Monday, October 08, 2007

Kant and the Analytic/Synthetic Distinction

Glach has a nice post on Kant's analytic/synthetic distinction. In the comments I say that the distinction is Wolffian; but this is a little misleading, because Wolff himself doesn't make the distinction. Rather, what Kant does is show that the Wolffian notion of analyticity makes it absolutely necessary for us to recognize a form of judgment distinct from analytic judgments, namely, synthetic judgments.

Looking at the relevant SEP article, by Georges Rey, I find myself a bit puzzled. The idea seems to be that the 'containment' criterion and the 'principle of contradiction' criterion for analyticity (which are both carried over from Wolff) are different. OK, but the example given is this:

(A) Bachelors are unmarried or the moon is blue.

And, says, Rey, "'Bachelors are unmarried or the moon is blue' is a logical consequence of 'Bachelors are unmarried' — its denial readily contradicts the latter — but clearly nothing about the color of the moon is remotely “contained in” the concept bachelor."

But this appears muddled to me. (A) is indeed a logical consequence of 'Bachelors are unmarried', but it does not follow from 'Bachelors are unmarried' by the principle of noncontradiction, but by the (obviously synthetic) principle of disjunction addition. To say that X follows from Y by logical consequence simply means that X follows from Y by some sort of necessity; but, of course, we have to distinguish between two ways necessity could be involved: the analytic and the synthetic. As Kant notes, "Analytic judgments (affirmative) are therefore those in which the connection of the predicate with the subject is thought through identity; those in which this connection is thought without identity should be entitled synthetic." But disjunction addition does not introduce an identity; it introduces new information, namely, the alternative, which may or may not be true. Kant's appeal to the principle of noncontradiction, in fact, is Wolffian; on a Wolffian scheme the criterion of possibility is the principle of noncontradiction, and what we do in analysis is draw out what is contained in the coherent concept by using only the principle of noncontradiction; when we have done so we have described a possible object, since every concept which does not violate the principle of noncontradiction has, on Wolff's view, a corresponding possible object. So if I'm analyzing a concept, e.g.,

Bachelor = ?

I can only introduce such information on the right hand side as must not be denied of the concept on the left hand side on pain of violating the principle of noncontradiction, e.g.,

Bachelor = Unmarried Man

(since it would be a contradiction to deny the predicate "unmarried man" of the subject, "bachelor"). But you can't even predicate "unmarried man or the moon is blue" of "bachelor" because "unmarried man or the moon is blue" is a nonsense predicate. "The moon is blue" is an alternative proposition, not part of what we are predicating of "bachelor". Thus we can't affirm or deny it of "bachelor", and the principle of noncontradiction, understood as the claim that we cannot affirm and deny the same thing of the same subject in the same respect, is not enough to get (A).

Incidentally, this is all connected with Kant's famous argument that existence is not a predicate. One might be tempted to say that existing dollar is a species of the genus possible dollar. But this would make every existence judgment either necessarily true or necessarily false. So existence judgments must be synthetic, if existence is predicated of subjects. Existence is thus a determination or 'mode' of possibility; "existence" functions as a determining predicate. What Kant points out is that this won't do, and his argument for it is a clever one. If "existence" is a determining predicate, it must add to the concept of the subject and enlarge it. But if we take "existence" to be a concept that is added to the concept of a possible object, the existing object is not the same as the possible object. Suppose I have a question about whether a treasure mentioned by my friend is real. I have a concept of the relevant treasure qua possible, and I am asking whether that very thing actually exists. Now suppose that the treasure at first does not exist, but then is later put together. In the earlier stage, we say of the possible object, treasure, that it does not exist; in the later stage we say of the very same possible object that it does. Even to make sense of the change we must be using the same concept. If existence were a determining predicate for possible being, though, the concept of existing treasure would never be the same concept of a possible object as the concept of possible treasure, because it has a determination, or additional feature, that distinguishes it from the concept of possible treasure. We could not, then, talk of a possible treasure becoming actual, any more than we can talk about a possible treasure becoming a possible cow. Possible objects don't change into different possible objects; they merely stay possible or begin to exist. As Kant says, "The real contains no more than the merely possible." It makes no difference to the concept of money in my bank account whether that possible money exists or not. Thus "existence" cannot be a feature added to the merely possible object to make it a different possible object; it must be that very possible object. It's just that this possible object may or may not be thought to exist.

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