It sets out how possible world semantics (PWS) solves the issue of substitution for modal logic.
I'm not a logician. I'm Happy to be corrected by those with a better understanding. But as I understand it, in PWS the existential and universal quantifiers are understood within each possible world, while the necessity and possibility quantifiers are understood across all possible worlds.
So within each possible world we can have different assignments of predicates to individuals.
We have lots of different possible worlds each with different bunches of the same individuals, being assigned different bunches of predicates.
If an individual or group of individuals has the same predicate in all possible worlds, it necessarily has that predicate: Bachelors are unmarried in all possible worlds.
If an individual or group of individuals does not have a predicate in any possible world, it is not possible.
If an individual or group sometimes has a given property, sometimes not, then it is a possible property.
But as I understand it, in PWS the existential and universal quantifiers are understood within each possible world, while the necessity and possibility quantifiers are understood across all possible worlds.
If an individual or group sometimes has a given property, sometimes not, then it is a possible property.
That's actually the definition of contingency. Possibility is just defined as truth in at least one world. Necessary truths, for example, are still possible truths because they fit that condition. Contingency means true in some worlds but false in others.
If an individual or group of individuals has the same predicate in all possible worlds, it necessarily has that predicate: Bachelors are unmarried in all possible worlds.
This has always been odd for me. It seems like one could have a married bachelor. What makes one married is to hold a certain legal status, yes? Well consider a state of affairs where there's a contradiction in the local laws. Law A says "Yada yada Those holding a marriage certificate are married" and Law J says "Etc etc Gay people cannot be married". Now some gay person managed to get married (certificate and all), and there is no judicial precedent in how judge which law overrules the other. On the usual assumption that law decides what is true in these cases (because that's how we know who is considered married), one would seem to have a married bachelor.
b. The Common Principle of all Analytical Judgments is the Law of Contradiction. --- All analytical judgments depend wholly on the law of Contradiction, and are in their nature a priori cognitions, whether the concepts that supply them with matter be empirical or not. For the predicate of an affirmative analytical judgment is already contained in the concept of the subject, of which it cannot be denied without contradiction. In the same way its opposite is necessarily denied of the subject in an analytical, but negative, judgment, by the same law of contradiction. Such is the nature of the judgments: all bodies are extended, and no bodies are unextended (i.e., simple).
For this very reason all analytic judgments are a priori even when the concepts are empirical, as, for example, "Gold is a yellow metal," for to know this I require no experience beyond my concept of gold as a yellow metal. It is, in fact, the very concept, and I need only analyze it, without looking beyond it elsewhere.
The law of contradiction holds in PWS. In no world can there be a contradiction. But there can be differences between worlds; so while my cat is all black in this world, in another possible world it might be all white; yet in no possible world is my cat both all black and all white.
Now Kant says that it is part of the concept of gold that it be a yellow metal, and hence that being a yellow metal is a priori.
And yet it is eminently possible that gold might be a different colour. So in some possible world there might be red gold.
So being yellow is not a necessary characteristic of gold.
SO it seems that either Kant was in error about gold, or that a priori and necessity are different things.
That's actually the definition of contingency. Possibility is just defined in truth in at least one world. Necessary truths, for example, are still possible truths. Contingency means true in some worlds but false in others.
This has always been odd for me. It seems like one could have a married bachelor. What makes one married is to hold a certain legal status, yes? Well consider a state of affairs where there's a contradiction in the local laws. Law A says "Yada yada Those holding a marriage certificate are married" and Law J says "Etc etc Gay people cannot be married". Now some gay person managed to get married (certificate and all), and there is no judicial precedent in how judge which law overrules the other. On the usual assumption that law decides what is true in these cases (because that's how we know who is considered married), one would seem to have a married bachelor.
That just looks like an invalid marriage to me. I don't see a philosophical issue here, just a legal one.
Reply to Banno But what would make it valid or not would be for a precedent to be set by a judge ruling on the case. Prior to that it's a contradiction in the law. One law says they're married (they hold the certificate) the other says they aren't (they're a gay couple), and it's the law which establishes who is married or not.
Reply to MindForged indeed; and if they are married, they are not bachelors; and if they are not married, they are. It's not a case of one without the other.
Terrapin StationJanuary 15, 2019 at 00:00#2462430 likes
"Gold is a yellow metal" or "a bachelor is an unmarried man"
All those types of statements really tell us is how an individual has formulated their concepts. It's telling us either what they require to call some x (some particular) an F (some type term), or alternately it's announcing terms they use as synonyms.
The only necessity invoked there is the stringent stipulation of the individual in question.
It explains what's really going on with those statements contra Kant's misconceptions, and it explains the only sense in which we could say that they're "necessary."
Reply to Terrapin Station You like the word really - what is really going on; what the statement really tells us. I'm not so keen. I still do not see how your post explains anything.
Deleted UserJanuary 15, 2019 at 01:17#2462570 likes
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Necessary statements are commands or policies, i.e. speech acts, whose origin of force is the intentions of the speaker or institution who asserted them. This includes metaphysical assertions, ethical assertions and all universally quantified 'propositions' over infinite domains in science and mathematics.
So "Bachelors are unmarried men", when interpreted as expressing a necessary truth, is to declare a policy allowing the substitution of the former as a synonym for the latter without exception. Hence the image of it holding in "all possible worlds".
However, when interpreted as expressing a publicly verifiable proposition "Bachelors are unmarried men" is both contingent and under-determined.
...then it seems right to say that if there is gold, then it is a metal and it is yellow...
I don't see that you can escape modality quite so easily. Suppose a mine starts digging out red gold. Same mailability, same atomic mass, same melting point. Would you say it is red gold, or not gold?
If being yellow is a part of the very concept of gold, you must say it is not gold.
The best way to understand them is by seeing how they are used in possible world semantics.
It's simply a way to parse any modal statement. Possible worlds are specified by our speculations. What if Tim Wood had been Jim wood? That can be parsed as: In some possible world, Tim wood is known as Jim Wood.
In some possible world, gold might be red. In no possible world could gold have a different atomic mass, because no longer would it be gold - it would be something else.
But in my opinion you're missing a deeper point. Perhaps this way. Posit something certain. Then subject it to your criticism that maybe someday somebody might dig up or discover.... Allow that, and absolutely nothing stands.
Perhaps I see see beyond your deeper point...
let's debar the Humpty Dumpty world where words mean whatever we choose.
Then if we find a red substance with otherwise the same properties as gold, we have a choice: is it gold, or is it not-gold? what attributes are essential to gold? Kant, and perhaps you, say colour is; i say it isn't.
you want to call it gold... but you want it to be different.
That's not an issue: I want my cornflakes not as they are in the pack, but slightly soggy from cold milk. I want my I want my beard longer. Such things do not make these not my cornflakes or this not my beard.
Deleted UserJanuary 15, 2019 at 02:14#2462770 likes
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The limits of imagination are the limits of the knowable. So for all practical purposes, the limits of imagination are the limits of what is. In cases where we can't imagine X, it seems we know a priori that X doesn't and can't exist. Necessarily, there is no X.
With a posteriori knowledge, we are being informed about what's out there. As long as we can imagine things being other than they are, there are only contingently true statements related to a posteriori knowledge.
schopenhauer1January 15, 2019 at 02:46#2462860 likes
Achieving almost complete incoherence! Is it the wanting that does not make these not your cornflakes or not your beard? Are possible worlds just a thought? We joke, but I'm serious. Semanticists can create any animal they feel they need for their ow purposes, but as with any errant creativity, their's is subject to disciplines and controls, and being kept in its cage. "Possibility" is possibility, not license.
tim wood, queston: What do you suppose a statement is about gold that is synthetic a priori?
schopenhauer1January 15, 2019 at 03:07#2462970 likes
Reply to Banno
I hate to smuggle in words where they were not explicitly stated but to get your point across to those who don't get Kripke and his idea of natural kinds, you should just mention that he is arguing for what is "essential" to the natural kind before it is no longer "that" particular natural kind. That might solve some confusion on what Kripke is actually doing.
Edit: Oh and he is doing it through the idea of how "names" designate the referent in all possible worlds. I realize you might want his methodology too since I know you are keen on making that distinction that he is mainly doing a grammatical project rather than metaphysics.
for what is "essential" to the natural kind before it is no longer "that" particular natural kind.
The unfortunate example provided by Kant, and critiqued by Kripke, is that gold is a yellow metal. Now Kripke and Kant would presumably agree that old is a metal - that something purported to be gold but which is not a metal, is not gold. Kant seems to think that this is also true for being yellow; that something purported to be gold, but which is not yellow, would not be gold. Kripke disagrees; and given that colour is a secondary characteristic, Kripke's view seems to me to be the better.
AH. Good question. You had best explain the difference, if we are going to proceed.
On the way to explaining bundle theory, Hume asks us to imagine an object that has no properties. He finds that he is not able to imagine it. He obviously has no problem saying the words, though.
Are you actually imagining that? Or just saying the words?
Hm. I cannot imagine the square root of -1. But I can bring the words together and then manipulate them to produce say a curve or an image of the Mandelbrot set.
Hm. I cannot imagine the square root of -1. But I can bring the words together and then manipulate them to produce say a curve or an image of the Mandelbrot set.
If you see no difference between imagining and "bringing words together," our experiences are too different to continue on.
Reply to frank Frank, I'm teasing the distinction Hume introduced to see if it can stand on it's own feet. Looks to me like it can't. (See me avoid the can't/Kant joke?)
The unfortunate example provided by Kant, and critiqued by Kripke, is that gold is a yellow metal. Now Kripke and Kant would presumably agree that old is a metal - that something purported to be gold but which is not a metal, is not gold. Kant seems to think that this is also true for being yellow; that something purported to be gold, but which is not yellow, would not be gold. Kripke disagrees; and given that colour is a secondary characteristic, Kripke's view seems to me to be the better.
I would agree with Kripke's assessment. But, I think Kant just missapplied gold when judging with this own theory. Gold being yellow is a posteriori, as Kripke agrees, and synthetic, not analytic. Unlike bachelor's being unamarried males, there is nothing in gold that automatically makes its definition of being yellow logically necessary- it could have been a different color.
The more interesting question is "What would Kant think of gold's atomic number of 79?". This to me seems like a synthetic a priori judgement. That is to say, you need to experience it in the world to know it (experiment), but it is universally and necessarily seen as true once it is discovered. I could be misapplying his terms myself though, that is where others can try to correct me.
The difference between Kant's approach and Kripke's approach, which @csalisbury was trying to bring up is one of areas of interest (which may be incommensurable). Kant is looking at things from an epistemological point of view and Kripke from a grammatical point of view. From Kant's epistemological point of view, he considers the very universal conditions for even observing the world in the first place. Thus, the reason gold is 79 in all possible worlds, is because of the necessity set up by our brains (time/space,categories of understanding). There is no way the substance we call gold could not be 79.
Kripke, on the other hand, isn't interested in necessities of human understanding like Kant is. He is purely focused on how we use names. Names are inherently arbitrary as what the actual utterance is. What isn't arbitrary is how the name then becomes "attached" (or rigidly designated), in his view. Thus, though we don't need any universal laws of human understanding to have a substance be named "gold", once that substance is named gold, and used over and over from that original instance, it becomes fixed in all possible worlds. These two starting points for understanding the world are very different. That is to say, Kant wasn't worried about how grammar works with names- he was worried about how things could be universally true despite having been derived at empirically. He was worried that Hume was right in his "Problem of Induction".. By Kant saying that universal necessities are actually transcendental (in the very fabric of our understanding of our world), that universal truths can be derived from empirical evidence.
schopenhauer1January 15, 2019 at 08:15#2463470 likes
@Banno I'd be willing to append my first statement above that they are incommensurable if, we consider that Kripke's project was more than grammatical, that his conclusions were also epistemological. That is to say, in truth-statements judgements about the world, we have found a new category that Kant didn't consider. However, the reason Kant didn't consider it, was he was not using the approach of names and grammar, which can arguably make them incommensurable, being two lines of investigation that may not go together.
However, following Kripke's own line of reasoning perhaps, we can say that, IF Kant was to have used a grammatical method (and applying it to modal logic), he would have also included necessary a posteriori statements in his schema. He would notice that you can have contingent "words" apply necessarily to a person or a kind.
However, we may still state that these are incommensurable approaches as Kant was looking at propositions and Kripke was looking at grammar and these two approaches are mutually exclusive.
Terrapin StationJanuary 15, 2019 at 11:01#2463640 likes
You like the word really - what is really going on; what the statement really tells us. I'm not so keen. I still do not see how your post explains anything.
Well, we'd need to check if you even understood my post, I suppose. How would you say what I said in your own words?
Terrapin StationJanuary 15, 2019 at 14:02#2463880 likes
Let me try this: is gold a yellow metal? Is gold any other color? Assuming the answer to these are yes and no respectively, then it seems right to say that if there is gold, then it is a metal and it is yellow, and, if it is either not metal or not yellow, then it is not gold.
So, when we're talking about this from the a priori context, the answer is "It depends on how you've formulated your concepts."
Hm. I cannot imagine the square root of -1. But I can bring the words together and then manipulate them to produce say a curve or an image of the Mandelbrot set.
Let's do a thought experiment and start by saying there are things we can't imagine (even in principle) and see where it leads.
I suppose it could be that much of what is entailed by that initial premise is beyond my imagining. Maybe the whole conclusion is. What's the point in trying to think it through when the truth is likely as not beyond my grasp?
And when the dust settles, I find that this skepticism is a deadend. The actual world is bounded by my imagination (for all practical purposes). What appears otherwise just hasn't been properly tackled yet.
If you look back, you'll see I said "for all practical purposes" the first time.
But there can be differences between worlds; so while my cat is all black in this world, in another possible world it might be all white; yet in no possible world is my cat both all black and all white.
How could your cat not be black in another possible world? I get how you might have adopted a white cat in this world had you so chosen, but I don't understand how you maintain your identity across worlds where you can have cats in each world of varying colors. Quoting Banno
So being yellow is not a necessary characteristic of gold.
This strikes me as a slippery slope into essentialism, where you're going to have to now identify what is a necessary characteristic of gold, if not its color. I don't follow why its color cannot be part of its arbitrary definition if we so choose. Does gold cease being gold under a red lamp? Sure, if we say so.
That just looks like an invalid marriage to me. I don't see a philosophical issue here, just a legal one
It would seem he was getting at what I was saying above. Things are whatever we say they are.
At any rate, doesn't your acceptance of the the logical necessity of analytic truths jettison Quine's well known objections?. https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction#Quine's_criticisms.
“....I apply the term transcendental to all knowledge which is not so much occupied with objects as with the mode of our cognition of these objects, so far as this mode of cognition is possible a priori....”
“....(Is there) a knowledge altogether independent of experience, and even of all sensuous impressions? Knowledge of this kind is called a priori....”
“...But the expression, "a priori," is not as yet definite enough...”
“...By the term "knowledge a priori," therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. Opposed to this is empirical knowledge, or that which is possible only a posteriori, that is, through experience. Knowledge a priori is either pure or impure. Pure knowledge a priori is that with which no empirical element is mixed up....”
“...The Human Intellect, even in an Unphilosophical State, is in Possession of Certain Cognitions "a priori"....”
A.) “...if we have a (judgement) which contains the idea of necessity in its very conception, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely priori....”
B.) “...an empirical judgement never exhibits strict and absolute, but only assumed and comparative universality (by induction); therefore, the most we can say is—so far as we have hitherto observed, there is no exception to this or that rule....”
C.) “...If, on the other hand, a cognition carries with it strict and absolute universality, that is, admits of no possible exception, it is not derived from experience, but is valid absolutely a priori....”
“....When strict universality characterizes a judgement, it necessarily indicates another peculiar source of knowledge, namely, a faculty of cognition a priori. Necessity and strict universality, therefore, are infallible tests for distinguishing pure (that is, a priori) from empirical knowledge, and are inseparably connected with each other....”
—————————————-
It doesn’t matter the objects in general we know about when considering knowledge itself, because such things are already given, or at least possibly given, by perception as appearances, but rather the theoretical, or indeed speculative, methodology under which human knowledge is possible. The old...knowledge *of* vs knowledge *that* dichotomy, so to speak, insofar as the judgements “gold is a yellow metal” and “water is a clear fluid” are understood empirically as immediate yet incomplete knowledge *of* gold and *of* water respectively. Reason wants it known under what conditions are we authorized to signify or designate gold and water.....and every other damn thing in the world....the way we do, such that knowledge *that* gold is a yellow metal and knowledge *that* water is a clear fluid, are derived from valid, that is, non-contradictory, cognitions.
Reason doesn’t want to know if any other immediate empirical intuition can be given to gold, but only that the intuition of, e.g., “yellow”, “metal”, actually does belong to it, not because perception, from which the empirical appearance comes, says so, but because understanding, from which such necessary justification alone comes, says so. But understanding does not intuit, it has no say in assigning “yellow” to “gold”, that having already been accomplished under the auspices of the faculty of intuition, which gives appearance to phenomena by means of imagination, and which then becomes rationally authorized as representation.
But we already know from experience what the intuitions of yellow and metal may represent, other than gold. We also know from experience the intuitions of clear and fluid may represent other than water. Therefore, we can say that the assignment of certain predicates to gold is an empirical cognition when gold is directly perceived, and, more importantly, we can thereafter cognize a priori, that gold is a yellow metal when no appearance of gold is given at all, because such appearance has already been represented and hence judged as non-contradictory. This is, of course, impure a priori knowledge, having it base in experience, no matter how remote. It is perhaps more easily considered as indirect, as opposed to direct, knowledge, although this qualification is not suggested as intrinsic to the transcendental philosophy of continental Enlightenment era epistemological theory.
Now of pure a priori knowledge, it must be admitted that whatever conditions, and therefore the principles which legislate those conditions, already explicit in impure and empirical knowledge cannot apply, for such is entirely circular and of no use whatsoever. That condition and principle being the logical law of non-contradiction, it follows that whatever legislation reason requires for pure a priori knowledge as its ends must have for its means some other fundamental ground. While it may be easy to dismiss the conditions given from experience, which the very idea of pure a priori requires, it is very far from easy to dismiss the cognitive operational procedure of human rationality. Therefore, a line must be drawn as to where and how we think objects, without there being objects to think about. If the line be drawn at the point where empirical influence stops, but the remainder of the cognitive system continues, such should be sufficient ground to establish the possibility of pure a priori knowledge. From the quotes above, they being taken in their respective order of print, it is clear knowledge works backwards, from itself, through cognition, through judgement, through understanding, through representation, through intuition. But all intuition is given from perception, which is always empirical, thus the line must be drawn before intuition when proceeding backwards, or that of which is a consequence of it. But if intuition is dismissed as a faculty for representation given to understanding, there must be some other source from which understanding may draw, in order to make its judgement, from which a cognition may follow and from that knowledge may follow.
This source resides in the understanding itself, they are the pure conceptions of the understanding, called noumena, and are, in effect, nothing more than the names of the properties or attributes a merely possible object, or, which is the same thing, an object as it will be represented upon the experience of it, must be given before any judgement whatsoever is possible of it. Because there are only these two sources of possible relations for the understanding to employ in its judgements, that is, intuitions and conceptions, and because intuitions, which have non-contradiction as their principle, have been dismissed in the determinations of pure a priori knowledge, the principle of necessity for the existence and the employment of the conceptions of the understanding, and furthermore the absolute universality of their application, serves as sufficient ground of pure a priori knowledge.
(Universality herein means only insofar as reason is investigating the realm of possibility; the pure conceptions of the understanding have no standing in what is called “transcendent”)
Does it matter if the pure conceptions of the understanding really exist? Does it matter they were incorporated post hoc ergo propter hoc as a means to inhibit infinite regress? No, not really, because we do not doubt we are in fact in possession of pure a priori knowledge, which makes explicit we must have pure a priori cognitions, which in its turn makes explicit we must have made pure a priori judgements, which in IT’S turn makes explicit we must have something purely a priori in our faculty of understanding. This is why it is said we do not and cannot know noumena as real objects of conception, even though we are permitted to name them because we think them as necessary, and if that is so, they are so much confused with the “thing-in-itself”, which we also know absolutely nothing about. Noumena, along with imagination and schemata, should be considered as a facilitators in the rational procedure of faculties, but not in themselves cognitive faculties.
All that remains, in the consideration of empirical, a priori and pure a priori understanding, judgement, cognition and knowledge, is whether or not the claim for the reality of pure a priori knowledge has something applicable to it. What can we know a priori? Simply put, anything we know that has no empirical content whatsoever is known a priori. Upon reduction of anything empirical or possibly empirical out from thought in general, all that remains is nothing but thought itself, the thought of something, and is purely a priori; that which exists as nothing more than a thought of something, is a proposition where the subject and predicate are connected by the pure conceptions of the understanding, whereby the predicate follows universally and necessarily from the subject. “Plurality is succession in time”, “No sum is less than its constituents”, “No cognition of three lines will ever allow cognition of a triangle” serve as examples of pure a priori knowledge. It should be noted, that because pure a priori knowledge has no empirical content, no truth value can be assigned to any pure a priori proposition, such truth coming from experience alone. These propositions serve only as the form this kind of knowledge must have.
These are the conditions for deriving the grounds of analytic and synthetic propositions, and the knowledge which follows from each of those kinds, and these from a particular epistemological theory. There is no reason to suppose this theory is better or worse than any other, even if it is logically consistent.
Only, I'm going to follow Davidson and say that incommensurability is not an option. If two groups of ideas don't meet well, then one or both of them are wrong.
SO while I take Kripke as approaching forma grammatical point of view, it's apparent that the grammar has epistemological implications for Kant. The necessities of human understanding are present in the way we use words.
SO here again is my question: Can we reconcile Kant's a priori with Kripke's necessity?
Was it just a mistake to include "yellow" in the essence of gold? Perhaps if we remove that, we have some agreement between Kripke and Kant. .
Was it just a mistake to include "yellow" in the essence of gold? Perhaps if we remove that, we have some agreement between Kripke and Kant. .
I think it was, especially keeping in mind the definition of analyticity and with Kripke's further critique using modal logic.
However what would this approach look like if there was agreement when one is using propositions and the other is using purely grammar- when one is looking how we understand the world using propositions, and one is using how we understand names using modal logic?
@Hanover, I think we ought take transworld identity as read for the purposes of this thread. I'm quite comfortable with Kripke's account, in Naming and Necessity Lecture 1, and given the substantial thread on that topic already in this forum, I don't have more to say.
So unless you have a very specific criticism of Kripke's attitude to transworld identity, I'm not interested in that approach.
However what would this approach look like if there was agreement when one is using propositions and one is using purely grammar- when one is looking how we understand the world using propositions, and one is using how we understand names using modal logic?
The difference is profound, while subtle.
SO one says that gold has an atomic mass of 79, and hence if some sample has another atomic mass, it is not gold.
The other says that gold has an atomic mass of 79, and hence if some sample has another atomic mass, we ought not call it "gold".
:wink:
Deleted UserJanuary 15, 2019 at 21:52#2464800 likes
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Yoohoo! Depends on a careful definition of what Kant meant by "yellow," don't you think? You can play with this all you want but the substantive issues don't go away.
No I don't. I certainly don't think that yellow is necessarily wrapped up in the meaning of gold, in the same way that bachelors is literally the definition of unmarried males. Yellow seems to me a contingent property of gold- it doesn't have to be a primary property. If it wasn't yellow, it wouldn't make it any less "gold". So that statement synthetic a posteriori.
However, if we took away the atomic number of 79, it certainly wouldn't be gold anymore. However, even according to Kant's own idea of judgements, this proposition wouldn't be analytic. It certainly is something I had to find out in the world (synthetic), but holds universally and necessarily true. However, you can correct me where you think I misapply Kant.
Eh? Really? There's gold that's not yellow (or "gold" as Banno would have it)?
I guess the point is- what makes gold essentially gold? Is it its yellowness? But, I see where you are coming from using Kant's own theory of categories. Before we can define gold, we must figure out what is legitimate in a definition. Kripke and @Banno are claiming that modal logic seems to indicate that only certain essential properties can be considered gold, otherwise it is not designating gold, really.
I can see where the clash comes in though. As I mentioned before, Kant is interested in how we understand the world through our transcendental lens. Thus other possible worlds logic would be conditioned by our very own epistemology. His work did not seem to go beyond the scope of what is possible outside of our own psychological understanding in this world.
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Terrapin StationJanuary 16, 2019 at 00:39#2465400 likes
Which Kant was careful to make clear and document.
Really, I don't remember Kant stressing that it purely depended on how individuals formulated their concepts, so that an a priori claim that holds for one person might not hold for another. Wouldn't that basically negate the idea of there being any necessary a priori claims in a broader context (rather than, as I noted, only possibly amounting to someone being stringent or stubborn in their concept-usage over time?)
schopenhauer1January 16, 2019 at 01:50#2465530 likes
But we do know gold is an element. AU, then, is AU wherever in the universe you go, in those places where there is gold (maybe none in some places in the universe, maybe where atoms cannot exist). That leaves the question, what does "gold" mean in the context of APW and PWS. My answer: it doesn't mean anything in those worlds because they're just conjectural worlds concocted to test certain logical propositions. Which means in brief, you can't get theah from heah, and you cant get heah from theah, as Bert says to Ernie. And "existence" in any such world does not imply existence in ours.
Kripke was concerned with names. That is the main point we must not forget with him. His question is, "How do proper names and natural kinds designate their referent?". Statements like, "Gold is a yellow metal" were not good enough for him. To him, these "descriptivist models" of names and natural kinds were too weak to really designate "that" kind of natural kind. For example, "The definition of gold is a metallic yellow substance" doesn't hold up. In another possible world, metallic, yellow, and substance might not be how to describe gold, but gold would still somehow retain its goldness in those worlds. It is considering what properties hold up in these worlds, that he considers the name gold to actually designate "that" kind of natural kind. Thus, since it is a name that is given to an object after experiencing an object and sensing it in the world, it is a posteriori. However, unlike most other a posteriori statements that are contingent, the NAME gold is always and necessarily attached (rigidly designated) to some essential property in all possible worlds (something like let's say the atomic number 79). If it doesn't have this essential property, the name "gold" does not rigidly designate that object. Thus he says that Kant is missing a category for necessary a posteriori judgements, like the ones (he thinks) are needed for rigidly designating proper names and natural kinds.
As far as Kant's synthetic a priori- I think I take back my statement that atomic number 79 being essential to gold is a synthetic a priori statement. In Kant's view, this should simply be synthetic a posteriori. It is gained through experience which makes it a posteriori and it is adding information that is not contained in the subject, so it is synthetic.
Synthetic a priori would be things like cause and effect and mathematics. You don't need to experience things in the world for them be proven, but they are also not contained in the subject by definition.
The question for me is, if ? is a priory, is ? also necessary?
Reply to schopenhauer1 So on your account, some things can be a posteriori and yet necessary - agreeing with Kripke. Gold having an atomic number of 79 being one of these.
And further, gold having atomic number 79 is synthetic; it brings together two distinct concepts, atomic number and gold, or if you prefer the phenomenological experience of gold.
So we have a necessary synthetic statement: gold has atomic number 79.
Or do we take the discovery of gold to be analytic, post hoc? The very idea of gold contains within it the idea of atomic number 79; to be gold is to have atomic number 79; only we needed to do some experiencing in order to learn this...
Or does this whole structure of a priori/a posteriori and synthetic/analytic fall apart on analysis?
AND is being a priory the same as being necessary?
schopenhauer1January 16, 2019 at 03:58#2465590 likes
So on your account, some things can be a posteriori and yet necessary - agreeing with Kripke. Gold having an atomic number of 79 being one of these.
And further, gold having atomic number 79 is synthetic; it brings together two distinct concepts, atomic number and gold, or if you prefer the phenomenological experience of gold.
Or do we take the discovery of gold to be analytic, post hoc? The very idea of gold contains within it the idea of atomic number 79; to be gold is to have atomic number 79; only we needed to do some experiencing in order to learn this...
Or does this whole structure of a priori/a posteriori and synthetic/analytic fall apart on analysis?
AND is being a priory the same as being necessary?
I think these are great questions and pretty much sums up this whole debate.
In order for any of this to work we have to have some basic terms that we all agree on (or at least think Kant agreed on). Let me start with the last question:
AND is being a priory the same as being necessary?
At first, I thought just that- Kant was saying a priori was just a synonym for universal and/or necessary. Now, I'm thinking it is a bit different. I think Kant's thoughts on a priori literally has to do with the term "prior to". That is to say, if terms are derived prior to (or outside of) experiential observations (with the senses usually), it is an a priori-type statement. Thus, geometric rules like "All triangles have corners that add up to 180 degrees" are not derived from experiential observations of the world (this is at least Kant's interpretation of what we are doing). One doesn't need to observe any particular thing in the world, just understand the concepts using our intuition on how triangles, corners, and degrees work when we make judgements on them. Synthetic means that the proposition is additive and not simply a tautology. Thus, 180 degrees, the concept, is not inherent in a triangle per se, but a conclusion only made through a priori investigation. Thus the sum of the degrees of a triangle is a synthetic a priori judgement.
So on your account, some things can be a posteriori and yet necessary - agreeing with Kripke. Gold having an atomic number of 79 being one of these.
Yes, if I was following Kripke's reasoning, there indeed does seem to be judgments that are made from observing the world, and as a byproduct of how we use language, create necessary a posteriori truth-statements.
And further, gold having atomic number 79 is synthetic; it brings together two distinct concepts, atomic number and gold, or if you prefer the phenomenological experience of gold.
So we have a necessary synthetic statement: gold has atomic number 79.
Technically, this would fall under necessary (if defined as being true in all possible worlds), and it is something that is additive, not just tautological in the subject.
Or do we take the discovery of gold to be analytic, post hoc? The very idea of gold contains within it the idea of atomic number 79; to be gold is to have atomic number 79; only we needed to do some experiencing in order to learn this...
This is I guess what I believe @tim wood (and maybe Kant?) believed. "Gold is the metal that has atomic number 79" would indeed be a tautology so, indeed this would be an analytical statement.
Or does this whole structure of a priori/a posteriori and synthetic/analytic fall apart on analysis?
And now we come to the real question at hand. It needs a much crisper demarcation between what counts as analytic and what does not, or this indeed does become arbitrary to the person using the concept. It breaks down unless there is absolute certainty on what fits under what category. If it breaks down, it becomes arbitrary as a way to distinguish truth statements.
Deleted UserJanuary 16, 2019 at 04:22#2465640 likes
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So. There are "possible worlds" where Banno isn't Banno. Of course, to be relevant, that Banno must be Banno. If not, then why would we think that the Banno in the other "possible world" that isn't Banno is Banno. In that world he may just be a cruller. If he is a cruller in that world, why would we think he is Banno. And if he is Banno, then the assumption that there are "possible worlds" where he isn't Banno collapses. Which means he is Banno. So Banno is Banno in all possible worlds. Which applies mutis mutandis to everything in all possible worlds. So there is no possible world wherein there is something that is not, in this world. Hmm.
Banno is indeed Banno in every possible world in which I exist. In no world am I a doughnut, a fruit cake or anything other than human. Although in some worlds my name is Tim Wood. I am not Banno in all possible worlds, since one can posit a possible world without me in it.
It seems that you are happy to accept that science has moved on since Kant. So has logic.
Metaphysician UndercoverJanuary 16, 2019 at 12:03#2466100 likes
It is necessary that a priori knowledge is necessary. It must be so because "a priori" refers to principles which cannot be justified by experience. Since they cannot be justified by experience, the only thing which makes them acceptable as true, is the assumption that they are necessary. If we reject their necessity then there would be absolutely no reason to accept them as true.
schopenhauer1January 16, 2019 at 12:13#2466120 likes
It is necessary that a priori knowledge is necessary.
Yes, I didn't mean that Kant didn't think a priori to be necessary. I just meant that being necessary isn't a fully sufficient definition of a priori.
Metaphysician UndercoverJanuary 16, 2019 at 12:20#2466130 likes
Reply to schopenhauer1
I agree, to discuss things in terms of necessity, is to use different categories than Kant uses.
There are two fundamentally different types of necessity, that which is prior to logical process, as needed for it, and that which is posterior to logical process, as that which is made necessary by logic. But this is not equivalent to Kant's a priori/a posteriori division.
We must be careful not to equivocate between these two senses of necessity, and I think Kant's categories may create ambiguity. His, are probably not the best that could be drawn..
schopenhauer1January 16, 2019 at 12:25#2466150 likes
We must be careful not to equivocate between these two senses of necessity, and I think Kant's categories may create ambiguity. His, are probably not the best that could be drawn..
Yes, I think this exercise is kind of proving that out. The fuzziness between what counts as analytic or synthetic in the definition of gold, for example makes that seem the case.
Metaphysician UndercoverJanuary 16, 2019 at 12:40#2466190 likes
Reply to schopenhauer1
The problem I see is that the principles by which we proceed into logical process, the propositions as premises, which are necessary for logic to proceed, are usually principles which are derived from experience. So if there is such a thing as "a priori" in Kant's sense, some sort of principles which are not derived from experience (and if I remember correctly, he provides a convincing argument for the reality of this), then these must be something like the rules of the logical processes themselves. It's questionable whether a priori principles could even be accurately put into words, because the use of words is learned from experience. For example, what would be the rule for counting? Add one. But even stating with "one", simple unity, is to take an empirically induced principle. If we do not start with one, what sort of rule for counting could we produce?
schopenhauer1January 16, 2019 at 13:31#2466300 likes
Add one. But even stating with "one", simple unity, is to take an empirically induced principle. If we do not start with one, what sort of rule for counting could we produce?
Yes, but did Kant himself think that "one simple unity" was empirical? I think to him, numbers themselves and counting were all a priori, though possibly synthetic. Again, that's where I get confused with Kant. He doesn't demarcate enough. His examples are kind of fuzzy and taken as givens of why they are a priori sometimes.
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Metaphysician UndercoverJanuary 16, 2019 at 14:25#2466510 likes
Yes, but did Kant himself think that "one simple unity" was empirical? I think to him, numbers themselves and counting were all a priori, though possibly synthetic.
I agree, I was using that as an example of why Kant's category of a priori is not very good. I think other comments on this thread have illustrated the same thing.
Again, that's where I get confused with Kant. He doesn't demarcate enough. His examples are kind of fuzzy and taken as givens of why they are a priori sometimes.
My opinion is that we must allow that there is such a thing a priori knowledge, but it would probably be impossible to give an example of it, because of the a posteriori basis of language itself. So a priori knowledge is not something which can be exemplified, but we can know from logical demonstration that there must be ( necessarily is) such a thing. That's why examples are always fuzzy and confusing.
Terrapin StationJanuary 16, 2019 at 14:58#2466600 likes
Banno is indeed Banno in every possible world in which I exist. In no world am I a doughnut, a fruit cake or anything other than human. Although in some worlds my name is Tim Wood. I am not Banno in all possible worlds, since one can posit a possible world without me in it.
It's not at all clear to me why that would be the case, though.
And I don't know how we'd convince anyone that it's not conceivable, because we do things like this in films all the time. For example, a witch or genie might turn a person into a dog, into a biscuit--whatever. It's not at all difficult to imagine that the person is now a dog or a biscuit. So how would we argue that in all possible worlds, the person can't be a biscuit?
There might be problems with the metaphysical plausibility of such things, but no moreso than that's a problem with any counterfactual scenario, because in all of them, we have to pretend that things can be different than they are yet still be the "same thing" somehow, which doesn't really make any metaphysical sense (at least to me as a nominalist).
2+1=3 in all possible worlds. If it did not, we would not be talking about 2,3,+, or =.
Water is H?O in all possible worlds. If it were not, we would not be discussing water.
If we can say this of numbers, and water, and even that the atomic number of Gold is 79 and to find something else would simply be to misuse the word "gold" -- why is it that color cannot function in the same way?
You say that it is a secondary characteristic. Perhaps because it just seems plausible that Gold could be some other color, perhaps if our eyes had different cones in them or something along those lines. But it seems to me that another could just insist that you're using the word "Gold" incorrectly if you're referring to something that is not yellow yet has all the other properties of Gold. They could insist that this is not Gold, clearly, because it is not yellow, but should be called Rold.
I mean why not?
Deleted UserJanuary 16, 2019 at 19:16#2467140 likes
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The why......
“.....Our knowledge springs from two main sources in the mind, first of which is the faculty or power of receiving representations; the second is the power of cognizing by means of these representations. Through the first an object is given to us; through the second, it is thought....”
“....We apply the term sensibility to the receptivity of the mind for impressions, we call the faculty of spontaneously producing representations, or the spontaneity of cognition, understanding....”
“....Neither of these faculties has a preference over the other. Without the sensuous faculty no object would be given to us, and without the understanding no object would be thought. Thoughts without content are void; intuitions without conceptions, blind. Hence it is as necessary for the mind to make its conceptions sensuous (that is, to join to them the object in intuition), as to make its intuitions intelligible (that is, to bring them under conceptions). Neither of these faculties can exchange its proper function. Understanding cannot intuit, and the sensuous faculty cannot think. In no other way than from the united operation of both, can knowledge arise....”
“....We therefore distinguish the science of the laws of sensibility, that is, aesthetic, from the science of the laws of the understanding, that is, logic....”
“....logic in its turn may be considered as twofold—namely, as logic of the general use, or of the particular use, of the understanding. The first contains the absolutely necessary laws of thought, without which no use whatsoever of the understanding is possible, and gives laws therefore to the understanding, without regard to the difference of objects on which it may be employed....”
“....general logic has nothing to do with the origin of our cognitions, but contemplates our representations, be they given primitively a priori in ourselves, or be they only of empirical origin, solely according to the laws which the understanding observes in employing them in the process of thought, in relation to each other. Consequently, general logic treats of the form of the understanding only, which can be applied to representations, from whatever source they may have arisen....”
“....All intuitions, as sensuous, depend on affections; conceptions, upon functions. Conceptions, then, are based on the spontaneity of thought, as sensuous intuitions are on the receptivity of impressions. Now, the understanding cannot make any other use of these conceptions than to judge by means of them...”
“....In all judgements wherein the relation of a subject to the predicate is cogitated, this relation is possible in two different ways. Either the predicate B belongs to the subject A, as somewhat which is contained (though covertly) in the conception A; or the predicate B lies completely out of the conception A, although it stands in connection with it. In the first instance, I term the judgement analytical, in the second, synthetical...”
“....The former may be called explicative, the latter augmentative judgements; because the former add in the predicate nothing to the conception of the subject, the latter add to our conceptions of the subject a predicate which was not contained in it, and which no analysis could ever have discovered therein....”
(Insert for clarity: “...analyse the conception, that is, become conscious of the manifold properties which I think in that conception,...”)
“....Judgements of experience, as such, are always synthetical. For it would be absurd to think of grounding an analytical judgement on experience, because in forming such a judgement I need not go out of the sphere of my conceptions, and therefore recourse to the testimony of experience is quite unnecessary....”
And the wherefore.......
“....But as in all the attempts hitherto made to answer the questions which reason is prompted by its very nature to propose to itself, for example, whether the world had a beginning, or has existed from eternity, it has always met with unavoidable contradictions (...), but it must be possible to arrive at certainty in regard to the question whether we know or do not know the things of which metaphysics treats....”
“....For what of analysis, that is, mere dissection of conceptions, is contained in one or other, is not the aim of, but only a preparation for metaphysics proper, which has for its object the extension, by means of synthesis, of our a priori knowledge. And for this purpose, mere analysis is of course useless, because it only shows what is contained in these conceptions, but not how we arrive, a priori, at them; and this it is her duty to show, in order to be able afterwards to determine their valid use in regard to all objects of experience, to all knowledge in general....”
————————————————————————
Logic is the law of thought, understanding is the means of thought, therefore logic rules understanding. Understanding manifests in judgements, judgements are of two kinds, one for objects, one for thought of objects. Therefore the laws of thought in the form of logic rules judgements. One form of logic, in which thought is transposed to intelligible communication, is the proposition. A logical proposition requires a subject and a predicate, and the relationship between them determines the kind and the source of the judgement being communicated.
Analytic propositions dissect conceptions in order to determine whether the conception in the predicate belongs to the conception in the subject by the logical law of identity, re: all dogs are canines.
Propositions where the conception in the predicate does not belong to the conception in the subject by identity, but must be connected to it by synthesis from an intuition of experience, earn the title synthetic propositions, re: all dogs have four legs.
Analytic judgements a priori occur when the relations in the conceptions in the predicate belong to the conceptions in the subject from the logical principles of universality and necessity, re: all bodies are in space.
Synthetic a priori judgements, synthetic in the method of their subject/predicate relation and a priori from the nature of the conceptions in them, are shown by any pure mathematical expression.
An analytic a posteriori proposition may be merely a tautology, hence useless, re: my hat is a hat.
Synthetic a posteriori propositions are redundancy in kind, for synthetic propositions are already completely empirical judgements, the concept in the predicate supplements the concept in the subject, even if not contained in it.
The proof of the possibility and validity of synthetic a priori propositions is given in mathematics and the principles for them are given to all natural sciences. Their true value, however, lays in their employment by reason in questions of metaphysics, which is in effect, the examination of grounds for possible truth.
Thus is the division into and function of differences in the approach to the attainment of knowledge, and the justification for synthetic a priori judgements being by far the most important.
Reply to tim wood Posit any world you like. This might have been where @frank was thinking with his talk of imagination. Whatever you want.
Is it possible?
PWS gives us a way of at least making sense of that question.
Posit a world that contains a square circle. Is it possible? No, because it leads to contradiction. Posit a world in which water is He?O. Is that possible?, no, because what we call water is H?O. SO a world in which what was called "water" was found to have the chemical structure He?O is a world in which "water" refers to something other than water.
A world in which gold is purple is just a world in which gold is not yellow. A world in which gold has the atomic number 63 is a world in which "gold" refers to something else.
Now while PWS was somewhat controversial for a wile, it has settled in as a neat way of dealing with counterfactuals, possibilities and necessities.
I don't. If non-contradiction applies in our world, why should it apply in another "possible" world. After all, we only need to "posit" them, not account for them.
Well, if contradictions are allowed, the word "possible" loses meaning. Possibility and impossibility imply constraints to worlds. If there are none then we might as well as get rid of the words "possible" and "impossible" as then everything would be possible.
Reply to Banno You were saying at one point that logic is a set of rules for the way we talk. I think logic is about the limits of imagination, and we discover those limits.
Quine pointed out that even if the way we talk is entirely conventional, it doesn't appear that the ability to apply logic to new situations can be learned second hand.
Deleted UserJanuary 17, 2019 at 22:56#2471770 likes
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Deleted UserJanuary 17, 2019 at 22:58#2471790 likes
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"all possible worlds" is a meaningful idea are content to have gold not be gold, but at the same time be gold, in various "possible worlds" (I do not know how that works...).
It doesn't because it is wrong. Gold is gold in every possible word in which it exists. Posit a world in which gold is purple, and get a possible world in which gold exists. Posit a world in which gold has the atomic number 1, and you will have to decide if in that world "gold" means hydrogen, or in which the atomic number system admits to fractions...
But it seems to me that another could just insist that you're using the word "Gold" incorrectly if you're referring to something that is not yellow yet has all the other properties of Gold. They could insist that this is not Gold, clearly, because it is not yellow, but should be called Rold.
Colloquially, isn't possible just self-consistent and either of non/hypothetical?
Self-consistent is at least the usual identity (ontological, propositional) and non-contradiction (propositional).
I guess that implicitly assumes our world is self-consistent, but that seems required for propositions to be meaningful anyway.
I don't mean to invoke humpty dumpty, it's just that to myself it seems that the invocation of atomic number is just as arbitrary as color in designating some aspect as a necessary feature.
For myself it does strike me as odd to say that the color of gold is known a priori. There's a sense in which I can make sense of it -- like, now that I think of Gold as golden it seems that I can think of gold in a purely conceptual sense and say that its color is now part of its concept. But, then, it seems to me that gold could have been other than golden.
However, from my perspective, it seems to me that gold could have been other than having 79 protons in its nucleus too. This was something we discovered a posteriori, and is not a necessary feature of gold -- that is, there is a possible world in which gold has more or less protons than 79. Your thought experiment would apply equally well here too -- imagine that we had some substance who retained the same ductility, the same color, the same melting point and freezing point, the same ratio for certain alloys, and in all other ways was the same as the gold we know in our actual world -- save for the number of protons we find in its nucleus.
Wouldn't we call this gold? Or would we call this something else?
To me I think it's similar to your color example. initially I wouldn't call something gold that happened to be red, but I'd say, perhaps, that it is red gold. And if we found some substance with a different number of protons in it then I'd say it is Gold-78 or some such, if I were being precise.
Sort of like how we came to know there are isotopes of various elements with differeing number of neutrons. They were similar in structure, but different in certain respects (and had different properties too because of that).
Comments (107)
The question for me is, if ? is a priory, is ? also necessary?
Kripke takes Kant as saying this.
It sets out how possible world semantics (PWS) solves the issue of substitution for modal logic.
I'm not a logician. I'm Happy to be corrected by those with a better understanding. But as I understand it, in PWS the existential and universal quantifiers are understood within each possible world, while the necessity and possibility quantifiers are understood across all possible worlds.
So within each possible world we can have different assignments of predicates to individuals.
We have lots of different possible worlds each with different bunches of the same individuals, being assigned different bunches of predicates.
If an individual or group of individuals has the same predicate in all possible worlds, it necessarily has that predicate: Bachelors are unmarried in all possible worlds.
If an individual or group of individuals does not have a predicate in any possible world, it is not possible.
If an individual or group sometimes has a given property, sometimes not, then it is a possible property.
This is correct.
Quoting Banno
That's actually the definition of contingency. Possibility is just defined as truth in at least one world. Necessary truths, for example, are still possible truths because they fit that condition. Contingency means true in some worlds but false in others.
Quoting Banno
This has always been odd for me. It seems like one could have a married bachelor. What makes one married is to hold a certain legal status, yes? Well consider a state of affairs where there's a contradiction in the local laws. Law A says "Yada yada Those holding a marriage certificate are married" and Law J says "Etc etc Gay people cannot be married". Now some gay person managed to get married (certificate and all), and there is no judicial precedent in how judge which law overrules the other. On the usual assumption that law decides what is true in these cases (because that's how we know who is considered married), one would seem to have a married bachelor.
The law of contradiction holds in PWS. In no world can there be a contradiction. But there can be differences between worlds; so while my cat is all black in this world, in another possible world it might be all white; yet in no possible world is my cat both all black and all white.
Now Kant says that it is part of the concept of gold that it be a yellow metal, and hence that being a yellow metal is a priori.
And yet it is eminently possible that gold might be a different colour. So in some possible world there might be red gold.
So being yellow is not a necessary characteristic of gold.
SO it seems that either Kant was in error about gold, or that a priori and necessity are different things.
Fair enough.
That just looks like an invalid marriage to me. I don't see a philosophical issue here, just a legal one.
All those types of statements really tell us is how an individual has formulated their concepts. It's telling us either what they require to call some x (some particular) an F (some type term), or alternately it's announcing terms they use as synonyms.
The only necessity invoked there is the stringent stipulation of the individual in question.
It explains what's really going on with those statements contra Kant's misconceptions, and it explains the only sense in which we could say that they're "necessary."
So "Bachelors are unmarried men", when interpreted as expressing a necessary truth, is to declare a policy allowing the substitution of the former as a synonym for the latter without exception. Hence the image of it holding in "all possible worlds".
However, when interpreted as expressing a publicly verifiable proposition "Bachelors are unmarried men" is both contingent and under-determined.
I don't see that you can escape modality quite so easily. Suppose a mine starts digging out red gold. Same mailability, same atomic mass, same melting point. Would you say it is red gold, or not gold?
If being yellow is a part of the very concept of gold, you must say it is not gold.
The best way to understand them is by seeing how they are used in possible world semantics.
It's simply a way to parse any modal statement. Possible worlds are specified by our speculations. What if Tim Wood had been Jim wood? That can be parsed as: In some possible world, Tim wood is known as Jim Wood.
In some possible world, gold might be red. In no possible world could gold have a different atomic mass, because no longer would it be gold - it would be something else.
2+1=3 in all possible worlds. If it did not, we would not be talking about 2,3,+, or =.
Water is H?O in all possible worlds. If it were not, we would not be discussing water.
no - hence my specification of atomic mass.
Perhaps I see see beyond your deeper point...
let's debar the Humpty Dumpty world where words mean whatever we choose.
Then if we find a red substance with otherwise the same properties as gold, we have a choice: is it gold, or is it not-gold? what attributes are essential to gold? Kant, and perhaps you, say colour is; i say it isn't.
TPF?
Quoting tim wood
That's not an issue: I want my cornflakes not as they are in the pack, but slightly soggy from cold milk. I want my I want my beard longer. Such things do not make these not my cornflakes or this not my beard.
The limits of imagination are the limits of the knowable. So for all practical purposes, the limits of imagination are the limits of what is. In cases where we can't imagine X, it seems we know a priori that X doesn't and can't exist. Necessarily, there is no X.
With a posteriori knowledge, we are being informed about what's out there. As long as we can imagine things being other than they are, there are only contingently true statements related to a posteriori knowledge.
tim wood, queston: What do you suppose a statement is about gold that is synthetic a priori?
One can imagine all sorts of things that are impossible.
Such as?
I hate to smuggle in words where they were not explicitly stated but to get your point across to those who don't get Kripke and his idea of natural kinds, you should just mention that he is arguing for what is "essential" to the natural kind before it is no longer "that" particular natural kind. That might solve some confusion on what Kripke is actually doing.
Edit: Oh and he is doing it through the idea of how "names" designate the referent in all possible worlds. I realize you might want his methodology too since I know you are keen on making that distinction that he is mainly doing a grammatical project rather than metaphysics.
I agree, but we need to keep one eye on the difference between essence for Kant and for Kripke.
As I understand Kant, the essential predicates are those that are contained in the subject.
For Kripke, the essential predicates are those that are true of the subject in every possible world.
In both cases we might argue Quoting schopenhauer1
The unfortunate example provided by Kant, and critiqued by Kripke, is that gold is a yellow metal. Now Kripke and Kant would presumably agree that old is a metal - that something purported to be gold but which is not a metal, is not gold. Kant seems to think that this is also true for being yellow; that something purported to be gold, but which is not yellow, would not be gold. Kripke disagrees; and given that colour is a secondary characteristic, Kripke's view seems to me to be the better.
On the way to explaining bundle theory, Hume asks us to imagine an object that has no properties. He finds that he is not able to imagine it. He obviously has no problem saying the words, though.
Do you need more of a dissection than that?
This is where we came in.
Quoting frank
Hm. I cannot imagine the square root of -1. But I can bring the words together and then manipulate them to produce say a curve or an image of the Mandelbrot set.
If you see no difference between imagining and "bringing words together," our experiences are too different to continue on.
You didnt avoid the can't/Kant joke because you pointed out that you were avoiding it.
Since your hemisphere is hogging the sunshine, I'm out. :yawn:
I would agree with Kripke's assessment. But, I think Kant just missapplied gold when judging with this own theory. Gold being yellow is a posteriori, as Kripke agrees, and synthetic, not analytic. Unlike bachelor's being unamarried males, there is nothing in gold that automatically makes its definition of being yellow logically necessary- it could have been a different color.
The more interesting question is "What would Kant think of gold's atomic number of 79?". This to me seems like a synthetic a priori judgement. That is to say, you need to experience it in the world to know it (experiment), but it is universally and necessarily seen as true once it is discovered. I could be misapplying his terms myself though, that is where others can try to correct me.
The difference between Kant's approach and Kripke's approach, which @csalisbury was trying to bring up is one of areas of interest (which may be incommensurable). Kant is looking at things from an epistemological point of view and Kripke from a grammatical point of view. From Kant's epistemological point of view, he considers the very universal conditions for even observing the world in the first place. Thus, the reason gold is 79 in all possible worlds, is because of the necessity set up by our brains (time/space,categories of understanding). There is no way the substance we call gold could not be 79.
Kripke, on the other hand, isn't interested in necessities of human understanding like Kant is. He is purely focused on how we use names. Names are inherently arbitrary as what the actual utterance is. What isn't arbitrary is how the name then becomes "attached" (or rigidly designated), in his view. Thus, though we don't need any universal laws of human understanding to have a substance be named "gold", once that substance is named gold, and used over and over from that original instance, it becomes fixed in all possible worlds. These two starting points for understanding the world are very different. That is to say, Kant wasn't worried about how grammar works with names- he was worried about how things could be universally true despite having been derived at empirically. He was worried that Hume was right in his "Problem of Induction".. By Kant saying that universal necessities are actually transcendental (in the very fabric of our understanding of our world), that universal truths can be derived from empirical evidence.
However, following Kripke's own line of reasoning perhaps, we can say that, IF Kant was to have used a grammatical method (and applying it to modal logic), he would have also included necessary a posteriori statements in his schema. He would notice that you can have contingent "words" apply necessarily to a person or a kind.
However, we may still state that these are incommensurable approaches as Kant was looking at propositions and Kripke was looking at grammar and these two approaches are mutually exclusive.
Well, we'd need to check if you even understood my post, I suppose. How would you say what I said in your own words?
So, when we're talking about this from the a priori context, the answer is "It depends on how you've formulated your concepts."
Let's do a thought experiment and start by saying there are things we can't imagine (even in principle) and see where it leads.
I suppose it could be that much of what is entailed by that initial premise is beyond my imagining. Maybe the whole conclusion is. What's the point in trying to think it through when the truth is likely as not beyond my grasp?
And when the dust settles, I find that this skepticism is a deadend. The actual world is bounded by my imagination (for all practical purposes). What appears otherwise just hasn't been properly tackled yet.
If you look back, you'll see I said "for all practical purposes" the first time.
How could your cat not be black in another possible world? I get how you might have adopted a white cat in this world had you so chosen, but I don't understand how you maintain your identity across worlds where you can have cats in each world of varying colors. Quoting Banno
This strikes me as a slippery slope into essentialism, where you're going to have to now identify what is a necessary characteristic of gold, if not its color. I don't follow why its color cannot be part of its arbitrary definition if we so choose. Does gold cease being gold under a red lamp? Sure, if we say so.
In response to @MindForged you stated Quoting Banno
It would seem he was getting at what I was saying above. Things are whatever we say they are.
At any rate, doesn't your acceptance of the the logical necessity of analytic truths jettison Quine's well known objections?. https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction#Quine's_criticisms.
“....(Is there) a knowledge altogether independent of experience, and even of all sensuous impressions? Knowledge of this kind is called a priori....”
“...But the expression, "a priori," is not as yet definite enough...”
“...By the term "knowledge a priori," therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience. Opposed to this is empirical knowledge, or that which is possible only a posteriori, that is, through experience. Knowledge a priori is either pure or impure. Pure knowledge a priori is that with which no empirical element is mixed up....”
“...The Human Intellect, even in an Unphilosophical State, is in Possession of Certain Cognitions "a priori"....”
A.) “...if we have a (judgement) which contains the idea of necessity in its very conception, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely priori....”
B.) “...an empirical judgement never exhibits strict and absolute, but only assumed and comparative universality (by induction); therefore, the most we can say is—so far as we have hitherto observed, there is no exception to this or that rule....”
C.) “...If, on the other hand, a cognition carries with it strict and absolute universality, that is, admits of no possible exception, it is not derived from experience, but is valid absolutely a priori....”
“....When strict universality characterizes a judgement, it necessarily indicates another peculiar source of knowledge, namely, a faculty of cognition a priori. Necessity and strict universality, therefore, are infallible tests for distinguishing pure (that is, a priori) from empirical knowledge, and are inseparably connected with each other....”
—————————————-
It doesn’t matter the objects in general we know about when considering knowledge itself, because such things are already given, or at least possibly given, by perception as appearances, but rather the theoretical, or indeed speculative, methodology under which human knowledge is possible. The old...knowledge *of* vs knowledge *that* dichotomy, so to speak, insofar as the judgements “gold is a yellow metal” and “water is a clear fluid” are understood empirically as immediate yet incomplete knowledge *of* gold and *of* water respectively. Reason wants it known under what conditions are we authorized to signify or designate gold and water.....and every other damn thing in the world....the way we do, such that knowledge *that* gold is a yellow metal and knowledge *that* water is a clear fluid, are derived from valid, that is, non-contradictory, cognitions.
Reason doesn’t want to know if any other immediate empirical intuition can be given to gold, but only that the intuition of, e.g., “yellow”, “metal”, actually does belong to it, not because perception, from which the empirical appearance comes, says so, but because understanding, from which such necessary justification alone comes, says so. But understanding does not intuit, it has no say in assigning “yellow” to “gold”, that having already been accomplished under the auspices of the faculty of intuition, which gives appearance to phenomena by means of imagination, and which then becomes rationally authorized as representation.
But we already know from experience what the intuitions of yellow and metal may represent, other than gold. We also know from experience the intuitions of clear and fluid may represent other than water. Therefore, we can say that the assignment of certain predicates to gold is an empirical cognition when gold is directly perceived, and, more importantly, we can thereafter cognize a priori, that gold is a yellow metal when no appearance of gold is given at all, because such appearance has already been represented and hence judged as non-contradictory. This is, of course, impure a priori knowledge, having it base in experience, no matter how remote. It is perhaps more easily considered as indirect, as opposed to direct, knowledge, although this qualification is not suggested as intrinsic to the transcendental philosophy of continental Enlightenment era epistemological theory.
Now of pure a priori knowledge, it must be admitted that whatever conditions, and therefore the principles which legislate those conditions, already explicit in impure and empirical knowledge cannot apply, for such is entirely circular and of no use whatsoever. That condition and principle being the logical law of non-contradiction, it follows that whatever legislation reason requires for pure a priori knowledge as its ends must have for its means some other fundamental ground. While it may be easy to dismiss the conditions given from experience, which the very idea of pure a priori requires, it is very far from easy to dismiss the cognitive operational procedure of human rationality. Therefore, a line must be drawn as to where and how we think objects, without there being objects to think about. If the line be drawn at the point where empirical influence stops, but the remainder of the cognitive system continues, such should be sufficient ground to establish the possibility of pure a priori knowledge. From the quotes above, they being taken in their respective order of print, it is clear knowledge works backwards, from itself, through cognition, through judgement, through understanding, through representation, through intuition. But all intuition is given from perception, which is always empirical, thus the line must be drawn before intuition when proceeding backwards, or that of which is a consequence of it. But if intuition is dismissed as a faculty for representation given to understanding, there must be some other source from which understanding may draw, in order to make its judgement, from which a cognition may follow and from that knowledge may follow.
This source resides in the understanding itself, they are the pure conceptions of the understanding, called noumena, and are, in effect, nothing more than the names of the properties or attributes a merely possible object, or, which is the same thing, an object as it will be represented upon the experience of it, must be given before any judgement whatsoever is possible of it. Because there are only these two sources of possible relations for the understanding to employ in its judgements, that is, intuitions and conceptions, and because intuitions, which have non-contradiction as their principle, have been dismissed in the determinations of pure a priori knowledge, the principle of necessity for the existence and the employment of the conceptions of the understanding, and furthermore the absolute universality of their application, serves as sufficient ground of pure a priori knowledge.
(Universality herein means only insofar as reason is investigating the realm of possibility; the pure conceptions of the understanding have no standing in what is called “transcendent”)
Does it matter if the pure conceptions of the understanding really exist? Does it matter they were incorporated post hoc ergo propter hoc as a means to inhibit infinite regress? No, not really, because we do not doubt we are in fact in possession of pure a priori knowledge, which makes explicit we must have pure a priori cognitions, which in its turn makes explicit we must have made pure a priori judgements, which in IT’S turn makes explicit we must have something purely a priori in our faculty of understanding. This is why it is said we do not and cannot know noumena as real objects of conception, even though we are permitted to name them because we think them as necessary, and if that is so, they are so much confused with the “thing-in-itself”, which we also know absolutely nothing about. Noumena, along with imagination and schemata, should be considered as a facilitators in the rational procedure of faculties, but not in themselves cognitive faculties.
All that remains, in the consideration of empirical, a priori and pure a priori understanding, judgement, cognition and knowledge, is whether or not the claim for the reality of pure a priori knowledge has something applicable to it. What can we know a priori? Simply put, anything we know that has no empirical content whatsoever is known a priori. Upon reduction of anything empirical or possibly empirical out from thought in general, all that remains is nothing but thought itself, the thought of something, and is purely a priori; that which exists as nothing more than a thought of something, is a proposition where the subject and predicate are connected by the pure conceptions of the understanding, whereby the predicate follows universally and necessarily from the subject. “Plurality is succession in time”, “No sum is less than its constituents”, “No cognition of three lines will ever allow cognition of a triangle” serve as examples of pure a priori knowledge. It should be noted, that because pure a priori knowledge has no empirical content, no truth value can be assigned to any pure a priori proposition, such truth coming from experience alone. These propositions serve only as the form this kind of knowledge must have.
These are the conditions for deriving the grounds of analytic and synthetic propositions, and the knowledge which follows from each of those kinds, and these from a particular epistemological theory. There is no reason to suppose this theory is better or worse than any other, even if it is logically consistent.
Only, I'm going to follow Davidson and say that incommensurability is not an option. If two groups of ideas don't meet well, then one or both of them are wrong.
SO while I take Kripke as approaching forma grammatical point of view, it's apparent that the grammar has epistemological implications for Kant. The necessities of human understanding are present in the way we use words.
SO here again is my question: Can we reconcile Kant's a priori with Kripke's necessity?
Was it just a mistake to include "yellow" in the essence of gold? Perhaps if we remove that, we have some agreement between Kripke and Kant. .
Give me an example...:razz:
Whereof we cannot speak, and so on. How does this part of the discussion relate back to Kant and Kripke?
Cool. Thank you.
Quoting Banno
I think it was, especially keeping in mind the definition of analyticity and with Kripke's further critique using modal logic.
However what would this approach look like if there was agreement when one is using propositions and the other is using purely grammar- when one is looking how we understand the world using propositions, and one is using how we understand names using modal logic?
So unless you have a very specific criticism of Kripke's attitude to transworld identity, I'm not interested in that approach.
The difference is profound, while subtle.
SO one says that gold has an atomic mass of 79, and hence if some sample has another atomic mass, it is not gold.
The other says that gold has an atomic mass of 79, and hence if some sample has another atomic mass, we ought not call it "gold".
:wink:
Some things that we know a priori are necessarily true, like the LONC. Kripke just adds that you also have a priori knowledge about your own choices.
No I don't. I certainly don't think that yellow is necessarily wrapped up in the meaning of gold, in the same way that bachelors is literally the definition of unmarried males. Yellow seems to me a contingent property of gold- it doesn't have to be a primary property. If it wasn't yellow, it wouldn't make it any less "gold". So that statement synthetic a posteriori.
However, if we took away the atomic number of 79, it certainly wouldn't be gold anymore. However, even according to Kant's own idea of judgements, this proposition wouldn't be analytic. It certainly is something I had to find out in the world (synthetic), but holds universally and necessarily true. However, you can correct me where you think I misapply Kant.
But of course we wouldn't want to just be adding auxiliary hypotheses in order to protect our pet theory.
Nah. Watched the Demonstration at the WA mint. They melt a gold bar and then set it. It's not yellow. It's - gold.
I guess the point is- what makes gold essentially gold? Is it its yellowness? But, I see where you are coming from using Kant's own theory of categories. Before we can define gold, we must figure out what is legitimate in a definition. Kripke and @Banno are claiming that modal logic seems to indicate that only certain essential properties can be considered gold, otherwise it is not designating gold, really.
I can see where the clash comes in though. As I mentioned before, Kant is interested in how we understand the world through our transcendental lens. Thus other possible worlds logic would be conditioned by our very own epistemology. His work did not seem to go beyond the scope of what is possible outside of our own psychological understanding in this world.
Really, I don't remember Kant stressing that it purely depended on how individuals formulated their concepts, so that an a priori claim that holds for one person might not hold for another. Wouldn't that basically negate the idea of there being any necessary a priori claims in a broader context (rather than, as I noted, only possibly amounting to someone being stringent or stubborn in their concept-usage over time?)
Kripke was concerned with names. That is the main point we must not forget with him. His question is, "How do proper names and natural kinds designate their referent?". Statements like, "Gold is a yellow metal" were not good enough for him. To him, these "descriptivist models" of names and natural kinds were too weak to really designate "that" kind of natural kind. For example, "The definition of gold is a metallic yellow substance" doesn't hold up. In another possible world, metallic, yellow, and substance might not be how to describe gold, but gold would still somehow retain its goldness in those worlds. It is considering what properties hold up in these worlds, that he considers the name gold to actually designate "that" kind of natural kind. Thus, since it is a name that is given to an object after experiencing an object and sensing it in the world, it is a posteriori. However, unlike most other a posteriori statements that are contingent, the NAME gold is always and necessarily attached (rigidly designated) to some essential property in all possible worlds (something like let's say the atomic number 79). If it doesn't have this essential property, the name "gold" does not rigidly designate that object. Thus he says that Kant is missing a category for necessary a posteriori judgements, like the ones (he thinks) are needed for rigidly designating proper names and natural kinds.
As far as Kant's synthetic a priori- I think I take back my statement that atomic number 79 being essential to gold is a synthetic a priori statement. In Kant's view, this should simply be synthetic a posteriori. It is gained through experience which makes it a posteriori and it is adding information that is not contained in the subject, so it is synthetic.
Synthetic a priori would be things like cause and effect and mathematics. You don't need to experience things in the world for them be proven, but they are also not contained in the subject by definition.
So on your account, some things can be a posteriori and yet necessary - agreeing with Kripke. Gold having an atomic number of 79 being one of these.
And further, gold having atomic number 79 is synthetic; it brings together two distinct concepts, atomic number and gold, or if you prefer the phenomenological experience of gold.
So we have a necessary synthetic statement: gold has atomic number 79.
Or do we take the discovery of gold to be analytic, post hoc? The very idea of gold contains within it the idea of atomic number 79; to be gold is to have atomic number 79; only we needed to do some experiencing in order to learn this...
Or does this whole structure of a priori/a posteriori and synthetic/analytic fall apart on analysis?
AND is being a priory the same as being necessary?
I think these are great questions and pretty much sums up this whole debate.
In order for any of this to work we have to have some basic terms that we all agree on (or at least think Kant agreed on). Let me start with the last question:
Quoting Banno
At first, I thought just that- Kant was saying a priori was just a synonym for universal and/or necessary. Now, I'm thinking it is a bit different. I think Kant's thoughts on a priori literally has to do with the term "prior to". That is to say, if terms are derived prior to (or outside of) experiential observations (with the senses usually), it is an a priori-type statement. Thus, geometric rules like "All triangles have corners that add up to 180 degrees" are not derived from experiential observations of the world (this is at least Kant's interpretation of what we are doing). One doesn't need to observe any particular thing in the world, just understand the concepts using our intuition on how triangles, corners, and degrees work when we make judgements on them. Synthetic means that the proposition is additive and not simply a tautology. Thus, 180 degrees, the concept, is not inherent in a triangle per se, but a conclusion only made through a priori investigation. Thus the sum of the degrees of a triangle is a synthetic a priori judgement.
Quoting Banno
Yes, if I was following Kripke's reasoning, there indeed does seem to be judgments that are made from observing the world, and as a byproduct of how we use language, create necessary a posteriori truth-statements.
Quoting Banno
Yes, I can agree with this.
Quoting Banno
Technically, this would fall under necessary (if defined as being true in all possible worlds), and it is something that is additive, not just tautological in the subject.
Quoting Banno
This is I guess what I believe @tim wood (and maybe Kant?) believed. "Gold is the metal that has atomic number 79" would indeed be a tautology so, indeed this would be an analytical statement.
Quoting Banno
And now we come to the real question at hand. It needs a much crisper demarcation between what counts as analytic and what does not, or this indeed does become arbitrary to the person using the concept. It breaks down unless there is absolute certainty on what fits under what category. If it breaks down, it becomes arbitrary as a way to distinguish truth statements.
Everybody seems to know what a possible world is - any world without a contradiction.
Does logical necessity imply existential necessity?
What do you mean by ''existential necessity''?
Banno is indeed Banno in every possible world in which I exist. In no world am I a doughnut, a fruit cake or anything other than human. Although in some worlds my name is Tim Wood. I am not Banno in all possible worlds, since one can posit a possible world without me in it.
It seems that you are happy to accept that science has moved on since Kant. So has logic.
Yes, I didn't mean that Kant didn't think a priori to be necessary. I just meant that being necessary isn't a fully sufficient definition of a priori.
I agree, to discuss things in terms of necessity, is to use different categories than Kant uses.
There are two fundamentally different types of necessity, that which is prior to logical process, as needed for it, and that which is posterior to logical process, as that which is made necessary by logic. But this is not equivalent to Kant's a priori/a posteriori division.
We must be careful not to equivocate between these two senses of necessity, and I think Kant's categories may create ambiguity. His, are probably not the best that could be drawn..
Yes, I think this exercise is kind of proving that out. The fuzziness between what counts as analytic or synthetic in the definition of gold, for example makes that seem the case.
The problem I see is that the principles by which we proceed into logical process, the propositions as premises, which are necessary for logic to proceed, are usually principles which are derived from experience. So if there is such a thing as "a priori" in Kant's sense, some sort of principles which are not derived from experience (and if I remember correctly, he provides a convincing argument for the reality of this), then these must be something like the rules of the logical processes themselves. It's questionable whether a priori principles could even be accurately put into words, because the use of words is learned from experience. For example, what would be the rule for counting? Add one. But even stating with "one", simple unity, is to take an empirically induced principle. If we do not start with one, what sort of rule for counting could we produce?
Yes, but did Kant himself think that "one simple unity" was empirical? I think to him, numbers themselves and counting were all a priori, though possibly synthetic. Again, that's where I get confused with Kant. He doesn't demarcate enough. His examples are kind of fuzzy and taken as givens of why they are a priori sometimes.
I agree, I was using that as an example of why Kant's category of a priori is not very good. I think other comments on this thread have illustrated the same thing.
Quoting schopenhauer1
My opinion is that we must allow that there is such a thing a priori knowledge, but it would probably be impossible to give an example of it, because of the a posteriori basis of language itself. So a priori knowledge is not something which can be exemplified, but we can know from logical demonstration that there must be ( necessarily is) such a thing. That's why examples are always fuzzy and confusing.
It's not at all clear to me why that would be the case, though.
And I don't know how we'd convince anyone that it's not conceivable, because we do things like this in films all the time. For example, a witch or genie might turn a person into a dog, into a biscuit--whatever. It's not at all difficult to imagine that the person is now a dog or a biscuit. So how would we argue that in all possible worlds, the person can't be a biscuit?
There might be problems with the metaphysical plausibility of such things, but no moreso than that's a problem with any counterfactual scenario, because in all of them, we have to pretend that things can be different than they are yet still be the "same thing" somehow, which doesn't really make any metaphysical sense (at least to me as a nominalist).
If we can say this of numbers, and water, and even that the atomic number of Gold is 79 and to find something else would simply be to misuse the word "gold" -- why is it that color cannot function in the same way?
You say that it is a secondary characteristic. Perhaps because it just seems plausible that Gold could be some other color, perhaps if our eyes had different cones in them or something along those lines. But it seems to me that another could just insist that you're using the word "Gold" incorrectly if you're referring to something that is not yellow yet has all the other properties of Gold. They could insist that this is not Gold, clearly, because it is not yellow, but should be called Rold.
I mean why not?
“.....Our knowledge springs from two main sources in the mind, first of which is the faculty or power of receiving representations; the second is the power of cognizing by means of these representations. Through the first an object is given to us; through the second, it is thought....”
“....We apply the term sensibility to the receptivity of the mind for impressions, we call the faculty of spontaneously producing representations, or the spontaneity of cognition, understanding....”
“....Neither of these faculties has a preference over the other. Without the sensuous faculty no object would be given to us, and without the understanding no object would be thought. Thoughts without content are void; intuitions without conceptions, blind. Hence it is as necessary for the mind to make its conceptions sensuous (that is, to join to them the object in intuition), as to make its intuitions intelligible (that is, to bring them under conceptions). Neither of these faculties can exchange its proper function. Understanding cannot intuit, and the sensuous faculty cannot think. In no other way than from the united operation of both, can knowledge arise....”
“....We therefore distinguish the science of the laws of sensibility, that is, aesthetic, from the science of the laws of the understanding, that is, logic....”
“....logic in its turn may be considered as twofold—namely, as logic of the general use, or of the particular use, of the understanding. The first contains the absolutely necessary laws of thought, without which no use whatsoever of the understanding is possible, and gives laws therefore to the understanding, without regard to the difference of objects on which it may be employed....”
“....general logic has nothing to do with the origin of our cognitions, but contemplates our representations, be they given primitively a priori in ourselves, or be they only of empirical origin, solely according to the laws which the understanding observes in employing them in the process of thought, in relation to each other. Consequently, general logic treats of the form of the understanding only, which can be applied to representations, from whatever source they may have arisen....”
“....All intuitions, as sensuous, depend on affections; conceptions, upon functions. Conceptions, then, are based on the spontaneity of thought, as sensuous intuitions are on the receptivity of impressions. Now, the understanding cannot make any other use of these conceptions than to judge by means of them...”
“....In all judgements wherein the relation of a subject to the predicate is cogitated, this relation is possible in two different ways. Either the predicate B belongs to the subject A, as somewhat which is contained (though covertly) in the conception A; or the predicate B lies completely out of the conception A, although it stands in connection with it. In the first instance, I term the judgement analytical, in the second, synthetical...”
“....The former may be called explicative, the latter augmentative judgements; because the former add in the predicate nothing to the conception of the subject, the latter add to our conceptions of the subject a predicate which was not contained in it, and which no analysis could ever have discovered therein....”
(Insert for clarity: “...analyse the conception, that is, become conscious of the manifold properties which I think in that conception,...”)
“....Judgements of experience, as such, are always synthetical. For it would be absurd to think of grounding an analytical judgement on experience, because in forming such a judgement I need not go out of the sphere of my conceptions, and therefore recourse to the testimony of experience is quite unnecessary....”
And the wherefore.......
“....But as in all the attempts hitherto made to answer the questions which reason is prompted by its very nature to propose to itself, for example, whether the world had a beginning, or has existed from eternity, it has always met with unavoidable contradictions (...), but it must be possible to arrive at certainty in regard to the question whether we know or do not know the things of which metaphysics treats....”
“....For what of analysis, that is, mere dissection of conceptions, is contained in one or other, is not the aim of, but only a preparation for metaphysics proper, which has for its object the extension, by means of synthesis, of our a priori knowledge. And for this purpose, mere analysis is of course useless, because it only shows what is contained in these conceptions, but not how we arrive, a priori, at them; and this it is her duty to show, in order to be able afterwards to determine their valid use in regard to all objects of experience, to all knowledge in general....”
————————————————————————
Logic is the law of thought, understanding is the means of thought, therefore logic rules understanding. Understanding manifests in judgements, judgements are of two kinds, one for objects, one for thought of objects. Therefore the laws of thought in the form of logic rules judgements. One form of logic, in which thought is transposed to intelligible communication, is the proposition. A logical proposition requires a subject and a predicate, and the relationship between them determines the kind and the source of the judgement being communicated.
Analytic propositions dissect conceptions in order to determine whether the conception in the predicate belongs to the conception in the subject by the logical law of identity, re: all dogs are canines.
Propositions where the conception in the predicate does not belong to the conception in the subject by identity, but must be connected to it by synthesis from an intuition of experience, earn the title synthetic propositions, re: all dogs have four legs.
Analytic judgements a priori occur when the relations in the conceptions in the predicate belong to the conceptions in the subject from the logical principles of universality and necessity, re: all bodies are in space.
Synthetic a priori judgements, synthetic in the method of their subject/predicate relation and a priori from the nature of the conceptions in them, are shown by any pure mathematical expression.
An analytic a posteriori proposition may be merely a tautology, hence useless, re: my hat is a hat.
Synthetic a posteriori propositions are redundancy in kind, for synthetic propositions are already completely empirical judgements, the concept in the predicate supplements the concept in the subject, even if not contained in it.
The proof of the possibility and validity of synthetic a priori propositions is given in mathematics and the principles for them are given to all natural sciences. Their true value, however, lays in their employment by reason in questions of metaphysics, which is in effect, the examination of grounds for possible truth.
Thus is the division into and function of differences in the approach to the attainment of knowledge, and the justification for synthetic a priori judgements being by far the most important.
Theoretically.
Is it possible?
PWS gives us a way of at least making sense of that question.
Posit a world that contains a square circle. Is it possible? No, because it leads to contradiction. Posit a world in which water is He?O. Is that possible?, no, because what we call water is H?O. SO a world in which what was called "water" was found to have the chemical structure He?O is a world in which "water" refers to something other than water.
A world in which gold is purple is just a world in which gold is not yellow. A world in which gold has the atomic number 63 is a world in which "gold" refers to something else.
Now while PWS was somewhat controversial for a wile, it has settled in as a neat way of dealing with counterfactuals, possibilities and necessities.
Well, if contradictions are allowed, the word "possible" loses meaning. Possibility and impossibility imply constraints to worlds. If there are none then we might as well as get rid of the words "possible" and "impossible" as then everything would be possible.
Quine pointed out that even if the way we talk is entirely conventional, it doesn't appear that the ability to apply logic to new situations can be learned second hand.
Quoting tim wood
It doesn't because it is wrong. Gold is gold in every possible word in which it exists. Posit a world in which gold is purple, and get a possible world in which gold exists. Posit a world in which gold has the atomic number 1, and you will have to decide if in that world "gold" means hydrogen, or in which the atomic number system admits to fractions...
Quoting tim woodNo; no possible world may contain a contradiction.
Quoting tim wood
Far from it. The whole point of the exercise is to allow for different truths in different worlds.
Of course they could. Humpy Dumpty beckons.
But what about you, Moli? What would you say?
For example, physical theories are only possible truths, they aren't necessary to hold in every world there is.
Self-consistent is at least the usual identity (ontological, propositional) and non-contradiction (propositional).
I guess that implicitly assumes our world is self-consistent, but that seems required for propositions to be meaningful anyway.
I don't mean to invoke humpty dumpty, it's just that to myself it seems that the invocation of atomic number is just as arbitrary as color in designating some aspect as a necessary feature.
For myself it does strike me as odd to say that the color of gold is known a priori. There's a sense in which I can make sense of it -- like, now that I think of Gold as golden it seems that I can think of gold in a purely conceptual sense and say that its color is now part of its concept. But, then, it seems to me that gold could have been other than golden.
However, from my perspective, it seems to me that gold could have been other than having 79 protons in its nucleus too. This was something we discovered a posteriori, and is not a necessary feature of gold -- that is, there is a possible world in which gold has more or less protons than 79. Your thought experiment would apply equally well here too -- imagine that we had some substance who retained the same ductility, the same color, the same melting point and freezing point, the same ratio for certain alloys, and in all other ways was the same as the gold we know in our actual world -- save for the number of protons we find in its nucleus.
Wouldn't we call this gold? Or would we call this something else?
To me I think it's similar to your color example. initially I wouldn't call something gold that happened to be red, but I'd say, perhaps, that it is red gold. And if we found some substance with a different number of protons in it then I'd say it is Gold-78 or some such, if I were being precise.
Sort of like how we came to know there are isotopes of various elements with differeing number of neutrons. They were similar in structure, but different in certain respects (and had different properties too because of that).