Gettier's Case II Is Bewitchment
Let us suppose that Smith has strong evidence for the following proposition:
(f) Jones owns a Ford. Smith's evidence might be that Jones has at all times in the past within Smith's
memory owned a car, and always a Ford, and that Jones has just offered Smith a
ride while driving a Ford.
Let us imagine, now, that Smith has another friend, Brown, of whose whereabouts he is totally ignorant. Smith selects three place names quite at random and constructs the following three propositions:
(g) Either Jones owns a Ford, or Brown is in Boston.
(h) Either Jones owns a Ford, or Brown is in Barcelona.
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.
Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (0, and proceeds to accept (g), (h), and (i) on the basis of (f). Smith has correctly inferred (g), (h), and (i) from a proposition for which he has strong evidence. Smith is therefore completely justified in believing each of these three propositions. Smith, of course, has no idea where Brown is.
But imagine now that two further conditions hold. First, Jones does not own a Ford, but is at present driving a rented car. And secondly, by the sheerest coincidence, and entirely unknown to Smith, the place mentioned in proposition (h) happens really to be the place where Brown is. If these two conditions hold, then Smith does not KNOW that (h) is true, even though (i) (h) is true, (ii) Smith does believe that (h) is true, and (iii) Smith is justified in believing that (h) is true.
While it is true that (g), (h), and (i) are entailed by (f), and it is also true that Smith could accept/believe that all three are valid forms of disjunction. It is not true that Smith could believe anything at all about Brown's location. I mean, Gettier clearly states that Smith is totally ignorant about that. Thus, Smith - himself - would not form belief about Brown's location. One cannot know they are ignorant about Brown's location and simultaneously form and/or hold a belief about where Brown is located.
The mistake here is conflating knowledge of the rules of entailment/disjunction with belief. Believing that (g), (h), and (i) are entailed by (f) is not equivalent to believing the disjunctions.
Comments (1001)
It is if you believe that f is true. For example, if I believe that it is Sunday and if I believe that it being Sunday entails that the Post Office isn't open then I must believe that the Post Office isn't open.
So if g, h, and i follow from f and if I believe that f is true then I must believe that g, h, and i are true.
Belief can be wrong....is the cup in the cupboard?. Reality and logic are not joined at the hip but they are generally pretty friendly.
Personally I don't think Gettier counter-examples knock down JTB, although they do make us analyse the 'J' part rather more closely.
And in both of Gettier's original cases he is explicit that his mark sees the entailment and makes the deduction, precisely because you can't assume that he did, even if it's the rational thing to do.
I think we can generally say that most uses of the word knowledge do incorporate the idea of being justified in some way, but keep in mind there are many ways of justifying a belief besides inductive and deductive arguments.
Accepting (f) isn't equivalent to believing that (f) is true. I've argued for this without subsequent refutation. Gettier starts with "accepts" and finishes with "believes". The two are not the same. I agree that if one believes that (f) is true, then one believes (f).
Accepting (f) only requires accepting that (f) follows the rules of correct inference, and as such it doesn't require and/or entail belief that (f) is true. Gettier's argument requires one to neglect that much.
Edited at a later date to add:
Jeesh! I have no idea wtf I was talking about here. I must've been waaaay tired. Replace (f) with (g), (h), and (i)... I think that's what I was talking about...
:-#
If you mean as this as a matter of psychology, then yeah, people have inconsistent beliefs. But they shouldn't.
"Years of Academy training wasted!"
Smith - himself - would not form belief about Brown's location. One cannot know they are ignorant about Brown's location and simultaneously form and/or hold a belief about where Brown is located.
The mistake here is conflating knowledge of the rules of entailment/disjunction with belief. Believing that (g), (h), and (i) are entailed by (f) is not equivalent to believing the disjunctions. Following established rules counts as being justified in putting those rules to use. Smith is justified in believing that he has followed the rules of correct inference to correctly/sensibly arrive at disjunction.
Moreover, it is humanly impossible to believe that (g), (h), and (i) are true. Gettier's case neglects this brute fact.
Sure you can. Anyone who said that I'm at home or at work or driving from one to the other would almost always be right. (I lead an exciting life.)
You are skirting around the issue with disjunction though.
There's a bit of irony here.
Gettier's case requires that.
g) Either Jones owns a Ford, or Brown is in Boston.
(h) Either Jones owns a Ford, or Brown is in Barcelona.
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.
One cannot believe that any of the three random locations are where Brown is if s/he is aware that they have no clue of Brown's whereabouts.
One can however, be aware that they have no clue where Brown is and accept that the rules of correct inference allow all three of these conjunctions.
Brown is in Barcelona.
Brown is in Brest-Litovsk.
One cannot believe that all three of these are true. One can believe that one of them is. One cannot believe that they are totally ignorant of Brown's location and also believe any of the three.
And yet...
One can believe that they are totally ignorant of Brown's location and accept that the rules of correct inference allow all and/or any of the three to be attached to another belief with the terms "either/or", and be properly called a "disjunction".
Recognizing that g, h, and i follow from f does not require belief that g, h, and i are true. One cannot believe that Brown is in three places at once, thus it cannot be the case that Smith believes g, h, and i. Believing all three follow from f is not the same as believing that any of the three say something true about Brown's location.
I can believe all three to some degree:
Boston: 10%
Barcelona: 20%
Brest-Litovsk: 70%
and I can believe 100% that he's in one of those three.
But I can't do this:
Boston: 50%
Barcelona: 50%
Brest-Litovsk: 50%
or I'm vulnerable to a Dutch Book.
But I can arrive at disjunction based on those percentages.
Consider these:
1. London is the capital city of England
2. Either London is the capital city of England or I am in London
3. Either London is the capital city of England or I am in Exeter
4. Either London is the capital city of England or I am in Ipswich
Do you accept that 2, 3, and 4 follow from 1? Do you believe that 1 is true? Do you believe that 2, 3, and 4 are all true?
Because they do follow, and they are all true. Being the rational person that I am, I believe that they are all true.
Your mistake is in thinking that I have to believe that I am in London or Exeter or Ipswich to believe that 2, 3, and 4 are true. I don't. I only need to believe that London is the capital city of England. Which is exactly why I believe the following to be true (and why they are both true):
5. Either London is the capital city of England or pigs can fly
6. Either London is the capital city of England or pigs can't fly
Agreed, but we seem to have drifted into the issue of what natural language disjunctions are. There are old arguments about their interpretation.
Interesting charge. Am I the only one here using common sense?
Gettier's case requires Smith to hold belief about Brown's location, for that is precisely the purported belief that is true. If believing that g, h, and i follow from f does not necessarily require belief about Brown's location then the whole thing is a sham... which it is.
Bewitchment.
Gettier's argument is this:
(1) If you are justified in believing p, then you are justified in believing p v q.
(2) You can have a justified true belief that p v q even if p if false, so long as q is true.
Nobody cares whether you actually form this belief. The issue is that if you did, you would have a justified true belief we are not inclined to count as knowledge.
(1) claims that entailment preserves justification, which is hardly objectionable. The natural approach, in light of (2), is to conclude that (1) is too simple, that we need an extra condition governing how entailment preserves justification.
Gettier's case requires Smith to hold belief about Brown's location, for that is precisely the purported belief that is true.
Are you denying this?
It's a hypothetical. He asks us to assume that Smith forms this belief. Your argument is that he doesn't, or can't, or shouldn't. What's not clear is your grounds for denying the premise.
This is a really important and constantly overlooked point, but making it is often like "speaking in parables to the blind", unfortunately.
No it doesn't. It only requires that you believe that Jones owns a Ford. That's the whole point. Given that "Either Jones owns a Ford or Smith is in Barcelona" follows from "Jones owns a Ford" then if you are justified in believing that "Jones owns a Ford" is true then you are justified in believing that "Either Jones owns a Ford or Smith is in Barcelona" is true. And if Smith is in Barcelona then "Either Jones owns a Ford or Smith is in Barcelona" is true, even if Jones doesn't own a Ford.
So you have a justified true belief if one operand of a disjunction is false but justifiably believed to be true and if the other is true but not justifiably believed to be true (or even justifiably believed to be false).
I don't need to believe that "pigs can fly" is true to believe that "either London is the capital city of England or pigs can fly" is true.
Then Smith does not believe that Brown is in Barcelona. If Smith does not believe that Brown in is Barcelona, then Smith does not have JTB, and that's the whole point. Believing that g, h, and i follow from f doesn't require belief about Brown's location. And yet, that is the only purported belief that is true here. It's not a belief of Smith's at all. It's a random statement about Brown's location.
Bewitchment.
Leave out knowledge and belief for a moment. If I am justified in asserting p, am I justified in asserting p v q?
To answer your question...
An either/or claim is a claim that one or the other is true. The problem with Gettier's case is that both could be. That is because they have nothing to do with one another. A proper either/or claim posits mutually exclusive propositions. The two cannot both be true. Thus, to put the two statements that Gettier has into an either/or form is ill-conceived.
I get that. But I wanted to clarify your views on the logical constants and standard inference rules.
Quoting creativesoul
And, as it turns out, you have a non-standard view of "or".
It's entirely possible that in everyday English usage, the exclusive "or" predominates. That's an empirical question. By "proper" do you mean "conforming to everyday usage"?
And would you, in general, reject inferring "p ? q" from "p"?
When one says either X or Y, do you think that it makes any sense at all to put it like that if both X and Y are true or could be so?
That's a linguistics question. In some cases, exclusive or is more natural, and in some cases inclusive.
There are reasons classical logic settled on the inclusive or. For instance, by De Morgan's law,
¬(A & B) ? ¬A ? ¬B
because it seems most natural to say that "A & B" can be false by either or both of A and B being false.
Certainly people use the exclusive or sometimes, but it's so well known that "or" is ambiguous that we have "but not both" to make it clear when the exclusive interpretation is intended.
I'll spell it out more clearly for you.
1. My belief that p is justified
2. From 1, my belief that p ? q is justified
3. p is false and q is true
4. From 3, p ? q is true
5. From 2 and 4, my belief that p ? q is justified and true
6. I know that r if my belief that r is justified and true
7. From 5 and 6, I know that p ? q
I do not see how setting out how A&B can be false is relevant to the case at hand. For one, it's not a counterexample of either/or. It may, however, shed some much needed light upon how combining two propositions/assertions/statements into one monolith is a mistake. It could offer enough evidence to show the equivocation of "true". It could also lead to a more productive direction by virtue of helping us to recognize how Gettier conflates propositions/assertions/statements with belief.
I understand the historical approach. I've seen the above 'proof' or something similar before, although 6 looks out of place. It should say I know that q if my belief that q is justified and true. The problem is, of course, that there is no belief that q. Never-the-less...
Smith does not hold/have belief about Brown's whereabouts. That's a given. As I've already spelled out for you, if Smith does not hold belief about Brown's whereabouts, then Smith cannot believe that Brown is in Barcelona. The statement that is true is the one about Brown's whereabouts. That is not a statement of Smith's belief.
The conflation is at 2. Belief that p v q does not require belief that q. Belief that q is precisely what the case requires in order to be a case of belief, regardless of whether or not it's justified or true.
r is just a placeholder, like p and q. It's the justified true belief definition of knowledge. In this case, r is p ? q, which is shown to be a justified true belief in 5.
I'm not saying that there's a belief that q. I'm saying that there's a belief that p ? q. So, no, there's no conflation at 2.
It just looks to me like you don't accept any of Gettier's premises, including the use of classical logic to analyse natural language.
Is there common ground for you and Gettier that I'm missing?
That is the problem.
If Smith can believe each of those three propositions, and those three propositions include contradictory statements about Brown's whereabouts, then either Smith believes Brown is in three places at once or believing each of those three propositions does not require belief about Brown's whereabouts. Since all three propositions include statements about Brown's whereabouts, and Smith has no idea where Brown is, it is clear that what Gettier counts as being justified in 'believing' each of those three propositions does not require belief that the statements about Brown's whereabouts are true.
So, then what does it mean to believe each of these three propositions if not believing that inferring p v q from p is justified?
Fair enough.
I suspect that there is much common ground.
He doesn't need to believe anything about Brown's location. He only needs to believe that Jones owns a Ford. That's just a fact about disjunctions.
Again, the following are both true, I believe both to be true, and I am justified in believing both to be true:
1. London is the capital city of England and/or pigs can fly
2. London is the capital city of England and/or pigs can't fly
I know both of these to be true. And by the same token, I know that the following are both true, even though I have no opinion on where you are:
3. London is the capital city of England and/or creativesoul is in London
4. London is the capital city of England and/or creativesoul is in Barcelona
Such as?
I understand all of that Michael.
I'd like you to answer the question...
What does it mean to believe each of these three propositions if not believing that inferring p v q from p is justified?
You believe that p v q is true if you believe that one or both of the operands is true.
That looks like an equivocation of "is true".
Believing that p is true or believing that q is true is to believe that p or q corresponds to fact/reality. Note that these are two separate statements. Believing that p v q is true if you believe that p or q corresponds to fact/reality is to believe that calling p v q "true" is consistent with the rules of correct inference.
I note also that your examples have a p that is true. Gettier's p is false. Not sure what the ramifications of that are, aside from whether or not one is justified in deriving p v q from a false p? Of course, all of this recent stuff is aside from my original objection(s). It's always interesting to look at Gettier cases none-the-less.
I think our differences involve the different conceptions/notions regarding what counts as belief.
In terms of the logic, nothing. In terms of our intuition regarding what counts as knowledge, everything. It shows that the JTB definition of knowledge isn't correct (or at least, isn't sufficient).
Is that different than believing that inferring p v q from p is justified?
You see, I know what it takes for p to be true. I know what it takes for q to be true. However, I do not understand how "is true" could mean the same thing when talking about what it takes for p v q to be true. It seems like the only criterion for p v q being true is either p or q being believed.
It has nothing to do with believing that p v q is a justified inference from p, so I don't understand why you're bringing it up. Gettier is simply saying that because p v q is entailed by p then if a belief that p is justified then ipso facto a belief that p v q is justified.
It's not. It's very basic logic, as shown in this truth table. p v q is true if one or both of p and q are true.
I'm bringing it up because believing that p v q is a justified inference from p has everything to do with the self-imposed bewitchment. I understand the historical approach. I understand that if one accepts all of Gettier's premisses, then the only substantive argument against his cases needs to involve justification.
I've no skin in the game either way as far as the justification aspect goes. My approach criticizes the belief aspect. So, set the preconceptions aside for a moment and follow along. That is the only way for you to understand how what I'm bringing up is relevant.
Whether or not p v q is entailed by p is determined solely by the rules of correct inference. As you, yourself, have said - that's just a fact about disjunction. I'm not denying that. I'm granting it. Gettier is saying that because Smith knows the rules(realizes the entailment), he proceeds to accept (g), (h), and (i) on the basis of (f). That much is clearly seen below...
Here is where the bewitchment begins. The key word here is "accept". Accepting (g), (h), and (i) on the basis of (f) requires only realizing and accepting(believing) that the rules of correct inference allow such a thing. That much is indisputable..
Notice that Gettier changes "accepts" to "believes". Smith is completely justified in believing that each of these three propositions follow the rules of correct inference, thus he believes that all three are valid. Believing that each of the three propositions are valid allows one to place 'is true' at the end, again based upon the rules.
Don't let that bewitch you.
Believing that each of the three is valid is remarkably different than believing each of the three correspond to fact/reality. They cannot all be true, even though - as a result of the rules - the terms "is true" can be affixed to each. Smith knows that. Believing all three requires believing that all three are true(as compared/contrasted to valid). Smith knows that. One cannot form and hold three contradictory beliefs simultaneously, although one can believe that three contradictory propositions are all valid. Smith does not believe all three propositions, even though he accepts that they are all valid inferences.
What I'm pointing out here is the equivocation of "is true" that is at hand. It bears witness to the fact that Gettier is conflating Smith's belief that each disjunction follows the rules of correct inference with Smith's believing that each one is true. One can believe that three contradictory propositions all follow from the same p. This allows one to affix each disjunction with 'is true', because in this situation 'is true' signifies valid inference, and all of this follows the rules of correct inference.
So, Smith's belief is that Jones owns a Ford, and that each of the three propositions derived from that follow the rules of logic.
That takes the steam out of it all, does it not?
It should be clear that by "accept" Gettier means "accept as true".
They could all be true, and would all be true if Jones owns a Ford. Just as both of the below are true:
1. London is the capital city of England and/or pigs can fly
2. London is the capital city of England and/or pigs can't fly
They're not contradictory propositions. Contradictory propositions cannot follow from the same p (unless p itself is a contradiction). It's simple logic.
If by "accept" Gettier means "accept as true", then he certainly means accept as valid. One cannot accept that all three are true, because they all three contradict one another. One can accept that all three are valid.
They don't contradict each other. I don't know why you keep claiming that they do. Again, both of these are true:
1. London is the capital city of England and/or pigs can fly
2. London is the capital city of England and/or pigs can't fly
That is precisely the bewitchment.
I know the distinction between being valid and true. The sentences are both true, because London is the capital city of England.
Compare with:
1. London is the capital city of France
2. London is the capital city of France or I am in France
3. London is the capital city of France or I am in Germany
2 and 3 are valid inferences from 1, but 1, 2, and 3 are all false.
He believes that all three are true by virtue of believing p and accepting the rules of valid inference.
It is the case that p v q follows from p, so Smith's belief that p v q is 'true'(valid) is justified by the rules and true - also by the rules. P is false, so Smith's belief that p is justified and false.
Yes, which is what Gettier said. And there is no problem with this.
Furthermore, if he really is justified in believing p, then because those three sentences really do follow from p, he really is justified in believing those three sentences.
See the post above.
1. London is the capital city of France
2. London is the capital city of France or I am in France
3. London is the capital city of France or I am in Germany
2 and 3 are valid inferences from 1, but 1, 2, and 3 are all false.
Now compare with:
4. London is the capital city of England
5. London is the capital city of England or I am in France
6. London is the capital city of England or I am in Germany
5 and 6 are valid inferences from 4, and 4, 5, and 6 are all true.
If I am justified in believing 4 then I am justified in believing 5 and 6. If I believe 5 and 6 then I know 5 and 6.
And contrary to your earlier claim, 5 and 6 are not contradictory (and neither are 2 and 3).
His belief isn't just that p ? q is a valid inference from p (as with 2 from 1 above), but also that p ? q is true (as with 5 above).
7. Jones owns a Ford
8. Jones owns a Ford or Brown is in Barclelona
9. Jones owns a Ford or Brown is in Boston
Smith doesn't just believe that 8 and 9 are valid inferences from 7 (as with 2 and 3 from 1 above) but also that 8 and 9 are true (as with 5 and 6 above).
And, again, 8 and 9 are not contradictory.
No. If he really is justified in believing p, then because those three sentences really do follow from p, then his accepting them as valid is justified and true.
He's also justified in believing that they are true.
In fact, even if he isn't justified in believing p, his accepting the inference as valid is justified and true, because validity doesn't require true premises.
But again, Gettier isn't saying "accepting as valid inferences", he's saying "accepting as true".
His believing that they are true is nothing more and nothing less than his believing that the rules of disjunction allow him to randomly add any other statement to his belief that p and then call it "true" as a result of his believing that p.
Or it's that he believes that the disjunction describes some fact about the world, like the disjunction "either there's something in your pocket or you're just happy to see me".
So it's not clear to me how your argument addresses Gettier at all. There's a true disjunction that is justifiably believed to be true. Under the JTB definition of knowledge, Smith knows that either Jones owns a Ford or Brown is in Barcelona. Nothing you've said refutes any of this.
The argument is really straightforward, as I explained here, and there's a difference between accepting that something is a valid inference and accepting that something is true, as I explained here.
But, of course, the main thing I've been trying to show you today is that the three propositions are not contradictory.
Jones owns a Ford or Brown is in Boston
These are both valid inferences from a belief that p. Because p is false, they cannot both be true. They cannot both be true, because p is false and they state contradictory locations regarding the whereabouts of Brown. Smith believes that p, and has no idea of Brown's location. So, to make a statement about Brown's location is to state something that Smith, himself, does not believe.
Smith can believe that the rules of disjunction allow him to randomly add any other statement to his belief that p and then call it "true" as a result of his believing that p.
Smith's belief is justified by the rules and true by the rules.
Of course it's about the content of g, h, and i.
I believe that "London is the capital city of England and/or pigs can fly" is true because of the content of that statement. It describes what I believe to be the fact that London is the capital city of England and/or pigs can fly.
Smith believes that "Jones owns a Ford and/or Brown is in Barcelona" is true because of the content of that statement. It describes what he believes to be the fact that Jones owns a Ford and/or Brown is in Barcelona.
Jane believes that "Jim either has something in his pocket or is happy to see Sarah" is true because of the content of that statement. It describes what she believes to be the fact that Jim either has something in his pocket or is happy to see Sarah.
Your objections just don't make any sense, and seem to rest on your own peculiar logic, given that you think that the three statements that can be inferred from p are contradictory.
Try again.
Smith doesn't believe that Brown is in three different locations. Your argument is based on a false premise.
Try again.
Read the whole post and think about it.
There's a difference between just believing that p ? q is a valid inference from p and also believing that p ? q is true.
Smith believes that p is true.
Smith believes that p ? q is a valid inference from p.
Therefore, Smith believes that p ? q is true.
The full argument is here. Nothing you've said has refuted it.
Do you disagree?
That takes the steam out of it all, does it not?
And that each of those propositions are true.
Quoting creativesoul
Yes. And he's justified in believing that p ? q. And p ? q is true. He has a justified true belief.
No, because he has a justified true belief that intuitively shouldn't be considered knowledge. Therefore, the JTB account of knowledge is lacking.
Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q).
The entire argument neglects what belief that p v q requires. As such it works from an ill-conceived criterion for what counts as belief.
Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q). That bit of knowledge effectively dissolves this particular Gettier problem.
1. My belief that p is justified
2. From 1, my belief that if p is true then so too is (p v q) is justified
3. p is false and q is true
4. From 3, p ? q is true
5. From 2 and 4 my belief that if p is true then soo too is (p v q) is justified and true
6. I know that r if my belief that r is justified and true
7. From 5 and 6, I know that if p is true then so too is (p v q).
No problem.
This isn't in conflict with what I had for 2:
2. From 1, my belief that p ? q is justified.
You haven't shown this to be false.
1. It is wrong to steal.
From this, we can infer:
2. It is wrong for me to steal
Using your logic, all I'm doing is inferring that one statement follows from another. But that's not all I'm doing. I'm also stating that 2 is true. And if we bring in belief:
1. I believe that it is wrong to steal
2. Therefore, I believe that it is wrong for me to steal
My belief isn't just that 1 is true and that 2 follows. It's also that 2 is true. There's nothing wrong with the argument I provided here. Smith has a justified true belief that shouldn't be considered knowledge. The Gettier case stands. Nothing you've said refutes this.
Well, I don't say things "anyway".
And yet you object? Upon what grounds? I've exhausted the notion of belief that (p v q) being used in this particular Gettier case. I've done so without conflicting what you claimed. What I had for 2 has much stronger justificatory ground as a result of all this. A rational person steps back and recognizes the relevance of this novel approach, then sees it through.
I used your logic by the way. If you want to argue you'll have to argue against this, for it's the only thing different between our arguments.
Believing that (p v q) is true, if based upon belief that p, is to believe that if p is true then so too is (p v q).
Applying the above bit of knowledge we arrive at...
1. My belief that p is justified
2. From 1, my belief that if p is true then so too is (p v q) is justified
3. p is false and q is true
4. From 3, p ? q is true
5. From 2 and 4 my belief that if p is true then soo too is (p v q) is justified and true
6. I know that r if my belief that r is justified and true
7. From 5 and 6, I know that if p is true then so too is (p v q).
No problem. Smith has JTB.
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, is to believe that if p or q is true then so too is (p v q).
That should do it.
It's also to believe that p ? q is true. Why is this so hard for you to understand?
Smith believes that the proposition "Jones owns a Ford or Brown is in Barcelona" describes some fact about the world, just as I believe that the proposition "either she's having a shower or she's having a bath" describes some fact about the world.
Your argument might be valid, but so is mine (or, rather, Gettier's). And my (Gettier's) argument shows that the JTB definition of knowledge is lacking.
Smith doesn't just believe that the inference is valid. He also believes that the inferred propositions are true. And, as I keep saying, nothing you're saying refutes this. You've just ignored it.
I'm tempted to be a smartass.
Re-read the quote you are addressing and pay close attention to how it begins.
That's like saying that to believe that "it is wrong for me to steal" is true is just to believe that if "it is wrong to steal" is true then "it is wrong for me to steal" is true.
You're setting up the belief just as:
B(p ? r).
I'm saying that the belief is:
B(r).
Where r is "it is wrong for me to steal" or "either she's in the shower or she's in the bath" or "Jones owns a Ford and/or Brown is in Barcelona".
How and/or if classical logic can account for what belief that (p v q) takes is of no concern of mine. I think that the issue is one that I struggled with. Your point is well taken though. Here's the fix...
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, is to know that if p or q is true then so too is (p v q).
Gettier attempts to take an account of thinking about thought/belief as though it were the same as thought/belief. It's not.
Does Smith also know that p v q would be true if q is, even though he has no opinion on the truth or falsehood of q?
It's worth looking at the scope of "know":
(1) I know that: p or q is true.
(2) I know that: p is true or q is true.
(3) I know that p is true or I know that q is true.
(1) and (2) are actually the same thing -- it's just the definition of "or".
(3) is a reason for (1) -- and thus (2) -- but the converse does not hold.
Remember Gettier???
It's really rather simple when you think about it. Lose the logic talk for a moment, for that is precisely what bewitches people...
If Smith believes that p, and then derives (p v q) from p, and realizes the entailment, then he knows the rules of disjunction. If he knows the rules of disjunction then he knows that (p v q) is true if either p or q is.
Gettier, and evidently everyone since doesn't take this brute fact into consideration.
That bit of knowledge regarding what belief that (p v q) takes dissolves this purported Gettier problem. It works from an utterly inadequate notion of belief that (p v q). That is of no surprise to me, because it is a consequence of the whole of philosophy having gotten thought/belief wrong, by virtue of not drawing and maintaining the crucial distinction between thought/belief and thinking about thought/belief. Belief that (p v q) requires the latter. Belief that p does not. Gettier's notion of belief that (p v q) doesn't take this into proper account, and cannot as a result of neglecting the aforementioned distinction.
You're forgetting that we are treated to a buffet of reasons for Smith to believe that p.
The issue is what belief that (p v q) requires in order for it to even form and/or be held.
No one called me out. However, the replies to that particular post now have a bit of different meaning to me than at the time. Here I was wondering what on earth some of you were thinking, when it would've been much more appropriate the other way around. Thanks for the charitable reading!
:D
I still have no idea what this is supposed to mean or what point you think you've made. In what way is Case II dissolved?
Fair enough Srap. I'm making quite the claim, aren't I? Extraordinary claims require extraordinary proof. I like that, and ought honor it.
I'm working on that now...
It is here that it would behoove us all to pause a moment and give this very careful attention. Granting all of the above, let us critically examine what Gettier is saying by virtue of assessing what it would actually take in order for one to even be able to do what Gettier says that Smith does.
Smith has justified belief that p. Smith constructs three propositions from his belief that p. Smith realizes the entailment of these three propositions. Smith accepts all three on the basis of his justified belief that p. Smith is therefore justified in believing each (p v q). Gettier stops here though, without putting it all together. Smith has three different beliefs that (p v q).
What does it take in order for Smith to even be able to do all of that?
If Smith believes that p, derives 3 versions of (p v q) from p, and realizes the entailment, then he knows the rules of correct inference. If he knows the rules of correct inference then he knows that (p v q) follows from p; He knows that the rules of correct inference presuppose the truth of the premisses; he knows that a valid inference is called "true" because validity preserves the truth of the premisses, and he also knows that the inference is true(as compared/contrasted to just valid) if, and only if, the premisses are true and the inference valid. Given that Smith knows all of the above...
Smith's 'belief' that (p v q) is not that (p v q) is true. Rather, it is that "(p v q) is true" is valid and that is justified true belief in all three cases. It is nothing less than knowledge that (p v q) follows from p. The truth conditions of p and q are irrelevant to knowing that (p v q) follows from p.
QED.
It's more than this, as I explained here.
You can believe that r follows from p and believe that r is false, and you can believe that r follows from p and believe that r is true. In Gettier's case, Smith doesn't just believe that r follows from p; he also believes that r is true.
Yes he does. He believes that r follows from p, that p is true, and so that r is true.
Quoting creativesoul
This doesn't make any sense. Inferences are valid, not propositions. "(p ? q) is true" is a proposition.
The below is an example of a valid inference:
1. p ? r
2. p
3. r
These are three separate propositions that can be true and believed in. You might believe 1, 2, and 3. You might believe 1 but not 2 or 3. You might believe 1 and 3 but not 2. You might believe 2 and 3 but not 1. You might believe 2 but not 1 or 3. You might believe 3 but not 1 or 2.
In Gettier's case, r is p ? q.
And he also believes that p ? q is true.
p ? q isn't an inference, and so isn't the sort of thing that is valid. It's a proposition that is either true or false.
He does take that into account. It's right there in your quoted passage: "Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed"
He does take it into proper account. Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of inference. Therefore, Smith believes that g, h, and i are true.
Compare with: Smith believes that f is false. Smith knows that g, h, and i follow from f as per the rules of inference. Smith believes that g and h are false and that i is true.
Believing that r follows from p is one thing. Believing that r is true (or false) is something else.
g, h, and i are not the sort of things that can be valid or invalid, as I keep saying. Inferences are valid, not propositions. g, h, and i are propositions. They are either true or false.
Smith believes that f is true. Smith knows that g, h, and i are valid inferences from f. Therefore, Smith believes that g, h, and i are true.
And Gettier would agree. The problem is that Smith has a justified true believe in g, h, and i. Therefore, the JTB definition of knowledge is lacking.
Hows that work?
Because propositions are not the sort of things that are valid or invalid. Inferences are valid or invalid. Propositions are true or false. g, h, and i are propositions.
This is basic logic.
This isn't mutually exclusive. He has a justified true belief that g, h, and i follow from f and a justified true belief that g, h, and i are true.
So then, propositions are not inferred?
Propositions are inferred, but they are not inferences. This is an inference:
1. Socrates is a man
2. All men are mortal
3. Therefore, Socrates is mortal
Each of the three propositions is either true or false, with the argument itself being valid or invalid. It doesn't make sense to say that "Socrates is mortal" is valid.
4. London is the capital city of England
5. Therefore, London is the capital city of England or I am a woman
Each of the two propositions is either true or false, with the argument itself being valid or invalid. It doesn't make sense to say that "London is the capital city of England or I am a woman" is valid.
So, conclusions aren't valid?
Where's the argument?
Does it make sense to say that "London is the capital city of England or I am a woman" is an invalid conclusion?
That is Smith's 'belief' that (p v q) is true.
It is nothing less than knowledge that (p v q) follows from p. The truth conditions of p and q are irrelevant to knowing that (p v q) follows from p.
That makes no sense at all. Either an inference is not inferred, or being inferred doesn't count as being an inference.
What follows below is self-contradiction...
Read this carefully people...
So then, g, h, and i are only valid inferences when you say so? What sense does this make?
On the one hand, you claim that g, h, and i are propositions not inferences, and because only inferences are valid, g, h, and i cannot be so. On the other hand, you say that Smith knows that g, h, and i are valid inferences from f.
The truth conditions of q have no bearing upon either Smith's belief or his knowledge.
He would believe that f, but would not know that h followed. Thus, his assertion would be unjustified, and the case ends there.
And if (f) were true, so would (g), (h), and (i) be.
It's rather the point that Smith thinks he is applying modus ponens but he isn't, because (f) is actually false. That's valid, in the sense that it will preserve truth, but there's no truth to preserve.
Gettier's claim is that if an inference is valid, it preserves justification as well as truth, and thus even though there was no truth to preserve, what justification Smith had for his belief that (f), is passed to (g), (h), and (i) by modus ponens.
Since (h) is true entirely by coincidence, Smith now has one justified true belief, (h), but he has increased his store of justified false beliefs:
(f) Jones owns a Ford;
(g) Either Jones owns a Ford, or Brown is in Boston;
(i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.
What will happen if he ever comes to correct his false belief (f)? Will he now have this inconsistent set of beliefs?
(g') Brown is in Boston;
(h') Brown is in Barcelona;
(i') Brown is in Brest-Litovsk.
No, as a matter of fact he won't: he believed he was applying modus ponens; once he knows that (f) is false, he will no longer infer (g), (h), and (i). Modus ponens is no use if (f) is false.
To believe that you have made a valid inference from a true premise is to believe that the conclusion is true. It is the whole point of making valid inferences. We only do this to get truths we do not yet know from truths that we do.
If you presented an argument here on this forum, what would you think of the following response?
And here you'd gone to all that trouble of establishing your premises and making careful inferences, all for nought ...
ADDED: Where I say "no truth" above, that's technically wrong, of course, because all of the conditionals are fine:
(f)?(g)
(f)?(h)
(f)?(i).
No. And neither does it make sense to say that a conclusion is valid. Arguments are valid or invalid; propositions (whether premise or conclusion) are true or false.
"London is the capital city of England or I am a woman" is a conclusion that follows from the premise "London is the capital city of England". The argument is valid. Given that the premise is true, so too is the conclusion, and so the argument is sound.
Quoting creativesoul
Here are three arguments:
1. London is the capital city of England
2. London is the capital city of England or I am a woman
2 follows from 1. 1 is true and 2 is true.
3. London is the capital city of France
4. London is the capital city of France or I am a woman
4 follows from 3. 3 is false and 4 is false.
5. London is the capital city of Germany
6. London is the capital city of Germany or I am a man
6 follows from 5. 5 is false and 6 is true.
There is more to Smith's belief than just believing that p ? q follows from p. He also believes that p is true and that p ? q is true. His argument is akin to the first of the three above.
Quoting creativesoul
Quoting creativesoul
Clearly there's some ambiguity here with the term "inference". On the one hand it can mean "a conclusion reached on the basis of evidence and reasoning", but I meant it in the sense of "the process of inferring something". I should have perhaps used the term "argument". Arguments are valid or invalid; propositions are true or false. g, h and i are propositions, not arguments, and so are either true or false, not either valid or invalid. Inferring g, h, and i from f is either valid or invalid.
Quoting creativesoul
There's more to it than this.
Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. And Smith believes that g, h, and i are true.
Again with my previous example:
I believe that "it is wrong to steal" is true. I know that "it is wrong for me to steal" follows from "it is wrong to steal" as per the rules of correct inference. And I believe that "it is wrong for me to steal" is true.
Compare with:
I believe that "it is right to steal" is false. I know that "it is right for me to steal" follows from "it is right to steal" as per the rules of correct inference. And I believe that "it is right for me to steal" is false.
And compare with:
I believe that "all Presidents are men" is false. I know that "President Trump is a man" follows from "all Presidents are men" as per the rules of correct inference. And I believe that "President Trump is a man" is true.
There are three things to consider here: 1. is the premise true? 2. does the conclusion follow from the premise? 3. is the conclusion true? For some reason you are ignoring 3. Why?
Quoting creativesoul
But it does follow. If "Jones owns a Ford" is true then "Jones owns a Ford or Brown is in Barcelona" is true. If he's justified in believing that Jones owns a Ford then he is justified in believing that Jones owns a Ford or Brown is in Barcelona.
Smith's justification for (f) is all relevant to (f). Smith's inferring (g), (h), and (i) from (f) has nothing to do with the justification for (f). This is obvious because Smith could have correctly inferred (g), (h), and (i) even if it were the case that (f) was unfounded. Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f).
I would disagree with Gettier's claim.
The position you're arguing for hinges upon the above. I appreciate the time and effort that you put into the posts here Michael. However, it is much more appropriate to make your case by virtue of using Gettier's example...
Could you?
Well, yes and no. He doesn't make the inference because his belief that (f) is justified, but Gettier claims that inference preserves what justification he has for that belief, just as it preserves truth.
Quoting creativesoul
The trouble with this view is that valid inference from unjustified belief would confer justification upon the conclusion of the inference.* Inference isn't supposed to do that. Valid inference doesn't confer truth upon your conclusion, but guarantees that if the premises are true then the conclusion is too. Inference itself is not the source of the conclusion's truth -- that's still the premises.
Quoting creativesoul
Yeah, like I've been saying for a while, you disagree with Gettier's premises. So you should be arguing that the quote above, beginning "Secondly, ...", is false.
* Here's an example of that:
I wake up on a Tuesday morning, groggy, remembering that I didn't have to get up yesterday, and thinking it's Monday and I have to be at work at 9. As it happens, Monday was a holiday and I have forgotten. I have a true belief that I need to be at work at 9, but it is not justified, as it is a valid inference from my unjustified belief that it is Monday, not Tuesday.
What makes the following claims true?
"1 is true and 2 is true"
"3 is false and 4 is false"
"5 is false and 6 is true"
"2 follows from 1"
"4 follows from 3"
"6 follows from 5"
What kind of answer are you expecting here?
Because it looks like you are asking, in so many words, for a theory of truth.
I would say that that would be the case if, and only if, P and Q have the same truth conditions.
Well, the theory of truth one works with is at hand, regardless of whether or not that is currently the focus of discussion. However, I am teasing out the differences between statements that are called 'true' by virtue of being a valid inference, and those that are true.
I strongly suspect that there is conflation between the two at work.
That would make them the same proposition.
Quoting creativesoul
"Called 'true'"? So you still don't accept that the conclusion is true?
Quoting creativesoul
There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true. It doesn't. If you don't think that, then you don't need two different kinds of truth. Or three. Or twelve. Truth is truth.
I would not claim that all valid inference is justified by virtue of being valid. Disjunctions are unique.
(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules.
Assuming a hypothetical "you"...
We agree here.
That's not going to work out. I can define all the logical constants in terms of disjunction and negation.
It feels like we're wandering around here. I'm having trouble keeping track of what you accept and what you don't.
You think/believe that every proposition has it's own unique set of truth conditions?
I do not accept Gettier's notion of belief. I've said that from the beginning. Our discussion allows those differences to show themselves. The formulation of JTB works from the same notion.
(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules.
What's wrong with the above Srap?
I think that's a pretty reasonable way to define propositions, yeah. You can express the same proposition in multiple ways, in multiple languages, and there will be all sorts of differences that logic just doesn't care about. Insofar as they have the same truth conditions they are different ways of expressing the same proposition.
Quoting creativesoul
Why not?
Quoting creativesoul
No they're not, not if we're talking about the logical constants. Are we talking about that, or are we talking about linguistics?
Quoting creativesoul
And you've not shown why this matters. At no point does Gettier attribute to Smith a belief in any of the "Q's".
Quoting creativesoul
Nope.
But I have shown why it matters. Assuming sincerity in speech, statements are statements of belief. Smith's lack of belief in Q shows that his belief that (p v q) has nothing at all to do with his belief except his belief that (p v q) follows from p.
That is JTB.
In this context: beliefs have propositional content. If that's what you mean, yes.
"I believe that ...", "I know that ...", "I suspect that ...", "I hope that ...", "I doubt that ..." -- these are all propositional attitudes. All of these words have other uses, none of which are relevant here.
... and is therefore true. That Smith believes (g), (h), and (i) -- i.e., believes all of them to be true -- is a premise of the argument.
What exactly are your grounds for rejecting this premise? That it is impossible for Smith to believe the conclusion of a valid argument from premises he believes? That it is not rational to do so? That as a matter of fact people do not do this?
Believing (f) and properly inferring (g), (h), and (i) from (f), why on earth should he not believe any of his own conclusions?
No!
This is an opportune reminder...
Allow me to hold a mirror up for you Srap.
His premiss works from an utterly inadequate notion of belief that (p v q).
QED.
He believes that they're all valid inferences.
Belief that (p v q) follows from p is knowing that if either p or q is true then so too is (p v q). That's it. There's nothing more to it.
The truth conditions of q are utterly irrelevant.
So let's say that I know that my girlfriend is in the bathroom washing. I believe that the disjunction "she's having a shower or she's having a bath" is true. Let's also assume that this isn't a dichotomy, and that she could in fact just be using the sink.
According to you, to believe that this sentence is true is just to believe that it follows from "she's having a shower" (and/or from "she's having a bath")? That's quite clearly wrong. Believing that a disjunction is true is no different in kind to believing that a conjunction is true, or to believing that a simple proposition such as "she's having a shower" is true.
Given the argument:
1. p
2. p ? r
3. r
One can believe in the truth (or falsity) of 1, 2, and 3. Contrary to your repeated claims, it isn't just a case of believing in the truth of 1 and 2.
I can believe that p is true, I can believe that if p is true then r is true, and I can believe that r is true. In our case, r is p ? q.
That would be clearly wrong. I agree that believing a disjunction is true is not equivalent to believing that it follows from p.
That is precisely my point. Smith's belief that (p v q) is of the latter, not the former.
There's a few remarkable differences between your example and the Gettier case. In your case, both statements(p & q) are about the same situation(your girlfriend's washing). You did not accept the disjunction as a result of recognizing the entailment. You believe that one or the other is true, and that it could be either. You asserted it as further clarification of your own belief. They're both kinds of washing, and you know that she's washing.
Smith doesn't believe that (p v q) is true. Smith didn't assert it as further clarification of his belief. He constructed g, h , and i by virtue of adding three different q's - none of which were belief. None of which were about p. All of which were propositions. His acceptance of g, h, and i is the result of realizing the entailment. He believed that each followed from p.
It's the notion of belief that that is at issue. More specifically, it seems to be an issue with how classical logic attempts to account for it. The shortcomings of logic is a topic in it's own right, so I'm trying to not focus too much upon that, although some of those shortcomings bear upon this particular Gettier case. I'm also trying to avoid talking about the content of thought/belief, but that is beginning to seem inevitable, it is most certainly germane.
To directly address the above quote:It is false. If there were no difference in kind, then there would be no difference between the content, but there is.
Belief that a simple proposition such as "she's having a shower" is true is to believe that "she's having a shower" corresponds to what she's doing in the bathroom.
Belief that a disjunction such as "she's having a shower or she's having a bath" is true, is to believe that one statement or the other corresponds to what she's doing in the bathroom.
Belief that the conjunction "she's having a shower, and she's having a bath" is to believe that both statements correspond to what she's doing in the bathroom.
Note that all three are about what she's doing in the bathroom. Further note the difference between the above disjunction and Smith's.
Seeing how none of the variables above have a meaningful value other than being a place-marker for any given proposition, all you're doing here is asserting conviction in the representational ability of this particular formulation.
How you arrive at r matters.
And to believe that a disjunction such as "Jones owns a Ford or Brown is in Barcelona" is true is to believe that one statement or the other corresponds to some fact about the world.
Can I surmise that each of these same propositions is about the same states of affairs?
The former is about the same fact, and it consists entirely in/of statements of belief about that fact. The latter is about different facts and does not consist entirely of belief about those facts.
The former clarifies belief about the same fact. The latter clarifies belief about the rules.
How you arrive at (p v q) matters.
The above is what (p v q) ought represent, but it doesn't. It represents more than that. It also represents Gettier's case where q isn't believed, there are two separate truth conditions for p and q, therefore Smith doesn't believe that a single state of affairs determines the truth/falsity of both.
That difference sheds light upon the problem.
How one arrives at (p v q) matters.
<shrug>
I believe that I am shorter than the Eiffel Tower. Do you want to call that one state of affairs? Two? Three? How would you decide?
Point taken. I would only note that the conversation focused upon what it would take in order for justification to be preserved from p to (p v q).
Do you still hold that every proposition has it's own unique truth conditions such that no two propositions have the same truth conditions?
Yes.
If one believes that either this(p) or that(q) is true, then one believes that both cannot be. That is not the case with Smith.
It would still be the case that Smith has validly inferred (p v q).
Both p and q would be true.
Smith would still believe that (p v q) is true if either p or q is. Smith would be correct in following the rules, but the rules would be wrong.
Would his belief that (p v q) still be true?
Yes, I've already explained the difference.
1. I am a woman
2. I am a woman or London is the capital city of France
I believe that p ? q is validly inferred, but that p ? q is false.
3. I am a woman
4. I am a woman or London is the capital city of England
I believe that p ? q is validly inferred, and that p ? q is true.
In Smith's case,
5. Jones owns a Ford
6. Jones owns a Ford or Brown is in Barcelona
Smith believes that p ? q is validly inferred, and that p ? q is true.
You're the one conflating, arguing that Smith believing that p ? q is true is just believing that p ? q is validly inferred. That's just not the case.
If one believes that either this(p) or that(q) is true, then one believes that both cannot be.
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, is to know that if p or q is true then so too is (p v q), and to believe that both cannot be.
Believing that "Either 'Jones owns a Ford' or 'Brown is in Barcelona'" is true, if based upon belief that Jones owns a Ford, and accepting the rules of correct inference is to know that if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true, then so too is "Either 'Jones owns a Ford' or 'Brown is in Barcelona'", and to believe that both 'Jones owns a Ford' and 'Brown is in Barcelona' cannot be.
Didn't you earlier claim that g, h, and i were all true?
:(
How so? What part of my post do you disagree with?
Quoting creativesoul
Gettier is using the inclusive or, not the exclusive or, as the exclusive or doesn't follow from p.
It's p ? q, not p ? q.
That's an oversimplification. See my last post above that sums up my notion of what Smith's belief that (p v q) is true consists in.
And it's wrong. Again:
1. I am a woman
2. I am a woman or London is the capital city of England
My belief that 2 is true isn't just a belief that 2 is validly inferred. Else you would have to say that I believe that 4 is true:
3. I am a woman
4. I am a woman or London is the capital city of France
Except I don't. I believe that 4 is false, even though it's validly inferred. There is a very clear difference between believing that p ? q is entailed by p and believing that p ? q is true. Smith believes that p ? q is true (and that it is entailed by p).
Smith cannot believe that both p and q could be true.
1. My name is Michael or my girlfriend is having a shower (p ? q)
2. My name is Michael or my girlfriend is having a bath (p ? r)
I believe that my name is Michael. If my name is Michael then both of 1 and 2 are true. Therefore, I believe that both 1 and 2 are true. Furthermore, I believe that my girlfriend could be having a shower, and so believe that both p and q could be true. And I believe that my girlfriend could be having a bath, and so believe that both p and r could be true.
Granted, I can't believe that p, q, and r are all true, as I can't believe that both q and r are true, but that's irrelevant to Gettier's argument.
Quote me and argue against the parts you say are wrong.
And again:
1. I am a woman
2. I am a woman or London is the capital city of France
I believe that p ? q is validly inferred, but that p ? q is false.
3. I am a woman
4. I am a woman or London is the capital city of England
I believe that p ? q is validly inferred, and that p ? q is true.
Smith's belief is of the latter kind. A valid inference with a true conclusion.
No, he cannot.
Gettier claims that Smith is totally ignorant about Brown's location. That is a problem for the inclusive notion. Smith does not believe any of the Q's. In order for Smith to believe that both p and q could be true, Smith must believe q. Gettier also claims that Smith believes all three. If Smith believes all three and believes that p and q can both be true, then he either holds contradictory belief about Brown's location or he holds belief about Brown's location. Neither is acceptable given that Smith is totally ignorant regarding Brown's whereabouts.
Smith doesn't need to believe that both are true. It's a disjunction, not a conjunction.
Your arguments are making less and less sense.
You mean this reason?
Quoting creativesoul
That's simply false.
Let's say that q is "creativesoul is over 40 years old". You're saying that I can only believe that q could be true if I believe that q is true? That is obviously wrong.
Also, he doesn't. He can believe that q is false and that p is true. The following is a disjunction that I believe to be true:
My name is Michael or pigs can fly.
And it's true. And I'm justified in believing that it's true.
We're getting back into your territory... My case cannot be made in those terms. I've removed the bit regarding inclusive/exclusive...
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, is to know that if p or q is true then so too is (p v q).
Believing that "Either 'Jones owns a Ford' or 'Brown is in Barcelona'" is true, if based upon belief that Jones owns a Ford, and accepting the rules of correct inference is to know that if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true, then so too is "Either 'Jones owns a Ford' or 'Brown is in Barcelona'".
What's your criticism here? Please use Gettier's case as a counter...
You're conflating again. Believing that p ? q is true is not the same thing as believing that p ? q is entailed by p. I can believe that p ? q is entailed by p but believe that p ? q is false (as with the example of "I am a woman or London is the capital city of France" being entailed by "I am a woman").
I'm setting out what is required in order to even be able to arrive at "Either 'Jones owns a Ford' or 'Brown is in Barcelona'" is true, if based upon belief that Jones owns a Ford.
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, requires knowing that if p or q is true then so too is (p v q).
I've changed the bit I think you took issue with.
So Smith believe that p ? q is true. And Smith is justified in believing that p ? q is true. And p ? q is true. Therefore, Smith has a justified true belief.
Nothing you've said refutes Gettier's argument.
Smith is wrong.
(p v q) is true because q is true.
Are you sure???
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, requires knowing that if p or q is true then so too is (p v q). Smith's knowing that if p or q is true, then so too is (p v q) and still believing that (p v q) is true despite not believing any of the Q's, is for Smith to believe that (p v q) is true because p is.
Smith has false belief.
(p v q) is true because q is true.
You're conflating "Smith believes that 'p ? q is true because p is true' is true" with "Smith believes that 'p ? q' is true because Smith believes that p is true".
Take this example:
1. I believe that "Donald Trump is the President" is true.
2. I believe that the President is elected by popular vote and that Donald Trump won the popular vote.
According to you, my belief that Donald Trump is the President is false because Donald Trump didn't win the popular vote (and nor is that how the President is elected). That's just wrong. My belief that Donald Trump is the President is a true belief, even though I believe it for a false reason.
Smith has a true belief, even though he has it for a false reason.
No, I'm claiming that Smith believes that p ? q is true, that Smith is justified in believing that p ? q is true, and that p ? q is true. He has a justified true belief.
Believing that (p v q) is true is much different than believing that (p v q) is true because p is. Smith holds the latter, not the former.
I've given the argument for that. Here it is again...
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, requires knowing that if p or q is true then so too is (p v q). Smith's knowing that and still believing (p v q) is true despite not believing any of the Q's, is for Smith to believe that (p v q) is true because p is.
Again, you're conflating "Smith believes that 'p ? q is true because p is true' is true" with "Smith believes that 'p ? q' is true because Smith believes that 'p' is true".
The situation at hand is the latter. I explained this more clearly with my example of Donald Trump being the President. I have a true belief arrived at from a false reason. Smith has a true belief arrived at from a false reason. But a true belief is a true belief nonetheless.
I wrote this...
...not this...
Yeah, the false belief that p.
I thought we'd been over this, for instance here.
It's still true that p entails p v q.
Believing that (p v q) is true, if based upon belief that p, and accepting the rules of correct inference, requires knowing that if p or q is true then so too is (p v q). Smith's knowing that if p or q is true, then so too is (p v q) and still believing that (p v q) is true despite not believing any of the Q's, is for Smith to believe that (p v q) is true because p is.
Smith believes that (p v q) is true because p is true.
Smith has false belief.
(p v q) is true because q is true.
You said: "[Smith believes] that p v q is true because p is". There are two different ways to interpret this:
1. Smith believes that "p ? q is true because p is true" is true, and
2. Smith believes that "p ? q" is true because Smith believes that "p" is true
You seem to think that it's just the first. But it isn't. It's also the second. To repeat my earlier example:
1. I believe that "Donald Trump is the President because Donald Trump won the popular vote, and the President is elected by popular vote" is true, and
2. I believe that "Donald Trump is the President" is true because I believe that "Donald Trump won the popular vote, and the President is elected by popular vote" is true
It doesn't matter why I believe that "Donald Trump is the President" is true – even if for a false reason. I do, and my belief is true.
It doesn't matter why Smith believes that "p ? q" is true – even if for a false reason. He does, and his belief is true.
As I said, Smith thinks he's applying modus ponens but he isn't, because p is false.* So yes there is also the false belief that modus ponens is applicable -- but we don't want to go too far down this road because at some point you have to actually make an inference, which is an action not a belief.
Just remember that, for all Smith knows, Brown is in Barcelona. He may not believe that Brown is in Barcelona, but he doesn't believe that he isn't either.
So this is not a case of (p & ~q)?(p v q).
* We're saying m.p. is used here because that's basically what Gettier does. You could also call deriving p v q from p (or from q) a "v introduction rule" as it would be in a natural deduction system.
ADDED: Keep in mind too that Smith thinks m.p. is applicable because he thinks p is true. And that is what he should think. He just happens to be wrong.
Believing that 'either Jones owns a Ford or Brown is in Barcelona' is true, if based upon belief that 'Jones owns a Ford' is true, and accepting the rules of correct inference, requires knowing that if 'Jones owns a Ford' or 'Brown is in Barcelona' is true then so too is 'Either Jones owns a Ford or Brown is in Barcelona'. Smith's knowing that and still accepting that 'Either Jones own a Ford or Brown is in Barcelona' is true despite not believing that 'Brown is in Barcelona' is true, is for Smith to believe that 'Either Jones owns a Ford or Brown is in Barcelona' is true because 'Jones own a Ford' is true.
Smith believes (p v q) is true because p is true.
Smith has false belief.
(p v q) is true because q is true.
2.Smith believes that (p v q) is true.
3.Smith does not believe that q is true.
4.Smith believes that (p v q) is true because p is true.
5.(p v q) is true because q is true
6.Smith holds false belief
What more could you ask for?
X-)
"Because" is a slippery word though.
We can talk loosely about this, and it usually does no harm. I could say something like "p's being true makes p v q true." Mathematicians talk this way, but again this is to speak loosely. That's not a good idea here.
(If we really want to say something like this, we should probably say that whatever makes p true also makes p v q true -- but this is just the sort of truth theorizing I don't think we need to do here.)
As I've said, I think the right thing to say is that Smith believes, correctly, that p entails p v q, and he believes, incorrectly, that p. With those two beliefs in hand, he applies modus ponens. This is exactly what Gettier describes, I think.
Look at your 4 the other way round: what makes 4 a false belief is precisely that p is false. That's another reason to split out p, which you have not done here, although Gettier does. Smith has lots of false beliefs, and they all flow from his false belief that p.
And because Smith believes that p, it makes sense to present 4 giving "believe" smaller scope:
4. Smith believes that p v q because Smith believes that p.
That's the other sense of "because" -- not the vaguely causal sense we had above, but the sense in which p is a reason for Smith to believe that p v q, and a good one. By burying p inside a more complex belief, you've left out the reasoning process Gettier attributes to Smith. And it's that reasoning process that carries justification.
At least we're getting closer now to confronting the actual problem.
My point is that Gettier's notion of Smith's belief is too simplistic.
An old friend of mine who's much more knowledgable with logical notation than I said this...
So the refutation rests on
Smith believes that: ((p v q) is true because p is true)
against
((p v q) is true because q is true)
interesting....
That's what Gettier tries to do Srap. It neglects to take the fact that Smith knows the truth conditions of (p v q) and doesn't believe q.
His belief that p is a justified false belief, yes. At least that's the premise, which hasn't been challenged here.
I'm not talking about his belief that p. That should be clear.
1.Smith knows that (p v q) is true if either p or q is true
2.Smith believes that (p v q) is true.
3.Smith does not believe that q is true.
4.Smith believes that (p v q) is true because p is true.
5.(p v q) is true because q is true
6.Smith holds false belief
What are you denying?
I heard you the first time. ;-)
Let me put it this way: your statement is just shorthand for this one
p & p?(p v q).
It's not like you can believe "p v q because p" without believing that p. You're just pushing the two premises together.
But you should be. I think you're trying to block the justification of p v q by hiding p, which is the only justified belief on the table.
2.Smith believes that (p v q) is true.
3.Smith does not believe that q is true.
4.Smith believes that (p v q) is true because p is true.
5.(p v q) is true because q is true
6.Smith holds false belief
What are you denying?
Justification is the whole point of the exercise.
Smith has loads of false beliefs, starting with p. What does that get you?
What point are you making?
I've said I object to 4 because it runs two premises together and obscures the main issue. I don't know if it's false, but it's not helpful.
What do you get if I grant 4?
Smith does not have a JTB to begin with. One cannot quite make the claim that Gettier shows a problem for JTB if Gettier's example is JFB... now can they?
;)
2 is the justified true belief.
Believing that 'either Jones owns a Ford or Brown is in Barcelona' is true, if based upon belief that 'Jones owns a Ford' is true, and accepting the rules of correct inference, requires knowing that if 'Jones owns a Ford' or 'Brown is in Barcelona' is true then so too is 'Either Jones owns a Ford or Brown is in Barcelona'. Smith's knowing that and still accepting that 'Either Jones own a Ford or Brown is in Barcelona' is true despite not believing that 'Brown is in Barcelona' is true, is for Smith to believe that 'Either Jones owns a Ford or Brown is in Barcelona' is true because 'Jones own a Ford' is true.
2 is what matters. It's the whole point of Case II.
We already have, as a premise, a justified false belief for Smith, namely p, which for some reason you don't like to talk about.
4 annoys me, but I'm not even sure it matters, unless the idea is to pretend that Smith doesn't believe that p.
The Gettier case annoys everyone since '63. That doesn't matter. Show me where that argument for 4 goes wrong.
As I said before, I think "A because B" is just shorthand for a modus ponens:
If B then A;
B;
therefore A.
As it happens, you had included the conditional in your premises (1 I think), but p was nowhere to be found.
If we have the conditional explicitly, that means p is presupposed by 4, and there's no need for that, because we've been told in so many words that Smith believes that p.
Natural language isn't shorthand for logical notation. It's quite the other way around, and if logic cannot take proper account of Smith's belief that (p v q) is true because p is true, then it's not a problem with Smith's belief(which happens to be belief about the rules). It's a problem for logic.
I granted Smith's belief that p. So yes, p is presupposed by 4. The focus is what Smith's belief that (p v q) requires in order for it to even be held by Smith. That's what the argument sets out, and it shows Gettier's error in his report of Smith's belief.
I presented it in natural language.
Arrrgh! :P
I do not know how else to describe it.
Believing that 'either Jones owns a Ford or Brown is in Barcelona' is true, if based upon belief that 'Jones owns a Ford' is true, and accepting the rules of correct inference, requires knowing that if 'Jones owns a Ford' or 'Brown is in Barcelona' is true then so too is 'Either Jones owns a Ford or Brown is in Barcelona'. Smith's knowing that and still accepting that 'Either Jones own a Ford or Brown is in Barcelona' is true despite not believing that 'Brown is in Barcelona' is true, is for Smith to believe that 'Either Jones owns a Ford or Brown is in Barcelona' is true because 'Jones own a Ford' is true.
Smith is aware of what it takes for (p v q) to be true. He knows that (p v q) can only be true if either p or q is. He does not believe that q is true. He does believe that (p v q) is true. He does not believe that (p v q) is true because q is true. He does believe that p is true. He believes that (p v q) is true because p is true.
P's being true or Q's being true is what makes (p v q) true.
;)
You've mentioned this several times. I see this as knowing the definition of "or".
If A or B, then A-or-B.
It seems interesting if you throw in "is true", but it's really not.
If A is true or B is true, then A-or-B is true.
But again that's just the definition.
I see it as knowing what makes (p v q) true.
We're not actually disagreeing. :-)
"p ? q" has three semantic components: p, q, and ?. You have to know what they all mean to know what "p ? q" means; you have to know whether p and q are true to know whether "p ? q" is true.
Understood. Invoking meaning could be helpful here, for you do not have to know whether p or q are true to know what makes (p v q) true.
2 and 4 are two separate, albeit related, beliefs. 2 is a true belief and 4 is a false belief.
Yet again, it doesn't matter if I believe that Donald Trump is the President for a false reason. My belief that Donald Trump is the President is true. And it doesn't matter if Smith believes that p ? q is true for a false reason. His belief that p ? q is true is true.
I don't think the Trump example is an adequate comparison...
I also do not think that "(p v q) is true" adequately explains Smith's belief. I'm saying that Smith's belief is false because it is belief about what makes (p v q) true as compared/contrasted to belief that (p v q) is true. The former is prior to the latter during actual thought/belief processes.
Smith's belief isn't properly accounted for by 2. That's the need filled by arguing for 4. Smith's belief that (p v q) is true is belief that (p v q) is true as a result of p's being true. In other words, Smith's belief that (p v q) is true consists of belief about what makes it so. It's belief about the truth conditions. That's the only way he could believe g, h, and i. It's not belief that (p v q) is true, per se. It's belief about what makes them so. He believes that they are true because p is true.
Smith is aware of what it takes for (p v q) to be true. He knows that (p v q) can only be true if either p or q is. He does not believe that q is true. He does believe that p is true. He does believe that (p v q) is true. He does not believe that (p v q) is true because q is true. He believes that (p v q) is true because p is true.
P's being true or Q's being true is what makes (p v q) true.
I am on the jury of the trial of Mr. X. Mr. X Is accused of killing Bob. I sit in the courtroom and see all the evidence. Everything points to Mr. X- he has no alibi, he was seen in the area during the murder, he owns the murder weapon, and all the forensic evidence indicates he killed Bob. He has a motive and multiple witnesses confirm his motive and the other facts surrounding the case.
Would you say I am justified in believing Mr. X committed the murder and killed Bob?
To some extent, you're agreeing with Gettier: the reliance on Smith's belief that Jones owns a Ford is the source of Gettier's claim that Smith's belief that Jones owns a Ford or Brown is in Barcelona is justified.
Almost everyone feels something is wrong here. Some accept that it's a refutation of the JTB theory of knowledge, but many don't. So the question is what is going wrong here?
You say that (h) is not an adequate characterization of the belief Smith holds. You want (h) to drag (f) along with it. (BTW, your argument was my very first reaction too, so I sympathize.)
I think now that going down this road eviscerates entailment in a way we don't want. If we have a web of beliefs, connected by various degrees of the relation "is a reason for", we still need to individuate those beliefs, even if they confront reality in groups or as a totality, not singly, because we have to be able to revise them individually.
I think the usual approach to Gettier is probably right: we feel that the justification Smith has for believing (f) turns out to be irrelevant to the truth of (h). It's that irrelevance we want to capture. We need rules about how justification passes from one belief to another, something more precise than Gettier's principle that entailment preserves justification just as it preserves truth.
Hey Srap.
Interestingly enough, I am agreeing with Gettier, at least as far as the justification aspect goes, and as everyone will soon see - it is not a problem for justified true belief, because Smith's belief is not true. I mean, I do think that Smith is completely justified in his belief that: ((p v q) is true because p is true). The difference between everyone(it seems) and myself is that I find very good reason to say that Smith's belief is false. Thought/belief is my forte, so to speak, and it is informing my approach here.
As you've noted, and is shown immediately above, I've argued that (h) is not an adequate characterization of the belief that Smith forms/holds. What Gettier claims is Smith's belief is utterly inadequate in it's explanatory power regarding what Smith's belief consists in/of. As I've been working through this, along with the help of others - including yourself - I'm beginning to realize something curious. My earlier thoughts were put into a rough argument. While reading through the objections...
What I'm attempting to set out is that the belief that Smith holds prior to his acceptance of g, h, and i ought be the focus. That belief is required in order to accept any and/or all three, and it seems to me that it is only that approach that puts a much needed finer point upon what Smith's belief that (p v q) actually consists in/of. However, in my earlier rough outline, that timeline wasn't adequately represented. As a result, you and others have rightly said that we could stop at 2. Or better yet - that the issue is/was Smith's JTB that (p v q) is true, and that that is prior to what I've set out.
I'm working on how to show that Smith's arrival at (p v q) is true is nothing more and nothing less than that it is true because p is true, as compared/contrasted with Smith's believing it is true because belief that p, and realizing that (p v q) follows from p. The former is Smith's belief about (p v q). The latter is Gettier's report of Smith's belief, and it leaves out the former. The former sets out what realizing that (p v q) follows from p, and then accepting g, h, and i as a result of that realization entails and/or implies.
That would put what I'm arguing for prior to what Gettier arrives at. An appropriate outline ought show that Smith's belief that: ((p v q) is true because p is true) is temporally prior to and therefore effectively exhausts Smith's belief that: ((p v q) is true). That would dissolve the problem.
That is to say that Smith's belief that: ((p v q) is true) is existentially contingent upon Smith's belief that: ((p v q) is true because p is true).
Interesting. My approach is from a completely different direction, namely a focus upon the belief aspect, it ignores the aforementioned irrelevance and instead sheds much needed light upon the fact that Gettier doesn't properly account for Smith's belief about (p v q). Smith's belief about (p v q) necessarily predates and informs Smith's belief that: ((p v q) is true). Smith's belief about (p v q) is that: ((p v q) is true because p is true).
Let me explain...
Smith's belief that: ((p) is true) is Smith's believing "Jones owns a Ford". Smith's belief does not consist in/of believing that: (the statement "Jones owns a Ford" is true), unless Smith himself has learned to isolate his own thought/belief. In other words, unless Smith is actively involved in thinking about thought/belief. This comes to bear when attempting to properly account for Smith's belief that:((p v q) is true because p is true).
Doesn't that effectively dissolve the 'problem' with case II?
I'll have lots more to say in a little while, but first there's this: if you're still talking about all this as adding a step before Smith gets to (h), it doesn't matter. It doesn't even matter if it's false. You have to block Smith's belief that (h) or block it from being justified.
Are you going back to denying that he ever believes (h)?
Smith gets to (g), (h), and (i) just fine. It's the step after, namely Smith's realizing the entailment, and accepting all three as true - as a result of that realization - that I'm unpacking.
I'm not denying that Smith believes (h). I'm providing excruciating detail of exactly what that consists in/of.
It does matter if Smith's belief is false. I'm not even sure how you could possibly think/believe that it doesn't.
Because it all starts with a false belief, (f).
Gettier wants to show that Smith arrives at JTB from a false p as a means of placing the notion of justification in question. I have no skin in the game, so to speak. It seems to me that you very well may. I haven't given the justification aspect any thought at all to speak of.
As I mentioned earlier, my forte is thought/belief. I hold that the whole of philosophy has gone horribly wrong regarding thought/belief, and that many - perhaps most - of the historical philosophical issues/problems share that hinge point. That is, that they are all logical consequences of getting thought/belief wrong. With that in mind...
Taking the justification of Smith's belief into consideration requires getting Smith's belief right.
If Smith believes that (h), and is justified in his belief that (h), then if (h) is true, which it is, then Smith should know that (h), which he clearly doesn't.
For judging Case II, nothing else is relevant.
:-|
Is that what I said?
That is precisely what needs a thorough unpacking.
That is most certainly relevant.
That IS Smith's belief that: ((p v q) is true because (p) is true)
Or... more specifically...
Smith's belief that: ((p v q) is true because (p) is true) is inferred from his belief that: ((p) is true), ((p v q) follows from p), ((p v q) is true if either (p) or (q) is true), and ((q) is not true).
Show me where it goes wrong.
Do you understand why that sentence is there?
BTW, I've considered arguing that this is simply false:
But that's a whole 'nother thing.
What else could such an imagining consist of if not exactly what I've painstakingly set out in such excruciating detail?
Smith's belief that: ((p v q) is true because (p) is true) is inferred from his belief that: ((p) is true), ((p v q) follows from p), ((p v q) is true if either (p) or (q) is true), and ((q) is not true).
It is not the case that (p v q) is true because (p) is true.
Why ought the justification aspect matter here?
:-|
As far as I can tell, no.
If Smith believes that (h), and is justified in his belief that (h), then if (h) is true, which it is, then Smith should know that (h), which he clearly doesn't.
For judging Case II, nothing else is relevant.
That is what the below unpacks, and what the earlier more condensed argument sets out as well as what the earlier long-form argument explains...
p1. 'Jones owns a Ford' is true
p2. 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'
p3. 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true
p4. 'Brown is in Barcelona' is not true
C. 'Either Jones owns a Ford or Brown is in Barcelona' is true because 'Jones owns a Ford' is true
No, it really hasn't.
Smith has a false belief that (f). From it he derives, by valid inference, a true belief that (h). I describe this as an application of modus ponens by Smith. I think that's accurate enough and it is roughly how Gettier presents it. You describe the modus ponens step as Smith forming a belief that (h) because (f). It makes no difference to the overall argument. Smith then concludes that (h), which is a justified and true belief that is apparently not knowledge.
As I said, modus ponens does not actually apply here because (f) is false, although the conditional (f)?(h) is true. Smith, however, believes that (f), and thus is entirely consistent in applying modus ponens. His trouble comes not from making an inference he shouldn't -- he should, given his belief that (f); his trouble comes from having that false belief that (f).
I think it would also be fair to say that his trouble comes from believing that the evidence he has for (f) is strong enough to warrant a claim to know that (f). It wasn't. But that's another story.
(1) Smith does not believe that (h).
(2) Smith's inference of (h) from (f) is faulty.
What is your claim?
Here that means "Brown is not in Barcelona," and we are given no such claim.
You figure Smith doesn't know that?
:-}
Why such resistance Srap?
Here's the thing...
What Gettier claims that Smith does requires precisely what I've just set out.
Yes, we know. I've said as much. It's right there in the text. So what?
That is not a belief of Smith.
These are not equivalent:
(1) Smith does not believe that Brown is in Barcelona.
(2) Smith believes that Brown is not in Barcelona.
If you choose to submit your solution for publication, the natural choice would be Analysis.
You are correct that is what Smith believes. But why does that mean the Gettier case is wrong? Smith does not need to believe q or use q as a point of inference to arrive at (p v q). The propostion q can be anything that is not ~p. It can even be something Smith does not really have any opinion on. All Smith needs to be justified in believing (p v q). And if Smith is justified in believing p is true, then, by extension, he is justified believing (p v q) is true, as only one of the propositions in a disjunction is required for it to be true.
In this case, Smith is justified in p and believes p. By extension, he is justified in believing (p v q) is true, though Smith is indifferent to q's truth value or thinks q is false (he might even be justified in believing q). Therefore, Smith is justified in believing (p v q).
Smith has justified belief in (p v q). He is two thirds the way there.
It turns out (p v q) is true, but not because p; p is false and q is true. Smith has a justified false belief that p, so he is still justified in (p v q). It's just that his grounds for justification are false. However, q is true. Therefore, Smith believes a true proposition (p v q) and is justified in believing (p v q). Therefore, Smith has knowledge under the traditional account of knowledge: he has justified, true belief. But this seems wrong. Smith does not have knowledge of (p v q). Therefore, the traditional account fails.
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((q) is not true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)
Smith's belief that: ((p v q) is true because (p) is true) is inferred from his belief that: ((p) is true), ((p v q) follows from p), ((p v q) is true if either (p) or (q) is true), and ((q) is not true).
Quoting Srap Tasmaner
That was a couple months ago in the "'True' and 'Truth'"" thread, and might be worth revisiting now.
P ? Q has four possible models:
(1) P=0, Q=0
(2) P=1, Q=0
(3) P=0, Q=1
(4) P=1, Q=1
The gist of the above remarks was that, to take Case II as the example, Smith's justification relates to the models in which P is true (2 or 4), but it turns out P ? Q is in fact true under the third model, in which only Q is true.
@creativesoul is arguing that because all of Smith's beliefs are formed under one of the interpretations in which P is true, that his belief does not include or encompass the interpretations in which P is false.
Michael Dummett makes a distinction (when talking about assertion, as usual -- here it is Smith's acceptance that is at issue) that may be helpful here: there are the grounds upon which you make an assertion (which he calls its "justification"), and then there is what you are committed to by making the assertion. It is clear that Smith's belief that P is the grounds upon which he accepts that P ? Q, but by accepting that P ? Q he is committed to accepting all four possible models.
The commitment part is what we rely on when we judge lucky guesses to be correct. If, on the basis of nothing more than a hunch, you were to wager that the Battle of Hastings was fought in 1066, your bet would pay off. It is also possible to get the right answer for the wrong reasons, rather than for no reason.
This distinction shows up in our language use in many ways. If you believe you will be off work in time to meet me for a 7:00 movie, and you promise to, you have committed to being there and that commitment doesn't change because you end up working late and standing me up. You have broken your promise. Misunderstandings too often arise because a person might have one thing in mind, but the plain language of what they say admits of another interpretation, and if they misspoke, perhaps only an interpretation they did not intend. "That's not what I meant!" "But that's what you said!"
We do not, in general, take the grounds upon which an assertion is made as constraining the commitment made by that assertion. If we did, much about our language use would be different, but one thing in particular. To assert, or in Smith's case to accept, that a proposition is true is generally to accept that it may be false. That's usually the point of making an assertion. You provide information to your audience by telling them something is the case that might not be. (I tell you I stopped at the store and got milk, because I might not have.)
The exception, of course, is statements that are necessarily true. To make an assertion in which you admit as possible only the models in which the statement is true is take the statement as true necessarily. (If this were generally the case, we would all of us believe whatever we believed to necessarily be the case.)
In this case, if Smith were to accept that "Jones owns a Ford or Brown is in Barcelona" only insofar as Jones owns a Ford, then he would be allowing no possibility that Jones does not own a Ford. He would be taking "Jones owns a Ford" to be a necessary truth.
Obviously, there is no support for this claim in the text.
Once again, that is correct only if "or" is taken exclusively.
I just showed how that works...
It is relevant. Smith accepts all three.
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((q) is not true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)
Smith's belief that:((p v q) is true because (p) is true) is inferred from his beliefs that:((p) is true), ((p v q) follows from p), ((p v q) is true if either (p) or (q) is true), and ((q) is not true).
You're on the wrong track, in my view. I have explained why as best I can.
The idea I sketched a couple months ago, that justification cannot cross the boundary between one interpretation and another, is essentially the mainstream response to Gettier, that something is needed to guarantee the relevance of the belief's justification to its truth for that belief to count as knowledge. You must get the right answer for the right (sort of) reasons.
Nothing Gettier states warrants such talk about Smith's belief.
The last comment here reminds me of Davidson...
I understand that the mainstream view focuses upon justification. Smith's belief, as I've just set it out, is not true. For Smith(given his strong belief that p), arriving at a complex thought/belief such as belief that:((p v q) is true) requires knowing what (p v q) means, what it takes for (p v q) to be true, and inferring what I've set out...
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
That's better. The "because (p) is true" in C1 is equivalent to and/or satisfies Gettier's own criterion of "on the basis of (f)..."
C2. ((p v q) is true)(from p3,C1)
Gettier wants to get to the above without going through C1, even though he explicitly states acceptance on the basis of (f). C2 doesn't adequately represent Smith's thought/belief, as Gettier himself sets out. It is only C1 that exhausts Smith's thought/belief, as Gettier himself sets out.
Smith's belief that:((p v q) is true because (p) is true) is not equivalent to belief that:((p v q) is true)
Salva veritate
Smith's acceptance of all three on the basis of (f) is...
Belief that:((g) is true because (f))
Belief that:((h) is true because (f))
Belief that:((i) is true because (f))
...and belief that:((p v q) is true) is inadequate. It is found to be sorely lacking.
Alright. I know that this is a common approach to the Gettier problem. I reject it as irrelevant. That claim carries with it a justificatory burden. I'll honor that.
The Gettier problem has as it's target Smith's beliefs. That is crucial to keep in mind. Gettier quite clearly sets out the thought/belief process that Smith goes through. Smith believes Jones owns a Ford. Smith isolates his own thought/belief by virtue of putting it in the following statement form:'Jones owns a Ford' or (f). He then constructs 3 propositions, (g), (h), and (i). The propositions all follow the rules of entailment. Smith realizes this much. Smith believes that (g), (h), and (i) follow from (f) because he believes that all three follow the rules of correct inference. So, Smith's belief that:((g), (h), and (i) are valid inferences) is correct, as Gettier says below.
Now, with regard to what Srap is talking about above, Smith's belief renders interpretations of "or" irrelevant because Smith's belief is explicit. Gettier claims that Smith accepts (g), (h), and (i) on the basis of (f). The argument provided below adds clarity to the understanding here. It sets out Smith's thought/belief process as Gettier sets out...
Smith believes that:
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
Smith has false belief. There is no issue with JTB.
Yes, he does. But he also has a true belief, and that is an issue.
You can keep repeating that Smith believes that p ? q is true because p is true, but this does nothing to address the fact that Smith believes that p ? q is true.
Smith's belief that:((p v q) is true because (p) is true) is not equivalent to belief that:((p v q) is true)
Salva veritate
Smith's acceptance of all three on the basis of (f) is...
Belief that:((g) is true because (f))
Belief that:((h) is true because (f))
Belief that:((i) is true because (f))
...and belief that:((p v q) is true) is inadequate. It is found to be sorely lacking in it's ability to meet Gettier's own criterion regarding the thought/belief process that Smith goes through; and it is quite the metacognitive process...
I know they're not equivalent. They're two different things that Smith believes, just as "Donald Trump is the President" and "Donald Trump is the President because he won the popular vote" are two different things that I believe.
In each of these cases there is a false belief and a true belief. You're ignoring the true belief, but it's the true belief that is relevant to the topic at hand.
I've already said that that objection is irrelevant. I suppose that charge carries a burden with it...
"Donald Trump is the President" is not existentially contingent upon "Donald Trump is the President because he won the popular vote." You can arrive at the former without going through the latter. That is not the case with Smith's thought/belief process.
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)
Now, as the above argument clearly shows, Smith cannot arrive at C2 without going through C1. That is according to Gettier's own descriptions of Smith's thought/belief processes.
False analogy.
And Smith can arrive at "p ? q" without going through "p". He could have believed "q", just as I could have believed "Donald Trump won the most electoral college votes".
So I don't understand your distinction. We both arrived at our belief from a false reason but could have arrived at our belief from a true reason. Regardless, my belief that Donald Trump is the President is true and Smith's belief that p ? q is true is true.
Given exactly what Gettier sets out, I have constructed an argument which is meant to represent Smith's thought/belief process.
But when I described my thought/belief processes that led me to believe that Donald Trump is the President you said it didn't matter. You're moving the goalposts.
Do I or do I not have a true belief that Donald Trump is the President, despite arriving at this belief from a false reason?
But let's do a different example that is similar to your argument:
p1. "John is a widower" is true
p2. "John was married" follows from "John is a widower"
p3. "John was married" is true if either "John is a widower" or "John is a divorcee" is true
C1 "John was married" is true because "John is a widower" is true
C2. "John was married" is true
But John isn't a widower; he's a divorcee. According to you, if I believe that John is a widower then I cannot have a true belief that John was married, because what I really have is the false belief that John was married because he is a widower.
This is clearly wrong. It doesn't matter why I believe that John was married. I do, and he was. People can have true beliefs arrived at from false reasons.
No, it's not the same as Gettier's case. First of all, it does not follow from the fact that Y follows from X that Y is true.
That's not what Gettier sets out.
Two completely different kinds of description Michael. The former argument represent Smith's thought/belief process as Gettier sets it out. The latter does not. The first premiss is the only thing close to being a parallel.
That was supposed to adequately represent my argument below. It doesn't.
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)
Alright. So we have three separate propositions at work here. John is a widower. John was married. John is a divorcee. They need to be put into the appropriate form. 'John is a divorcee' is a parallel to q. You would need to be totally ignorant regarding John's marital status, otherwise there is no parallel to Gettier's description of Smith's thought/belief process. So, with that in mind, we arrive at the following parallels...
A. "Either John is a widower or John is a divorcee" could parallel (p v q)
B. "Either John was married or John was a divorcee" could parallel (p v q)
B makes no sense at all, for if you're totally ignorant about John's marital status, then you could not hold strong justified belief about it. Since that is the case, B is rejected. That leaves us with A. Let's work through it...
p1. ((p) is true)
p2. ((p v q) follows from (p))(from a)
p3. ((p v q) is true if either (p) or (q) is true)(from a,b)
C1. ((p v q) is true because (p) is true)(from p1,p3)
C2. ((p v q) is true)(from p3,C1)
p1. ((John is a widower) is true)
p2. ((Either John is a widower or John is a divorcee) follows from (John is a widower))
p3. ((Either John is a widower or John is a divorcee) is true if either (John is a widower) or (John is a divorcee) is true)
C1. ((Either John is a widower or John is a divorcee) is true because (John is a widower) is true)
C2. ((Either John is a widower or John is a divorcee) is true)
That's what it would look like, and it suffers the same fate as Smith's belief.
Srap I'm working on a response to all sorts of other stuff you've mentioned here. Now seems a good time to get into that stuff. I mean, since I've finally come to acceptable terms with exactly what I'm trying to set out. Thanks to an old friend of mine who gave me the appropriate tools...
;)
I'm not ignoring your last post. Much of it has been addressed. None-the-less, I plan on attending to it...
;)
I believe that A is true. I believe that B is true if A is true. Therefore, I believe that B is true. B is true. Therefore, I have a true belief, even if A is false. This is the form that all of these arguments follow.
I believe that John was married because he is a widower. John isn't a widower, but my belief that John was married is still a true belief.
I believe that Trump is the President because he won the popular vote. Trump didn't win the popular vote, but my belief that Trump is the President is still a true belief.
I believe that p ? q is true because p is true. p isn't true, but my belief that p ? q is true is still a true belief.
You can keep insisting that these aren't comparable, but they are. I can't put it any simpler for you. Smith has a true belief.
That's not what Gettier sets out.
Perhaps maybe it simply place certain kinds of entailment under scrutiny. As you say, each thought/belief has it's own set of truth conditions(although, unlike yourself, I think that some share those).
My formulation of Smith's thought/belief process avoids the issue, does it not?
Smith does not believe that:((h) is true) That is too simplistic an account. Rather, Smith believes that:((h) is true because (f)). Gettier says much the same thing when he writes...
Salva veritate
Belief that:((h) is true) is not equivalent to belief that:((h) is true because (f))
Seems to me that Smith's belief is explicit. As above, Smith believes that:((p v q) is true because (p)). That most certainly does not obligate Smith to accept different senses of "or". As a matter of fact, I think that in order to validly criticize another's argument(Smith's belief in this case), the first step is to accept their meaning; sense; definitions; etc. Given that, it doesn't make any sense to misattribute meaning to Smith's thought/belief as a means for scrutinizing it. That's what non-sequiturs(strawdogs) are made of. The notable exception, of course, is if one can effectively show that something is wrong with their usage(equivocation, nonsensical, etc.).
I'm wondering if these sorts of considerations are even able to arise if it turns out that the Gettier problem is nothing more than a half-century worth of misunderstanding.
Belief that:((p v q) is true) is inferred from belief that:((p v q) is true because (p) is true) which is inferred from his belief that:((p) is true), ((p v q) follows from (p)), and ((p v q) is true if either (p) or (q) is true).
Salva veritate
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p) is true).
As above... Therefore the traditional means of accounting for Smith's thought/belief process fails. The traditional account remains untouched. Smith has false belief. False belief is not a problem for JTB no matter how it is arrived at.
No.
1. Your reading of Gettier's original paper is wrong on its face and you're never going to convince anyone.
2. Even if you were right, and there was something faulty in Gettier's original cases, no one would care. Once you've seen the trick, it is child's play to construct new Gettier-type cases. The Gettier problem is this whole family of cases, and its seemingly endless adaptability. There is no broad agreement on any version of the JTB theory that meets our intuition of what counts as knowledge while blocking the creation of a Gettier-type case to undermine that specific approach.
Gratuitous assertions won't do at this juncture in the discussion. I'll convince anyone and everyone who is capable of following along.
If it's a Gettier case, then it ought follow the thought/belief process that Gettier himself lays out. If it does then you'll end up with false belief. False belief, no matter how it is arrived at, does not pose a problem for JTB.
Show me how one arrives at belief that:((p v q) is true) without going through the thought/belief process that I've been painstakingly laying out since the very beginning of this thread.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
Quoting creativesoul
It's exactly that. "A" is "p" and "B" is "p ? q".
Could you write this out in formal logic, or, at least, explain what it is the formal relationship between the two propositions: [(p v q) is true] and [(p) is true]?
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
1. S believes P
2. S deduces Q from P
3. S believes Q
4, S is justified in believing P
5. S is justified in believing Q
I'm not misreading. I'm strongly asserting that 1 and 2 are not always adequate for believing Q. In Case II, another deduction is necessary for arriving at belief that:((p v q) is true).
They are if you're a rational person. How can you believe A but not believe some B that you recognise to follow from it? You'd have to be an idiot.
Now, now.
Heh, I can see how that could be misread. I was saying that the person who believes A but not what they recognise to follow from A is an idiot. I wasn't calling creative an idiot. ;)
It's still not a nice word to use, Mr. Michael. Now mind your manners, there's a good boy. ;-)
P: My username is Chany.
I think I'm pretty justified in believing P is true.
Q: There are currently 300 billion flying pigs on the earth.
I think I'm pretty sure this is false.
P v Q.
I arrive at this by the addition rule of logic. I am justified in believing it is true. I believe it is true. It has to be, because P is true. If I were taking a test and I was asked, "is (P v Q) true or false," I'd answer true and be absolutely correct.
Is this wrong in any way?
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
Fill it out.
Not a Gettier case though.
C2. p ? q is true (from C1).
This is the Gettier case.
Smith cannot get to belief that:((p v q) is true) without ((p v q) is true because (p)).
Belief that:((p v q) is true) is not equivalent to ((p v q) is true because (p)).
The "because" is the other necessary deduction.
I know they're not equivalent. But the latter entails the former, and the former is true. Smith has a true belief.
Let's change P: I am not adopted.
I think I am fairly justified in this belief. No one said anything, I look like a bit like my father, and such.
Let's change Q: Michael lives in New York City.
I have no idea whether this is true or not. I suspend judgement. I can't be justified in believing Q.
Now, we look at (P v Q).
I am justified in believing (P v Q) is true on account of my justification in P.
Is this correct?
Smith cannot arrive at belief that:((p v q) is true) with a single deduction. Gettier's formulation for Smith's arrival at belief that:((p v q) is true) is found to be utterly inadequate as a direct result. To arrive at belief that:((p v q) is true) Smith must go through belief that:((p v q) is true because (p)). The argument shows precisely that.
Salva veritate is germane because belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former cannot be substituted for the latter, for it leaves out the necessary deduction within Smith's thought/belief process. The latter is Smith's thought/belief.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
You arrive at true belief. The justification aspect is not a current concern of mine. Also not a Gettier case.
You still haven't explained what this proposition in formal logic. What does "because" translate as?
I'm not saying that they can be substituted. I'm saying that the latter entails the former.
If I believe that Donald Trump is the President because he won the popular vote then I believe that Donald Trump is the President. If Smith believes that p ? q is true because p is true then Smith believes that p ? q is true.
In both of our cases we have a false belief and a true belief. You haven't shown that Smith doesn't have this true belief. You're just ignoring it and falsely claiming that the buck stops at the false belief.
Am I justified in P and can I use my justification in P and basic rules of logic to arrive at (P v Q). I am justified in believing (P v Q). I do not care about the actual truth values of these various propositions. I currently only care whether I would be justified in (P v Q).
I hate to ask this, but this symbol "?" means therefore, correct? I thought the triangle was inverted. Or is that simply to seperate the two propositions?
? is because and ? is therefore. I believe it's just a way to reverse the order.
Justification is not my concern. Smith holds false belief. False belief is not a problem for JTB. Gettier's Case II is not a problem for JTB.
On the way to my belief that Donald Trump is the President I form the belief that Donald Trump is the President because he won the popular vote. But why does that matter? My belief that Donald Trump is the President is true nonetheless.
It's not necessary. He could have arrived at that belief by believing that q is true, just as I could have arrived at my belief by believing that Donald Trump won the most electoral college votes. It's just that in this case we didn't. But again, why does that matter? My belief that Donald Trump is the President is true nonetheless and Smith's belief that p ? q is true is true nonetheless.
Salva veritate is germane because belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former cannot be substituted for the latter, for it leaves out the necessary deduction within Smith's thought/belief process. The latter is Smith's thought/belief.
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
Fill it out Michael...
That's Gettier's Case II being adequately taken account of.
Are you going to use p2 for anything?
Also, p3 is just P?Q?P?Q.
p2 accounts for the single deduction in Gettier's formulation.
I believe that Donald Trump is the President because he won the popular vote. This is a false belief, but my belief that Donald Trump is the President is true.
Smith believes that p ? q is true because p is true. This is a false belief, but his belief that p ? q is true is true.
How do these situations differ?
Mirror mirror...
It's a premise not used in your deduction anywhere.
:s
Not following Srap...
You derive C1 from p1 and p3. What do you use p2 for?
So what does Gettier use p2 for?
It matters because the only way that Smith can arrive at belief that:((p v q) is true) is via belief that:((p v q) is true because (p)).
The argument shows that.
The gravity is immense Michael. Set your preconceptions aside for a moment, and re- read my earlier post laying out the justificatory ground for the argument I've presented against Gettier.
No it isn't. He can get there via the belief that q is true. Or he can get their via trusting his friend who tells him that p ? q is true.
That's not what Gettier set out.
Don't get into it...
;)
Thought/belief has not been adequately represented by the whole of philosophy. That's another thread in it's own right, although this one sheds a bit of light on that. What can I say, I like to start with a 'bang!'...
O:)
All you seem to be saying is that Smith only believes that p ? q is true because he believes that p is true. But again, how is that any different to me only believing that Donald Trump is the President because I believe that he won the popular vote?
:-O
This coming from one who accused me of misreading...
No. He didn't.
So, how is Smith's belief any different to my belief? We both believe that some A is true because some B is true, even though our respective Bs are false.
But Smith believes (P v Q) as a proposition.
A1. I believe that John is a bachelor
A2. If John is a bachelor then John is a man
A3. I believe that John is a man because he is a bachelor
A4. I believe that John is a man
A5. John isn't a bachelor
A6. John is a man
Do I have a true belief? Yes. My belief that John is a man.
B1. I believe that p is true
B2. If p is true then p ? q is true
B3. I believe that p ? q is true because p is true
B4. I believe that p ? q is true
B5. p isn't true
B6. p ? q is true
Do I have a true belief? Yes. My belief that p ? q is true.
So, @creativesoul, how do you address this? Is the logic in A different to the logic in B? Or is A4 not a true belief that I have? Because it seems obvious to me that the logic is the same and that A4 is a true belief that I have. Therefore B4 is also a true belief that I have.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
Fill it out with your candidate for a belief that:((p v q) is true) Michael.
"Each of these propositions is entailed by (f). Imagine that Smith realizes the entailment of each of these propositions he has constructed by (0, and proceeds to accept (g), (h), and (i) on the basis of (f)."
Yes?
That is Smith's deduction.
Yes. It's really that simple.
And because you can't assume that Smith knows the law of addition, Gettier specifies that he does; and because you can't assume that he actually makes the inference he is entitled to, Gettier specifies that he does.
Not like Gettier Case II.
Again. Not like Gettier Case II.
That's exactly Gettier's Case II.
It is wrong.
It doesn't follow that thought/belief process...
That's a quote from Gettier explaining why Smith believes (g), (h), and (i). Smith believes (f) and Smith recognizes (g), for example, is entailed by (f) and accepts (g) as true. Therefore, Smith believes (g) on the basis of (f). Therefore, Smith believes (g).
Put another way, Smith believes the P. Smith recognizes (P v Q) follows from P. Michael is correct: Gettier says that Smith believes (P v Q). And what does Gettier say is Smith's reasoning for his belief? Smith believes P and recognizes (P v Q) is entailed by belief in P.
No it's not. It's another way of saying "P entails Q".
You have a typo there. You meant "(g), for example, is entailed by (f)".
Thanks. Fixed.
Yes. I know what it is. The full text of Case II preceding his conclusion that Smith is justified in believing Q is below. It warrants very careful attention...
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q.
Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true).
So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. So, as Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i). All of which are (p v q). So, Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing in the above two quotes about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith hasn't yet gotten to the point where he has formed and/or holds belief that:((p v q) is true)...
But oddly enough, Gettier concludes that that is the case, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
"Imagine that Smith realizes the entailment of each of these propositions he has constructed by (0, and proceeds to accept (g), (h), and (i) on the basis of (f)."
Gettier literally just says that Smith accepts (g), (h), and (i) as true propositions. In other words, Smith believes they are true; Smith believes (g), (h), and (i). These propositions are Q in this quote:
S is Smith. P is (f). Q is (g)/(h)/(i) (they all work). Gettier wants to emphasize that Smith's beliefs are all justified. Smith is justified in his beliefs and makes valid inferences from these beliefs towards different beliefs.
Smith believes C1. From C1, we know that Smith also believes C2: (p v q)- its the conclusion in Smith's internal argument, an argument indicated by "because" in C1. Smith's C1 is false because (p) is not true. However, Smith still believes C2- (p v q)- and is justified in that belief. And, it turns out, that (p v q) is true, as (q) is true. Smith has justified true belief, but he does not have knowledge.
The above quotation is about justification, not about the truth value of the statements. Smith doesn't say anything about Smith's beliefs as he is explaining Smith's justification because he already showed Smith's beliefs by saying Smith accepts (believes) the propositions (f) and (f)'s entailments: (g), (h), and (i).
Except you don't show the actual deduction of p?q. In truth, it's barely a deduction at all. It's just or introduction.
Ah. There it is once again.
The conflation of being true and being called "true" as the result of being the conclusion of a valid inference. Validity is insufficient for truth.
If Smith is rational, he wouldn't do that.
Why ought I need to show it?
Smiths belief that:((p v q) follows from (p)) shows it.
No it doesn't. That's a conditional. It says only that if p, then p?q. We have p, therefore we have p?q.
And Gettier characterizes this conditional as a true belief of Smith. That is, p?q does in fact follow from p -- it's not "merely", so to speak, a belief of Smith. It's one of Gettier's conditions that the entailment be correct.
2. P.
Therefore,
3. Q
If I say, "I accept Q because of the argument is valid and sound," it is equivalent to saying "I believe Q is true." Q follows from the argument above.
That's what I said...
Smith holds the belief that:((p v q) follows from (p)).
That is a true belief, not that it matters.
Fill out Smith's belief using modus ponens...
For example, I believe the government should legalize pot. Why? Because of various arguments I've seen for it. My belief is legalizing pot is the conclusion of arguments. But I still believe the proposition "the government should legalize pot."
Again, please write your proposition out in formal logic or explain how the word "because" functions in logic.
I'm not even understanding what you're trying to say...
I've put forth Smith's thought/belief process...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
That is Smith's belief. Gettier wants to say that Smith believes that:((p v q) is true), and he wants us to think/believe that Smith can arrive at that from, or as a result of arriving at p2. He neglects to consider that p3 and C1 are necessary. And, as I've argued ad nauseum...
Salva veritate
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)).
The "because" in C1 is the deduction that is missing from the Gettier formulation. It is a necessary step in believing this particular Q.
First, it's not. If it was, it would be only symbols with no words.
In C1, what does "because" translate to in formal logic? Does it signify a conjuction, like "and" does? Does it signify a conclusion, like "therefore" does?
Just to be clear, you are claiming that Smith does not actually believe that p?q is true, right?
I'm saying that:
Smith's belief that Q is nothing less than belief that:((p v q) is true because (p))
Does Smith believe that pvq is true?
I'm curious though. If Smith does go through the process I've set out and arrives at C2, doesn't that nullify his justification?
It's an invalid inference. My solution is good both ways, right?
:-*
So does Smith believe that "Jones owns a Ford or Brown is in Barcelona" is true?
EDIT: left off "is true".
But he does not believe that Jones owns a Ford or Brown is in Barcelona?
So he does believe "Jones owns a Ford or Brown is in Barcelona" is true?
Believing "'Jones owns a Ford or Brown is in Barcelona' is true" is not equivalent to belief that:((p v q) is true because (p)).
Does Smith believe that Jones owns a Ford or Brown is in Barcelona?
But he does not believe that Jones owns a Ford or Brown is in Barcelona?
But he does not believe that Jones owns a Ford or Brown is in Barcelona?
O:)
But he does not believe that Jones owns a Ford or Brown is in Barcelona, and he does not believe that "Jones owns a Ford or Brown is in Barcelona" is true?
QED?
So Smith does believe that "Either Jones owns a Ford or Brown is in Barcelona" is true?
Salva veritate
So Smith does not believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?
But he does not believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?
Does Smith believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?
Does Smith believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true?
So Smith believes that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford, and he does not believe that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true.
Is that correct?
I've said nothing about what Smith does not believe.
Quoting creativesoul
Notice anything odd here:
Where does Gettier say that Smith believes that Jones owns a Ford?
Continue...
I think I'd read somewhere before that there are doubts about how Gettier's original cases are constructed, but I hadn't though much about it, as we had other fish to fry in this thread. (As I said before, no one particularly cares because it's the not these particular cases but the pattern that's of interest.)
At any rate, none of us paid much attention to this.
So the form of the argument is actually this:
1. Smith has strong evidence for (f)
2. If (f) entails (h), evidence for (f) is evidence for (h)
3. (f) entails (h)
4. Smith's evidence for (f) is evidence for (h) (from 1-3)
5. Smith accepts (h) on the basis of the evidence he has for (f)
He certainly could accept (f) on the basis of the evidence he has. If that evidence is strong enough for him to accept (h), it's certainly strong enough for him to accept (f). But as it happens, Gettier never says that he does.
6. Smith's evidence for (f) justifies his belief that (h)
7. (h) is true
Should probably change that to:
6a. If the evidence for (h) is strong enough, it justifies Smith's belief that (h)
6b. Smith's evidence for (h) is strong enough (from 1 and 4)
6c. Smith's evidence for (h) justifies his belief that (h)
Hmmm...
Doesn't that involve p's being believed with strong ground but false? Each and every time?
Do you mean besides all of the cases inspired by Gettier?
No. Many involve something like faulty definite descriptions along the lines of Case I, and many involve more than a passing resemblance to the argument from illusion.
I suppose the SEP article is good, but I haven't looked in a while. I remember finding this article helpful.
More specifically, do they all follow Gettier's above formulation and if so, do all the Q's involve disjunction?
The upshot for our discussion here:
Everywhere I said all Smith's troubles flow from his having a false belief that Jones owns a Ford, I was wrong.
Everywhere you suggested that Smith really only believes that Jones owns a Ford, you were wrong.
Yes to the first, no to the second.
For instance, there's the dog-sheep:
You see in a field what looks to be a sheep and form the belief, based on direct observation, that there is a sheep in the field you are observing. But what you observe is actually a dog disguised (?) as a sheep. But there is in fact a sheep in that field; it's just behind a rise where you can't see it.
Your direct observation of the dog-sheep justifies your that there is a sheep in the field, and there is, but this doesn't seem like knowledge.
I'm not even sure what that means Srap. I don't remember ever saying that. False belief does not make a good starting point...
Good one.
Seriously. Show me.
Yeah. I vaguely remember reading something like this before... and barns. Never really gave it much thought though. Today's the day...
It doesn't follow that formulation.
I'm corn-fused.
:P
Edited to add: Oh yeah... it satisfies JTB. Epistemic luck. Yup. It does place justification under duress though, doesn't it?
Those are from the first 5 pages:
Quoting creativesoul
Quoting creativesoul
Quoting creativesoul
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Quoting creativesoul
Quoting creativesoul
Quoting creativesoul
These are from the last five pages:
Quoting creativesoul
Quoting creativesoul
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You can't seriously suggest that you haven't been arguing that Smith believed P?Q only because he believed P, and that you almost continually, with a few momentary lapses, refused to allow that Smith actually believed P?Q.
We were both wrong there. Gettier never attributes to Smith the belief that Jones owns a Ford. The only beliefs he ever attributes to Smith are (g), (h), and (i).
We were both wrong. Let's leave it at that.
I was most certainly wrong regarding the above...
X-)
I stand by all the rest. Gettier most certainly attributes belief that Jones owns a Ford to Smith. The entire case fills out his formulation preceding the cases in his original paper.
From the Lycan paper I linked:
The idea here is that Henry's belief is too lucky -- if he had happened to form the same belief looking at one of the other "barns", he'd be wrong. So there is some doubt about whether his current belief counts as knowledge.
This is a slightly different way of putting the pieces together, but is still a Gettier descendant.
That one's wrong too!
:P
No he really doesn't and I suspect it was deliberate.
Again. Don't see the problem. If it is a barn, then his belief is true. If it is not, then his belief is false. That one's quite a stretch on the imagination as well. I mean, we can all think of some logically possible world in which things make different kinds of sense.
We get that wrong and we get something or other wrong about everything ever spoken and/or written.
It's ambiguous.
"S is justified in believing that P" could mean:
(1) If S were to believe that P, his belief that P would be justified, or
(2) S believes that P and his belief is justified.
In the quote you gave, Gettier seems to conflate the two, but it's harmless because he's talking about this:
That is, the belief that P is one of the three conditions, listed here in TBJ order. I say conflation is harmless here because he's specifically talking about cases where all of (i), (ii), and (iii) hold.
In the specific cases he offers -- I just glanced at Case I -- he does not attribute the belief for which there is justification, but only uses it as the premise from which a different belief is derived.
Looks like a problem with entailment. Truth conditions matter.
Same pattern as in Case II: Smith has strong evidence for the conjunctive proposition (d), but Gettier never says that he accepts it, only that he derives (e) from it, and that (d) is false while (e) is true. Smith does accept (e).
Here, he says "on the grounds of (d)", where in Case II he says "on the basis of (f)". That's somewhat ambiguous. Could mean that he's accepted (d) (and (f) in Case II), but then Gettier is explicit about him accepting (e) (and (g), (h), and (i) in Case II) so why not say so explicitly? His preamble I think does not require that the antecedent be believed, only that it be justified, since all we're going to get from these antecedents is justification anyway, as they never turn out to be true.
Well you know I don't agree there.
If he believes that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford then he believes that the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true. And if the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true because Brown is in Barcelona then the proposition "Either Jones owns a Ford or Brown is in Barcelona" is true.
So Smith has a true belief.
I've addressed your confusion here. Nobody is saying that validity is sufficient for truth. Validity is one thing and truth is another. I've provided examples of valid arguments with false conclusions and valid arguments with true conclusions. Smith's case is a valid argument with a true conclusion.
Quoting creativesoul
He also holds the belief that p is true, and so also holds the belief that p ? q is true.
The first is in thinking that the following is an exhaustive account of Smith's beliefs:
1. p
2. p ? p ? q
But it isn't. There is also the conclusion:
3. p ? q
The second is in thinking that Smith's belief on p ? q being true is only:
4. p ? q ? p
But it isn't. It's also:
5. p ? q
And before you respond yet again with "salva veritate", I'm not saying that p ? q ? p is equivalent to p ? q, just as I'm not saying that p is equivalent to p ? q. I'm saying that p ? q ? p entails p ? q, just as I'm saying that p entails p ? q.
This is a valid argument:
1. p
2. p ? p ? q
3. p ? q
Therefore the rational person who believes 1 and 2 will also believe 3. Consider:
4. Socrates is a man
5. If Socrates is a man then Socrates is mortal
6. Therefore, Socrates is mortal
A valid argument. Therefore the rational person who believes 4 and 5 will also believe 6.
It is true that Smith might not be rational and might not believe 3 (or 6) even though he believes 1 and 2 (or 4 and 5), but that's irrelevant. Gettier asserts that he is rational and does.
The problem that Gettier raises is that if Smith believes 3 because he believes 1 and 2 – and if 1 is justified but false, and 2 and 3 are true – then Smith has a justified true belief that intuitively isn't knowledge.
If all you're saying is that a belief in 3 doesn't necessarily follow from a belief in 1 and 2 then you're addressing a red herring.
Can't get to 3 from 1 and 2. Can't get to 6 from 4 and 5. Missing premiss in both.
False premisses and valid form cannot yield true conclusions.
Gettier's Case II has Smith working from a false premiss. For whatever reason, convention has been bewitched for half a century. I've shown that arriving at belief that:((p v q) is true) because (p)) requires more than one deduction. Gettier's formulation requires only one. One cannot arrive at belief that:((p v q) is true). Can't be done. Prior to ever getting there, one must first go through belief that:((p v q) is true if...) and belief that:((p v q) is true because(insert appropriate corresponding belief to the prior 'if')).
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q)) is true because (p))(from p1,p3)
That's the solution. Gettier gets to p2(longwindedly) and wants to claim that 'therefore' Smith believes that ((p v q) is true). I've already argued for all this without subsequent refutation.
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q.
Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true).
So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. So, as Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i). All of which are (p v q). So, Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing in the above two quotes about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith hasn't yet gotten to the point where he has formed and/or holds belief that:((p v q) is true)...
But oddly enough, Gettier concludes that that is the case, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds that belief. I've shown all sorts of problems with Gettier's account. That want of Gettier is yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because(p)). We cannot swap one for the other. The latter consists in part of the deduction missing in Gettier's account.
Salva veritate
QED
What's the difference between a premise and an inference rule?
And what would that be?
True premisses and valid form cannot yield false conclusions.
False premisses and valid form cannot yield true conclusions.
Gettier's Case II has Smith working from a false premiss. For whatever reason, convention has been bewitched for half a century. I've shown that arriving at belief that:((p v q) is true) because (p)) requires more than one deduction. Gettier's formulation requires only one. One cannot arrive at belief that:((p v q) is true). It can't be done, unless that is; one wants to conflate being true with being called "true" as a result of being the product of a valid inference. Validity is insufficient for truth. Prior to ever getting to belief that:((p v q) is true), one must first go through belief that:((p v q) is true if...) and belief that:((p v q) is true because(insert belief statement(s) corresponding to the prior 'if')). That holds for any and all interpretations thereof.
Salva veritate
What I'm saying is that the following is not only my argument. It is not only an adequate account of Smith's thought/belief process, but it is also necessary for any and all disjunction. It's a formula that doubles as a solution. This can be tested by virtue of filling it out...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))(from p1,p3)
That's huge.
Yes they can.
1. If my name is Susan then I am a man
2. My name is Susan
3. Therefore, I am a man
False premises, true conclusion.
Quoting creativesoul
Yes you can. They're valid. The second is the stereotypical syllogism.
The rational and wise person knows that validity is insufficient for truth.
Show me don't tell me.
Nobody is saying that the conclusion is true because the argument is valid. There are two different parts to this scenario. The argument is valid and the conclusion is true.
Quoting creativesoul
I've set it out many times. Here it is again:
1. I am a woman
2. I am a woman or London is the capital city of France
Valid with a false conclusion.
3. I am a woman
4. I am a woman or London is the capital city of England
Valid with a true conclusion.
5. Jones owns a Ford
6. Jones owns a Ford or Brown is in Barcelona
Valid with a true conclusion.
Quoting creativesoul
The examples I have given are valid.
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...( ))
C1. ((p v q) is true because(insert belief statement(s) corresponding to the prior 'if'))(from p1,p3)
Fill it out...
Hmmm...
Must take more time than I had imagined.
No. You're missing the point.
Smith - himself - would not form belief about Brown's location. One cannot know they are ignorant about Brown's location and simultaneously form and/or hold a belief about where Brown is located.
The mistake here is conflating knowledge of the rules of entailment/disjunction with belief. Believing that (g), (h), and (i) are entailed by (f) is not equivalent to believing the disjunctions. Following established rules counts as being justified in putting those rules to use. Smith is justified in believing that he has followed the rules of correct inference to correctly/sensibly arrive at disjunction.
He doesn't need to form a belief about Brown's location to believe that "Jones owns a Ford or Smith is in Barcelona" is true. He only needs to believe that Jones owns a Ford.
No it isn't. I believe all of these to be true:
1. London is the capital city of England or pigs can fly
2. London is the capital city of England or pigs can't fly
3. London is the capital city of England or there are no pigs
I believe them to be true because I believe that London is the capital city of England and that if London is the capital city of England then 1, 2, and 3 are true. Incidentally, 1, 2, and 3 are true.
You seem to not understand disjunctions.
As a simple task, which of 1, 2, and 3 do you believe to be true and which do you believe to be false?
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
QED
8-)
I understand disjunctions just fine. You do not seem to understand irrelevance.
Then tell me which of these you believe to be true and which you believe to be false:
1. London is the capital city of England or pigs can fly
2. London is the capital city of England or pigs can't fly
3. London is the capital city of England or there are no pigs
I believe all three to be true.
Fill it out.
Refute the argument. Start at the top.
Then you don't understand disjunctions. If you understand disjunctions (and if you believe that London is the capital city of England) then you will believe that those three disjunctions are true. Here's a truth table to make it clear:
Brace yourself Michael...
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert appropriate belief statement(s) about truth condition(s))
C1. ((p v q) is true because (insert belief statement(s) corresponding to 'if' in p3))(from p1,p3)
C2. p ? q (from C1)
This is the true belief.
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
QED
You get thought/belief wrong, then you get something or other wrong about every utterance throughout human history, regardless of individual(cultural, familial, and/or historical) particulars...
I believe that John is a bachelor. I believe that "John is a bachelor" is true. I believe that "John is a man" follows from "John is a bachelor". I believe that "John is a man" is true if "John is a bachelor" is true. I believe that "John is a man" is true because John is a bachelor.
John is a man but isn't a bachelor. So my belief that 1) ["John is a man" is true because John is a bachelor] is false, but my belief that 2) ["John is a man" is true] is true.
Smith's belief that 1) ["Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford] is false, but his belief that 2) ["Jones owns a Ford or Brown is in Barcelona" is true] is true.
Ignoring 2 doesn't make it go away.
One can have a true belief arrived at from a false reason.
Follow Gettier's formula, and you'll find yourself at p2
False premisses and an invalid form/inference can get you there. So what? It's irrelevant to the argument being made and you know it.
Look at the notation.
It isn't. If the conclusion is true and if I believe that the conclusion is true then I have a true belief. It doesn't matter if I believe it to be true because I believe a false premise to be true.
I believe that John is a man because he is a bachelor. My premise "John is a bachelor" is false but my conclusion "John is a man" is true. I have a true belief (and a false one).
You'll be at p2
Fill it out.
p1. ((p) is true)
p2. ((p v q) follows from (p))
The above exhausts Gettier's thought/belief process as described above. You don't get here...
One must first arrive at belief that:((p v q) is true) before one can be justified in believing that:((p v q) is true). One cannot arrive there without going through another deduction...
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
That's specific to Case II. All cases require these two steps. Fill it out.
Are you claiming that there is/are no other truth condition(s) and/or justificatory ground for your belief that John is a man?
Can I get paid yet?
Start from the top...
Yes. I have simply been told by a person I trust that John is a bachelor. If it would make it a better example, let's use a gender-neutral name like "Max" instead of "John", or even an online alias like "creativesoul".
I only believe that this person is a man because I believe that this person is a bachelor. This person isn't a bachelor but is a man. I have a true belief (as well as a false one).
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
QED
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))(from p1,p3)
It's worth noting here that there are no disjunctions immune. None. When we fill in the blanks accordingly, there are no problems with any of the conclusions. None.
It is also worth mentioning that this isn't an outright and total rejection of Gettier's formula. In the main, it shows us that that particular formula is inadequate in it's ability to take proper account of how one arrives at believing a disjunction. That is not to say that the formulation is inadequate for taking account of all believing any and all Q's. To quite the contrary...
It is to say that it is inadequate for taking account of Q's that are disjunctions. Not all Q's require another deduction to arrive at believing them...
1. London is the capital city of England or pigs can fly
2. London is the capital city of England or pigs can't fly
3. London is the capital city of England or there are no pigs
S/he claimed that s/he believed London is the capital city of England.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
There's the formula. Let's fill it it out in numerical order.
Michael believes London is the capital city of England. Michael believes that: 'London is the capital city of England' is a true proposition(p1); the disjunction 'London is the capital city of England or 'Pigs can fly' follows from 'London is the capital city of England'(p2); the disjunction 'London is the capital city of England or 'Pigs can fly' is true if either 'London is the capital city of England' or 'Pigs can fly' is true. Michael believes that the disjunction 'London is the capital city of England' or 'Pigs can fly' is true because London is the capital city of England.
No problem there.
Michael believes London is the capital city of England. Michael believes that: 'London is the capital city of England' is a true proposition(p1); the disjunction 'London is the capital city of England or 'Pigs can't fly' follows from 'London is the capital city of England'(p2); the disjunction 'London is the capital city of England or 'Pigs can't fly' is true if either 'London is the capital city of England' or 'Pigs can't fly' is true. Michael believes that the disjunction 'London is the capital city of England' or 'Pigs can't fly' is true because London is the capital city of England.
No problem there.
3 is no different...
No problems, but not like Case II to begin with.
This is also not like Case II.
With regard to my argument. I'm not ignoring it. I've rendered it inadequate. Belief that ((p v q) is true because (p)) cannot be gotten around. One never gets to belief that:((p v q) is true). It stops at the former for reasons already argued for ad nauseum without subsequent refutation...
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))(from p1,p3)
S believes P, P entails Q, S deduces Q from P and accepts Q as a result of that deduction only gets us to belief that:((p v q) follows from (p)).
Therefore S does not yet believe that:((Q) is true)
Half a century of bewitchment.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))(from p1,p3)
An insincere purveyor of disjunction cannot pass through. I'm gonna be famous...
X-)
You're misreading. Let's replace the terms with a real example:
Smith believes that Max is a bachelor, Max being a bachelor entails that Max is a man, Smith deduces that Max is a man from Max being a bachelor and accepts that Max is a man as a result of that deduction.
The accepts Q is Gettier saying that Smith believes that Q is true. He accepts that Q is true because he accepts that P is true and accepts that P entails Q.
We can set it out more clearly here:
1. S believes P
2. P entails Q
3. S deduces Q from P
4. S accepts Q
For some reason you're conflating 3 and 4. This is wrong. Gettier isn't repeating himself. Compare with:
1. S doesn't believe P
2. P entails Q
3. S deduces Q from P
4. S doesn't accept Q
Notice that in both cases Smith accepts that Q follows from P, but in the first case he accepts Q and in the second case he doesn't. So contrary to your repeated claims, Gettier's example (the first case) doesn't just get us to the belief that p ? q follows from p. It also gets us to the belief that p ? q (a belief that we don't get to in the second case).
I've explained this to you several times. In both of these cases I believe that p ? q follows from p:
I am a woman
I am a woman or London is the capital city of England
I am a woman
I am a woman or London is the capital city of France
But in the first case I also believe that p ? q. And the same with Smith: he doesn't just believe that p ? q follows from p; he also believes that p ? q.
Smith's belief isn't just on the validity of the inference. It's also on the truth of the conclusion (and the premise).
No it doesn't. If you believe that p ? q ? p then you believe that p ? q.
It doesn't make sense to say "I believe that Donald Trump is the President because he won the popular vote but I don't believe that Donald Trump is the President".
And it doesn't make sense to say "I believe that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford but I don't believe that Jones owns a Ford or Brown is in Barcelona".
Gettier claims that Smith believes that:((p v q) is true). Belief that:((p v q) is true) is the aim.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
You cannot get to Gettier's aim without going through all of the above. Salva veritate
Half a century of bewitchment.
It doesn't make sense to say "I believe that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford but I don't believe that Jones owns a Ford or Brown is in Barcelona".
If Smith believes that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford then ipso facto Smith believes that Jones owns a Ford or Brown is in Barcelona. Smith has a true belief. This is basic logic.
Furthermore, Gettier states that Smith does in fact believe that Jones owns a Ford or Brown is in Barcelona.
It's a proof, and you know it.
Fill it out, or show what step is not necessary. Gettier sets out one deduction. One deduction is insufficient.
1. p
2. p ? p ? q
3. p ? q
This is a valid argument. Therefore the rational person who believes 1 and 2 will also believe 3. And Gettier states that Smith is a rational person and believes 3.
Start at the top...
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
That is Smith's believing Q as the result of another deduction.
QED
I need not refute that. It's irrelevant
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
S cannot arrive at belief that:((p v q) is true) without going through all of the above. Salva veritate
It isn't irrelevant. Smith believes that p ? q is true, and p ? q is true. Therefore, Smith has a true belief.
Isn't Smith's true belief improperly justified? He believes p v q, because he believes p; and yet ~p, but q.
Does Smith have a justified true belief? p v q is justified by q; it is true; and it is believed by Smith; but Smith thinks it is justified by p.
So does Smith know (p v q)? One could go either way, but I'd say that he does not know (p v q), because what he believes justifies knowing (p v q) is false.
Right, that's part of Gettier's setup. The only belief he attributes the Smith is the belief that p v q; he seems purposefully to avoid attributing p, which will turn out to be false anyway. Gettier only relies on p for justification, not for truth.
For Creative, it must.
Which of you is correct?
@creativesoul has nothing to say about justification, as he will tell you himself. His issue is something about the psychology of logic, I think.
creative isn't even talking about justification. He's saying that Smith doesn't believe p ? q.
I assume everyone who accepts the JTB account of knowledge feels the same way, else having both justification and truth would be redundant.
Alright, let's find agreement...
Smith believes P, deduces Q from P and accepts Q as a result...
Agreed?
What does that consist in/of?
That's the question at hand. I say that it doesn't include believing Q. Gettier seems to agree, because his next line is...
..."therefore S is justified in believing Q".
Seems that Srap and Michael hold otherwise.
Belief is at the beginning and the end...
Now...
Look at the proof.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Gettier only gets to p2 prior to his conclusion that S believes Q. It takes more than that.
The most interesting aspect to me is the fact that that same thought/belief process is necessary and sufficient for believing any and all Q's when Q is a disjunction derived from belief by a rational person. No disjunction is immune. It exhausts them all, without question. Here it is prior to being filled out...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
Fill it out, and you'll never arrive at a problem for JTB. The added benefit, of course, is that it stops an insincere purveyor of disjunction dead in his/her tracks.
I'm gonna be famous.
X-)
The Merrillian Lie-Trap
Not all Q's are arrived at by virtue of one deduction. The astute reader will note that almost all of Michael's counterexamples were belief of a simple variety. There were no disjunctions that were problematic... and there will not ever be.
Modus Ponens cannot account for disjunction. Believing Q when Q is a disjunction is not that simple... as my solution clearly shows.
That is the real problem and the so-called Gettier 'problem' lands quite squarely in the scope of consequence. Ah, but I digress...
Salva veritate
This is quite simply not true. We can clearly see for ourselves that Gettier attributes belief that p to Smith. The formula begins with S's believing P, and Case II fills that out by virtue of Smith's believing Jones owns a Ford.
In fairness to Michael, he is simply parroting Gettier, who was mistaken to begin with. That is proven by the fact that if Gettier had considered this... openly... he would have noted that another deduction was necessary for believing Q.
C1 exhausts Smith's believing Q.
Salva veritate
I am guessing that this is why the account is of interest to Creative, with his odd understanding of thought/belief.
But in any case, it appears to me that justification is the issue.
Quoting Michael
Having both justification and truth is far from redundant. it is not the case that the justification and the thing justified are the same.
This should read:
((p v q) is true if...(insert true statement(s) regarding what makes this particular disjunction true)
"Smith believes p, therefore (p v q)" is a non sequitur. It should be "p, therefore (p v q)".
Or alternately,
"Smith believes p, therefore Smith believes (p v q)"
Smith's beliefs about p or q imply nothing about the truth of p or the truth of q.
So although Smith thinks he has a justified true belief, and hence knows that p v q, he is wrong because the justification is false.
What do you mean by the justification being false? In Gettier's example, the justification is "Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and that Jones has just offered Smith a ride while driving a Ford". These are all facts. So is he justified in believing that Jones owns a Ford? If so then he's justified in believing that Jones owns or Ford or Brown is in Barcelona.
Quoting Banno
I thought you were saying that a belief isn't justified if it's false.
I'll repeat (and add to) my previous explanation here:
1. Smith's belief that p is justified by r
2. p ? p ? q
3. From 1 and 2, Smith's belief that p ? q is justified by r
4. p is false and q is true
5. q ? p ? q
6. From 4 and 5, p ? q is true
7. From 3 and 6, Smith has a justified true belief
p is "Jones owns a Ford", q is "Brown is in Barcelona", and r is "Jones has at all times in the past within Smith's memory owned a car, and always a Ford, and Jones has just offered Smith a ride while driving a Ford".
Yes it can. This is valid:
1. p
2. p ? p ? q
3. p ? q
When you have time. Read the following carefully... It is where I'm at in all this. Still honing it. p3 needs left alone. It's not an argument per se, it's a report of the thought/belief process necessary for arriving at believing Q when Q is a disjunction arrived at from believing P following Gettier's formulation...
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
That is Smith's believing Q as the result of another deduction.
QED
It does if you accept epistemic closure.
But even if you don't, Gettier states that Smith does believe Q. He's a rational person who believes that this argument is valid and that the premises are true, and so therefore that the conclusion is true:
1. p
2. p ? p ? q
3. p ? q
To try to argue that Smith doesn't actually believe p ? q is completely misplaced. You might as well try to argue that Jones does in fact own a Ford.
So let's put it to you. Do you believe that this statement is true?
London is the capital city of England and/or I was born in Leeds.
Well I just waded through all this, and I have to admit to some skimming. I'll make a few preliminary remarks, and see who wants to swallow them whole and who wants to bite their heads off.
1. (p v q) appears to say more than p, but actually says less. 'The glass contains water or the glass contains vodka' says less than 'The glass contains water'.
2. Nobody in the real world forms arbitrary unrelated disjunctions of things they believe and things they have no belief about, or believe to be false, except for rhetorical purposes, or I'm a monkey's uncle.
3. I'm not a monkey's uncle.
4. Logical implication is a justification.
5. Think of a whole number between 1 and 100. I have justification on the grounds of probability for believing that it is not 92. I have the same justification for thinking it is not any of the other numbers. So I can form the propositions: 1. You did not think of 1, 2. You did not think of 2, and so on. All are equally justified, all but one are correct, all are equally believed.
6. Nevertheless, I have no idea which number you thought of.
I'm not crazy about this one. (But agree with everything else.) I'd rather say something more like what Gettier says: whatever justification the premises have, the conclusion inherits. As I said earlier, inference is not expected to confer truth, but to preserve it.
Quoting Srap Tasmaner
Belief, nor justification, nor inference confer truth. Per Gettier, one can have justified false beliefs. Put truth back on the shelf a minute. Consider justification, consider inference. Can we say that inference transforms one or more propositions into another proposition? Can we say that it would be foolish, if not impossible to believe, and thus to honestly assert a proposition one does not believe, unless bracketed in an "If (p)"? So one makes inferences from (justified?) beliefs to new propositions that are justified by the inference. One does not, thought one theoretically could, infer (p v q) from p, because - there's no point, apart from sowing dissent in the ranks of philosophers.
(a) If I have performed the rain dance, it will rain tomorrow.
(b) I have performed the rain dance.
(c) It will rain tomorrow.
(a) is justified inductively (probabilistically?) by the fact (videos enclosed) that I have performed the rain dance five times, and each time it has rained the next day.
(b) is justified by my memory augmented by the video (enclosed).
(c) is justified by inference.
Where is your belief at this point? I'm betting you are somewhat sceptical of (a) because (insert long-winded justification of choice). Your justification and mine are competing, conflicting.
Yes. Should have made it clearer that inference preserving truth is something like a precedent for what we expect inference to do with justification.
On belief and assertion, I defer to Moore's paradox: asserting that P appears to carry with it a non-cancelable implicature that I believe that P. You can modify your degree of belief with "I'm not sure but I think" and the like, but you can't set it to zero.
Naturally if your belief in the premises of an inference is less than 100%, your belief in the conclusion should be less than 100%. Being the conclusion of an inference doesn't add or subtract certainty. -- We're talking here about perfect entailment. If you only have "If P, then it's likely that Q", that's a whole 'nother deal.
When I first saw Gettier, I had a similar reaction as creative, and as you're hinting at here -- that the "if p" tags along. As it turns out, this is the aspect of modus ponens that Tarski highlights by calling it the "rule of detachment" -- you get to detach the conclusion from the argument for it.
And I think that's right, with the proviso that your degree of belief in the conclusion, or the degree to which belief is justified, will track your degree of belief in your premises, or the degree to which those beliefs are justified.
When you have time. Read the following carefully... It is where I'm at in all this. Still honing it. p3 needs left alone. It's not an argument per se, it's a report of the thought/belief process necessary for arriving at believing Q when Q is a disjunction arrived at from believing P following Gettier's formulation...
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
That is Smith's believing Q as the result of another deduction.
QED
Indeed. Well put. That is precisely one point I've been making. Here's the thing...
Gettier, and evidently many others want to say that Smith can get to belief that:((p v q) is true). That is their aim. The target. The candidate. The problem is that one cannot arrive at that without going through belief that ((p v q) is true if... (insert belief about the truth conditions of this particular disjunction)), and ((p v q) is true because...(insert belief corresponding to the "if" in p3)).
Once one arrives here, there's nothing more to the belief, and certainly nothing less.Salva veritate
Given the formula in the beginning of his paper, Gettier does not - cannot - take account of what it takes to arrive at believing Q when Q is a disjunction deduced fro believing P. There's nothing about Smith's thought/belief regarding the truth conditions of the disjunction. Michael has left that fact sorely neglected.
My argument, is about what the thought/belief consists in/of. It seems that you've understood. No surprise given that you've been one of the few who've been able to follow my position regarding thought/belief. Thanks for joining in, by the way...
As you say...
There is, and I haven't. One of the truth conditions of "Jones owns a Ford or Brown is in Barcelona" is Jones owning a Ford, which Smith believes.
How many times do we have to go over this? Smith doesn't just believe that (g), (h), and (i) are entailed by (f). He also believes (f), and so also believes (g), (h), and (i). I explained this simple fact to you in the very first reply.
To repeat my earlier question, do you believe that this statement is true?
London is the capital city of England and/or I was born in Leeds.
I assume that you do, because I assume that you believe that London is the capital city of England. If you were being honest then you would admit to this. And with that, your argument against Gettier fails.
A few possible counters:
I don't think the Gettier problem is really new. I think it was mentioned as early as the Theatetus or however you spell it.
Also, there's something fishy about investigating commonsense beliefs by means of formal logic in a thought experiment where we imagine people constructing formal structures in order to deduce things. It seems like a weird scenario bound to produce nonsense.
Michael, try my newly minted Anti-Gettier.
Given that it is the case that it rains every day, do you believe that "if I do the rain dance it will rain tomorrow"?
Logic insists it is true; common sense insists that if you believe in the efficacy of rain dances, you've gone badly wrong somewhere.
I seems to me that the logic of conditionals, conjunctions, disjunctions, fails to take any account of semantic content.
I'm wondering if all the difficulties can be resolved by adding a fourth criterion to the tradition: Knowledge is justified true meaningful belief. This would allow me to answer your question, "No. I believe London is the capital of England, and where you were born has nothing to do with it." And it would allow you to answer me, "No, I believe it will rain tomorrow whether you dance or not"
And these "no's" are denials of significance rather than of logic.
I will say my prayers before bedtime, and/or someone will die in the night. Justified true belief. Forming meaningless connectives is like dividing by zero; there ought to be a law against it.
Yes. To believe that this conditional is true is not (necessarily) to believe that the antecedent is the cause of the consequent.
Quoting unenlightened
If you have to add to the JTB account of knowledge in light of Gettier's argument then you've agreed with Gettier that the JTB account of knowledge fails (or at least isn't sufficient).
Such JTB+X accounts of knowledge are a direct response to the apparent validity of the Gettier cases.
Quoting Michael
Well is this not exactly what @creativesoul has been trying to articulate, that one can assent to the truth only by denying the meaning? When someone says 'Hands up or I shoot', the convention is that if you put your hands up, they don't shoot, and if you put your hands up and they shoot you anyway, you are entitled to be pissed off, and they might as well not have said anything.
Hey Pneum!
When you have time. Read the following carefully... It is where I'm at in all this. Still honing it. p3 needs left alone. It's not an argument per se, it's a report of the thought/belief process necessary for arriving at believing Q when Q is a disjunction arrived at from believing P following Gettier's formulation.
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
That is Smith's believing Q as the result of another deduction.
QED
That's an implied exclusive or. The Gettier case is an explicit inclusive or.
And I don't actually understand how this relates to what I said to you. I was addressing your material conditional, whereas with creative we are talking about disjunctions.
You mean this???
Gratuitous assertions won't do at this juncture Michael. I've detailed exactly what believing any and all Q's requires when Q is a disjunction deduced from believing P. Show me which step is unnecessary.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
Gettier only gets to p2. I've successfully argued for this without subsequent refutation or due attention.
I've clearly shown that p3 and C1 are left completely unaccounted for in Gettier's paper. Arriving at believing Q when Q is a disjunction deduced from believing P requires another deduction. That deduction is clearly accounted for in my formula, but is left neglected in Gettier's.
So, you could show which step in my formula is unnecessary for believing a disjunction. You could show how believing Q requires only one deduction from P. You could always just take the argument from the top. You could always just imagine any disjunction you like... fill in my formula... and look at the results. There is never a problem.
Fill it out...
Yes. If I believe that (f) is true and if I believe that (g), (h), and (i) are entailed by (f) then I will believe that (g), (h), and (i) are true. That's straightforward rationality.
So contrary to your repeated strawmen, nobody here is saying that "believing that (g), (h), and (i) are entailed by (f) is equivalent to believing the disjunctions".
p2. ((p v q) follows from (p))
That's where you get.
It doesn't make Q true. It makes Q the conclusion of a valid inference.
Yes it does. It's modus ponens. This is elementary logic.
1. p
2. p ? p ? q
3. p ? q
Are you sure you want to argue this?
X-)
p1. ((p) is true)
p2. ((p v q) follows from (p))
That's where you get.
3 in the quote above doesn't follow from p2 unless by "true" you mean being the result of a valid inference.
Quoting creativesoul
If 1 is true and if 2 is true then 3 is true. Modus ponens. Again, elementary logic.
I'm not saying it does. It follows from 2 and 1. It's a syllogism with a major and minor premise.
Perhaps I should spell it out like this for you:
1. p
2. p ? p ? q
3. p ? q (from 1 and 2)
I'm not saying that it is. I'm saying that if Smith is rational and if he recognises that the argument is valid and if he believes that the premises are true then he will believe that the conclusion is true.
In Gettier's case, the argument is valid, Smith is rational, and Smith believes that the premises are true. So Smith believes that the conclusion is true.
Modus ponens doesn't help your report of Smith's belief. 1 is false and you know it. So, it is not the case that if 1 is true and 2 is true then 3 is true. 1 is false and yet you want 3 to be true. Your argument requires it.
Again elementary logic.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
Gettier only gets to p2. I've successfully argued for this without subsequent refutation or due attention.
I've clearly shown that p3 and C1 are left completely unaccounted for in Gettier's paper. Arriving at believing Q when Q is a disjunction deduced from believing P requires another deduction. That deduction is clearly accounted for in my formula, but is left neglected in Gettier's.
So, you could show which step in my formula is unnecessary for believing a disjunction. You could show how believing Q requires only one deduction from P. You could always just take the argument from the top. You could always just imagine any disjunction you like... fill in my formula... and look at the results. There is never a problem.
Fill it out...
We're talking about what Smith believes to be true. If he believes that the premises of a valid argument are true then he will believe that the conclusion is true.
Quoting creativesoul
We're talking about belief at the moment. You're trying to argue that Smith doesn't believe that 3 is true, despite believing that 1 and 2 are true. This is wrong. Smith is a rational person. He believes that the argument is valid and that the premises are true. Therefore he believes that the conclusion is true.
Is that clear enough?
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
That is Smith's believing Q as the result of another deduction.
QED
1. Smith believes that p
2. Smith believes that p ? p ? q
3. From 1 and 2, Smith believes that p ? q
4. Smith's belief that p is justified by r
5. p ? p ? q
6. From 4 and 5, Smith's belief that p ? q is justified by r
7. p is false and q is true
8. q ? p ? q
9. From 7 and 8, p ? q is true
10. From 6 and 9, Smith has a justified true belief
London is the capital city of England and/or I was born in Leeds.
Now from here, you and Gettier want to say that Smith believes that the disjunction 'Jones owns a Ford or Brown is in Barcelona' is true.
Is that right?
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Elegance
Yes. But Gettier doesn't just want to say it. He does say it. It's one of those premises that it doesn't make sense to refute, like "Jones was renting a Ford".
C2. p ? q is true (from C1)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
C2. p ? q is true (from C1)
Salva veritate
How many times am I going to explain this? I'm not saying that they're equivalent. This is just a strawman.
I'm saying that the latter entails the former.
Why do you keep saying this? It has no bearing on our discussion.
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
There are no problems with this formula. Imagine any disjunction arrived at by virtue of deducing it from believing P. Fill it out.
I'm not saying that there are problems. I'm saying that it's incomplete, which is why I am filling it out:
C2. p ? q is true (from C1)
No, yours are. You've said "False premisses and valid form cannot yield true conclusions". And of the following you've said "Can't get to 3 from 1 and 2. Can't get to 6 from 4 and 5":
You're just wrong on all accounts.
It bears on the discussion by virtue of pointing out that the two are not equivalent.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p))
The former neglects the other deduction. The latter exhausts the former, but not the other way around. The latter is utterly inadequate for representing the necessary thought/belief process required for believing Q when Q is a disjunction arrived at from believing P.
Irrelevant.
Use a disjunction. Apply my formula. Show a problem with the result.
But I'm not saying that they're equivalent. I'm saying that the latter entails the former.
If I believe that Donald Trump is the President because he won the popular vote then I believe that Donald Trump is the President.
So if I believe that Jones owns a Ford or Brown is in Barcelona because Jones owns a Ford then I believe that Jones owns a Ford or Brown is in Barcelona.
1. p
2. p ? p ? q
3. p ? q
I swear you're just being wilfully ignorant now. But then you've repeatedly shown that you don't understand basic logic, so perhaps it isn't wilful.
There's something missing. Do you not notice?
"All men are mortal" is missing from the latter. p v q is true because p is missing from the former.
There isn't. They're valid. It's modus ponens.
I've little to no reason to continue this discussion. You deny a clearly missing premiss, and are attempting to brow beat me with man-made rules that do not take proper account of actual thought/belief processes...
1. p
2. p ? p ? q
3. p ? q
And in English
1. London is the capital city of England
2. If London is the capital city of England then by entailment London is the capital city of England and/or I was born in Leeds
3. Therefore, London is the capital city of England and/or I was born in Leeds
Because there isn't one. Just look up modus ponens:
If something is F, it is G.
a is F.
Therefore, a is G.
If Socrates is a man then he is mortal
Socrates is a man
Therefore, Socrates is mortal
I believe that London is the capital city of England, and so I believe that "London is the capital city of England or pigs can fly" is true.
Smith believes that Jones owns a Ford, and so he believes that "Jones owns a Ford or Brown is in Barcelona" is true.
Knowing what a disjunction means requires knowing what makes it true.
Yes, and he believes it to be true. And it's true. So he has a true belief.
Believing Q, when Q is a disjunction deduced from believing P...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
His believing Q is exhausted by C1.
Salva veritate
See p3 and C1???
Gettier and you have not - cannot - properly take account of that and yet you agree that it's necessary.
No it isn't. There's also:
C2. p v q is true
My belief that Donald Trump is the President isn't exhausted by:
C1. Donald Trump is the President because he won the popular vote
There's also:
C2. Donald Trump is the President
No you haven't. You've denied it. But it's a fact of logic that C1. p ? q ? p entails C2. p ? q.
Show where Gettier or your report of Smith's thought/belief process accounts for this.
p3 and C1 do so very nicely.
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
His believing Q is exhausted by C1.
Salva veritate
See p3 and C1???
Gettier and you have not - cannot - properly take account of that and yet you agree that it's necessary.
Take it from the top...
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true).
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's belief that:((p v q) is true). S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that it takes more than one deduction for S to arrive at belief that:((p v q) is true), and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than belief that:((p v q) is true) and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
That is Smith's believing Q as the result of another deduction.
QED
Show where Gettier or your report of Smith's thought/belief process accounts for this.
Where is any of that accounted for in Gettier's paper?
p3 and C1 do so quite nicely.
Michael knows what this means:
(c) If unenlightened does the rain dance, it will rain tomorrow.
He also believes it and believes it is justified (because it rains every day) and true.
The guy's clearly not worth talking to. :D
(p1) Whatever unenlightened does, it will rain tomorrow.
(p1) is true, and entails (c). (c) is patent nonsense. Michael has to claim that (c) is not patent nonsense, and therefore has to claim that it does not mean what we all understand it to mean. Only by denying the common meaning can he maintain that logic preserves truth.
But if logic cannot follow the workings of language, and help us untangle sense from nonsense, we might as well forget logic. Language and meaning is prior to logic; logic must enhance our understanding, not ride roughshod over it.
Looking at the problem again, notice that (p1) means that what unenlightened does is unconnected to the rain, whereas (c) makes just such a connection. It is the making of this connection that is illegitimate, and makes a nonsense from sense. So I propose a new rule:
Thou shalt not connect the unconnected. (p v q) for example is empty rhetoric - empty of meaning or false, unless there is a connection between p and q, because it declares that there is such a connection.
Thus we allow, 'Socrates is a man, and all men are mortal', and 'the glass contains water and/or vodka', but not, 'the glass contains water, and/or all men are mortal'.
If c makes a connection then c isn't justified by the fact that it rains every day. You're equivocating.
Either "if ... then" implies a causal connection, in which case the claim isn't justified, or it's justified, in which case it doesn't imply a causal connection.
So you need to disambiguate into one of these two:
1. If unenlightened does a rain dance then it will cause it to rain tomorrow
2. If unenlightened does a rain dance then perhaps incidentally it will rain tomorrow
The latter is what I believe to be true (assuming that it rains everyday, and that this justifies believing that it will rain tomorrow).
"London is the capital city of England or pigs can fly" is true if London is the capital city of England or if pigs can fly, and so if I believe that London is the capital city of England then I will believe that "London is the capital city of England or pigs can fly" is true.
I believe that there is no connection between the name of the capital of England and the aerial abilities of pigs. So I believe you are making an unjustified disjunction devoid of meaning. All you really believe, and all you can honestly assert is that London is the capital of England. As it happens, I can assure you that pigs can and do fly on a regular basis, but they invariably fly as baggage, so you are unlikely to have noticed them unless you are involved with baggage handling.
The relevance of this is that it solves the problems raised by Gettier, and prevents people from claiming as 'logical truth' certain things that are patent nonsense.
Except "London is the capital city of England or pigs can fly" isn't nonsense. It's a meaningful English statement which is true if London is the capital city of England or if pigs can fly.
There doesn't need to be a connection between the operands for a disjunction to make sense.
Surely you understand what I mean when I say that one or both of "London is the capital city of England" and "pigs can fly" is true? Because that's all the disjunction is saying.
Indeed, I understand and accept your conjunction as phrased in the first sentence, because there is a connection made between the statements mentioned as distinct from used concerning their truth or falsity. But this connection is not made when they are conjoined in use in the disjunction. A claim that mentions statements is not identical to a claim that uses them, and your use of quotation marks indicates that you understand that.
""London is the capital of England" is true" means the same as "London is the capital of England" - or so it can be argued, anyway. But it cannot be argued that ""Pigs can fly" is false" means the same as "Pigs can fly". And since the claim is that one statement can be false, the identity you propose cannot be maintained.
So you're saying that the following two propositions are different?
1. "London is the capital city of England or pigs can fly" is true
2. One of both of "London is the capital city of England" and "pigs can fly" is true
Because it seems to me, to channel my inner creativesoul, that this is a case of salva veritate.
Regardless, you can always apply Gettier's reasoning to the second.
I don't think you can. Smith's belief that "at least one of two statements, 1 and 2, is true" is not the same as the belief that "statement1 and/or statement 2", for reasons that you have dismissed without criticism. Now Smith, by hypothesis, does not know or understand unenlightened's law, so we must forgive him if he conflates them. Nevertheless, if we asked him to justify his belief, he would say something like, " well I've no idea about 2 but I'm sure of 1 because... " you know the story.
And that would satisfy you, but not me, creative, or Gettier. Gettier says Smith has a justified true belief that is not knowledge, creative says that he does not believe what he says he believes, And I say it's all you logicians fault for neglecting the meaning of language and only looking at the form.
I don't understand your reasons. To say that "London is the capital city of England" is true is to say that London is the capital city of England and to say that "pigs can fly" is true is to say that pigs can fly. And so to say that one or both of "London is the capital city of England" and "pigs can fly" is true is to say that London is the capital city of England and/or pigs can fly.
1 and 2 say the same thing. Compare with:
3. "London is the capital city of England and pigs can't fly" is true
4. Both "London is the capital city of England" and "pigs can't fly" are true
T(p) ? T(q) is equivalent to T(p ? q).
5. "London is the capital city of England or pigs can fly" is false
6. One or both of "London is the capital city of England" and "pigs can fly" is false
That 5 and 6 are not equivalent is not that 1 and 2 are not equivalent. The semantics of "true" and "false" make a difference.
1. One or both of "Jones owns a Ford" and "Brown is in Barcelona" is true
A belief in 1 is justified if one is justified in believing that Jones owns a Ford, and a belief in 1 is true if Brown is in Barcelona. Smith has a justified true belief.
Because the disjunction is explicitly saying that one or other may be false. So it does not say p is true it says p might be false, but in case p is false, then q must be true. And it also says that q might be false, but in case q is false p must be true.
But since there is in fact no connection between p and q, there is no justification for saying it.
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
Gettier is proposing a thought/belief process for arriving at believing Q when Q is a disjunction deduced from believing P. Case II fills that out, but it doesn't account for p3 and C1, which are necessary for a rational person to arrive at believing Q.
Gettier's reasoning is flawed because it's based upon a grossly inadequate (mis)understanding of what Smith's believing Q requires. Smith is purportedly rational. Smith's arrival at believing Q requires and is exhausted by C1. That holds good for every imaginable disjunction arrived at from belief that:((p) is true). There is never a problem of any kind.
Believing a disjunction - for a rational person - is nothing more and nothing less than knowing what it means which requires knowing what makes it true and believing that those conditions have been met.
Gettier nowhere says that Smith believes Jones owns a Ford, only that he has good evidence for this belief. Let's say he thinks it highly probable.
We can represent Smith's belief thus: label a jar "Jones", and put 90 red marbles and 10 blue marbles in it. Red will represent "true" and blue "false".
Smith has no reason to think Brown is in Barcelona, so let's label another jar "Barcelona", and in this one we'll put 1 red and 99 blues. It's a long shot, but possible.
Smith should expect that if he draws a marble from "Jones" that the chances of it's being red are 9 in 10. If he draws a marble from "Barcelona", the chances of it's being red are 1 in 100.
What are the chances that, if he draws a marble from each, at least one of them will be red? I can tell you: it's 0.90 + 0.01 - (0.90)(0.01), which is 0.901.
No rational person would think it's reasonable to believe A but unreasonable to believe A ? B.
Then I must be an unreasonable person, because I think that to reason thus: "Probably A, but if not A then definitely B" is cuckoo.
This doesn't seem like the correct interpretation of the disjunction at all.
Let's say that there's a group of kids, and I believe that one of them is mine. If someone were to ask me "is one of those kids yours?" I will answer "yes". Am I saying that if it isn't the one I think it is then it must be one of the others? Not at all. But I'm still saying that one of them is mine, and it's true that one of them is mine if in fact one of them is mine.
Now replace a group of kids with a group of sentences, with one of which I believe to be true.
That puts the probability of A ? B at 1. I put it at 0.901. Why would you put it at 1?
Suppose you're also pretty confident that Brown is in Barcelona, and we put 90 reds and 10 blues in "Barcelona" as well. Then the probability of getting at least one red is 0.90 + 0.90 - (0.90)(0.90), which is 0.99. Still not 1.
For comparison, if "Jones" has only red marbles in it, guess what the probability is that, drawing a marble from each jar, at least one of them will be red.
Because A ? B ?(¬A?B), I guess.
That means ?-introduction comes to P?(¬P?Q) for any Q, which, duh.
I suppose that means that the term "or" suffers from the same sort of problem as the term "if ... then ..." (which unenlightened brought up earlier with the example of the rain dance). But I don't think this undermines Gettier's reasoning either way, so it seems a sort of misplaced criticism.
So to rephrase the issue, and continue with my earlier example, if I believe that my child is eating cake, and if I believe that three children are eating cake, then I believe that the statement "my child is one of the three eating cake" is true. This seems perfectly reasonable.
Agreed. People find material implication and inclusive disjunction counterintuitive, and then mistake their objections to them for objections to arguments that use them.
That's the problem.
My argument shows it and dissolves any and all issues with believing disjunction by virtue of showing the difference... clearly.
The justification for Smith saying it, is the fact that there is no connection. "Either Jones owns a Ford or Brown is in Barcelona" is Smith's certainty being put on display. The problem, of course, is that Gettier's account is inadequate for properly representing Smith's believing the disjunction.
This changes with Gettier though. Gettier knows Jones does not own a Ford. Gettier knows Brown is in Barcelona. Gettier also knows that Smith believes the disjunction because Smith believes Jones owns a Ford. If we fill out my solution with Gettier's belief we arrive at a different disjunction(s) than Smith. None of which are problematic.
Nothing at all unreasonable there.
I would just note something that is not like Gettier Case II. Michael is talking about combining two separate beliefs of his own. Case II only uses one belief of Smith's.
The similarity is that what's being derived has two different sets of truth conditions being combined into one. That is notable, I think, because of the historical notion of "proposition". A disjunction is called a "proposition", as is a conjunction. However, a disjunction consists of two separate propositions, each with it's own set of truth conditions, and in Case II, one of which need not be believed by the speaker/author.
Propositions are not equivalent to belief.
If I believe that the statement "Jones owns a Ford" is true and written in this book, and if I believe that "Brown is in Barcelona" is also written in this book, then I believe that the statement "one of the two statements written in this book" is true.
How is that any different to saying "I believe that this or that statement is true"? Or "I believe that 'Jones owns a Ford' is true or 'Brown is in Barcelona' is true"? Or "I believe that Jones owns a Ford or Brown is in Barcelona"?
Quoting creativesoul
Exactly so. which is to say it is rhetorical. It only follows and then trivially if he is right about Jones.
Quoting creativesoul
Yes, Gettier has authorial infallibility. He knows what he knows absolutely in his invented world, and he knows in this instance that Smith does not know what he rationally believes. But since Smith is defined to be rational, he knows that his rational belief p can be false and he knows that its falsehood does not imply the the truth of q. So he cannot believe (p v q) precisely because that implies that if perchance he is wrong about p, then q would be true. It is impossible for him to assent to this because even Gettier tells us, for realism's sake, that he forms several disjunctions mutually contradictory under ~p which is infallibly true, unknown to Smith.
Sure, but we're talking about belief. If I believe that one of the kids in the phone booth is mine I don't necessarily believe that if it's not Bill then it's Ted. I might believe that it's definitely Bill and definitely not Ted. But it's still the case that I believe that one of the kids in the phone booth is mine.
So you believe it's Bill, and you don't believe it's Ted. But should it turn out that Bill is not yours, because your wife had an affair, you do not thereby conclude you have fathered Ted.
p1. (B v T)
p2. ~B
c1 T
p1. (B v T)
p3. ~T
c2. B
I think this demonstrates the implications I have indicated, and the necessity of including falsehood in any expression of a disjunction. To believe the disjunction is to believe " if it's not Bill, it must be Ted." And that is unbelievable. But note that when you paraphrase the disjunction informally as "one of the kids in the phone booth is mine", you contrive to avoid the implication by avoiding the disjunction. That's cheating.
I believe that it's true, even though I don't believe that if it's not Donald Trump then it's Hillary Clinton.
But what you present here is a perfectly valid disjunction that I would have assented to before knowing the result of the election "Either Trump or Clinton will be President". You need to do better than keep asking these rhetorical and irrelevant questions. The disjunction is valid because if either one of them was not elected, the other would have been, in other words there is a real connection between the two sides of the disjunction. Now do try and address the argument a little.
If I believe that Donald Trump is the President then I will believe that "Donald Trump is the President or Hillary Clinton is the President" is true.
If I believe that Bill is my child then I will believe that "Bill is my child or Ted is my child" is true.
If I believe that Jones owns a Ford then I will believe that "Jones owns a Ford or Brown is in Barcelona" is true.
If believe that p then I will believe that "p ? q" is true.
I am justified in believing that Donald Trump is the President. Therefore I am justified in believing that "Donald Trump is the President or Hillary Clinton is the President" is true. Donald Trump isn't the President but Hillary Clinton is the President. "Donald Trump is the President or Hillary Clinton is the President" is true. I have a justified true belief.
Let's not. Let's look at the formal implications of a disjunction that I laid out and you ignored.
The formal implication of a disjunction is that if "p" is true then "p ? q" is true. Therefore the rational person who believes that "p" is true will believe that "p ? q" is true.
This just doesn't make sense:
1. I believe that "p" is true
2. I believe that if "p" is true then "p ? q" is true
3. I don't believe that "p ? q" is true
Because if you don't believe that "p ? q" is true then you believe that both "p" and "q" are false, but it's been established that you believe that "p" is true.
Quoting unenlightened
Yes. So if I believe p1 and p2 then I will believe c1, and if I believe p1 and p3 then I will believe c2. What's the problem?
Quoting unenlightened
But it's basic logic, so I don't see how you can question it. If "p" is true then "p ? q" is true. Because "p ? q" is true if "p" is true (or if "q" is true).
You seem to be pushing for a logic where "p" is true but "p ? q" isn't. I don't know how you can expect that to work. It's alien to every truth table I know.
Quite simply, what you're saying is illogical.
I think it's called "Gettier" ;) . I'll try and formalise things as best I can.
On your side, we have:
a. If p then (p v q).
And on my side, we have:
b. If (p v q) then (if ~p then q).
The problem with putting these together is that (a) is conditional on p and (b) is a conditional on ~p.
This is not a problem under infallibility since both conditions cannot be met. But Gettier specifies that Smith believes p, but ~p. And this brings both conditionals into play at once. So we now have
c. If S believes p, then S believes (p v q)
d. If S believes (p v q) then S believes (if ~p then q)
This leads to:
e. If S believes p, then S believes that (if ~p then q).
Now (e) states that if S believes p, then S believes that if ~p, absolutely any and every proposition is true, including contradictions. I think it vastly overstates anyone's confidence in their beliefs. I am pretty damn sure that Trump is the president, but not so sure as to believe that if I am wrong about that, a thousand devils inhabit my left knee and also do not. After all, someone might have just assassinated the fruitcake (hope springs eternal). In other words, the formalisms of infallibility do not transfer to fallible beliefs.
I think we both want to escape (e) and our difference is more or less whether it is better to reject (c) or (d).
Edit. It occurs to me that the explosion at (e) is the equivalent of the formalism that from (p & ~p) anything follows. And that is what Gettier has set up for us - Smith believes p but ~p.
1. Smith believes that if "p" is true then "p ? q" is true
2. Smith believes that if "p" is false then "p ? q" might be false, and so doesn't believe that if "p" is false then "q" is true
I don't know how to formally reconcile these.
1. p
2. p ? p ? q
3. p ? q
4. p ? q ? ¬p ? q
5. ¬p ? q
6. p ? ¬p ? q
6 is the principle of explosion, a valid rule of inference. Therefore, if Smith believes that "p" is true then it is correct to believe that if "p" is false then "q" is true.
So now we bracket that...
S believes {
1. p
2. p ? p ? q
3. p ? q
4. p ? q ? ¬p ? q
5. ¬p ? q
6. p ? ¬p ? q) }
7. ¬p (Gettier's stipulation)
And we have arrived at my (e), which is the explosion of belief. This is too volatile a situation to be tolerated. One false belief plus formal logic lead to the total collapse of knowledge.
I don't know about anyone else, but I am going to forbid S from moving from 1 to 2 unless p is a tautology, on the grounds that all other beliefs are not certain and therefore have the form "Believably p, but (&) conceivably ¬p". Now if S takes my advice and substitutes this formula for 1, then 2 does not follow from 'conceivably ¬p', and the bomb is defused.
1. One or both of "Jones owns a Ford" and "Brown is in Barcelona" is true
If it helps, this proposition can be presented to Smith ahead of time. It is only later that he is presented with evidence that Jones owns a Ford. Does he believe that 1 is true? I say he does.
There's also relevance logic that denies disjunctive syllogism, which is what I was arguing for earlier. In relevance logic, p entails p ? q but p ? q doesn't entail ¬p ? q.
No that won't do. Firstly, it is more like your 3 than your 1. And secondly, they could both have been true.
Quoting Michael
That makes perfect sense to me, because what I have done is to divide the claim into two parallel but opposed logical realms, the believable and the conceivable. So the claim "S believes p" is not expressed by S as "p". Instead, because Gettier has had the decency after all this time to let him know that he can have justified false beliefs, S says
1a. " Believably p, but conceivably ¬p." In this way he runs 2 arguments in superposition :
2a. Believably (p v q) but conceivably ¬(p v q)
And so on. And the two lines of argument remain in superposition until either Jones or Gettier confirms absolutely that either his belief or his unbelieved contrary conception is uniquely true, at which point he sensibly discards whichever line starts with the untrue premis.
Sorry, meant "is true" not "is false".
That might be more fun.
Because Smith believes p and because p entails p ? q, Smith believes p ? (p ? q).
p ? (p ? q) doesn't entail ¬p ? q, so Smith doesn't believe ¬p ? q.
Or to make it stronger, because Smith believes p ? ¬q and because p ? ¬q entails p ? q, Smith believes p ? ¬q ? (p ? q).
p ? ¬q ? (p ? q) doesn't entail ¬p ? q, so Smith doesn't believe ¬p ? q.
?
Are you using "entail" in some special sense?
Isn't this what "probably p" already says? Why do this superposition analysis at all? Do belief and conception vary freely, or is there some relation there? If you just stick with probability, it's direct: as p seems less probable, ¬p seems more probable. Isn't that more sensible?
Quoting unenlightened
That says "Believably ¬p?q but conceivably p?q", but again manages to lose the connection between them. For any q, either p implies it or ¬p does, and if one doesn't, then the other definitely does.
Are we trying to reinvent "or" here?
It just doesn't matter if his holding that belief is also bizarre. There are two elements to a coincidence. Of course his holding that belief is bizarre! It's an abuse of logic. But if, for whatever peculiar and idiosyncratic reasons, he is inclined to form such a belief, it will be true and justified but not knowledge. You either accept that, and scrap JTB, or you block the supposed justification.
ADDED: Or I guess you could say that JTB "almost always" works, or "usually" works, or works for "normal" cases -- @Fafner is making a related argument elsewhere.
What I'm trying to get at is:
¬p ? q ? (¬p ? ¬q)
The point is that if I'm asked what would follow if ¬p then I would withdraw the disjunction rather assert q.
Whereas unenlightened is saying:
¬p ? (p ? q) ? q
Yes, you could use probably and possibly instead. I think the superposition idea is a neat way of doing it, but if we go your way, we have something like this:]S believes {
1. Probably p & possibly ¬p
2. p ? p ? q
[s]3. p ? q
4. p ? q ? ¬p ? q
5. ¬p ? q
6. p ? ¬p ? q)[/s] }
7. ¬p (Gettier's stipulation)
Without the unadorned premise "p", one cannot make the move to (p v q), and Gettier's justified true belief that is not knowledge cannot arise.
If his belief is just "probably [Jones owns a Ford] and possibly not [Jones owns a Ford]" then his belief is true even if Jones doesn't own a Ford.
Whereas if his belief is false if Jones doesn't own a Ford then the first premise is the unadorned "p".
Smith's belief that Jones owns a Ford is true if and only if Jones owns a Ford. So his belief is the unadorned "p".
Now this I agree with completely!
But this is not an issue with logic per see, but something else. That something else could be Grice's maxims, for instance.
So this is similar to the path of constraining justification: there are other rules besides logic in play.
Smith's belief that Jones owns a Ford is false, Gettier insists. Jones does not own a Ford.
Yes. But my point is that premise 1 is "p", not "probably p and possibly not p".
I think the issue is that whereas this is valid:
1. p
2. p ? q
3. ¬p ? q
This probably isn't:
1. B(p)
2. B(p ? q)
3. B(¬p ? q)
Perhaps relevance logic is more appropriate here, denying the disjunctive syllogism (but maintaining the disjunction introduction).
If you have "probably", you don't need "possibly" to stand in for "improbably": "probably" already covers both. "Possibly" is already in the background underwriting "probably".
Quoting Michael
Well this second 3 is still a conditional. We don't yet have something like
4. B(¬p)
That would force us to conclude that q. Once we get 4, our beliefs are inconsistent and something must be done.
I don't think it's really about that.
I believe that if your name is John then your name is John or pigs can fly, but I don't believe that if your name isn't John then pigs can fly. So 3. alone is a problem.
But that's just the usual issue with material implication.
Hmm. Not right.
We do want the other principle at work to relate directly to our standards of rationality.
Yes yes, premise 1 is p, the disjunction applies, and explosion happens such that Smith believes anything and anything because with authorial infallibility, ¬p. I think I have offered a way out that preserves both knowledge and logic. If you don't want to buy it, find your own way out, or a hole in my logic.
Quoting Srap Tasmaner Whatever dude. As long as it is clear that you can't derive the disjunction. Annoyingly, Michael's quote ate my vital strike.
Don't know anything about relevance logic, but my intuition throughout has been that the justification for believing p turns out to be irrelevant to the truth of p v q.
And I'm not willing yet either to give up using or forbid others from using standard rules of inference.
We don't like the result, agreed. So we need some other rule to override here. The natural choice, to almost everyone, is to say that the belief of Smith's that turns out to be true is not in fact justified.
2. p ? p ? q you can keep with my blessing, along with the other rules of inference, because you don't have "p", you only have "probably p" which does not get you to (p v q).
I'd still say this is unclear in Gettier's text, and what's more it's an interesting case, because we often do want to reason from premises we only hold probable.
But it gets you "probably p v q" doesn't it? That's all Gettier needs p for.
You seem to be conflating. It isn't:
¬p ? Smith believes q
Rather it's (allegedly):
1. Smith believes that ¬p ? q
At the moment the truth of any proposition isn't relevant. We're just discussing what Smith believes. Specifically, does he believe p ? q?
And I still find this peculiar. Gettier tells us in so many words that he accepts (g), (h), and (i). The argument has to be that he shouldn't or couldn't. I guess you could go with "wouldn't" but that's not especially persuasive.
I think this is the problem:
1. I believe ¬q
2. ¬q ? ¬p ? ¬q
3. I believe ¬p ? ¬q
4. I believe p
5. p ? p ? q
6. I believe p ? q
7. p ? q ? ¬p ? q
8. I believe ¬p ? q
The issue is that the rules of entailment can lead to having contradictory beliefs (3 and 8). unenlightened overcomes the contradiction by denying 6. I overcome the contradiction by denying 8.
I think if you believe probably A, then you (should) believe probably what's entailed by A, and that's how Gettier treats justification.
Look at the jars again. "Jones" is likely to give red, so "Jones" or "Barcelona" is likely to give red. It's just not true that if you get a blue from "Jones" you'll definitely get a red from "Barcelona". There's no reason to think that and I don't think Smith does as a matter of fact. **
Similarly probably (p v q) includes improbably ¬(p v q), not improbably (¬p v q). The "or" is inside what is believed probably, not outside, as above.
Taking a step back: if I have reason to believe you own a Ford, then I have reason to believe you own a vehicle, because owning a Ford entails owning a vehicle. That's Gettier's claim, that entailment preserves justification just as it preserves truth, however much or little there is.
** ADDED: Again, it's a bizarre bit of luck that Smith draws the one lonely red from "Barcelona".
Where does 1 come from? Smith does not believe Brown is in Barcelona, but he doesn't believe Brown is not in Barcelona.
If he did, the whole exercise makes no sense.
Just an example of how the rules of entailment can lead to contradictory beliefs.
Okay. I'll look again, but doesn't that mean your premises must have been inconsistent?
Say "p" is "London is the capital city of England" and "q" is "pigs can fly".
3. p v ¬q
8. p v q
9. (p v ¬q) & (p v q)
10. (T v T) & (T v F)
11. T
3 and 8 are not contradictory. You have p as a premise, so you can get anything you like from ¬p. Also, you could save some time by just deriving both p v q and p v ¬q from p. q doesn't matter since you've already got p. That is, you don't need ¬q as a premise here at all.
Once again, I think we're really taking about Material Implication: Miracle or Menace?
We can leave out my habitual translation:
9. (¬p?¬q) & (¬p?q)
10. (F?T) & (F?F)
11. T
As I said, it's all of those false premises in 10 that are annoying.
I have "I believe p" as a premise. Does that not make a difference?
Right, I mean exactly that: if you believe that p, there's nothing contradictory about believing that ¬p?q and believing ¬p?¬q. It just means you get material implication.
If Jones owns a Ford then either 'Jones owns a Ford' or 'Brown is in Barcelona' is true. Jones owns a Ford. Therefore, either 'Jones owns a Ford' or 'Brown is in Barcelona' is true.
What's the problem?
:-|
That's justified true belief about disjunction(the rules of correct inference). It's not believing the disjunction. That requires what I've been setting out...
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
The above holds good for every imaginable disjunction arrived at from belief that:((p) is true). There is never a problem of any kind. It's a solution. Believing a disjunction - for a rational person - is nothing more and nothing less than knowing what makes it true and believing that those conditions have been met.
It seems that some want to skip p3 and C1 and arrive directly at belief that:((p v q) is true) simply because the rules say that it follows from ((p) is true). As I've just shown in the last post, if Smith used modus ponens to arrive at belief, he would arrive at believing that either 'p' or 'q' is true. But Smith doesn't believe that either 'p' or 'q' is true. Thus, Smith wouldn't use modus ponens to arrive at believing that:((p v q) is true).
This is worth quoting again.
If someone tells Smith that as a matter of fact Jones does not own a Ford, what happens to my jars?
We dump all the reds out of "Jones" and leave just a blue; "Barcelona" still has 99 blues and the one red. Chances, drawing one from each jar, of getting at least one red? 0 + 0.01 - (0)(0.01), so just 0.01.
Yeah, that's a belief you're unlikely to hold.
In my last response, I ignored -- God knows why -- that in my model, we've got a probability for q, so some of that was crosstalk.
I am actually interested in what you were getting at with "Probably p, but if not then definitely q", the crossover from probable or partial belief to belief, assertion, placing a bet, answering a question on a test, or any other way of acting on a belief that commits you to accepting the consequences of so acting, positive or negative.
But I don't think it's relevant to Gettier's argument. We clearly can and do and probably should and must commit in this way. Smith does, and does so with some justification. That's all Gettier needs.
S believes {1. p , 2. (p v q)}
Reality {3. ¬p , 4. (¬p v q)}
Logic (p v q) & (¬p v q) ? q
In a way, this is an ancient problem; Descartes was looking for certainty. Logic cannot cope with a false premise, it falls apart. But false beliefs happen to humans. We need to reason about reality and apply our beliefs to it, but logic only deals in certainties. Reality is never wrong, logic is never wrong, but S and possibly one or two other folk are sometimes wrong. And one wrong belief for a logician leads to explosion.
So S and the rest of us need to take account of our fallibility in reasoning about our beliefs.
Logic never asserts anything about reality. One might say that it it only ever asserts implications - "If (premises) then (conclusion)". Reality is pure infallible assertion "¬p, q ..." So there is never a conflict between them.
But S fallibly asserts p, logically concludes (p v "I am a monkey's uncle"), and ends up lost in the
jungle.
So he needs to keep hold of the fallibility of the assertion, and convey it through the argument in the same way that pure logic prefaces all its assertions with an "if".
So I'm trying to find ways of doing that, with "believably p" or "probably p". And conclusions logically derived from such fallible assertions then have to carry the logical caveat "If really p, then (p v q)"
The result of this is S's belief is not the bald (p v q) any more, but retains the condition (that p) attached to it. S doesn't believe (p v q) unconditionally as Gettier and others here claim, but the conditional, "If really p, then (p v q)".
And this means that he cannot then be said to have the belief Gettier needs him to have, to break the conception of knowledge.
The third step makes no sense in context.
You should have it as this, where B(r) is "Smith believes r":
1. B(p)
2. B(p ? q)
3. ¬p
4. q
5. ¬p ? q
6. B(p ? q) ? (¬p ? q)
Yes it does. It expresses the part of the story where Gettier infallibly tells us That Smith is wrong about Jones owning a Ford. It's like when God says "Let there be light". It is so, whether He has gotten around to giving you eyes or not. That's another teaching story, but it works the same way - the story is the story and you have to make sense of it the way it is.
The bit in bold is the bit that doesn't make sense:
(p ? q) ? (¬p ? q) ? q
It's not that at all. It's:
B(p ? q) ? (¬p ? q)
There's no false premise. Smith's belief that p is false, but the premise "Smith believes p" is true.
Smith's argument is:
1. p
2. p ? p ? q
3. p ? q
He recognises it as valid, he believes the premises, and so he believes the conclusion.
Gettier's argument is:
1. Smith believes p
2. Smith believes p ? p ? q
3. Smith believes p ? q
4. ¬p
5. q
6. p ? q
Smith's belief 3 is true because of 6.
I don't understand your notation. What's B?
A false belief isn't nonsense. It's just false. If you have a cat and I believe that you don't have a cat then the principle of explosion doesn't come into play (as you suggested earlier).
It's just the case that:
1. A believes p
2. ¬p
There's only an issue when we have one of these situations:
1. A believes p
2. A believes ¬p
1. p
2. ¬p
Nothing like this shows up In Gettier's reasoning.
So Smith has the false belief p, which Gettier accepts. But he also has the true belief p ? q. So I don't actually understand your criticism.
That has been my justified belief for some time. ;)
My version of the story goes like this: Smith puts the odds of Jones owning a Ford at 9-1, and the odds of Brown being in Barcelona at 1-99, so the odds of at least one being the case are a little better than 9-1. Then what? He makes a prediction, and he acts on that prediction. If you never actually place your bet, you don't get paid. If you never actually test a hypothesis, you don't learn anything.
Gettier tells us that Smith accepts (g), (h), and (i). Suppose Smith could ask someone who knows. If he started with (h), he would get the answer he expected, and continue to believe (h). But if he also asked about (g), and then about (i) too, he would not get the answers he expected.
Once he gets "false" for (g), he knows Smith doesn't own a Ford, right? The result for (i) confirms this, and now Smith will be strongly inclined to believe that Brown is in Barcelona.
But it's not that simple. There could be another factor here: can Smith tell the difference between Brown being in Barcelona, on the one hand, and his informant telling him the truth about (h) but lying about (g) and (i)? Can Smith tell the difference between testing "p v q" and testing "(p v q) & (z v x)"? There's nothing for it but to keep forming hypotheses and keep testing.
And so must we. We have to actually plump for "p v q" and get on with it, and be prepared to revise our beliefs as we go. That's why Gettier is useful: it could always turn out to be the truth of q reinforcing your belief that p. Science is hard.
Now, how do you test "If really p, then p v q"?
My view is that you don't test it because it's a matter of pure logic. Science doesn't formulate unconnected disjunctions and then try and establish which arm is true. Nor for that matter does the average Smith. Though logic permits the move, it's not a useful, revealing move as far as I can see.
The sort of thing science busies itself with is connected disjunctions - "the glass contains water or vodka" - and then we get the hydrometer out. "The glass contains water or my neighbour has a beard" is not something it is sensible to consider, never mind claim as a belief, or try and test.
Then what if Smith has strong evidence to suggest that it's water, but in fact it's vodka? He has a justified true belief that "the glass contains water or vodka".
Say he buys a bottle of Evian from Tesco, but some prankster in the factory has switched the contents.
If Smith has a justified belief that the glass contains water, why would he want to think, claim or believe that it contains water or vodka? He wouldn't, he would think claim and believe it contains water - wrongly. The circumstance where he would perhaps form the disjunction is if he saw that it contained a clear, colourless liquid, and that someone had sipped from it (not white spirit then), but didn't know exactly what liquid. If he thinks he knows what is in the glass, he has no reason to think the disjunction. And then it is as arbitrary and pointless as an unconnected disjunction.
That misses the point.
Quoting Srap Tasmaner
Gettier just constructs an artificial example to show how this works. It happens when you think you're testing p but you're actually testing p v q v r.
Favour us with a less artificial example, you have my attention.
The fundamental issue I take with your account is that it sets up a bizarre situation where:
1. I know that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. I believe that Jones owns a Ford, and
3. I don't believe that "Jones owns a Ford or Brown is in Barcelona" is true.
I think that your "solution" to the Gettier problem is far more counter-intuitive than just accepting that knowledge isn't simply justified true belief.
Other Gettier situations – such as correctly believing that Max is a man because of false evidence that Max is a bachelor – also show issues with the JTB definition of knowledge, so trying to save it from the disjunction case seems like a wasted effort anyway.
You may be right. I'm just exploring, but the way you tell it, I don't see Max as much of a problem. But I agree that there is a problem with JTB anyway. That's why all this is interesting. Does Gettier 'get at' the problem? Do you or he have a solution? Epistemology is a bit of a mess, and it seems to have infected politics.
To further show how the use of "p v q" is utterly inadequate, we all need to consider some other aspects of Smith's thought/belief. Smith must think about the rules of correct inference. The earlier post of Smith running modus ponens through his mind is a more than apt demonstration of the distinction between thought/belief about the rules. Belief that P and belief that Q are belief statements about the world while belief that:((p v q) is true)) is belief about the rules. Gettier claims Smith recognized the entailment, which is thinking about the rules of correct inference. Smith must think about the rules. Gettier's paper does not take proper account of this.
Who here would argue that thinking about the rules of correct inference is not required in order to arrive at believing Q ,when Q is derived from P, P entails Q, and the thinking/believing agent recognizes this entailment and the proceed to accept Q on the basis of P?
The process I'm setting out, when absent, results in a Smith that cannot believe a disjunction because without thinking about the rules, one cannot recognize the entailment.
Again, rational people do not assent to believing Q unless they understand what Q means, Q's following from P's notwithstanding. Rational people do not assent to believing Q simply because they believe P and some folk say that Q's following from P is necessary and sufficient for believing Q.
That is particularly germane when believing Q is believing a disjunction.
If it's true that one statement follows from(and/or is entailed by) another then it is so solely by virtue of the rules of correct inference saying so. One statement's following from another, in and of itself, neither warrants believing nor counts as believing the statement which is said to follow.
That is particularly germane when discussing believing a disjunction.
Various attempts have been made in recent years to state necessary and sufficient conditions for someone's knowing a given proposition.
To this there is only thing to state...
One must believe a proposition in order to know it. Smith does not believe that ((p v q) is true) except in the sense that "true" indicates being the result of correct inference. Gettier's formula does not have what it takes for Smith to arrive at believing Q.
One of the two statements is believed. To state that one or the other is true is to believe that they both could be. It shows uncertainty where none exists. One of the two is believed.
This is interesting.
I'm curious. How exactly have you come to differentiate Smith's argument from Gettiers? Furthermore, does it even make sense to say that Smith has an argument? Seems to me that he clearly has a thought/belief process that is laid out by Gettier himself.
"Jones owns a Ford" is true. "Jones owns a Ford" entails "Either Jones owns a Ford or Brown is in Barcelona". Therefore, "Either Jones owns a Ford or Brown is in Barcelona" is true.
Is that an accurate rendition of what you're claiming Smith's 'argument' is?
There's coffee.
There had been, a long time ago, a study linking coffee consumption to increased risk of cancer. But coffee drinkers are more likely to be smokers. Controlling for smoking, coffee's risk was downgraded. Then it went back up. The latest I think is that there's a risk associated with very hot drinks, not coffee per se.
Tests produce results, but they don't tell you why they produce the result they do. That's why justification can point away from the truth instead of toward it.
Yes. Except I wouldn't use the "either ... or ..." terminology as that implies an exclusive or, which isn't actually entailed by Jones owning a Ford. Gettier clearly meant for it to be an inclusive or, and so "Jones owns a Ford or Brown is in Barcelona" is the better wording. Charitable readings and all.
Quoting creativesoul
No it isn't. The statement "London is the capital city of England or pigs can fly" is true if London is the capital city of England. Therefore I believe that the statement "London is the capital city of England or pigs can fly" is true because I believe that London is the capital city of England. Given that the statement is true even if pigs can't fly, I can believe that the statement is true even if I believe that pigs can't fly.
Like unenlightened you're setting up a situation where:
1. I know that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. I believe that Jones owns a Ford, and
3. I don't believe that "Jones owns a Ford or Brown is in Barcelona" is true.
This strikes me as untenable. Anyone in this situation is clearly suffering from cognitive dissonance. And although it's entirely possible that Smith is in this state of cognitive dissonance, it's also entirely possible that he isn't, and Gettier is quite within his right to assert that Smith isn't.
Besides, Smith likely does believe that "Brown is in Barcelona" could be true. So your counter-argument isn't actually a counter-argument at all.
Well you have set up the beginning of a Gettier; Smith reads the study and believes that coffee causes cancer, a JFB. And then he sets up a connected disjunction "coffee causes cancer, or something else that coffee drinkers do causes cancer." Which is perfectly reasonable, and leads to further investigation. It is in fact a way of sceptically questioning his belief. Whereas Smith's arbitrary disjunction per Gettier does the opposite, it relies entirely on the unquestioned truth of his belief to make a claim that has no value in itself and can lead only to the entrenchment of his belief. It neither leads to a test of his belief nor an expansion of his knowledge in terms of Jones' whereabouts or anything else.
And since we all agree that it is possible and quite likely that we we all have the odd justified false belief, our attitude as scientists and equally as philosophers ought to be, because we are justified in being, sceptical rather than complacent concerning our beliefs.
And then, even if he is so ill-advised as to form the logically implied assertion, ((p v ae) v q), he is safe from ever believing or seeming to believe q, because (p v ae) is necessarily true, given justification - J, even if the substance of "ae" is that J is a lie, or an hallucination, and so it can be safely reasoned from.
Salva veritate
He also has a true belief. "Jones owns a Ford or Brown is in Barcelona" is true if Brown is in Barcelona. Brown is in Barcelona, therefore "Jones owns a Ford or Brown is in Barcelona" is true. Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because he believes that Jones owns a Ford and knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford.
Again, you're setting up the untenable situation where:
1. I know that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. I believe that Jones owns a Ford, and
3. I don't believe that "Jones owns a Ford or Brown is in Barcelona" is true.
It's nonsense.
No.
When you combine the two statements into one monolith and talk about Smith's belief like you've done above, you must remember and properly take into account that Smith's belief is about the rules of correct inference. If Smith believes that the disjunction is true if either one of the disjuncts is true, then he holds true belief about what makes the disjunction true.
That is not equivalent to believing the disjunction.
Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford. Just like you believe your disjunction is true because London is the capital city of England.
That's a very poor reading of what I've set out here. What follows immediately below is the thought/belief process that is required in order to arrive at believing Q when Q is a disjunction. Which part are you denying?
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
It's exactly what you're saying. You're saying that Smith doesn't believe that "Jones owns a Ford or Brown is in Barcelona" is true, despite the fact that he believes that Jones owns a Ford and knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford. It's untenable.
It's a simple fact that:
1. Smith knows that "Jones owns a Ford or Brown is in Barcelona" is true if Jones owns a Ford,
2. Smith believes that Jones owns a Ford, and so
3. Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true.
And given that "Jones owns a Ford or Brown is in Barcelona" is true because Brown is in Barcelona, Smith's belief that "Jones owns a Ford or Brown is in Barcelona" is true is true.
What follows immediately below is the thought/belief process that is required in order to arrive at believing Q when Q is a disjunction. Which part are you denying?
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
Again the pattern of oversimplifying Smith's believing a disjunction continues unabated, despite the fact that Michael himself follows the below...
It's a simple fact that:
1. Smith knows that "Jones owns a Ford or Brown is in Barcelona" is true if either "Jones owns a Ford" or "Brown is in Barcelona" is true.(p3)
2. Smith believes that Jones owns a Ford.(p1)
3. Smith believes that "Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford.(C1)
Precisely. Now account for it correctly.
I predict great success for the hypothesis that it was either coffee or something else. But the issue is getting past tautology and giving some substance to the something else. (We're also in the neighborhood of Nelson Goodman's discussion of ceteris paribus in FF&F.)
Here's another tack. Smith's original approach to Jones's car ownership is in part an abduction: if Jones owns a Ford, he'll drive a Ford. There's additional support for the abductive thesis in Jones's history of Ford ownership. An alternative abductive thesis would have been that Jones is renting a Ford, but there's no additional support for that.
The two abductive theses are connected by having a common result, that Jones drives a Ford. Which brings us to an issue we haven't specifically discussed, which is disjunction elimination. That works like this:
1. A?C
2. B?C
3. A v B
4. C
Given that Jones drives a Ford, we could form the abductive hypothesis that Jones owns a Ford or Jones rents a Ford. That's clearly an improvement, as it would in fact be true. But it's not a foolproof method. Maybe Jones borrowed a Ford. How can you be sure you've thought of every possible explanation of Jones driving a Ford? (Or coffee drinkers getting cancer.)
On the other end, I think what bothers people about (g), (h), and (i), the arbitrariness of those distinctions, is that it's not obvious how you could eliminate them. What would be a consequence either of Jones owning a Ford or Brown being in Barcelona?
This is actually the same problem as above. It's the sort of thing that the TV show House relied on. "By any chance, have you been to Barcelona recently?" Wildly unconnected underlying issues can produce similar symptoms.
Charitable readings and all...
Smith doesn't believe that Brown is in Barcelona. So Smith's thought/belief process - since it involves invoking an inclusive 'or' - is about the rules of correct inference. And yet that is not being taken into proper account.
Do you mean to say that (g)-(i) are exclusive disjunctions, and that each of these exclusive disjunctions is entailed by (f)? That just seems wrong. For it's logically possible that Jones owns a Ford while Brown is in any one of those three locations.
If instead you mean that (g)-(i) are ordinary (inclusive) disjunctions, then they are trivially entailed by (f). In that case these propositions should not be expressed with the form "either (f) or (p)", but rather with the more modest form "(f) or (p)".
Redraft accordingly:
(f) Jones owns a Ford.
(g') Jones owns a Ford, or Brown is in Boston.
(h') Jones owns a Ford, or Brown is in Barcelona.
(i') Jones owns a Ford, or Brown is in Brest-Litovsk.
Smith believes that (f).
If Smith believes that (f), and Smith's beliefs are rational, and Smith understands the conventional meaning of logical disjunction, then:
1. Smith's beliefs are consistent with (g')-(i').
2. Smith is disposed to assent to (g')-(i')
None of those propositions commit Smith to having any expectations about the whereabouts of Brown. The belief that (f) does not commit Smith to having expectations about the whereabouts of Brown. Consider:
(u) Jones owns a Ford, or Brown is a unicorn.
The belief that (f) does not commit Smith to having beliefs about Brown or about unicorns. If Smith is rational then his beliefs are consistent with (u). If Smith is rational and understands the conventions of propositional logic, then Smith is disposed to assent to (u).
To all appearances, the truth of the second term in each disjunction is independent of the truth of (f) -- not only as a matter of logical form, but also as a matter of fact. Such propositions are utterly arbitrary and uninformative. To believe them, to have beliefs consistent with them, or to be disposed to assent to them, is merely to be a rational person who believes that one term in the disjunction is true.
I see nothing especially troubling in this way of speaking.
The trouble comes this way:
If you have good reason to believe that p, then you have good reason to believe that p v q, and if p v q is true you have a well-founded true belief, but it is possible for p to be false and q true, in which case your reasons for believing that p turn out to be irrelevant.
Indeed. The trouble comes when those pontificating about Smith's thought/belief process conflate his belief that:((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true)) and ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if')) with belief that:((p v q) is true). The latter cannot exhaust the former, and thus belief that:((p v q) is true) is not an adequate representation of Smith's belief.
1. Mary tells Smith that she will give him £10 if Jones owns a Ford or if Brown is in Barcelona
2. Smith believes that Jones owns a Ford
3. So, Smith believes that Mary will give him £10
4. Jones doesn't own a Ford but Brown is in Barcelona
He might be wrong in believing that she will give him £10 because Jones owns a Ford, but he's right in believing that she will give him £10.
You're playing silly word games that do nothing to refute Gettier's argument. You ain't gettin' famous for it.
There's no word games being played Michael. I'm letting the fly out of the bottle.
Indeed, the whole idea is that such a formulation is necessarily true. Because otherwise S is only reasoning about his beliefs and giving substance to nothing. "I believe p, therefore I believe p v q." I tells us nothing about the world.
To put it another way, if S or any other philosopher wants to adhere to the strict implications of logic, they have to do so from the start. What is hidden in Gettier's account is what I have been accused of here, which is conflating what S believes with what Gettier defines to be the truth in his world. S believes p, but S doesn't assert ' I believe p', he asserts 'p'. He is not entitled to assert 'p' as a logical necessity, but he can assert my disjunction (p v ae) which is necessary and says in effect 'what I believe is true unless I am wrong in my belief.' It is S's failure to acknowledge in his assertion the real possibility of error on his part that leads him and us into the logical quagmire when he then makes strict logical deductions.
Smith must think about the rules of correct inference. The earlier post of Smith running modus ponens through his mind is a more than apt demonstration of what that looks like. Belief that P and belief that Q are belief statements about the world while belief that:((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true)) and ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if')) is belief about the rules. Gettier claims Smith recognized the entailment, which is thinking about the rules of correct inference. Smith must think about the rules. Gettier's paper does not take proper account of this.
Who here would argue that thinking about the rules of correct inference is not required in order to arrive at believing Q ,when Q is derived from P, P entails Q, and the thinking/believing agent recognizes this entailment and the proceed to accept Q on the basis of P?
The process I'm setting out, when absent, results in a Smith that cannot believe a disjunction because without thinking about the rules, one cannot recognize the entailment.
Again, rational people do not assent to believing Q unless they understand what Q means, Q's following from P's notwithstanding. Rational people do not assent to believing Q simply because they believe P and some folk say that Q's following from P is necessary and sufficient for believing Q.
That is particularly germane when believing Q is believing a disjunction.
If it's true that one statement follows from(and/or is entailed by) another then it is so solely by virtue of the rules of correct inference saying so. One statement's following from another, in and of itself, neither warrants believing nor counts as believing the statement which is said to follow.
That is particularly germane when discussing believing a disjunction.
Various attempts have been made in recent years to state necessary and sufficient conditions for someone's knowing a given proposition.
To this there is only thing to state...
One must believe a proposition in order to know it. Smith does not believe that ((p v q) is true) except in the sense that "true" indicates being the result of correct inference. Gettier's formula does not have what it takes for Smith to arrive at believing Q.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
The above is what believing Q requires when Q is a disjunction arrived at from believing P. Gettier's account of Smith's thought/belief process only gets to p2.
Smith believes that he will receive payment. His belief is true. You're just playing word games.
I'm charging you with inadequately accounting for Smith's thought/belief by virtue of not taking account of the process that is necessary for believing a disjunction. The oversimplification that both you and Gettier are guilty of results in the Gettier problem. It's not a problem for believing a disjunction. It's a problem with how that's being accounted for. It's a pseudo-problem:The self-induced bewitchment of inadequate language use.
That's not a word game, and you know it.
A proper account of believing a disjunction has been offered. There are no problems with it, and no disjunction is immune. None. Here it is again...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
That is what it takes. That is what it consists in/of. I've invited you and/or anyone else to imagine a disjunction arrived at by a rational agent on the basis of believing P that is not completely exhausted by the above solution. There are no problems. Fill it out.
The added beauty, of course, is that this eliminates any and all confusion about senses of 'or' as well as the fact that an insincere purveyor of disjunction cannot get through it, for it puts his/her actual belief on display for everyone to see. It also stops Gettier and anyone else from just mentioning - in passing - that Smith recognizes the entailment. The solution above spells out exactly what that means by virtue of showing what it requires.
Set it out in a way that follows Gettier's formula, then we'll talk...
1. Mary tells Smith that she will give him £10 if Jones owns a Ford or if Brown is in Barcelona
2. Smith believes that Jones owns a Ford
3. So, Smith believes that Mary will give him £10
4. Jones doesn't own a Ford but Brown is in Barcelona
Mary will give him £10. Smith has a true belief.
Set it out by adding the values...
If you believe that p and refuse to believe that p v q, then your beliefs are inconsistent. If you hold inconsistent beliefs then you are vulnerable to a Dutch book, as follows.
You're a bookie and you believe the odds that Jones owns a Ford are 10-to-1, and those are the odds you offer. That is, if Jones does own a Ford, you pay out just $11 on a $10 bet that Jones owns a Ford - Jones owning a Ford is the heavy favorite -and nothing on bets that he doesn't; if Jones does not own a Ford, you pay out nothing on bets that he does, and $110 on bets that he does not.
For some reason, you think it's less likely that Jones owns a Ford or Brown is in Boston than it is that Jones owns a Ford. (No matter where Brown is, the chances are at least equal. You don't agree.) You set the odds that Jones owns a Ford or Brown is in Boston at even money. That is, if either is true, you pay out $20 on a $10 bet that either is true, and nothing on a bet that both are false; if both are false, you pay out nothing on a bet that at least one is true, and $20 on a $10 bet that both are false. (If you think it's irrational to believe that Jones owns a Ford or Brown is in Boston, you might even offer something crazy like 1000-to-1 against. You just have no opinion and offer even money.)
Suppose I strongly believe Jones owns a Ford, and I bet $10 that he does and another $10 that Jones owns a Ford or Brown is in Boston. I figure I'll win both. Here are my actual payouts:
Ford & Boston: $31
Ford & not Boston: $31
No Ford & Boston: $20
No Ford & not Boston: $0
It costs me $20 to play, so my results range from clearing $11 to losing $20.
Now suppose instead I bet $10 that Jones does not own a Ford, and I bet $50 that Jones owns a Ford or Brown is in Boston. Here are my payouts:
Ford & Boston: $100
Ford & not Boston: $100
No Ford & Boston: $210
No Ford & not Boston: $110
The point here is that it only costs me $60 to play. No matter what happens, I clear at least $40. For nothing. With no risk whatsoever. No matter what Jones owns or where Brown is, I am guaranteed to clear at least $40.
Appendix
Assuming a negligible chance that Brown is in Boston and that you're right about the likelihood of Jones owning a Ford, these are the expected payouts:
First player: about $28 for a $20 stake;
Second player, who makes the Dutch book against you: about $100 on a $60 stake.
Gettier's scenario (no Ford, not Boston):
First player loses $20 to you;
Second player takes $50 from you.
Getting thought/belief right is necessary for getting the above right. I've shown that believing Q when Q is a disjunction arrived at from believing P is not adequately accounted for in terms of belief that:((p v q) is true). Believing Q in these cases requires thinking about the rules. As such it needs to be represented and/or properly accounted for.
I hope it's clear from my preceding remarks that I agree: (p V q) is not an adequate representation of Smith's belief in the case we began by considering.
Who says it is?
To say it is not an adequate representation of Smith's belief is not to say it can have no part in an adequate representation of Smith's belief.
For one thing, Smith believes
1. p [for reasons assumed in the scenario]
2. if p then (p V q) [empty formalism]
3. p V q [by inference from 1 and 2]
For another, Smith believes or is disposed to affirm that he has no idea whether q is true -- which is not the same as merely believing the tautology (q V ~q).
Quoting Srap Tasmaner
Is there some reason to insist that we cannot have justified true beliefs of this sort? To say p is justified in some epistemic context is not to say p is justified in an epistemic context that includes all the relevant facts. Such cases may lead to trouble for the one who believes that p, but I don't see what special difficulties they present for our analysis of these cases.
My reasons for believing p are not "irrelevant" to my judgment (p V q) in the case you've just described. They are the reasons that justify my judgment that p, and it's only this judgment which grounds the inference to (p V q).
That whole epistemic context is reflected in my disposition to alter my judgments in light of future changes to my view of the relevant facts. Such changes alter the balance of reasons for judging that p, which undermines the chain of inferences that had previously supported the claim (p V q).
All of which goes to show how the reasons that support the judgment that p are crucial to the judgment that (p V q) in this case.
Surely we're agreed on such matters? There must be something else at issue here....
The original paper...
That's been shown to be an inadequate account of what believing a disjunction requires...
No. But for many philosophers the intuition here is that the justified true beliefs in Gettier cases are not knowledge, so it's a problem for such accounts of what knowledge is.
My reasons for believing that p are obviously relevant to my believing that p v q, but it will turn out they have nothing to do with what makes p v q true. It's a bit of luck that I believe p v q for one reason but it turns out to be true for another. (Abusing the word "reason", I know.)
This thread is almost entirely about the B in JTB, for reasons that pass understanding.
It's not clear to me what position you take yourself to be arguing against or what position you take yourself to be defending, nor how your position is related to Gettier's .
"S believes that p" does not entail that p is true.
"S's belief, that p, is a justified belief" does not entail that p is true, nor that p is justified in every epistemic context.
"S knows that p" entails that p is true.
"T asserts that S knows p" does not entail that S knows p, and does not entail that p is true, even when T = S.
Sometimes knowledge claims are false claims. Like Wittgenstein says:
Gettier's paper is a critique of the concept of knowledge, not a critique of belief and justification, and not a critique of the validity of disjunction. It seems to me he takes ordinary epistemological concepts of belief, justification, and truth for granted in his paper. For instance:
Indeed, and this is really annoying. If justified true belief does not amount to knowledge, then what the eff is knowledge and what does amount to it? Where I'm at with this at the moment is that Smith does not arrive at his belief 'p' by formal logic, but by informal induction, and therefore he is not entitled (by logic) to treat his belief as a certainty, which is required to form the disjunction with a random 'q'. If Smith had the humility to assert in the first place, not 'p', but '(p v (I falsely believe p))', which is all he can confidently assert, he would save himself from justified true beliefs that he did not know, and us from a lot of head-scratching.
Together with abduction, yes. This is how we reason about matters of fact, sure.
Quoting unenlightened
Which he needn't; he only needs his belief to be justified. As Gettier puts this, he has "strong evidence" for (f).
Quoting unenlightened
No, it's clearly not, as my jar model shows. You can form a disjunction of beliefs held only probable, not certain.
Quoting unenlightened
But that just is to assert that p. Of course to say something is the case is to recognize that it might not be - it's the main reason we bother to make assertions. They are informative precisely because the facts they communicate are usually contingently so. And to recognize that is to recognize that you could be wrong. No one takes everything he says to be a necessary truth. But by asserting you commit yourself to the consequences of being right or being wrong. You place your bet, you answer the test questions, you test your hypothesis. What alternative is there?
I don't think humility saves you from Gettier. Suppose Smith never assents to p v q unadorned, but only as probable. We could still have a situation where Smith is right about the probability of p v q (and this is all we're talking about, not its truth) but his subjective probabilities are swapped: it's actually the "Jones" jar that is nearly all blue and the "Barcelona" jar that's nearly all red. Same problem, even without any claim of certainty or any belief held unconditionally true.
Weasel words these, if you don't mind my saying. If I'm right about something, probability no longer applies. If improbably I have the winning lottery ticket, what are the chances I have won the lottery?
?
I mean something as simple as this: I think there are 4 beers in the fridge because I think there are 3 Guinness and 1 Bud Light. Sadly, there's 1 Guinness and 3 Bud Light. I'm right about how many, but I've got the proportion wrong.
If you think about my stupid jars, it's obvious how this works.
If I'm weaseling about anything, it's that there are objective probabilities to get right or wrong. Sometimes there are, as with the jars. And sometimes you can be wrong about how probable an event is. I'm not offering a position in which there is no objective truth. Gettier gets dramatically reworked if you do that.
Understood and unsurprising given the novelty of my approach/position.
Gettier claims to show a case that satisfies the JTB formulation of knowing a proposition. The proposition in this case is a disjunction. Gettier claims that Smith meets the JTB criterion for knowing a disjunction. Gettier sets out a formula in the beginning of the paper that Smith's thought/belief process(as described by Gettier) follows in Case II.
1. I am claiming that believing a disjunction is necessary for knowing one
2. Believing a disjunction is not being taken proper account of
3. Belief that:((p v q) is true) is an utterly inadequate account of what believing a disjunction consists in/of
4. An adequate account of believing a disjunction clearly shows that Smith's belief is false
5. False belief is not a problem for JTB, no matter how it is arrived at
6. The underlying problem in Case II is a grossly inadequate (mis)understanding of what believing a disjunction consists in/of
It strikes me that perhaps you've not seen this...
I would concur.
This is not always true. To be as precise as ordinary language allows:S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's believing a disjunction.
This I outright deny.
Gettier's aims at a case that Smith forms/holds a Justified True Belief that:((p v q) is true) by virtue of going through the thought/belief process set out in the above formulation beginning with "Secondly..." Belief that:((p v q) is true) is the only value appropriate for Q in that formulation, for Q is (p v q) and believing Q is nothing less than belief that (p v q) is true. Hence, believing Q is belief that:((p v q) is true).
I will show that Gettier's formulation is inadequate regarding it's ability to take proper account of the thought/belief process required for S's believing a disjunction. S cannot arrive at that without another step that Gettier leaves out. To be clear, if the astute reader looks carefully at that formulation, s/he will note that only one deduction is purportedly necessary in order to satisfy the formulation. Namely, S's deducing Q from P.
I'm strongly asserting that [i]it takes more than one deduction for S to arrive at believing a disjunction, and since that is the case, it only follows that Gettier's criterion is inadequate. That will be clearly shown.
To be clear, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction then S is not necessarily justified in believing Q, for - in this case in particular - believing Q is nothing less than believing a disjunction and S cannot arrive at that following Gettier's formulation. Belief that:((p v q) is true) requires yet another deduction that is left sorely unaccounted for in Gettier's formulation. It's been said heretofore, but it now bears repeating...
S must first arrive at a belief before we can say that S is justified in forming/holding that belief. In Gettier Case II, the above formulation is utterly inadequate for S's arriving at belief that:((p v q) is true). The following argument represents the process of thought/belief that is necessary prior to even being able to arrive at believing Q and is an exhaustive account thereof. The term "because" in C1 is the necessary but missing deduction in Gettier's formula.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Note the above stopping point. The quote ends at the precise point where Gettier's next line concludes(by necessary implication) that Smith believes Q. Believing Q is precisely what's at issue here. Q is (p v q). Believing (p v q) is believing that (p v q) is true. Hence, Smith's believing Q is nothing less than Smith's belief that:((p v q) is true). So, using Case II, Gettier has filled out his earlier formulation. Here it is again...
Note here that this quote's stopping point coincides with Case II's, as shown directly above. As Gettier says, Smith believes Jones owns a Ford. Smith constructs (g), (h), and (i); all of which are (p v q). Smith believes p, and deduces (p v q) from p and accepts (p v q) as a result of this deduction. There is nothing about Smith's thought/belief process that the first two premisses below cannot effectively exhaust...
p1. ((p) is true)
p2. ((p v q) follows from (p))
Now, it is well worth mentioning here that nowhere in any of this(the above direct quotes from Gettier) is anything at all about Smith's believing Q. That is of irrevocable significance. It is a crucial point to consider here. Smith has yet to have gotten to the point where he has formed and/or holds belief that:((p v q) is true). Gettier thinks otherwise, as is shown by his saying...
...and...
He lost sight of exactly what believing Q requires. It requires precisely what follows...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))(from p1,p3)
Thus, we can clearly see that Gettier's formulation is inadequate to account for the belief that he needs for Smith to hold in order to make his case. Getting to belief that:((p v q) is true) requires both p3. and C1. Further we can also see that Smith's belief is not true, for he does not ever get to belief that:((p v q) is true). Gettier wants us to believe that Smith holds the belief that:((p v q) is true). This post has shown all sorts of problems with Gettier's formulation, and the aforementioned want of Gettier is just yet another.
Belief that:((p v q) is true) is not equivalent to belief that:((p v q) is true because (p)). The former is existentially contingent upon the latter and has a different set of truth conditions. The latter consists in part of the deduction missing in Gettier's account. The missing necessary deduction clearly shows that Smith's belief is false, Gettier's formulation is inadequate, and the 'problem' regarding Case II is non-existent.
Salva veritate
Smith believes Jones owns a Ford. Smith believes that 'Jones owns a Ford' is true. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' follows from 'Jones owns a Ford'. Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true if either 'Jones owns a Ford' or 'Brown is in Barcelona' is true.
Smith believes that 'Either Jones owns a Ford or Brown is in Barcelona' is true because Jones owns a Ford.
That is Smith's believing Q, as the result of another deduction and it is false.
QED
Seems that Gettier does as well as many many others including yourself. I mean, you say so immediately after saying that (p v q) is not an adequate representation of Smith's belief.
Gettier claims that Smith believes that "Either Jones owns a Ford or Brown is in Barcelona" is true. I'm objecting that this account of Smith's believing Q is utterly inadequate. Believing Q when Q is a disjunction requires thinking about the rules of correct inference because believing a disjunction requires considering what makes the disjunction true.
My solution shows this and in doing so it also shows that Smith's belief is false. Given that Smith has false belief, Gettier has lost all justificatory ground regarding Case II. His critique of JTB is based upon falsehood. Smith's belief is not true. Gettier's Case II is unfounded...
----------------------------------------------------------------------------------------------------------------------
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
The above holds good for every imaginable disjunction arrived at from belief that:((p) is true). There is never a problem of any kind. It's a solution. Believing a disjunction - for a rational person - is nothing more and nothing less than knowing what makes it true and believing that those conditions have been met. Smith's thought/belief process for arriving at believing all three of his own disjunctions is adequately represented below...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if (p) or (q) is true)
C1. ((p v q) is true because (p))
No he doesn't. He shows a case of Smith having a justified true belief that isn't knowledge.
I was more or less going from the three formulations of S knows that P...
Smith's belief is false. That's what matters...
Gettier mistakenly claims to have satisfied the (JTB)necessary and sufficient conditions for knowing P, while failing miserably at providing the necessary and sufficient conditions for believing Q when Q is a disjunction arrived at from believing P.
Gettier gives two special cases in which a justified true belief arguably does not count as knowledge, due to inadequate fit between the justification for the proposition and the truth of the proposition in question.
I suppose one might conclude that, though JTB may be necessary for knowledge, it is not sufficient.
That's not a troubling claim in my book. Even less so, given that Gettier's first case involves a superficial error of description, and his second case involves an arbitrary and artificial inference. Does anyone really believe that way? What is in fact believed when such sentences are uttered in such contexts?
Quoting Srap Tasmaner
Plato proposes that justification (account, logos) be added to true belief as a criterion for knowledge, to rule out cases in which a belief is only "accidentally" true.
Gettier helps us further specify the conception of knowledge as justified true belief, by indicating cases in which a justification for an accidentally true belief does not function the way the believer intends.
In both of Gettier's original cases, we expect the lucky believer, apprised of the relevant facts, to think something like "That's not what I meant".
His beliefs about the relevant state of affairs are on the whole contrary to fact, even though that view of the state of affairs disposes him to assent to a single proposition that is arbitrarily true with respect to his beliefs.
We might say the target propositions do not really reflect what is believed, and insist that beliefs be represented more thoroughly with respect to epistemic context.
Or we might say the ascribed "beliefs" are not really justified, though they seem justified from the point of view of the local epistemic context. A belief is true or false, independent of our grasp of the truth value of the proposition believed. Likewise, we might say, a justification for that proposition is "fit" or "unfit", independent of our grasp of the fitness of that justification.
Along such lines we could advocate for something like "fitness" as a "fourth criterion" to round off JTB, yielding Fit Justified True Belief. (Or try fullness, completeness, adequacy….). But this is only to clarify the original conception of "justification". For the thought was never that any old story that sounds good to me is good enough to warrant my beliefs, but rather that my story must line up with the relevant facts.
That sort of response should fly just as well for Barn Façade variations on Gettier's theme.
What about my example of Mary giving Smith £10?
1. Mary tells Smith that she will give him £10 if Jones owns a Ford or if Brown is in Barcelona
2. Smith justifiably believes that Jones owns a Ford
3. So, Smith justifiably believes that Mary will give him £10
4. Jones doesn't own a Ford but Brown is in Barcelona
Is this "unfit" justification? Is this a case of "that's not what I meant"?
Are you saying that a belief is only justified if it's true?
Smith has false belief.
Smith believes that Mary will give him £10.
Smith has a true belief.
He's correct in his belief that Mary will give him £10, but incorrect in his belief that she will do so because Jones owns a Ford.
This is the nonsense scenario you're setting up: "I believe that Mary will give me £10 because Jones owns a Ford, but I don't believe that Mary will give me £10". It's utter rubbish.
Quick note on the linguistics here:
(1) Mary gave me £10 because I won; and
(2) Mary didn't give me £10 because I won
usually both presuppose that Mary gave me £10.
The point of the statement is to highlight the reason for the action. The implication of the negative statement is that there was some other reason for the action taken. (Compare: "Mary didn't give me £10 because I didn't win.")
You get this a lot in Hollywood screenplays: "I didn't put you in the game because you're my son. I put you in the game because you earned it."
Similarly, someone could tell Smith, "Mary didn't give you £10 because Jones owns a Ford; she gave you £10 because Brown is in Barcelona."
That doesn't follow from what I've been arguing. You'll have to do better than that Michael.
What grounds this move to split up Smith's belief? On what basis do you posit Smith holding two beliefs?
Mary says she'll pay Smith if either this or that is the case. Smith understands this. Smith believes Mary will pay him because this is the case.
You want to remove the operative content of Smith's thought/belief, and by doing so create a problem that is otherwise not there.
Smith's belief is about and therefore must include his considering the conditions under which Mary will pay him.
The fact that there are two parts to Smith's belief. 1) Mary will give him £10, and 2) she will do this because Jones owns a Ford.
If someone were to ask Smith if he believes that Mary will give him £10, he will say that he does. It's really simple. You're clutching at straws.
Just "because"?
The astute reader will note that Michael just conceded, perhaps unwittingly, that there are two parts of Smith's belief that:Mary will pay him because Jones owns a Ford.
Michael wants to eliminate one part. Doing so renders an incomplete account of Smith's belief. This is clear for all to see. "Mary will pay me" does not mean the same thing as "Mary will pay me because Jones owns a Ford".
Salva veritate
The problem is not with Smith's belief. The problem is how it's being accounted for.
I'm not saying they do, so this is a straw man. I'm saying that if he believes that Mary will pay me because Jones owns a Ford then he believes that Mary will pay me. I've gone over this several times.
p ? r ? p
If Jones crashed his car into a tree then Jones crashed his car. If I believe that Jones crashed his car into a tree then I believe that Jones crashed his car. How is this so hard for you to understand?
I honestly think you're just being dishonest at this point.
But you are right; instead of being false, in this case the justification is insufficient.
Just wondering.
All Gettier says is that the Smith has "strong evidence" for the proposition that Jones owns a Ford.
Do you recommend holding out for justification that absolutely guarantees truth?
What irks me about Gettier is that he appears to be assaulting a straw man. Who is it that believes knowledge is exactly justified true belief?
Well, it was over fifty years ago. A simpler time.
Plus, it's a theory with some pedigree.
Plus, "justification" is a pretty flexible word. Informally, I think of JTB just as getting the right answer for the right reasons. That sounds plausible doesn't it?
Quoting Banno
I don't know. But you can arbitrarily strengthen the justification and still be vulnerable to Gettier. At least it seems that way. I think the impulse to say that if a belief were really justified, you know, really, properly justified, the way God intended and no cheating, then it would have to be true -- I think this impulse is mistaken.
The time I've spent in this thread (time I will never get back) has led me me to think that the point of Gettier is this: justification can point away from truth instead of toward it. I find that pretty interesting.
Is that so? Who, before Gettier, took it seriously?
If we understand the arrow above to be justifies or some cognate...
Then if the consequent is true, it is justified by any antecedent, true or false.
So anything justifies a truth.
Just sayin'.
Gettier cites the Theaetetus, Chisholm, and Ayer, for starters. Obviously the stars of Chisholm and Ayer have dimmed somewhat since then. Besides explicit support, I think the thrust of foundationalism, of empiricism in general, is toward such a position: a true belief grounded in experience, in the testimony of your senses, is the foundation of knowledge, that sort of thing.
Also, I think Gettier spurred many to consider defending the theory, because it feels like his argument is a parlor trick in some way.
Quoting Banno
The problem here is that you're switching in the middle from talking about justification to talking about truth. We expect both of these to hold, given that p?q:
(1) If p is true, then q is true;
(2) If I am justified in asserting (or believing) that p, then I am justified in asserting (or believing) that q.
But we cannot expect to freely mix and match:
(1*) If p is true, then I am justified in asserting q;
(2*) If I am justified in asserting that p, then q is true.
(1*) fails because I may have no idea that p; (2*) fails because I may be justified in asserting p though p and q both be false.
Inference does not confer either truth or justification; it only preserves whatever truth or justification is to be found in the premises.
But that's not right. The Theaetetus is famously inconclusive as to a definition of knowledge, and instead is perhaps best seen as arguing against empiricism, showing that the logos) must be taken as granted, in a neat parallel with Wittgenstein.
Quoting Srap Tasmaner
"If..."
I really have no idea what you're up to.
I'm thinking that knowledge is not as useful a term in epistemology as perhaps truth and certainty and belief. And that justification is near useless.
All just musings.
The irony...
This coming from one who's position rests upon knowingly and admittedly changing the meaning of Smith's belief...
I believe that:Mary will pay me because Jones owns a Ford is not equivalent to I believe that:Mary will pay me.
The former is an adequate account of Smith's belief. The latter is an oversimplification that leads to the very problems we're discussing.
Mary says she'll pay Smith if either this or that is the case. Smith understands this, and believes Mary will pay him because this is the case. You want to remove the understanding from Smith's thought/belief, and by doing so create a problem that is otherwise not there.
Smith's belief includes his considering the conditions under which Mary will pay him and believing that those conditions have been met. Leaving that part out of Smith's belief eliminates Smith's consideration of the truth conditions that are specific to believing a disjunction. That not only changes the meaning of Smith's belief, but it also changes whether or not it is true.
You admit that much, but then insist upon continuing to simplify it to the point of changing the meaning anyway.
To answer your earlier question Banno.
Regarding JTB, I have no skin in the game either way. What's important to me is getting thought/belief right...
A proper account of believing a disjunction has been offered. There are no problems with it, and no disjunction is immune. None. Here it is again...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
That is what believing a disjunction takes. That is what it consists in/of. I've invited anyone to imagine a disjunction arrived at by a rational agent on the basis of believing P that is not completely exhausted by the above solution. There are no problems. Fill it out.
The added beauty, of course, is that this eliminates any and all confusion about senses of 'or' as well as the fact that an insincere purveyor of disjunction cannot get through it, for it puts his/her actual belief on display for everyone to see. It also stops Gettier and anyone else from just mentioning - in passing - that Smith recognizes the entailment. The solution above spells out exactly what that means by virtue of showing what it requires.
How does knowledge sit with thought?
Smith is claimed to believe a disjunction.
The appropriate question for Smith is not "Do you believe that Mary will pay you?", for that is not asking about a disjunction. "Mary will pay you" is not a disjunction. Smith believes a disjunction.
Do you believe that Mary will pay you because Jones owns a Ford or because Brown is in Barcelona?
Solely by virtue of drawing and maintaining a meaningful distinction between knowledge and thought.
I've no issue with JTB counting as some knowledge. Although, I do tend to cast a critical eye upon a notion of justification pointing towards and setting aside something that requires language.
It's the belief part that matter most. If we get thought/belief wrong, then we'll have something or other wrong about everything ever thought, believed, spoken, written, and/or recorded.
Quoting Banno
A different vantage: Justification is useful in discerning mistakes of reasoning (self-deceptions and the like) in that it follows the principle of noncontradiction. Where a falsehood is denoted as a self-deception (or some other kind of deception), a falsehood will contradict both that which is true (i.e., a non-deception) as well as any other deception that is of a different ilk. Assuming any form of realism, there will always be something true. So justification, by means of remaining noncontradictory, serves to ensure that one’s beliefs remains accordant to what is real - i.e., from the vantage of correspondence to what is real, true. Even the most elaborate coherency between willfully given deceptions, in light of their being something true, will eventually be evidenced non-justifiable given its contradiction to that which is true - this, at least, given a sufficiently long enough chain of justifications. It may not always pinpoint what is true, but a contradiction will always pinpoint that there is a falsity somewhere.
If anyone cares to comment, I’m interested in how this sits with others?
If you're interested, page 40 is a good starting point...
thanks
Am I the only one who finds this unacceptable?
And yet Gettier used the "either ... or ..." terminology.
A proper account of believing a disjunction has been offered. There are no problems with it, and no disjunction is immune. None. Here it is again...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
That is what believing a disjunction takes. That is what it consists in/of. I've invited anyone to imagine a disjunction arrived at by a rational agent on the basis of believing P that is not completely exhausted by the above solution. There are no problems. Fill it out.
The added beauty, of course, is that this eliminates any and all confusion about senses of 'or' as well as the fact that an insincere purveyor of disjunction cannot get through it, for it puts his/her actual belief on display for everyone to see. It also stops Gettier and anyone else from just mentioning - in passing - that Smith recognizes the entailment. The solution above spells out exactly what that means by virtue of showing what it requires.
You mean <snip the bit that proves creativesoul wrong>?
I haven't said they are, so again this is a straw man.
I'm not going to continue discussing with you if you're going to resort to such dishonesty.
So far as I can see, Gettier problems don't give us reason to reject the conception of knowledge as justified true belief, they only present eccentric breakdown cases that push us to clarify. I've suggested we might respond to the issue by clearing up the relevant conception of belief, which seems to be creativesoul's approach, or by clearing up the relevant conception of justification, or both.
Quoting unenlightened
I'm not sure I follow.
Knowledge is not the same thing as certainty. I can know the way from here to the grocery store, even while doubting that I know the way. Belief and knowledge are compatible with doubt.
In Case I, Smith is not certain that Jones will get the job, nor certain that Jones has ten coins in his pocket. He only has "strong evidence" to support those claims.
In Case II, he has "strong evidence" that Jones owns a Ford. It's not made explicit how Gettier makes sense of the warrant for "Brown is not in Boston, Barcelona, or Brest-Litovsk". Say: Smith has a good idea of the history of Brown's whereabouts and Brown's plans for the next few weeks, thus believes accordingly it's extremely unlikely that Brown's at any of those three places, so has good reason to assume Brown's not in any of those three places.
In each case, there's no question of certainty, but only strong evidence that provides defeasible warrant for premises that ground the inference leading to the proposition in question.
So far as I can see, the problem is not that Smith is certain when he shouldn't be, but rather that Smith makes valid inferences based on false premises, and still winds up latching onto true conclusions. The lack of fit is so severe that we're forced to deny that Smith knows what he's talking about when he affirms the true propositions in question.
This problem remains whether or not Smith's beliefs account for the possibility of error.
The first problem that comes to mind is that (p2) can fill in the blank at (p3), which makes (p3) redundant.
(p V q) is true if p.
All that remains is to provide warrant for p.
I'm not aware of having said that.
I do say that "(p V q)" can and should have a place in an adequate representation of Smith's belief. That's not the same as doing the job all by itself.
So far as I can see, we need to add the premise that supports the inference to (p V q), and also the warrant for that premise.
Does it help if we adjust to reflect the exclusive disjunction in Gettier's paper:
1. p [for reasons assumed in the scenario]
2. ~q [for reasons assumed in the scenario]
3. if (p and ~q) then (either p or q) [empty formalism]
4. either p or q [by inference from 1, 2, 3]
Agreed, at least for the sake of argument.
Quoting creativesoul
Agreed, in that Smith's belief is not an isolated "belief in a disjunction", but has an epistemic structure. I've sketched my take on that structure, and I'm not sure I understand your take.
Quoting creativesoul
Agreed, same as (2).
Quoting creativesoul
Every account on the table clearly shows that the premise p is false and that the premise ~q is false. That's the problem. The justification is flawed because it's based on false premises, but it still reaches a true conclusion by way of valid inferences.
Is there something else you show to be false, some other proposition relevant to the problem?
Quoting creativesoul
Agreed.
But valid inferences from false premises to true conclusions arguably pose a problem worth addressing, at least given the peculiar character of the Gettier cases.
Quoting creativesoul
I'm still not clear on what your view of "believing a disjunction" amounts to.
I agree that clarifying the "representation" of the relevant belief is a promising approach to the problem, and that the complete picture should include more than "Smith believes that (p V q)" [or more than "Smith believes that (either p V q)", to follow Gettier's example more closely].
I've suggested that clarifying the relevant sense of "justification" is another promising approach.
You're not alone, and I wish I could make clearer to others what is very clear to me.
Quoting Cabbage Farmer
The argument is that if S has a justified belief p, then by pure logic he has a justified belief (p v q), where q is any proposition whatsoever. I don't think he can justify the second belief because it relies entirely on the truth of p, and not at all on the justification or the belief of p. Now to believe p is to believe the truth of p, but this belief is still not the truth of p, but only the belief of p.
Everyone seems to agree with Gettier that we can have justified false beliefs, but this is not reflected or accounted for in the proposition S makes his argument from. He believes p with good reason, but he is not thereby entitled to argue formally from p, but only from (p v I am mistaken about p). And from that premise, he cannot logically move to (p v q), but only to ((p v I am mistaken about p) v q) which is harmless.
If S knows p, then by force of logic, he knows (p v q). This works, because if he knows p, then p is true, by the definition of knowledge. But he doesn't know p and cannot possibly know p, because p is not true, and it is because beliefs are not always true that the truth preserving logic does not work for beliefs.
@Cabbage Farmer describes Smith somewhere as having a defeasible warrant to assert that p, and that's all he needs.
Think about how reductio works: assume that p, and then show that p leads to a contradiction or a known falsehood. And then plain old modus tollens.
It's the same thing here: Smith has strong evidence that Jones owns a Ford, but his belief is defeasible. If Jones walked in the office one day and said, "I don't know why I bought Fords all these years, this Chevy I just bought is fantastic!" Then poof, there goes Smith's belief that Jones owns a Ford. Why? Because Smith can immediately see that his theory would predict Jones not saying this. (The switch from material to subjunctive conditionals has a little wiggle room.)
There is all the reason in the world to reason from premises not known to be true, precisely so you can test them, expose them to possible defeaters. You can reason from premises you believe false as if they were true, precisely in order to show that they are false. (Again there may be a switch to counterfactual conditionals.)
In short, I think you're always entitled to inference. Inference is innocent. The credence you give your premises is usually the issue. If you hold certain what you shouldn't, then you block the modus tollens that would revise your belief. If you never infer, you block the modus tollens that would revise your belief.
No, that's not all he needs, and that is my whole point. From "defeasibly p", (p v q) does not follow. In logic a thing follows or it doesn't; there is no 'defeasibly follows'.
Redundancy applies if there is no meaningful difference in the change being made. You're suggesting that Smith holds the belief that:((p v q) is true if (p v q) follows from (p)). So the solution would look like this after filling in the blanks...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if (p v q) follows from (p))
C1. ((p v q) is true because (p v q) follows from (p))
It doesn't seem redundant from here. In such a scenario, Smith hods false belief about what makes a disjunction true. It does not follow from the fact that (p v q) follows from (p) that (p v q) is true. Being the result of a valid inference is insufficient for being true. That scenario also posits a Smith that does not take into consideration the actual truth conditions of (p v q). Rational people do not assent to believing a disjunction if they do not know what it means. Knowing what makes a disjunction true is knowing what it means. Rational people would know what makes a disjunction true and assent to believing a disjunction based upon believing that those conditions have been met. That is what my solution puts on display...
We agree that whether B follows from A is purely a matter of logic, nothing to do with belief. I don't know why you think I'm arguing for extra logical constants. I've never ever said anything remotely like that.
If you infer B from your belief that A, and if your belief that A is defeasible, then so too should your belief that B be. That's normal inference, not some special kind just for defeasible beliefs.
Suppose you think A might be the case, but it's difficult to test for directly, but you know that A?B, and it's comparatively easy to test for B. If B comes back false, you apply modus tollens and conclude ¬A.
One way to look at this is like so:
1. A?B
2. ¬B
? 3. ¬A
That is, in the Great Book of Established Truth, A was never entered at all.
But in practice what happens is more like this:
1. A?B
--- 1.1. Assume A
--- 1.2. B
--- Test B
--- 2. ¬B
--- 2.1. A??
3. ¬A
To get to the point of having something to test, you take A hypothetically, and infer B from it.
I think most scientists would be inclined to say there is no Great Book of Established Truth. Instead there is the Great Book of Not Disconfirmed Hypotheses. If B comes back true (as best we can tell), that's another tally mark for A, and that's the best we can do. That's why we have the book, to keep track of the A's that are doing pretty well in the confirmation department. As Hume said, all arguments about matters of fact are probable, not demonstrative. You can have a Great Book of Established Truth if you want, but you might as well leave it in the Math Dept. because they're the only ones who'll ever put anything in it.
If later there's even better evidence against B, they may both have to be moved to whatever the current volume is of the Great Book of Discredited Hypotheses.
** ADDED: We could of course have a "defeasibly follows from" in the sense that we could hold A?B to be only probable. It's a premise too, no real difference from holding A to be only probable. That's not our situation here, because though we can write P?P ? Q if we want, that's not really a premise. We're not entertaining the option that it could be false. It's an inference rule rather than a premise, and should really be written P?P ? Q, or [math]\small \frac{P}{P \lor Q}[/math].
Quoting Cabbage Farmer
This is to say that believing a disjunction has some sort of epistemic structure. You offered the following...
1. p [for reasons assumed in the scenario]
2. ~q [for reasons assumed in the scenario]
3. if (p and ~q) then (either p or q) [empty formalism]
4. either p or q [by inference from 1, 2, 3]
I can understand why it would seem to be helpful to formally set out an exclusive 'or'. I mean, Smith's thought/belief process results in his believing a disjunction, and he is admittedly ignorant about Brown's location, so he would not believe anything at all about Brown's location.
It seems very clear to me that there is a stark contrast between formalization of thought/belief(taking an account of thought/belief) and how thought/belief actually works. That is partially understood by virtue of our recognizing the performative contradiction inherently within 3 that would surely carry over to 4 if we were to take your offering as an adequate account of Smith's believing a disjunction. Belief that either p or q is true, in the sense of truth that is presupposed within all thought/belief and statements thereof, is to believe that either could be the case. Smith believes neither that p could be false nor that q could be true. For him to think/believe and/or state that either p or q could be true would be for him to arrive at self-contradiction.
However...
Smith can believe that (p v q) follows from (p) despite his not believing (q). Believing that a disjunction follows from a belief is not equivalent to believing a disjunction. The former is belief about the rules of correct inference, and the latter is believing that the truth conditions of a particular disjunction have been met. You've set out the former while leaving the latter sorely neglected. I've found focusing upon q to be entirely irrelevant, for Smith does not believe any of the q's, and we are taking an account of Smith's thought/belief process on his way to arriving at believing a disjunction.
Given that, what is there in your above epistemic structural offering that is both germane and not effectively exhausted by p1 and p2 below?
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
Quoting Cabbage Farmer
This doesn't make much sense to me. I'm saying that belief that:((p v q) is true) is not an adequate account of believing a disjunction. You've agreed to this and subsequently offered an account of believing a disjunction that results in belief that:(p or q) which is exactly what I've shown to be inadequate.
Quoting Cabbage Farmer
This is prima facie evidence that you've not understood what I've argued.
I understand that historically people have understood the problem to be that Smith arrives at JTB by virtue of working from false premisses and valid inference/form. I understand that folk want to take an account of Smith's thought/belief process by virtue of displaying some logical argument or another. I'm saying that they're all found to be sorely lacking in much the same way... explanatory power.
None of them can account for Smith's considering the truth conditions of his particular disjunctions and subsequently concluding that the disjunction is true because those conditions have been met.
That's precisely what believing a disjunction requires. When that is properly accounted for, it becomes crystal clear that Smith forms and holds false belief. The scope of those consequences are daunting. The Gettier 'problem' is irrefutably shown to be nothing more than an utterly inadequate account of what believing a disjunction requires and/or consists in/of.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
Quoting Cabbage Farmer
The 'argument' I'm putting forth is the thought/belief process that is required for a rational agent to arrive at believing Q when Q is a disjunction deduced from believing P. Believing a disjunction is not belief that:((p v q) is true). Believing a disjunction requires considering what makes that particular disjunction true and believing that those conditions have been met. Thus, Smith's believing all three of his particular disjunctions consists exactly in/of the thought/belief process I've set out.
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if either (p) or (q) is true)
C1. ((p v q) is true because (p))
Jones owns a Ford. "Jones owns a Ford" is true. "Either Jones owns a Ford or Brown is in Barcelona" follows from "Jones owns a Ford". "Either Jones owns a Ford or Brown is in Barcelona" is true if either "Jones owns a Ford" or "Brown is in Barcelona" is true. "Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford.
Smith does not have true belief.
Justification does not appear in the Theaetetus; it's a modern variant. In the Theaetetus the third component is the Logos; analysed in various ways. The idea is perhaps a sort of coherentism - a piece of knowledge has to fit in with the other stuff you know.
So one big flaw in Gettier is that he takes the justification to be one or two supporting propositions, and not holistic.
I don't think he does. The way Gettier sketches in the "strong evidence" Smith has is clearly just a gesture toward whatever we would generally count as strong evidence:
So do you have some thoughts on justification? What is this holism of which you speak?
A nice small bit of context may serve us well.
I strongly suggest that if one is offering a critique on the JTB concept of knowledge that s/he had better get belief right. Gettier aims at satisfying three popular formulations of knowledge as JTB. Those three formulations claim to set out the necessary and sufficient conditions for knowing a given proposition.
Something that has not been given due attention...
The necessary and sufficient conditions for knowing a proposition must exhaust the necessary and sufficient conditions for believing one. The necessary and sufficient conditions for believing a proposition vary according to the complexity of the proposition. The necessary and sufficient conditions for knowing a proposition vary in accordance to the complexity of the belief.
This is not reflected in any of the three formulations for JTB. It is also not reflected in Gettier's formulation. His cases follow the outline of his formulation, so this is also not reflected in either of those cases.
That gets to the root of the problem(s).
That is another root of the problem(s) and leads to the performative contradiction mentioned earlier when we confuse Smith's believing that:((p v q) follows from (p)) with Smith's believing that:((p or q) is true).
In the dream of Socrates, the account that accompanies true belief is an analysis of the complex in terms of the simple. The rejection of that account in the Theaetetus curiously parallels the move from logical atomism to meaning as use in analytic philosophy.
An intersting notion. So Moore might believe he has a hand, and yet doubt it. Or Moore might know he has a hand, and yet doubt it. But not Moore might be certain he has a hand, and yet doubt it.
That might be right.
Yes, this seems like another example. On the basis of his strong evidence that Jones owns a Ford, Smith might feel the bet's practically a sure thing. If he learns how he came to get the payout, he'll recognize it was pure luck.
Of course he still gets the payout, just like he still gets a hold of true claims in Gettier's original examples. But he gets them by a stroke of luck, not by virtue of understanding the relevant facts.
Quoting Michael
That's a fair analysis on the surface of the problem, but arguably leaves too much out of the picture.
How is the isolated claim "Mary will give me £10" supported in the context of Smith's beliefs? creativesoul has been arguing that we need a more thorough representation of Smith's beliefs in order to make sense of the problem. I'm inclined to agree.
We can't adequately understand what Smith believes -- we can't adequately interpret his propositional attitude with respect to the proposition we purport to represent by way of the English sentence "Mary will give me £10" -- without getting some of Smith's reasons into the picture. We need to show a relation among Smith's beliefs that supports the belief in question.
I suppose a JTB account of knowledge always requires us to dig deeper than a single knowledge claim, to show how the claim is justified for a given believer. In Gettier's cases, that digging turns up such a mess, it seems unreasonable to count them as cases of "knowing" -- as Smith himself would be prepared to admit, were he apprised of the relevant facts.
Quoting Michael
No.
What counts as a sound justification from Smith's ill-informed point of view does not count as a sound justification from any well-informed point of view. Smith's "argument" is valid but not sound, as it depends on false premises.
Once Smith is apprised of the relevant facts, he realizes that he only got hold of a true conclusion by chance, not by sound reasoning. What had previously seemed a sound justification now turns out to be an unsound justification, because the premises on which it was based now appear to be false. (Not all variations on Gettier's theme turn on false premises in such an obvious way, so I'm not suggesting that "soundness" is the road to a general solution.)
It's interesting that philosophers like Gettier seem prepared to count such valid inference from false premises as "complete justification", while presumably they would not count invalid inference from true (or false) premises as justification. Why treat the norms of inference as if they were more objective than the facts? On the other hand, why not treat justifications involving invalid inferences as nonetheless justifications for the one who doesn't notice his fallacy?
My suggestion is that we make a theoretical distinction between a claim i) "justified" from an ill-informed epistemic context or finite point of view, and ii) "justified" from a well-informed epistemic context or omniscient point of view. Then we might say, the J in JTB is justification in sense (ii).
This seems in line with Plato's original suggestion. I suppose it also makes justification a mercurial little trickster like truth and knowledge.
We count claims as true, as known, as justified, each of us from his own point of view. But we take for granted that there is a fact of the matter that determines whether we are correct in those judgments.
Except when there is no fact of the matter.
This bit I can agree with: In Gettier's cases, Smith believes that p but does not know that p, because p is in fact and unbeknownst to Smith, false.
That's why his justification for the disjunction is problematic. It's a valid argument from false premises that accidentally lands on a true conclusion. It seems to me Smith's ignorance is the whole problem, and this is what is preserved on what I take to be a common response to the puzzle: Smith does not know that p, and he does not know that (p V q), although (p V q) is true in fact and Smith believes with justification that (p V q).
I still don't see how adding skeptical couching helps to address this specific problem.
However one couches it, the sceptical element amounts to, by malign accident, improbable circumstance, alternative interpretation of the evidence, or whatever, '~p'.
This gives a weighted disjunction, (p(99%) v ~p(1%)). And that does not lead to (p v q). It's so simple it seems to be invisible to everyone, but as soon as it is possible that ~p, the damaging disjunction (p v q) cannot be made at all.
What I'm suggesting is that
(p AND (IF p THEN (p V q))
is already enough to give a truth condition for (p V q). Or in other words:
(p V q) is true if p.
I'm not sure what else you think is required, or how your view is coordinated with ordinary propositional logic. So far as I can see, all that's missing is sufficient warrant for the claim that p, which is provided by Gettier.
Which is not to say that (p V q), taken in isolation, is an adequate representation of Smith's belief in Gettier II.
Quoting creativesoul
I only offer to revert to the exclusive disjunction because it seems to be the form of the thought Gettier intends to put in Smith's head.
Quoting creativesoul
That sounds right. I suppose we're all talking about best practices for formalization of the case at hand.
Quoting creativesoul
What contradiction is inherent in (3), and how does it carry over to (4)?
Quoting creativesoul
The exclusive disjunction is true if and only if one but not both of the terms in the disjunction are true. That's the logical form of exclusive disjunction.
I suppose believing that an exclusive disjunction is true, or having beliefs with the form of an exclusive disjunction, requires believing that one but not both of the terms in the disjunction are true. For instance, by believing that p and believing that ~q.
Quoting creativesoul
I wouldn't say "could". We have no indication that Smith thinks it's impossible that ~p and impossible that q. And we have no indication he counts himself absolutely certain that p and ~q.
None of that is required for us to count Smith as believing with justification that p and ~q.
Quoting creativesoul
I reject this claim. I take the following to be consistent statements:
I believe that p and that possibly ~p. I believe that p, and I believe it's possible that my belief-that-p is wrong. I have beliefs and I believe it's possible that any of my beliefs are wrong.
I know that p but it's possible that I am wrong and that ~p. I have knowledge but it's possible that any knowledge claim of mine is wrong.
Moreover, I take it this way of speaking is consistent with Gettier's arguments.
Quoting creativesoul
Of course he can. His belief in that implication should not be influenced by his beliefs about the truth values of p and q.
Quoting creativesoul
The truth of an inclusive disjunction follows from the truth of any of its terms.
To believe that one or more of those terms is true is to have beliefs in accord with the truth of the disjunction, and is to be disposed to assent to the claim expressed in the disjunction.
Moreover, if Smith is rational and understands the conventions of formal logic, and believes that p, and entertains the proposition (p V q) in light of his belief that p, we should be surprised indeed if he does not acknowledge that he believes that (p V q) is true.
Quoting creativesoul
The truth conditions of (p V q) are met as soon as the truth conditions of p are met. Or as soon as the truth conditions of q are met. Or as soon as the truth conditions of (p AND q) are met.
It seems this is the point you're neglecting, which has sent you off on a search for red herring.
Smith believes that p.
Smith does not merely believe that there are abstract inferential relations between any pair of propositions and their disjunction. He believes the truth condition for a particular disjunctive claim has been satisfied. He believes that Jones owns a Ford.
Quoting creativesoul
I don't think I've neglected anything. We only need to focus on q if we want to follow Gettier and analyze the case as an exclusive disjunction. Smith's beliefs about q are quite relevant in that case. Because in that case, Smith must believe he has strong evidence for both p and ~q.
I'm happy to go with the flow here and focus on the case as if Smith had constructed an arbitrary inclusive disjunction instead of an arbitrary exclusive disjunction. I don't think it makes much difference for the underlying issue.
Quoting creativesoul
That's my point. We don't need the rest of it.
The relevant epistemic structure is exhausted by:
warrant for p
belief that p
understanding that (IF p THEN (p V q))
That's enough to make Smith disposed to assent to (p v q), and enough to make Smith's beliefs accord with (p V q).
Add that, given that epistemic context, Smith entertains the proposition (p V q) and makes a rational judgment. In my book that's enough to attribute to Smith the belief that (p V q).
Quoting creativesoul
I have agreed that (p V q) is not in itself an adequate representation of Smith's belief. I have offered what I take to be an adequate representation, which consists of more than the mere claim (p V q).
You have claimed repeatedly, but not shown to my satisfaction, that my sketch is inadequate. You have insisted that something extra is required, but you have not made clear why or what the extra item is supposed to be.
By now it seems we're going in circles. This is beginning to get tiresome.
Quoting creativesoul
I might argue this discussion is prima facie evidence that you don't understand what you've argued. Instead let's proceed by assuming that neither of us adequately understands the other's point of view, and that neither of us completely understands his own point of view, at least until such time as we may attain some sort of mutually satisfactory resolution.
Quoting creativesoul
I don't know what all the others have said.
In my view Smith's "belief" is justified in one sense, and not justified in a stricter sense. And his "belief" is not adequately represented by the isolated disjunctive claim, but only by that claim in the context of his supporting beliefs about the facts of the case, which supporting beliefs function as his justification for the isolated claim in question.
Quoting creativesoul
Why can't they? The truth of p is a truth condition for (p V q). Smith believes that p, and has strong reasons for believing that p. What is left unexplained?
Perhaps the abstract symbols are causing the confusion? I'll reiterate, Smith's beliefs here aren't merely about abstract inferential relations. He believes:
Jones owns a Ford.
IF Jones owns a Ford, THEN (Jones owns a Ford OR Brown is in Barcelona)
THEREFORE (Jones owns a Ford OR Brown is in Barcelona)
Quoting creativesoul
So far as I can see, it's already accounted for by Gettier. It's already clear that Smith's view of the facts is incorrect because he holds a false belief; and clear that accordingly his beliefs about the broader context are flawed; and clear accordingly that his justification for the disjunction is, though reasonable in context, sorely off the mark.
Quoting creativesoul
I don't see anything daunting about the Gettier problems, and I'm not sure you have worked out a coherent response to them. I do think they're interesting puzzles that force epistemologists to clear up their conception of knowledge as JTB. And I think your approach -- clearing up the representation of Smith's beliefs -- is promising in its broad features.
Your attempt to "solve" Gettier II by focusing on the formal features of "believing a disjunction" -- even if it were successful -- might leave dissatisfied those of us who'd prefer a single unified solution to all Gettier-type problems. Not all Gettier problems involve disjunction.
The above marks a common point of conflation. The below marks a typical red herring response to the above...
A careful reader will note that the objection does not offer an example of believing the disjunction. Rather, it poses a single statement as the belief candidate, namely "the Post Office isn't open". The problem of course, is that "the Post Office isn't open" is not a disjunction.
So in your view we are only entitled to infer p v q from p if p is a necessary truth.
No, only if it is an actual truth. Only if it is known, because then it is true. If it is only believed then it may not be true. But in practice, beliefs are normally not known to be knowledge unless they are necessary. But this is not merely 'my view', it is the way logic works, as developed over the millennia.
What's missing is an adequate account of believing a disjunction. Belief that:((p v q) is true if (p) is true) is necessary but insufficient for believing this particular disjunction. Believing it requires another deduction.
What you've offered covers one aspect of what believing a disjunction requires. That is, belief that:((p v q) is true if (p) is true) is a perfect representation of an agent's considering the truth conditions regarding what it would take for a disjunction to be true if and when it is deduced from belief that:((p) is true). In Gettier's second case, what you've presented would cover an exclusive 'or', and would be in complete agreement/congruence with p3 of my solution.
p3.((p v q) is true if... (insert belief statement(s) regarding what makes this particular disjunction true))
Filling it out...
p3.((p v q) is true if (p) is true)
We're after the agent's believing the disjunction. That requires one more deduction.
C1.((p v q) is true because (p))
The notation I'm using packs as much as possible into the belief statement, as it should on my view given that belief is the target. That said, I'm not well-versed in any formal notation.
------------------------------------------------------------------------------------------------------------------------
I want to note that you shouldn't take anything I say personally. My apologies for the poorly worded bits about misunderstandings, and not openly accepting some responsibility for them. My position carries quite the burden, and I gladly accept it...
That said, this post left much out. I think, however, that it gets to the heart of what you've asked for.
Aren't you just conflating validity with soundness? I just don't understand the idea that inference is only possible from actual truths.
Quoting unenlightened
What's a person to do then? Suppose I think I know that A. Should I infer B from it? Or only if I know that I know? Maybe I only think I know that I know ...
No.
IF p, then (p v q). That's valid, sound, true and contentless.
But if not, then q can really just fuck off.
Quoting Srap Tasmaner
A person is to acknowledge the fallibility of his beliefs and refrain from making arbitrary unconnected pointless disjunctions of them as if they were necessarily true, because they ain't.
Smith's considering the truth conditions of his particular disjunctions and subsequently concluding that the disjunction is true because those conditions have been met.
p1.If P then Q
p2.P
C.Therefore Q(from 1 and 2)
If modus ponens is used as a means for accounting for Smith's thought/belief process leading up to his believing a disjunction, then that thought/belief process would certainly include Smith's concluding that the disjunction is true because the truth conditions have been met(from 1 and 2). That cannot be left out, for doing so renders an incomplete account of Smith's belief. The incomplete account has a very different meaning.
If "Jones owns a Ford" is true then "either Jones owns a Ford or Brown is in Barcelona" is true. "Jones owns a Ford" is true. Therefore, "either Jones owns a Ford or Brown is in Barcelona" is true because "Jones owns a Ford" is true and if "Jones owns a Ford" is true then "either Jones owns a Ford or Brown is in Barcelona" is true.
Smith has false belief.
Belief that:((p v q) is true because ((p) is true) and (if (p) is true then ((p v q) is true)) is not equivalent to belief that:((p v q) is true).
p2. ((p) is true)
C. ((p v q) is true because ((p) is true) and (if (p) is true then ((p or q) is true)).
That is taking proper account of Smith's thinking about the truth conditions(from 1 and 2), and subsequently believing the disjunction as a result of believing that those conditions have been met. That is what has been left completely unexplained by every account on the table except my own...
I would readily agree that not all Gettier problems involve disjunction. They do all involve his formula though, and it has been proven to be inadequate for providing the necessary and sufficient conditions for believing all Q's.
It's only sound if p is true.
Quoting unenlightened
The conclusion of an inference merits no more or less credence than what you grant your premises. If you're uncertain about your premises, then you should be just that uncertain about your conclusions.
Why in your view is that not a sufficient acknowledgement of fallibility?
I agree, of course, that there is something odd about Smith's inference. Maybe there should be another rule brought to bear here. I just don't know what that rule would be.
If r, and S believes r, and r is justified, then by definition S knows r
by presenting a case in which S would, by this definition, be said to know r; and yet our intuition says otherwise.
And it might go like this:
S believes p
If p, then (p v q)
therefore S believes (p v q)
At this point one might object that adding the disjunction is infelicitous, since one cannot substitute into belief statements salva veritate. Is that one of Un's points?
Leaving that aside, how must the argument proceed? Is (p v q) justified?
Well, ex hypothesi, q is true but not p. So for the argument to work, the following substitution must work;
p is justified, therefore (p v q) is justified.
again, it is debatable that this can be done salva veritate.
As it turns out, and unbeknownst to S,
q and ~p, therefore (p v q)
bring down: If r, and S believes r, and r is justified, then by definition S knows r
Substitute (p v q) for r, and take (p v q) as true since q is true. Discarding the two salva veritate objections,
S believes (p v q)
and
q is justified, therefore (p v q) is justified
So therefore, by definition, S knows (p v q)
But S holds that (p v q) is justified because p is justified, not because q is justified. That is, S was wrong in thinking he had an adequate justification for (p v q).
SO I see three objections:
1. Substitution into belief statements can fail salva veritate
2. Substitution into Justification statements can fail salva veritate
3. S has in inadequate justification for (p v q).
Not that it matters, but I think you want that to be a conjunction.
I don't think we're talking about substitution here exactly. No one thinks p v q is equivalent to p; it's inferred from p. And explicitly we're not inferring what Smith believes. Smith makes these inferences and we're just told that he does.
If someone objects, what you gonna do?
S believes p
p is justified
p
Therefore S knows p
against
S believes p
p is justified
~p
Sam does not know p.
and against
S believes p
S believes p is justified
S believes S knows p
~p
In which case S is mistaken - all within the scope of S's belief.
We should be perhaps even more surprised if he was asked which of the following was a more accurate rendition/account/representation of his believing the disjunction, and he did not immediately confirm the second...
"Either Jones owns a Ford or Brown is in Barcelona" is true.
OR
"Either Jones owns a Ford or Brown is in Barcelona" is true because Jones owns a Ford.
This is even clearer if we put all three on display...
To drive the point home, the same holds with Case I. We should be quite surprised if Smith was asked which of the following was a more accurate rendition/account/representation of his belief(s), and he did confirm the second...
Jones has ten coins in his pocket. Jones is the man who will get the job.
OR
The man with ten coins in his pocket will get the job.
We're told that S has evidence of p, that S knows that p ? q follows from p, and so that S has evidence of p ? q. We're also told that S, recognising that he has evidence of p ? q, believes p ? q.
The relevant quote from Gettier:
Trying to argue that Smith doesn't believe p ? q doesn't make sense. You might as well try to argue that Jones owns a Ford or that Brown isn't in Barcelona.
He has evidence of p, and p ? q follows from p, and so he has evidence of p ? q.
Should I believe the following?
London is the capital city of England or pigs can fly.
I say I should. I have evidence that London is the capital city of England.
Exactly.
So far as I can see, it's best way to align this family of terms to reflect ordinary usage and to clean up the epistemologist's shop.
We can extend the treatment to "certainty": So long as we mean mere practical certainty or a feeling of sureness, but not absolute theoretical certainty, certainty is compatible with doubt.
More importantly, it just seems to be the case that minds like ours never or almost never attain absolute certainty, though many of us seem awfully sure of ourselves sometimes.
I've heard fallibilism is quite fashionable in the schools in our time.
More importantly, it just seems to be the case that minds like ours never or almost never attain absolute certainty.
According to your calculus, does (p(99%) V ~p(1%)) imply ((p V q)99%)? Or how are your probabilistic weightings related to propositional logic?
How does the weighted disjunction address the Gettier cases? Does Smith believe ((p V q)99%), on your account?
No, it's always sound, because it already has your 'if' incorporated. I put it in capitals so you would notice. It is contentless because it does not claim that p is true. S wrongly makes the claim, that p is true, and then uses this formula to arrive illegitimately at (p v q).
Quoting Srap Tasmaner
Where do you derive this principle from? It isn't a law of logic. If I might use an analogy, the higher you want to build, the more secure you need to make your foundations. But suppose it is true...
Consider q, that S has no reason at all to believe, except that Jones must be somewhere. Let's say q(0.01%)
Then q is (100 times) less likely than ~p.
The weight of incredibility of q exceeds the strength of credence of the premise, p on which it (p v q) rests.
It often seems professional epistemologists count it their duty to construct and assault straw men. Consider their collective abuse of the moldy old straw man they call "the skeptic".
I'm not into theory-building, but I'm inclined to think that JTB stands as a fair account of our use of "knowing" language. That's not necessarily the same thing as an account of what knowledge is; but only something like a theoretical model or analysis of the conditions under which we count ourselves entitled or unentitled to assign "knowing" predicates to subjects, to say that S knows that p.
Here's an argument:
Everyone in this room is happy.
Steve is in this room.
? Steve is happy.
That's a valid argument, whether or not either of the premises are true. If both of the premises are true, then it is also a sound argument.
I have taken you to be saying that Sharon is only entitled to make such an inference as shown above if the premises are true. It is conceivable that the premises are true but Sharon does not know this, in which case she is entitled to make an inference that she does not know she is entitled to make. And so it may be. If Sharon does know that the premises are true, then she also knows she is entitled to make the inference.
I have argued that making such valid inferences is one of the ways Sharon will try to determine whether the premises are true, by further exposing them to confirmation or disconfirmation. In this example, she would determine that Steve is in this room and then try to determine whether Steve is happy. If he is, the universal premise is partially confirmed; if he is not, then the universal premise is partially disconfirmed, but may still survive a reformulation like "Everyone in this room but Steve is happy," or "Almost everyone in this room is happy."
On my approach, Sharon knows the argument is valid, so she can come to know whether "Everyone in this room is happy" is true by assuming it true, hypothetically, making an inference and thus a prediction about each person in the room, and then testing those predictions.
She could also make no such hypothesis, and no such predications, but just ask everyone, tally them up and find that everyone or everyone but Steve is happy, whatever. There's really not much difference in this case.
The difference is that my approach obviously scales up and allows the use of statistics and probability, besides recognizing that raw fact-gathering is not the only thing we care about. We also need to make predictions, so we need to be good at it.
The curious thing is, by the time Sharon knows she is entitled to make the inference, she no longer needs to.
Suppose now Sharon shares her results with a colleague, Carol. Carol notices Steve's name on the list of people in this room, and, knowing Sharon's results, infers that Steve is happy. But do we just say that Carol knows that everyone in this room is happy the same as Sharon does? Isn't it rather the case that Carol is taking Sharon's results as given, for whatever reasons good or bad? That she is assuming Sharon's result is correct? And then she could test it, by, for instance, asking Steve if he is happy, thus confirming or disconfirming Sharon's result.
This hypothesis-prediction-test-revision cycle seems eminently rational to me and depends on making valid hypothetical inferences of unknown soundness.
What here do you disagree with?
[Disjunctive syllogism stuff in a future post.]
Nothing much.
I'll just note that science, probability, and induction/abduction are what S does to arrive at his belief p. No quarrel with him there.
Yes absolutely.
Broad Agreement feels good.
https://plato.stanford.edu/entries/closure-epistemic/#SkeAnt
It's not a calculus, merely annotation. In propositional logic, "probably p" or "believed p" does not add up to p, but to (p v ~p)
So what about the disjunctive syllogism?
If I assign to A a probability of r, and to B a probability of s, what probability should I assign to ~A & B? (That is, to ~A & (A v B).) That would be (1 - r)s. Since the probability of A v B is r + s - rs, it's also pr(A) + pr(~A & B). If pr(A v B) = 1, then if pr(A) goes to 0, pr(B) = 1. So there's no weirdness treating the usual disjunctive syllogism as a special case of standard probability.
I don't have Smith assigning a probability of 1 to Jones owning a Ford, and I don't have him assigning a probability of 0 to Brown being in, say, Barcelona. Those are assumptions of mine that I think are defensible from the text-- and from life-- but there's certainly room to argue otherwise.
So what should Smith's view be of the possibility that Jones does not own a Ford but Brown is indeed in Barcelona? Given probabilities of 0.90 for the Ford and 0.01 for Barcelona, he should assign a probability of 0.001 to Barcelona but no Ford. As it should be, since pr(Ford & Barcelona) = 0.901. So that's at least consistent.
But it has to be admitted that what I'm doing here is not-- what should we call it?-- "simply" inferring one belief from another. I allow Smith to form the prediction that Ford or Barcelona based on his hypothesis that Jones owns a Ford, but then in order to assign probabilities to it and to the disjunctive syllogism (to its premises actually, since he already has a prior for Barcelona), he does the math.
Thus I never see Smith being in the position of saying, "Probably A, but if not then definitely B."
Quoting unenlightened
Yeah, I have no justification for that (my thing about the credence you give a conclusion). I think it's a reasonable rule of thumb, something like Hume's saying that "the wise man proportions his belief to the evidence." For instance, in the case at hand of addition, the likelihood of A v B is higher than the likelihood of A, but that's because I'm smuggling in a prior for B.
As a matter of fact-- and this gets to your second point-- if A entails B, then the likelihood of B is at least as high as that of A. (If all F are G, there are at least as many G as F.)
So while there's intuitive support for the general idea of firm foundations and less and less certainty the farther your chain of inference carries you from those foundations, you have to be careful. If your theory as a whole is thought of as just a big conjunction of all of your current beliefs, and if some of those are less than certain, then all of them being true is less likely than some of them taken alone, because when you multiply the independent ones, their product is necessarily smaller. Sure. But our theories are more complicated than big conjunctions. There's a lot of dependence, entailments, conditional probabilities and disjunctions in there.
So I don't see Smith as overstepping the bounds of reason and landing in a puddle of nonsense. I see him as a victim of chance. Something extraordinarily unlikely happens, and it will challenge his otherwise orderly process of belief formation.
Quoting Cabbage Farmer
Quoting Cabbage Farmer
Here I think we are getting closer to what is going on in the Theaetetus.
One way we can be certain is when we take things as the bedrock of our discussion. In this sense, doubt is dismissed as not having a place in the discussion. So, for example, this is not a discussion about the comparative benefits of diesel and petrol engines, and thinking it so is to misunderstand what is going on. Or, to use the all-pervasive example, one does not doubt that a bishop moves diagonally while playing chess.
The problem here is the philosopher's game of putting "absolute" in front of "certainty" and thinking that this means something. Outside of philosophy, minds like ours always or almost always certain. Few folk check that they have an arm before they reach for the fork. It's not the sort of thing that one doubts, outside the philosopher's parlour.
And here is where the logos differs from justification. @Hanover brought this to mind elsewhere. When you learn that the cup is red (again), are you learning something about the cup, or something about the use of the word "red"? Well, one hand washes the other. When you learn that r justifies p, you learn more than just that r materially implies p; you learn a new way of using "r" and "p". It does not automatically follow that, if r justifies p, it justifies p v q.
Until it was pointed out that philosophers ought know how to use words.
To paraphrase, there are ways of knowing that are not exhibited in statements, but shown in what we do.
These are missing from Gettier.
I'm actually quite aware of that. However, the focus is squarely upon the necessary and sufficient conditions for believing a disjunction. So, it's not that I've neglected that point. Rather, it seems irrelevant to the focus.
Agreed. Where is that being properly accounted for aside from the conclusion of my solution?
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) about what makes this particular disjunction true))
C1. ((p v q) is true because...(insert belief statement(s) corresponding to the prior "if" in p3))
I've already touched on this, but in this post I'm arguing against the notion that p3 and C1 aren't necessary for believing a disjunction, and that we could simplify my solution by replacing them with ((p v q) is true if (p) is true). As before, belief that:((p v q) is true if (p) is true) IS p3 in the solution. So, it's clearly necessary, however it's also insufficient. Believing a disjunction requires more than belief that:((p) is true, deducing (p v q) from belief that:((p) is true, and thinking about the truth conditions of (p v q). That's as far as ((p V q) is true if (p) is true gets us. That's as far as p3 gets us. Believing the disjunction takes another deduction, or as you said earlier...
That is precisely what's been missing in every account but my own. That rational judgment is the conclusion itself...
((p v q) is true because (p))
As previously skirted around, when formalized, that judgment and what it rests it's laurels on is not absent. To quite the contrary it is contained within parenthesis to tell the reader what grounds the conclusion and looks like this... (from1,2) etc.
So then, why is it left absent in the account of what believing a disjunction requires?
It's what we're not told that matters, because that's what's missing, and that's the problem.
Gettier says nothing at all about Smith deducing that (p or q) is true. Gettier's formula is missing a necessary deduction. That's been adequately argued for without subsequent refutation nor even due attention from you.
Believing a disjunction requires and is entirely exhausted by the following...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) about what makes this particular disjunction true))
C1. ((p v q) is true because...(insert belief statement(s) corresponding to the prior "if" in p3))
I supposed I'm baffled by the fact that some people would rather continue traveling down a path that Gettier paved with an utterly inadequate criterion for what counts as believing a disjunction.
I mean, there it is. That's what it takes, and nothing less...
Examine it. Check it out. Fill it out. Imagine any disjunction you like that follows Gettier's formula, and plug in the values accordingly. You'll never arrive at anything that constitutes being a problem for JTB. That holds good for any and all disjunctions deduced from believing P. There are no exceptions...
The irony...
There is no stronger justificatory ground for believing that Gettier got it wrong.
I know he did.
X-)
Smith believes the following:
p1.Jones owns a Ford.
Smith constructs the following:
Either Jones owns a Ford, or Brown is in Boston.
Either Jones owns a Ford, or Brown is in Barcelona.
Either Jones owns a Ford, or Brown is in Brest-Litovsk
Smith believes all three are entailed by Jones owns a Ford.
p2."Either Jones owns a Ford, or Brown is in Boston" follows from Jones owns a Ford.
p2."Either Jones owns a Ford, or Brown is in Barcelona" follows from Jones owns a Ford.
p2."Either Jones owns a Ford, or Brown is in Brest-Litovsk" follows from Jones owns a Ford.
Therefore Smith believes all three.
C."Either Jones owns a Ford, or Brown is in Boston" is true.
C."Either Jones owns a Ford, or Brown is in Barcelona" is true.
C."Either Jones owns a Ford, or Brown is in Brest-Litovsk" is true.
Really now???
p2."Either Jones owns a Ford, or Brown is in Boston" follows from Jones owns a Ford.
p2."Either Jones owns a Ford, or Brown is in Barcelona" follows from Jones owns a Ford.
p2."Either Jones owns a Ford, or Brown is in Brest-Litovsk" follows from Jones owns a Ford.
C."Either Jones owns a Ford, or Brown is in Boston" is true because Jones owns a Ford.
C."Either Jones owns a Ford, or Brown is in Barcelona" is true because Jones owns a Ford.
C."Either Jones owns a Ford, or Brown is in Brest-Litovsk" is true because Jones owns a Ford.
Ground is important no?
What is a justified true belief if not a well-grounded true belief?
8-)
Well let me ask you a question in return. If you have a reasonable belief p, and a reasonable unconnected scepticism q (say p - that aspirin is an effective painkiller, and q - that Bluebeard's treasure is buried on Easter Island), what is to be gained by forming the disjunction, (p v q) ? How does S advance his knowledge, or understanding or in any way profit from forming his disjunction? Does it enable a test of p, or the building of a deeper theory or something?
(p V ~p) is mere tautology.
(p V ~p) is true, whether or not p.
probably p is an informative and definitive claim.
probably p can serve as a reasonable justification for further claims or actions, at least in some contexts.
probably p has its own formal implications:
IF (probably p) THEN (probably (p V q)).
I've never studied probabilistic logic, but I reckon the probability that (p V q) can't be any lower than the probability that p, and can't be any lower than the probability that q.
It's been a while since I've looked at that dialogue. In my recollection, it's a conversation about knowledge, not certainty, though of course I might be mistaken. Perhaps you'll do me the favor of correcting my memory, by reminding me how the concept of certainty figures in that fine old legend.
Or is there some other way in which we're approaching Theaetetus?
Quoting Banno
I wouldn't call that certainty, just a framing assumption.
We take claims for granted temporarily, for the sake of argument, for the sake of conversation, and thereby rule out whole regions of discourse for a while, to make room for the theme we've agreed to address.
A beautiful convention, without which there's little hope of progress in a diverse discursive community.
Quoting Banno
That sounds right to me.
I might add "Ordinarily one does not doubt that a bishop moves diagonally while playing chess." For even such a simple rule might be doubted in some contexts: while learning the rules of the game, in a moment of confusion, in an altered state of consciousness, in a context of skeptical doubt....
Quoting Banno
I take it "absolute certainty" means something along the lines of: 100% certain, beyond the possibility of doubt, beyond the possibility of error, not possibly false, indubitable in any discursive context whatsoever.... I agree the concept seems fanciful. I'm inclined to say that nothing is absolutely certain in this sense, and that the term is another one of those philosopher's fictions that make a laughing stock of their art when it's employed as anything more than a foil.
Thankfully practical certainty is the ordinary condition of human agents in the course of their ordinary affairs. So far as I can see, this only means that normally we're sure enough to act without question, without further checking, ascertaining, assuring, proving, testing, confirming, investigating.... Without any practical doubt, without any practical reason for doubt.
That natural confidence is often disrupted by circumstances. We learn by experience that our perceptual judgments and memories are fallible, that our calculations and inferences are fallible. Sometimes our expectations go unsatisfied or our plans go awry. Sometimes our conceptualizations turn out to have been confused or our interpretations turn out to have been biased. Sometimes what seems sure enough to us is doubted or denied by others; sometimes we doubt or deny what seems sure enough to others.
The care and method we employ in ascertaining the correctness of our judgments may vary along with our purposes and circumstances, including our assessment of the chance for error and our evaluation of the consequences of error.
Being practically certain, or feeling absolutely certain, is not the same as holding a claim that is absolutely immune to doubt.
Practical certainty is compatible with doubt -- in the study as well as in the marketplace.
Quoting Banno
I'm not sure how this coordinates with our discussion of certainty. In any case, it seems the answer depends on what you're ignorant of at the time you "learn that the cup is red".
If you already know what those words mean, then it may be you're color blind, or looking for red cups in the dark or in green light, and have finally determined that the cup in front of you is the red one you were looking for.
If you don't know what those words mean, but already have concepts of "red" and "cup", as one who doesn't speak English might, then you may only be learning the meaning of those English words, how they map onto your concepts and your native language.
If you don't have the concepts corresponding to the words "red" and "cup", then you may be acquiring those concepts for the first time, like a child, learning to pick out new sorts of things on the basis of perception, and learning to coordinate those things, and thoughts about those things, with the corresponding words in the English language.
Quoting Banno
Do you mean to say it does not "automatically follow", in the head of every person who learns that r justifies p? In other words, not everyone who learns that r justifies p will immediately infer that r justifies (p V q)?
That seems like a psychological point, not a logical one. I suppose I agree with the psychological point. But I would expect that, at least once a person has acquired a grasp of the form of basic propositional logic, he will be disposed to assent to the claim "r justifies (p V q)" as soon as he is disposed to assent to the claim "r justifies p".
Perhaps we might say Gettier's puzzles are neutral with respect to the distinction. They seem directly concerned with knowing-that, not knowing-how. Nonetheless, his problematization of justified true belief as a model for knowledge would have implications for justified true beliefs about know-how, and justified true beliefs involved in know-how.
It's tempting to suppose that models of knowing-that and models of knowing-how could be reconciled by subsuming either one into the other, and that perhaps neither has priority. If that can be done, it seems the way is open to a unified account of both sorts of knowing.
The carpenter has a special sort of know-how. He also knows that he has this know how. He believes that he can construct and repair various sorts of wooden object. His belief is justified -- not necessarily by sentences, but by deeds and memory of deeds that may be expressed in sentences if need be. He can demonstrate the skill, and he can instruct others. His demonstration and instruction may, but need not, involve speech.
Perhaps Plato shows his bias as a member of a class of privileged Athenian teachers whose reputation and livelihood depend on their expertise in literacy and rhetoric, when he suggests that true belief doesn't count as knowledge unless it's accompanied by a linguistic account. Or perhaps he doesn't mean that the account must be spoken, but only that it must be expressible in speech -- a rational understanding, a reasonably informed grasp of the matter that could, but need not, be expressed in language by a competent speaker. Or perhaps he glosses over this distinction without recognizing it, due to the richness and ambiguity of the term logos, or his own habits and biases.
By a more recent convention, we model beliefs and justifications as "propositions" and "propositional attitudes" expressed in language, but I see no reason to insist, and good reason to deny, that all beliefs and justifications have an essentially linguistic form. So far as I know, these conventions typically take for granted that the propositions do not have an essentially linguistic form, though of course we give them linguistic expression when we speak about them.
Yes, it certainly seems on the face of it that a deduction from probable p inherits (at least) the same probability.
IF (Improbably~p) THEN (improbably ~p v q)
This seems to be just as valid, only less probable.
IF (probably p) THEN (probably (p v ~q).
IF (Improbably~p) THEN (improbably ~p v ~q)
And these too. Does that worry you at all? It worries me.
Epistemic paradoxes.
Yes! It appears to be totally unmotivated, doesn't it? At the very least, it violates Grice's "Be relevant" maxim. It even seems to edge toward the logically tenuous mental gymnastics we associate with conspiracy theories. If this is science, it's pretty bad science, right?
I see the main issue as coincidental confirmation, so I'm ignoring Gettier's agenda most of the time. I imagine Smith learning that "Jones owns a Ford or Brown is in Barcelona" is true, but not learning what makes it true, and thus treating it as confirmation of his hypothesis that Jones owns a Ford. I have also imagined Smith not forming the disjunction at all, but simply making a test that he thinks is of Jones owning a Ford but is actually a test of "Jones owns a Ford or Brown is in Barcelona".
Suppose that's what happens, but then through other channels Smith discovers Jones does not own a Ford.* He might forget all about it, but if he is a good scientist, that unexplained positive will bug him. To get to the bottom of that, he'll have to be able to form this goofy disjunction.
Think about the discovery of cosmic microwave background radiation, how it went and how it could have gone. Suppose, contrary to fact, there is no CMB, and Penzias and Wilson were looking for it. They get this noise, check their equipment out, and think they've found it, but the source of the noise was actually pigeons nesting in their dish. What actually happened is the opposite: they weren't looking for it, checked their equipment, chased off the pigeons, and it was still there. They determine its characteristics as best they can, but have no idea what it is until someone tells them about the prediction that the Big Bang would cause such a thing.
Brown being in Barcelona is the pigeons in the first scenario and the CMB in the second. It's the unknown unknown. And when there are unknown unknowns, you can mistake noise for signal and signal for noise. To suss out what's going on you may eventually have to form odd disjunctions involving pigeons and the Big Bang.
That's my big picture version of what's going on. I think Gettier's examples are outlandish in order to make any claim of knowledge implausible, but he could have made them simpler. For example:
My hunch is that Smith's disjunctions are unacceptable in part as a matter of linguistics, and insofar as that supports our communal rationality, he is violating a norm of some kind. They can also be criticized as you have done here, as being unmotivated, even pointless. In fact, I mentioned this about a week ago: if a disjunction is part of an argument from cases, what is the result both of these produce that could eliminate the disjunction? (Compare the CMB story, where pigeons and Big Bangs both result in noise.)
I have no idea-- finally answering your specific question-- and I think the lack of apparent rationale is why we are inclined to reject them. My thought when I brought this up before is that it explains our feeling that these disjunctions are arbitrary. And I suspect we could even measure that: how unlikely would an event be that could be caused (or enabled?) either by Jones owning a Ford or Brown being in Barcelona? I think most of us would guess pretty dang unlikely. (But keep in mind the Connections TV show!)
I think this is the neighborhood where most discussion of Gettier sets up shop. Is there something about the conditions (beyond Smith's control) that makes this not knowledge? Is it something in Smith's behavior, some norm of rationality he has violated?
* Coincidentally, I have driven three different Fords for several years each without owning any of them.
Logic cannot account for truth(as correspondence to fact/reality). Rather, it presupposes it by virtue of assuming the truth of it's premisses, and aims to preserve it by virtue of establishing and following 'the rules' for 'correct' inference.
All thought/belief presupposes it's own correspondence to fact/reality somewhere along the line. Thought/belief consists - in part - of the presupposition of truth(as correspondence). Because thought/belief consists of the presupposition of truth, and neither logic nor formal notation can account for truth, then neither logic, nor formal notation can properly account for thinking/believing that something or other is true, believing a disjunction notwithstanding.
The attribution and/or recognition of causality is among the most rudimentary forms of thought/belief formation. So, it is of no real surprise that some folk would believe that if we force our thoughts to follow some logical structural form then doing so would cause us to arrive at true belief, as long as we start with true premisses.
It doesn't work that way unless we've gotten the rules right. If we can follow all the rules and still arrive at something that we all find unacceptable, then something is wrong with the rules.
:-|
The positive note here is that we can use ordinary language as a means to set out thought/belief processes that attempt to strictly adhere to disciplined convention. That's what I've done here, and in doing so, shed some much needed light upon the fact that believing a disjunction consists of more than Gettier or anyone else since, has properly accounted for.
The rules say that disjunction follows from a belief that p is true. The rules say that if that belief is true then so too is the disjunction. The rules say that if I follow them and arrive at believing that disjunction, then I have arrived at a belief that based upon good reason. I mean, after-all it's based upon the rules. The rules say that that is a well-grounded belief. It even encapsulates the ground within parentheses as a means for showing it.
However...
The rules do not require that that ground be properly taken account of when we are reporting upon that belief. Hmmmm...
Funny that. Look at all the trouble that that oversight has gotten us into.
When the ground is properly accounted for there is no problem, because believing a disjunction is nothing more and nothing less than believing it is true because p. So, it's a problem regarding how believing a disjunction has been taken into account for over half a century.
For anyone who wants to argue the semantics of 'or', I point you towards the solution. Fill it out, and then get back to me.
For anyone else who thinks/believes that I've only touched upon disjunction, I ask that you present a case that satisfies JTB but we shouldn't count it as knowledge, and in doing so, make certain that you take proper account of the ground by virtue of stating that the conclusion has been reached and/or is drawn because the ground(is true)...
Then look at the results.
I think I've done quite a bit more than that. It will take while to sink in though. Paradigm shift is long overdue.
Delusions of grandeur...
I'm gonna be famous.
I only addressed the OP, where tracking failed. I didn't read the whole thread so I could have missed the memo. Maybe write a paper in academic rigour?
X-)
If you want, you could start at page 40 or so, and let me know what you think. Weaknesses, etc.
Don't think I can trump what has already been said. Anyway, looking forward to reading a paper on it.
Quoting unenlightened
I'm not sure it's valid.
I take it the probability of (~p V q) will be very high when the probability of q is very high, regardless of the probability of ~p. Thus the improbability of ~p does not adequately inform our judgment about the probability of (~p V q). For the improbability of a disjunction requires the improbability of both of its terms, while the probability of a disjunction requires merely the probability of at least one of its terms.
Given an infinite number of such cases selected at random (cases in which it's improbable that ~p, but we have no idea whether it's probable that q), it may be reasonable to expect that (~p V q) will be false more often than (p V q) will be false. But it seems to me a statistical judgment of this sort is not the same thing as an inference in one particular case from the improbability of ~p to the improbability of (~p V q).
I recall von Mises makes a similar point in Probability, Statistics, and Truth, but I don't have my hard copy and haven't managed to find the passage online today.
Quoting unenlightened
This one has the same basic form as
IF (probably p) THEN (probably (p V q)).
Moreover, I take it the two claims are consistent. So we might say, further:
IF (probably p) THEN ((probably (p V q)) AND (probably (p V ~q)))
Quoting unenlightened
I'm not sure this is valid either, for the same reasons as the first formula above.
Perhaps it may help to compare: If I roll a twelve-sided die (p) and a four-sided die (q) together, what is the probability that at least one of the two dice lands on a value greater greater than 4?
Quoting unenlightened
I have yet to see reason for concern.
Quoting unenlightened
This is interesting, but suggests primarily that a rational believer would not thus lump together such beliefs without constraint. It seems to me the problem should be resolved by recharacterizing the judgment informed by a grasp of the odds. Kyburg, or the designer of the "policy" Kyburg criticizes, has smuggled irrationally expressed beliefs into a rational person's head.
Do you mean to suggest that this puzzle involving an irrational conjunction of inadequately expressed probabilistic judgments somehow informs our discussion about an inference in one particular case, from a probabilistic judgment that p to a probabilistic judgment that (p V q)?
Perhaps you would care to expand on the point. For one thing, does it matter that Kyburg's case involves conjunction, while our case involves inclusive disjunction? For another, what is there in our case corresponding to the contradiction generated by Kyburg's make-believe irrational believer? It's obvious where the contradiction lies in Kyburg's case, but so far you've given me no reason to suspect there's such a contradiction in the case at issue in our conversation. What have I missed?
It strikes me Kyburg's is another case in which probabilistic judgment over many instances is confused with probabilistic judgment in a single instance. In Kyburg's case the error's even worse, if the make-believe believer has leapt from the sound inference "Ticket n is (99:100) likely to lose" to the invalid non-probabilistic inference "Ticket n will lose". Whereas in our case, no one has been so foolish as to strip the probabilism off the claim. The cases also differ in that Kyburg's case has an explicitly mathematical form, whereas in our case Smith's probabilistic judgments do not have a clear mathematical form.
Quoting unenlightened
Is there something in this article especially relevant to our case?
Confusion and paradox are not the same.
It seems a safe bet that either my intuitions are confused and there is a paradox; or there is no paradox and your intuitions are confused.
I'll summarize my prima facie intuitions below. Let's kick them around, to see if they're consistent, and to see if we agree that they're reasonable. And to see if there are any typos...
Granting that we're judging a single particular case, with information about one term and no information about the other term of a disjunction:
VALID
(antecedent is sufficient to inform judgement that disjunction is probable)
IF (probably p) THEN (probably (p V q))
IF (probably p) THEN (probably (p V ~q))
IF (probably ~p) THEN (probably (~p V q))
IF (probably ~p) THEN (probably (~p V ~q))
IF (improbably p) THEN (probably (~p V q))
IF (improbably p) THEN (probably (~p V ~q))
IF (improbably ~p) THEN (probably (p V q))
IF (improbably ~p) THEN (probably (p V ~q))
INVALID
(antecedent is insufficient to inform judgment that disjunction is improbable)
IF (probably p) THEN (improbably (~p V q))
IF (probably p) THEN (improbably (~p V ~q))
IF (probably ~p) THEN (improbably (p V q))
IF (probably ~p) THEN (improbably (p V ~q))
IF (improbably p) THEN (improbably (p V q))
IF (improbably p) THEN (improbably (p V ~q))
IF (improbably ~p) THEN (improbably (~p V q))
IF (improbably ~p) THEN (improbably (~p V ~q))
Good exercise for a knucklehead like me.
It might help to make explicit:
IF (probably p) THEN (improbably ~p)
IF (probably ~p) THEN (improbably p)
IF (improbably p) THEN (probably ~p)
IF (improbably ~p) THEN (probably p)
And then put it together:
IF (probably p) THEN:
improbably ~p
probably (p V q)
BUT NOT NECESSARILY: improbably (~p V q)
IF (probably ~p) THEN:
improbably p
probably (~p V q)
BUT NOT NECESSARILY: improbably (p V q)
IF (improbably p) THEN:
probably ~p
probably (~p V q)
BUT NOT NECESSARILY: improbably (p V q)
IF (improbably ~p) THEN:
probably p
probably (p V q)
BUT NOT NECESSARILY: improbably (~p V q)
Of course we'd have to draw up different sets of tables for conjunction or exclusive disjunction.
I'm still not sure what our discussion about probabilistic inference has to do with Gettier's paper. Is it your position that whenever rational people recognize that their reasonable expectations are grounded merely in "strong evidence", there is an essentially probabilistic deep-structure to their expectations, according to which their assertions like "Jones owns a Ford" cannot be evaluated as true or false, but must be reinterpreted as assertions like "It's sufficiently probable that Jones owns a Ford", or perhaps "I have good reason to claim that it's sufficiently probable that Jones owns a Ford"?
Along those lines, perhaps the beliefs we really "have" are beliefs about the probability of propositions, or about a given individual's being justified in making claims about the probability of propositions.... As a wholehearted skeptic, that strikes me as a line of thought worth pursuing, and I suppose there may indeed be something like this sort of structure underlying ordinary belief.
But how would that pursuit inform our view of Gettier's little essay?
At some point in the mesh of justifications and probabilistic judgments, a proposition becomes actionable, and its alternatives become negligible. Given his justifications and the probabilistic deep-structure of his expectations at the time we meet him, the rational Smith is prepared to act, until further notice, as if it were the case that Jones owns a Ford, as if it were the case that Brown is not in Barcelona, and thus as if it were the case that (EITHER Jones owns a Ford OR Brown is in Barcelona) is true. And Smith will have achieved this result by way of the same unhappy accident that we find in Gettier's paper, before and after all this additional trouble with probabilism.
Thus even the skeptic or probabilist may acknowledge that a traditional analysis of ordinary human beliefs in terms of "propositions held to be true" is a reasonable and useful simplification of the deep structure you've indicated.
So far as I can see, that brings us right back to the beginning: How, according to you, is recourse to probabilistic analysis of Gettier's puzzles relevant to our evaluation of Gettier's arguments and our assessment of the conception of justified true belief as a criterion for knowledge?
Well, the use of "probably" and "improbably" isn't very useful. Try replacing it with percentages, where (for example) "probably" is ">= 75%" and "improbably" is "<= 25%". That then gives us:
If p >= 75% then ¬p <= 25%
Now if we consider a disjunction then this gives us:
If p >= 75% then p ? q >= 75%
So let's take each of unenlightened's examples:
Quoting unenlightened
If ¬p <= 25% then ¬p ? q ...?
Not enough info.
If p >= 75% then p ? ¬q >= 75%
If ¬p <= 25% then ¬p ? ¬q ...?
Not enough info.
Thanks for crunching the numbers for us! I'm relieved to find that the math, at least, confirms my intuitions.
I was running with unenlightened's usage of the terms "probable" and "improbable". But I am, moreover, inclined to say that ordinary conceptions of probability, and of the logical form of probabilistic judgment, are conceptually prior to, or at least historically prior to and conceptually distinguishable from, mathematical models of probability and probabilistic judgment.
I speak analogously about the priority of ordinary number-concepts and numerical judgments, and about the priority of pre-numerical quantitative concepts and judgments (more/less, greater/fewer, bigger/smaller, lighter/heavier, faster/slower), as compared to the more refined conceptualizations obtained by the construction and analysis of sophisticated mathematical models of such concepts.
In our case, I would say there is a logic of probability that is prior to, or distinguishable from, mathematical models of probability. This is no mere academic point: It seems that most probabilistic judgments by ordinary humans do not have an explicitly numerical form, and in some cases it's not clear what numerical analysis could possibly be given to express a probabilistic judgment.
Accordingly, I take it there's some good sense to the sort of claims that unenlightened and I have been trafficking in.
One glaring thing we've neglected so far is an evaluation of equiprobables. My preference is to avoid expanding the set of values. So rather than three values (probable, equiprobable, improbable), I'd try lumping equiprobable into one of the other two terms. It seems more fitting to call a 50/50 chance improbable than to call it probable, so I'd start out by lumping the equiprobable with the improbable.
I haven't bothered to sort through the implications.
If p is probable then ¬p is not probable
If p is probable then p ? q is probable
If ¬p is not probable then ¬p ? q is ...? Not enough info.
If p is probable then p ? ¬q is probable
If ¬p is not probable then ¬p ? ¬q is ...? Not enough info.
Ok, let's go back to the beginning. Gettier's claim is that B(p) -> B(p v q) for all q. My complaint about this is that the logic conserves truth, but belief is not truth. Now the difficulty with all the analysis above is that it separates the probable and improbable in order to then apply the rules of logic. The reason for bringing up probability was to try and get at the difference between belief and truth.
Now my suggestion has been that the way to express this is as a disjunction, (p v ~p), which we can annotate with percentages to illustrate the inclination of the belief, thus: (p75% v ~p25%). In this way the belief and the doubt are kept in one expression that can be asserted as true of necessity, and that truth can thence conserved by logical operations.
So then the Gettier disjunction becomes ((p75% v ~p25%) v (q1%)), or S could make the conjunction, ((p75% v ~p25%) & (q1% v ~q99%)). The point being that to make the disjunction with an arbitrary q, the first term must be true100%.
No it's not. His claim is that J(p) ? J(p ? q). He then says that Smith believes p ? q.
It preserves justification as well. If there are good reasons to believe p then there are good reasons to believe p ? q. How could it be any other way?
It doesn't make much sense to say that I'm justified in believing that London is the capital city of England but not justified in believing that London is the capital city of England or pigs can fly (or for a less silly example, that London is the capital city of England or unenlightened has brown eyes).
If p is true then p ? q is true. Therefore, if there is strong evidence that p is true then there is strong evidence that p ? q is true. If one has strong evidence that p ? q is true then one is justified in believing that p ? q is true.
Smith has strong evidence that p is true and so strong evidence that p ? q is true and so is justified in believing that p ? q is true.
That argument is invalid.
It is if you accept the principle that evidence is closed under entailment (or, more specifically, under disjunction introduction), which I do. Although clearly you don't. I honestly don't know how to go about convincing you of it. It's so obvious to me as to be pretty much axiomatic (like disjunction introduction itself).
So asking me to prove that evidence of p is evidence of p ? q is like asking me to prove that p ? q is true if p is true. All I can do is repeat examples in the hopes that eventually it'll get through.
I have evidence that "I have hazel eyes or unenlightened has brown eyes" is true. That evidence is evidence that I have hazel eyes; namely, what I see in the mirror.
Are you saying that I don't have evidence that "I have hazel eyes or unenlightened has brown eyes" is true? That strikes me as absurd.
No. The argument you presented is invalid. How you go about convincing me is to present a valid argument. I accept the premise, but I reject the conclusion, until you present a valid argument.
It's valid if the principle of closure under entailment is correct.
But your argument is invalid.
Let me give you a clue. The premise that you need is something like this:
If p is true then p ? q is true.
If there is strong evidence that p is true, then p is true.
Therefore, if there is strong evidence that p is true then there is strong evidence that p ? q is true.
Unfortunately, the premise that you need is not true, even according to Gettier.
That's not my argument. And I don't understand what that second premise is doing.
Apart from the second premise, it is an exact quote of your argument. The second premise is the hidden premise that would make your argument valid.
Then let's make it clearer for you by making the principle of closure explicit.
Evidence is closed under disjunction introduction.
"I have hazel eyes" entails by disjunction introduction "I have hazel eyes or unenlightened has brown eyes".
Therefore, strong evidence that "I have hazel eyes" is true is strong evidence that "I have hazel eyes or unenlightened has brown eyes" is true.
Adding to my argument changes my argument. I don't accept that second premise.
Quoting unenlightened
I don't need that second premise.
I take this to mean, for our purposes, that what works for truth also works for evidence.
Ok. Now you need to argue that, because that is what we are disputing. You still haven't presented a valid argument.
Quoting Michael
Yes, I am charitably making your invalid argument valid. You need another premise of some sort.
Quoting Michael
Cool. then we have no argument; you are pontificating, and I am absurd. Have fun.
It's hardly pontificating. It's stating a simple fact that to have evidence that p ? q is true is to have evidence that p is true, to have evidence that q is true, or to have evidence that both p and q are true.
So pooh-pooh with a "have fun" all you like. I'm content with my reasonable (and correct) account.
There is nothing I want to say to cause you any discontent. Perish the thought!
We don't have to do it this way.
I didn't bother with conditional probabilities before, but it's the natural way to model Smith's belief.
If [math]\small J[/math] is Jones owning a Ford, and [math]\small D[/math] is the evidence Smith is relying on, then the belief he holds highly probable is not really just [math]\small J[/math] but [math]\small J \mid D[/math], the probability of [math]\small J [/math] given [math]\small D[/math]. And it's dead easy to show that for any [math]\small X[/math]
[math]\small P(J \lor X \mid D) ? P(J \mid D)[/math].
Besides which, shouldn't your conclusion be "If there is strong evidence that p, then p v q"?
Yes, it's like betting on the favourite and buying a lottery ticket.
It works equally well if one is betting against the favourite.
P(~J?X?D)?P(J?D).
The more random shit you believe, the more likely you are to be right about something or other. But this does not amount to a system I would be prepared to try at the casino, or a justification for believing random shit.
Quoting Srap Tasmaner
It's not my conclusion, it's Michael's. I only provided the middle premise, to illustrate that his argument needed one.
Quoting Michael
It seems we're in agreement on the underlying logic.
The primary operator in all thought/belief and the formation thereof is the presupposition of correspondence with/to: fact; reality; the case at hand; the way things are/were; the universe; etc.(correspondence henceforth). At the moment of conception, all agents capable of drawing associations/correlations/connections between 'objects' of physiological sensory perception are completely void thereof. Thought/belief - like knowledge - is accrued. As such, it begins with simple/basic/rudimentary associations/correlations drawn between 'objects' of physiological sensory perception and/or the agents 'own' state of mind, and it grows in it's complexity. Initial thought/belief formation instantiates the presupposition of truth and the attribution of meaning inherent to all thought/belief and statements thereof.
Thought/belief is prior language. Correspondence to fact/reality is presupposed within thought/belief formation long before language acquisition has begun in earnest. Correspondence is presupposed prior language, because association/correlation presupposes the existence of it's own content. Some of those associations/correlations correspond to fact/reality. True thought/belief is prior to language. So, either truth exists without language, or true thought/belief exists without truth.
Being the result of a valid inference is existentially contingent upon language. Correspondence is not. The former does not constitute the latter. Our knowing that much also allows us to know that being the result of a valid inference alone does not necessarily constitute being either well-grounded or true. In addition, it only follows that validity is existentially contingent upon the presupposition of correspondence and the attribution of meaning, including but not limited to the recognition/attribution of causality.
Smith's accepts all three disjunctions based upon his well-grounded belief that Jones owns a Ford, if we adhere strictly to Gettier's account of Smith's reasoning for accepting the disjunctions based upon that belief. Smith is purportedly 'justified in believing' all three propositions because he believes Jones owns a Ford and recognizes the entailment of each of the three 'propositions'.
Here, it is crucial to note that Smith holds more than one belief about the disjunctions. He believes that they follow the rules of correct inference. That belief is true. He believes that all three are true if, and only if, the truth conditions are met. That belief is true. He believes that all three are true because Jones owns a Ford. That is the part left out by those who report upon Smith's belief, even when the reporter includes this crucial step when reporting upon their own thought/belief. Believing a disjunction requires precisely the process I've outlined. A proper account of believing a disjunction has been offered. There are no problems with it, and no disjunction is immune. None. Here it is again...
p1. ((p) is true)
p2. ((p v q) follows from (p))
p3. ((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
C1. ((p v q) is true because... (insert belief statement(s) corresponding to the prior 'if'))
That is what believing a disjunction consists in/of. I've invited anyone to imagine a disjunction arrived at by a rational agent on the basis of believing P that is not completely exhausted by the above solution. There are no problems. Fill it out.
Not sure why you think this.
Here's a diagram for what I said, which was [math]\small P(J \lor X \mid D) ? P(J \mid D) [/math]:
That seems pretty straightforward: we start with the yellow and green bits and pick up the blue as well. The blue might be empty, but we still know yellow+green+blue ? yellow+green.
Now here's yours, which was [math]\small P(\neg J \lor X \mid D)?P(J \mid D)[/math]:
Your claim is that orange+blue+green?yellow+green. Maybe, maybe not. Depends on whether orange+blue?yellow, doesn't it? And our hypothesis was that yellow+green is pretty big: Smith has strong evidence for his belief.
Two more points. Another interpretation of Smith's belief would be:
[math]\small P(J \mid D \lor X)[/math]
which looks like this:
That adds in the light blue bit. I don't think there's any reason to do this though, because all of Smith's reasoning is relative to [math]\small D[/math], his reasons for believing Jones owns a Ford. Adding the light blue bit doesn't change the argument anyway. It's just a bigger version of the "?" we've already got.
Now what about [math]\small X \cap D[/math]? Are the reasons Smith has for believing Jones owns a Ford reasons to believe Brown is in Barcelona? Well, they're not reasons to believe he isn't: there's no reason to think that Jones having always owned a car and always a Ford and now driving a Ford, etc., precludes Brown from being in Barcelona. So there's no reason to think [math]\small D[/math] and [math]\small X[/math] are disjoint. But it doesn't give you much to go on, so when I assigned a prior to [math]\small P(X \mid D)[/math], I made it tiny, and that seems reasonable to me.
((Apologies for the crumminess of the diagrams.))
Sorry, typo.
P(~J?X?D)?P(~J?D).
LOL.
Gettier is certain that he has made a case of Smith having justified true belief that ought not count as knowledge. His certainty is grounded upon the idea that believing a disjunction does not need to include the agents' believing that it's true because the truth conditions have been met. His certainty is based upon a partial account of believing a disjunction. When an account of believing a disjunction neglects the steps necessary for how one arrives at such a belief, it is an inadequate account. When such neglect changes the very meaning of the belief itself, the result is something other than the actual belief that is supposed to be under scrutiny. If the alternative is true, but the actual belief is false, then...
Bewitchment. Self-induced by inadequate language use.
That is Smith's belief.
It doesn't talk about the rules... it follows them. Our talk about Smith's belief ought include not only applying the rules to it, but also showing that Smith's belief has been arrived at by virtue of following them. That requires including the ground. Leaving that out is akin to removing the ground necessary not only for Smith's arriving at the believing that statement, but also for our adequately accounting of it.
Yeah, that's an option.
Conjunctions would be easy, I guess-- just two beliefs instead of three. And you could work up an approach that doesn't treat disjunctions, conditionals, counterfactuals as being potential truth-bearers at all. (Just inference rules or habits.) What about negatives?!
It's worth playing around with.
The truth-bearing approach works from the historical and quite mistaken presupposition that truth is existentially contingent upon language. It also claims that statements(etc.) are true solely by virtue of expressing a true proposition. That unnecessarily multiplies the level of difficulty inherent to taking proper account of what sorts of things can be true/false and what makes them so. We're still left with the same set of questions, and we've overcomplicated the pursuit.
In addition, any and all positions that work from the presupposition that truth requires language cannot admit of true/false pre-linguistic and/or non-linguistic thought/belief despite everyday happenings/events bearing witness to the brute fact that they are being continuously formed and held prior to language. Language creation requires pre-existing thought/belief. Language discovery requires the same. Language acquisition requires the same. Formal language requires natural. Natural requires thought/belief. Thought/belief presupposes it's own correspondence to fact/reality, as do belief statements. Propositions do not. Why continue using frameworks that do not take this into proper account?
It makes no sense whatsoever to posit that Smith's belief consists of that which he does not believe.
That's what Gettier proposes by claiming that Smith is completely justified in believing (g), (h), and (i). That, in and of itself, either renders the notion of belief incoherent and/or unintelligible, or it is prima facie evidence that Gettier works from an utterly inadequate notion thereof.
Neither is acceptable.
Propositions are not equivalent to belief statements.
"Either Jones owns a Ford, or Brown is in Boston."
"Either Jones owns a Ford, or Brown is in Barcelona."
"Either Jones owns a Ford, or Brown is in Brest-Litovsk."
Smith has no belief regarding Brown's whereabouts. And yet, for half a century, everyone has ignored the fact that Gettier claims that Smith's belief consists of that which he does not believe. During the same timeframe, everyone has agreed with Gettier that Smith's belief is true solely by virtue of where Brown is located even though Smith holds no belief regarding Brown's whereabouts.
That's impossible. Smith does not believe that Brown is in Barcelona, so Brown's being in Barcelona cannot make Smith's belief true.
Here's where a defender of Gettier will invoke the rules of disjunction. One can believe a disjunction is true if s/he believes that one, the other, or both are true. I would agree and demand that Smith's belief be adequately accounted for. Particularly, our account of Smith's belief ought not claim that it contains something that he does not believe. The disjunctions, as written above, contain a statement that Smith does not believe. Granted, they are part of the disjunctions, and Smith does believe the disjunctions are true. It is clear that our account of Smith's believing the disjunctions ought reflect the fact that Smith does not believe anything at all about Brown's whereabouts. Gettier says as much in his narrative, and yet neglects to adequately represent what Smith does believe.
Smith believes that all three disjunctions are true because Jones owns a Ford.
One of the disjunctions is true, because Brown is in Barcelona.
Smith holds false belief.
What sense does it make to offer an account of belief which contains that which is not believed?
None.
Sure, a disjunction can contain a statement which is not believed, and it does in the case of Smith. However, since that is the case, and Smith does not believe the statement, then our account of Smith's belief ought reflect that fact.
Smith believes that all three disjunctions are true because Jones owns a Ford.
One can state something that they do not believe. One can construct disjunctions that contain statements that one does not believe. Gettier had Smith do just that, and he had Smith deliberately misrepresent his own thought/belief in the process. Gettier posited this situation for rhetorical effect, and it worked.
Think about what happens when one states something that s/he does not believe. Just for argument's sake, would we claim that they have true belief if what they claimed were true, despite the fact that they did not believe it when uttering it?
Of course not.
It's all about belief. Justified. True. Belief.
I suggest that we learn to correct our accounting errors.
This presupposes belief that p or q is true if p is true.
Smith believes p is true and so is justified in believing that p ? q is true because p.
How could it be any other way?
g is false.
i is false.
h is true because q.
I have false belief on all three counts.
This works from the mistaken presupposition that the content of g, h, and i are equivalent to the content of Smith's believing g, h, and i.
It's not.
The part above that says ", and so Smith believes g, h, and i" doesn't follow from what precedes it. It ought read ", and so Smith believes that g, h, and i are true because f". If any of the three are true for any reason other than f being true, then Smith has false belief.
So, then an adequate account of your belief would be...
You believe that either London is the capital city of England or pigs can fly is true because London is the capital city of England.
You believe that either London is the capital city of England or pigs can't fly is true because London is the capital city of England.
That was from page 5.
Smith believes p v q is true because p.
It is ok to say that we're "defining thought/belief", as long as we keep certain facts in mind. We can get it wrong. Thought/belief formation happens long prior to language creation and/or acquisition begins in earnest. It requires an agent capable of drawing mental correlations/connections/associations between 'objects' of physiological sensory perception and/or itself.
There are no examples to the contrary.
That said, all usage of "thought" and "belief" consists entirely of mental correlations drawn between 'objects' of physiological sensory perception and/or oneself. There are no exceptions. All predication is correlation. Not all correlation is predication.
By virtue of drawing the aforementioned correlations, all initial thought/belief formation simultaneously and autonomously presupposes correspondence to fact/reality/events/happenings, attributes meaning, and presupposes the existence of it's own content, regardless of subsequent further qualification(real, imagined, or otherwise).
At conception, the agent is completely void of thought/belief. It doesn't have what all known examples take. This is the only reasonable presupposition to work from if we take care to choose our premisses carefully. Thought/belief is accrued, begins simply, and changes according to the complexity of the specific correlations involved.
Logic and all it's man-made rules consist of quite the complex set of mental correlations. As such it is existentially contingent upon more simple thought/belief formation. Logic is existentially contingent upon thought/belief. Thought/belief presupposes truth and meaning. Logic does as well by virtue of presupposing the truth of it's premisses.
Logic is existentially contingent upon thought/belief formation, not the other way around. Because that is the case, it only makes sense to conclude that the content of thought/belief cannot be adequately accounted for solely in terms of logical form.
8-)
The above works from an utterly inadequate, and all too common, (mis)conception of belief. Belief statements are always believed by the speaker. Statements that are always believed by the speaker do not include statements that are not(believed by the speaker). Disjunctions can.
Disjunctions are not belief statements.
During sincere speech acts, when someone is taking about the world and/or themselves, s/he is talking in ways that represent their own belief. One cannot believe a statement that s/he does not think is true. Sincere speech acts do not include statements that are not believed. Disjunctions can.
Disjunctions are neither always sincere speech acts, nor belief statements.
When sensibly talking in terms of belief that 'X', X is always a belief statement. The history of philosophy has held that the value of 'X' can be satisfied by virtue of using a proposition. Propositions include disjunctions. Disjunctions are not belief statements. Propositions are not always belief statements. When sensibly talking in terms of belief that 'X', X cannot be a disjunction.
In order to know that 'X is true', one must believe 'X'. When sensibly talking in terms of knowing that 'X', X cannot be a disjunction.
((p) is true)
((p v q) follows from (p))
((p v q) is true if...(insert belief statement(s) regarding what makes this particular disjunction true))
((p v q) is true because...(insert belief statements corresponding to the above "if"))
The above clearly puts the necessary thought/belief process for believing a disjunction on display for all to see. It reports upon the necessary content within believing a disjunction. Since Gettier's case hinges upon what counts as believing a disjunction, it lands squarely within the applicable bounds/scope of the above solution.
This account is also quite amenable to the common sense groundwork at the top of this post. Gettier's report of Smith's belief is not.