Gettier Problem Contradiction
Gettier Problem
Edmund Gettier in a 1963 paper titled "Is Justified True Belief Knowledge?" raised doubts, as the title of the paper indicates, as to whether or not Justified True Belief counts as knowledge.
The Justified True Belief JTB definition of knowledge is as follows;
A knows (has knowledge of) P (a proposition) IF AND ONLY IF:
1. P is justified
2. S believes P
3. P is true
I will discuss one particular example of the many Gettier Problems - the link I provided will take you to the wikipedia page that has a list of them.
What I want to discuss here is a contradiction that, in my opinion, undermines Gettier's stand that there are justified true beliefs that aren't knowledge. The contradiction that I'm talking about it is how Gettier first asserts that a given proposition p is knowledge based on JTB theory of knowledge. Gettier then follows this up with the claim that p is not knowledge but he does this using, again, the JTB theory of knowledge.
Let's see how Gettier tries to eat his cake and have it too with the help of one of his well-known examples, that of a Smith and a Jones competing for the same job. The employer talks to Smith and informs Smith that Jones will get the job AND Smith having counted the number of coins in Jones' pocket (Jones has 10 coins in his pocket) concludes that the man who'll get the job has 10 coins in his pocket. Unbeknownst to Smith, Smith himself has 10 coins in his pocket and the employer changes his mind and awards the job to Smith.
It's clear that:
1. Smith is justified in believing the person who gets the job has 10 coins in his pocket
2. It's true that the person who gets the job has 10 coins in his pocket is true
3. Smith believes that the person who gets the job has 10 coins in his pocket
In other words Smith has knowledge concerning the person who gets the job.
Then Edmund Gettier goes on to claim that Smith, in fact, doesn't have knowledge but that means either 1) Gettier is saying Smith doesn't have knowledge because one or more of the three conditions of the JTB theory is/are unfulfilled OR 2) Gettier has a different theory of knowledge in which setting Smith's belief is not knowledge.
Since Gettier doesn't offer a different theory of knowledge, it follows that 1) Getttier is saying Smith doesn't have knowledge because one or more of the three conditions of the JTB theory is/are unfulfilled. If so, then which of the JTB theory conditions is/are not being met here? It can't be the truth of the proposition "the person who gets the job has 10 coins in his pocket" because it is true. It can't be the belief "the person who gets the job has 10 coins in his pocket". Ergo, it must be the justification that's problematic. This leads to a contradiction: Gettier is claiming that, on one hand, that Smith has a justified true belief and, on the other hand, that Smith has an unjustified true belief.
Edmund Gettier in a 1963 paper titled "Is Justified True Belief Knowledge?" raised doubts, as the title of the paper indicates, as to whether or not Justified True Belief counts as knowledge.
The Justified True Belief JTB definition of knowledge is as follows;
A knows (has knowledge of) P (a proposition) IF AND ONLY IF:
1. P is justified
2. S believes P
3. P is true
I will discuss one particular example of the many Gettier Problems - the link I provided will take you to the wikipedia page that has a list of them.
What I want to discuss here is a contradiction that, in my opinion, undermines Gettier's stand that there are justified true beliefs that aren't knowledge. The contradiction that I'm talking about it is how Gettier first asserts that a given proposition p is knowledge based on JTB theory of knowledge. Gettier then follows this up with the claim that p is not knowledge but he does this using, again, the JTB theory of knowledge.
Let's see how Gettier tries to eat his cake and have it too with the help of one of his well-known examples, that of a Smith and a Jones competing for the same job. The employer talks to Smith and informs Smith that Jones will get the job AND Smith having counted the number of coins in Jones' pocket (Jones has 10 coins in his pocket) concludes that the man who'll get the job has 10 coins in his pocket. Unbeknownst to Smith, Smith himself has 10 coins in his pocket and the employer changes his mind and awards the job to Smith.
It's clear that:
1. Smith is justified in believing the person who gets the job has 10 coins in his pocket
2. It's true that the person who gets the job has 10 coins in his pocket is true
3. Smith believes that the person who gets the job has 10 coins in his pocket
In other words Smith has knowledge concerning the person who gets the job.
Then Edmund Gettier goes on to claim that Smith, in fact, doesn't have knowledge but that means either 1) Gettier is saying Smith doesn't have knowledge because one or more of the three conditions of the JTB theory is/are unfulfilled OR 2) Gettier has a different theory of knowledge in which setting Smith's belief is not knowledge.
Since Gettier doesn't offer a different theory of knowledge, it follows that 1) Getttier is saying Smith doesn't have knowledge because one or more of the three conditions of the JTB theory is/are unfulfilled. If so, then which of the JTB theory conditions is/are not being met here? It can't be the truth of the proposition "the person who gets the job has 10 coins in his pocket" because it is true. It can't be the belief "the person who gets the job has 10 coins in his pocket". Ergo, it must be the justification that's problematic. This leads to a contradiction: Gettier is claiming that, on one hand, that Smith has a justified true belief and, on the other hand, that Smith has an unjustified true belief.
Comments (39)
I think what Gettier is doing is appealing to our folk intuitions about knowledge, saying that we would normally not say that Smith knew. That then contradicts the supposed JTB claim that Smith did know, and so supposedly shows that JTB does not track our usual sense of knowledge.
Quoting TheMadFool
I think that this is correct. Our folk understanding of knowledge doesn’t track with the kind of “justification” Gettier claims JTB claims Smith has. I think on our folk understanding, Smith’s belief was not adequately justified, and that is why his belief does not conform to our folk concept of knowledge. JTB thus stands as a sound analysis of our folk concept of knowledge.
I'm not an expert but I don't get how folk intuition can be part of a philosopher's tool kit. I can imagine folk intuition being subjected to philosophical inquiry but not as a process in philosophy.
https://en.wikipedia.org/wiki/Intuition_pump
Like you say philosophy often starts with our intuitions about things and then analyzes them. In the case of knowledge, we analyze our pre-theoretical, folk idea of it in terms of JTB. Gettier is trying to show that JTB is not an accurate analysis of that, by showing where the JTB results differ from what we want to say is or isn’t knowledge.
That's not what I'm getting at. What I meant to show was the Gettier was contradicting himself. Smith, in his example, has knowledge because he fulfills the criteria of the JTB theory and also, here's the contradiction, lacks knowledge precisely because he fails to fulfill the justification condition of the JTB theory. How can Smith both satisfy the JTB and not satisfy it?
I see but do you agree that once philosophy begins to delve into an issue that issue formalized so as to be sufficiently removed from folk intuition even to the extent that it becomes unintelligble to our intuitions?
No, quite the opposite. For example, the common folk concept of free will predates concerns about whether determinism would inhibit it. We had a notion of freely willing vs not freely willing before it occurred to anyone to ask whether a deterministic universe would mean that nobody was ever freely willing. Then after two millennia of people debating free will vs determinism, you've got a bunch of philosophers who simply cannot conceive of a notion of "free will" that might be compatible with determinism: free will in their minds has just become the antonym of determinism, and determinism the antonym of free will. But if you step back and as whether that analysis of the concept tracks with our common pre-theoretic folk understanding of it, you find it doesn't, and we need to find a different analysis of the concept that does track with that understanding. Otherwise, "free will" in philosophy becomes some technical term that doesn't mean what people ordinarily mean by it, and any philosophical results about "free will" don't actually tell us anything about free will as people ordinarily mean it.
Likewise, if Gettier was right (I don't think he is) that a JTB account of knowledge did not track with our common pre-theoretic folk understanding of knowledge, that would show that JTB is not a correct analysis of what it's supposed to analyze (knowledge). We could then either insist that JTB is definitionally what it means to "know", and let there be a technical term of art in philosophy called "knowledge" that isn't knowledge as we ordinarily mean it; or we could re-analyze knowledge into something other than JTB, to have a useful analysis of knowledge as we ordinarily mean it.
SO Gettier doesn't add much to the sum total of philosophy by showing that JTB is at the least questionable. His is an impoverished account of knowledge. A decent account would be able to explain both how we know Jones has 10 coins in his pocket and how we know how to ride a bike.
Look at how tim wood approaches the issue (below):
Quoting tim wood
:chin:
No, what Gettier has shown here is that Smith can have a justified true belief, yet fail to have knowledge (since Smith's belief was true by luck). So there must be some other further condition required for knowledge. Gettier doesn't elaborate on what that further condition might be, but the problem here is that Smith's reasoning depended on a false premise, namely, that Jones would get the job. So a candidate fourth condition would be that knowledge doesn't depend on false premises.
My understanding of the problem is that Smith fails (1) on account of, in the original thought experiment, Smith deriving his knowledge that the man who gets the job has 10 coins in his pocket from the untrue belief that Jones will get the job plus the true belief that Jones has 10 coins in his pocket. His belief is unjustified, and yet true, and therefore not knowledge.
That would be this:
Quoting Responses to Gettier - Wikipedia
Whereas Gettier's intention was to setup the case such that Smith's belief was justified and true, but not knowledge. If Smith's belief were unjustified, the case wouldn't undermine the JTB account of knowledge.
Thanks Andrew, I've obviously conflated Gettier with his critics. Also obviously, I agree with those critics. It is fundamentally a belief based on ignorance, and is unjustified on those grounds.
Quoting Pfhorrest
Yes, and perhaps a folk understanding of justification too, not obviously applicable to epistemology. His justification is of the moral sort: "Well, how did I know my colleague had fabricated all of the data?!?," i.e. treats beliefs based on ignorance or lies as equally justified as beliefs based on experience and facts. Justification is something I expect to be based on more, such as waiting for the facts to come in, getting a fuller picture, weighing and discounting other possibilities.
The question itself highlights the possibility that the employer might change their mind. Did Smith consider this and dismiss it? If so, was he justified? If not, does that make it any more justified?
What is the role of luck in Smith's situation exactly? Firstly, the fact that truth is a condition in JTB theory in addition to justification suggests that justification alone is not enough to establish truth - in other words, the necessity of truth as an extra condition implies a forethought that luck plays a part in knowledge, no? Otherwise, why include truth at all as part of knowledge in the JTB theory? If that's the case, Gettier hasn't actually noticed anything that wasn't there already. However, it's true that Gettier laid it [the problem of luck] wide open for all to see.
Secondly, when you say "Smith's reasoning depended on a false premise" aren't you also saying, as a consequence, that Smith's justification is flawed or, to make the long story short, Smith is actually unjustified? Doesn't that contradict the JTB theory and mean that Smith actually doen't have knowledge but not because of a reason other than failing to satisfy the conditions of the JTB theory as Gettier seems to be implying?
If Smith is unjustifed then how can he have knowledge based on the JTB theory which explicitly requires justification?
As per the comment of mine you quoted, he does not. If I believe when I roll a die the number will be 6 because I had a dream about it, and it turns out 6, that is not spooky knowledge. It is a mere accident.
I think Gettier's definition of justified belief was Plato's idea of "being able to give account". By that definition, Smith is justified and has knowledge. He then applies a different definition of knowledge (a more sensible one), and implicitly a different definition of justified belief, to say Smith does not have knowledge. He is inconsistent imo.
What's this "different definition of justified belief" Gettier uses?
As Pfhorrest has already said, he is using some implicit common sense definition. We can't say exactly, since it is implicit. His implicit definition of justified belief appears to be something like Plato's. His implicit definition of knowledge is clearly different, since it does not match what the JBT yields with Plato's definition of justified belief.
Well, I don't know how that got past the philosophy chekpoint. Interesting if what you say is correct. Pfhorrest seems to have been on the right track. Do you have any idea how to make Gettier's definition of knowledge make the transition from folk intuition to philosophical formalism if that's the correct word?
My understanding is that responses have been of two kinds: refine the definition of justified belief, or add a fourth condition that allows for a Platonic justified belief without calling it knowledge. So the latter address your question, I think. For example, criteria are added to disallow accidental justified belief, or other kinds of belief in error. But one can just incorporate that into the definition of "justified". That's really what it boils down to: What constitutes justified belief?
If we agree with Gettier that Smith has a justified belief, then a justified belief can be one that is based on lies, misinformation, out-of-date information, etc. and, most importantly, gullibility and closed-mindedness. If Trump tells me the US have built 2,000 km of wall and he's only built 3 km, I am justified in believing this, e.g. justified in telling everyone that this is true and saying anyone who says any different is a liar.
But I have other means of telling how much new wall there is. I can check facts for myself and not just believe the first person and call the case closed. Likewise Smith was perfectly able to justify his belief that Jones would get the job by waiting for facts, such as a confirmation letter, or lack of one. The outcome of the employer changing their mind or making a mistake was always possible, but apparently not considered, or considered and dismissed for unknown reasons. Smith could have counted the number of coins in his own pocket and justified his belief that way, but apparently chose not to. On bases such as these, the belief is not justified because Smith did everything he could to be ignorant of the facts and prejudicial about outcomes, and this would have been evident in his own testimony. You could argue that he could not really account for his belief satisfactorily.
My response to this problem is similar to that of Robert Nozick: I say that knowledge is believing something because it is true, such that not only does one believe it, and it is true, but if it weren't true one wouldn't believe it.
This last condition can, I think, be considered a different sense of "justification" from the Platonic one, and so salvage the traditional definition of knowledge, albeit only by turning the concept of justification on its head, which I argue needs to be done anyway to have a workably rational method of deciding what to believe (critical rationalism or falsificationism).
[quote=Wikipedia]The main idea behind Gettier's examples is that the justification for the belief is flawed or incorrect, but the belief turns out to be true by sheer luck. Thus, a general scenario can be constructed as such:
Bob believes proposition A is true because of argument B. Argument B is flawed, but A turns out to be true by a different argument C. Since A is true, Bob believes A is true, and Bob has justification for A, all of the conditions (JTB) are satisfied. However, Bob has no knowledge of A.[/quote]
In other words there is a justification for the proposition A although Bob is unaware of it.
The problem is Bob doesn't know the correct justification. Basically if we were to apply the JTB theory to the justification itself instead of the propositon A we get the following:
D = argument C is the correct justification for proposition A
1. D is true
2. D is justified
But
3. Bob doesn't believe D
Therefore Bob doesn't have knowledge of the justification for proposition A.
In other words, Gettier problems track back to ignorance of the true justification for propostion A. Gettier problems can be explained within the framework of the JTB theory.
The "true" JTB form of Bob's having knowledge reads as below:
1. Proposition A is true
2. Propostion A is justified [by argument C]
3. Bob believes proposition A
Since for Bob proposition 2 is not satisfied, Bob's belief in proposition A is unjustified and so, Bob doesn't have knowledge
I agree that's what the Wikipedia article says, which is I think in turn paraphrasing what Gettier says. I don't think it's true, though.
Plato's original loose definition of a justified belief ruled out making someone believe something that was true through trickery (e.g. a sophist convincing a jury of something true) and this is typically extended to coincidental guessing (I believe the die will turn a 6, it does turn a 6, which cannot be justified [except maybe by time-travel :rofl: ]). I think the same holds for ignorance.
Quoting TheMadFool
Yes, that's a good way to put it. The original idea behind justifiable belief is to be able to account for one's belief. Smith cannot properly account for the belief "the man who gets the job has 10 coins in his pocket" because he does not know he has 10 coins in his pocket or that he will get the job, i.e. his justification will itself be false.
Quoting TheMadFool
:up:
The luck element is that some person other than Jones happened to fulfill the justification criteria. Smith's belief was true despite the false premise.
If Jones had got the job, then Smith's belief is attributed to his having met that standard of justification before forming his belief, not luck. The purpose of the justification condition is not to guarantee the truth, which would be impractical, if not impossible (and would make the truth condition redundant). It's instead to make sure that only people who have made an appropriate effort in forming their beliefs have knowledge attributed to them.
Quoting TheMadFool
No, that would just be using a different definition of "justified" to what Gettier is using. The case assumes that Smith is justified in believing that Jones will get the job and has ten coins in his pocket (which is a justified false belief and so not knowledge). So Smith is also justified in believing that a person with ten coins in his pocket will get the job (which is a justified, true belief but also not knowledge because it derives from the earlier false belief).
Agreed.
Quoting Andrew M
Agreed.
Quoting Andrew M
1. What definition of justification is Gettier using?
2. We know for sure that Gettier is using the JTB theory to infer that Smith has a justified, true belief but there's another definition of knowledge that makes Gettier claim that Smith doesn't have knowledge. What is this "another definition of knowledge"?
Just what you might expect in ordinary, everyday life. If Alice looks out the window and says it is raining outside then Bob, in the next room, has justification for believing it's raining outside. He doesn't need to also verify all the relevant premises that that belief is based on (e.g., that Alice isn't hallucinating, or that the water is not coming from a garden hose unbeknownst to Alice, etc.), which would be impractical.
Quoting TheMadFool
People's common intuitions about knowledge with respect to Gettier scenarios.
See https://en.wikipedia.org/wiki/Gettier_problem#Experimental_research
Unacceptable for the reason that the Alice-Bob story still employs the JTB theory, the very theory that is supposedly wrong or incomplete.
Quoting Andrew M
So, this is intuition vs rigorous formalism
I don't think Gettier would say what he said if he didn't have very good reasons for doing so. There's more to it than that.
The Alice-Bob story is an everyday scenario where Bob forms his belief that it is raining for a legitimate reason (i.e., he justifiably forms his belief). That's the kind of scenario that a theory of knowledge is intended to describe, whether it's JTB or any other theory.
Now consider a planet orbiting a star. That can be described using Newton's theory of gravity. However it turns out that there are cases (such as with Mercury's orbit) where Newton's theory makes the wrong prediction.
Just as we can observe a planet's orbit, so we can observe how people use knowledge terms in everyday scenarios. In a Gettier scenario, JTB makes the wrong prediction (i.e., it predicts that Smith has knowledge whereas people don't regard Smith's belief as knowledge).
Arguably, to say that Smith lacks knowledge, Gettier needs a theory of knowledge based on which he can make such a claim, no? What's this theory is all I'm asking.
Gettier didn't need a theory (beyond the JTB theory he was challenging), he just needed to be aware of people's ordinary use of the terms "know", "knowledge", etc. He was able to identify scenarios where people regarded a person's belief as true and justifiably held, but they didn't also regard it as knowledge (also subsequently shown experimentally across different cultures). Note that he wasn't the first to recognize this - see Russell's stopped clock case which is perhaps a more straightforward scenario.
That's the parallel of people observing Mercury's position and noticing that it wasn't where Newton's theory said it should be. Those people didn't have a better theory - that would have to wait until Einstein came along.
As for what a better theory might be, I think the "no false premises" approach is basically right (but note the possible objections at that link).
Are you suggesting that Gettier problems are based on [weak] intuition rather than [strong] rational analysis? Gettier doesn't seem to have shared that sentiment as the title of his article - Is justified true belief knowledge? - suggests an intent to make a strong refutation of JTB theory.
By the way, any ideas on the exact nature of the people's ordinary use of the terms "know", and "knowledge"? That people don't find the JTB theory sufficient to describe knowledge bespeaks a need for something else over and above JTB.
Here's a possible scenario for Russell's clock (based on an earlier thread).
(1) Alice: What's the time?
(2) Bob: 3pm.
(3) Alice: How do you know?
(4) Bob: I looked at the clock just now
(5) Alice: Ah, OK.
(6) Carol: That clock is broken.
(7) Alice: Oh. So what time is it?
(8) Carol: I'll check the internet time clock ... It actually is 3pm.
(9) Alice: Really? (laughs) OK.
Note that the word "know" is only used once in that exchange. Yet an analysis shows, for Alice, a Gettiered JTB (at 5) and knowledge (at 9).
There are close parallels with the soundness of an argument here, and the no false premises response, which I agree is a partial solution, is treating the justification as if it were an argument for the belief, which suggests that something like validity should also be a requirement: it is not enough that the premises of the justification are true, they must also be relevant in some sense.
The problem here seems to be that if you apply 'no false premises' recursively to the premises, and also require them make a valid argument for the belief, you end up with the requirement that only proofs are acceptable as justifications.
I agree with you that this would not be very useful, but I am beginning to wonder whether, unless we accept either that view, or the view that knowledge is a matter of believing a fact simpliciter, then we must recognize that knowledge is a conditional thing.
A Bayesean might propose that a justification should increase the likelihood that the belief is of a fact (which is a weakened form of validity and soundness; those two, in combination, raise the probability that the argument is correct to 1), and that the resulting conditional probability is a measure of the strength of that knowledge. In the clock example, the argument behind the justification at step 4 presumably includes the premise that the clock normally runs reliably, a claim that has a certain probability attached to it, which is used to update the prior (which, in some circumstances, might simply be that there is a 1/24 probability that it is 3-something pm.) The new fact introduced by Carol at 6 reverts the probability that it is actually 3pm to whatever the prior was before Bob mentioned looking at the clock (such as the afforementioned 1/24.) When Carol checks on the internet at step 8, they get a different justification to substitute for the original.
A similar observation can be made about Gettier's first case: when it is revealed that Smith, not Jones, got the job, the conditional probability behind Smith's belief crashes to the probability that Smith's unexamined pocket contains ten coins. The discovery that it does constitutes a new justification.
This is just off the top of my head; I would be surprised if there are not paradoxes arising from this view.
Another aspect of Gettier's examples is that there is no causal connection: whether someone has 10 coins in their pocket, and who gets chosen for the job, have no causal relationship, and neither do Jones' car ownership and Brown's location in the second case (note that this causal disconnect is absent in the clock example.)
As these issues lie at the foundations of epistemology, they are not trivial.
Thanks! It occurred to me just now that a simplified definition along these lines might be that a justification has to be a valid argument that is more likely sound than not.
On the other hand, having a quantitative concept of justification seems to fit with the jury instruction to return guilty if the premise that the defendant committed the crime is true 'beyond reasonable doubt', and also with the phrase that 'extraordinary claims require extrordinary evidence'. As probability is constrained between 0 and 1, the odds that the justification is sound might be a better measure, in order to encompass both extraordinary evidence and unreasonable doubt (Update: maybe the log of the odds? The odds itself asymptotically approaches the probability when the latter is small, and they both approach zero, which means that a metric using either probability or odds would not discriminate much between extraordinary claims and claims that are merely improbable.).
In either variant of this view, Gettier's second case still seems problematical, but perhaps we can dispose of it by noting that proposition h (the one that Gettier regards as problematical for JTB) is a disjunction of two beliefs, only one of which (Jones owns a Ford) could be knowledge by either of the definitions I gave above. If the other belief (that Brown is in Barcelona) happens to be true, then this would establish that the proposition h states a fact, but not that Smith has a justification for believing it, as the only justifications he has for h concern only Jones' car, and they turn out to be false. Here we have the disjunction of two propositions, neither of which are part of Smith's knowledge, so it seems reasonable to say that their disjunction is not known by Smith, either.
Yes. And if the argument is sound, then the person has knowledge. Obviously there is no guarantee of that since the conclusion or a premise could be false (unbeknownst to them). But that's the trade-off that has to be made for claims to be justifiable at all, and therefore for knowledge to be possible.
Quoting A Raybould
Yes, in some contexts the standard for justification is higher.
Quoting A Raybould
Works for me.
Interesting point. Gettier's claim is that the JTB definition can be satisfied (e.g. by the example you give), yet still not count as knowledge. But if Gettier knows exactly why the example doesn't count as knowledge, then he should be able to give an alternative definition, or provide an additional clause, which he doesn't. And if he doesn't know why the example doesn't count as knowledge, then what reason does he have for the claim that it doesn't?
My take on this is that Gettier is basing his claim on a presumption made by the JTB definition itself, which is that the truth of a belief is not sufficient for knowledge because a belief can be true purely by accident. So another clause is needed, and that, according to the JTB definition, is justification. Gettier's point is that justification doesn't do the job it's intended for, since, as the relevant examples show, a belief being justified doesn't necessarily prevent it from being true purely by accident.
One may question whether non-accidental truth is necessary for knowledge, but that is already presumed by the JTB definition, which is Gettier's target.