Is anyone aware of any books or articles that explicitly discuss the relationship between Kant’s notion of the Synthetic a Priori [judgment], e.g. “every color is extended,” "Nothing can be simultaneously red and green all over," “2+2=4,” etc. (to the extent such a notion retains viability after Quines Two Dogmas), and Wittgenstein’s notion, in On Certainty, of hinge propositions (see OC, §§341-3), such as “My body has never disappeared and reappeared again after an interval.” (OC 101): That is, propositions that are not necessarily/exclusively empirical, i.e. whose function is not necessarily/exclusively to describe the world, but, rather [or additionally] to provide the norms/rules that make empirical investigation possible. (I would also appreciate, and consider an "answer," the commentary of any user that has considered the relationship between these concepts.)
Hinge propositions are much more subtle concept than synthetic a priori judgements.
Synthetic a priori judgements are equivalent to what Wittgenstein calls tautologies in the Tractatus (or contradictions when they are false):
4.461 The proposition shows what it says, the tautology and the contradiction that they say nothing.
The tautology has no truth-conditions, for it is unconditionally true; and the contradiction is on no condition true.
Tautology and contradiction are without sense. (Like the point from which two arrows go out in opposite directions.)
(I know, e.g. nothing about the weather, when I know that it rains or does not rain.)
In other words synthetic judgements are ones that cannot ever be challenged or disproved.
Hinge propositions on the other hand are propositions that can be challenged potentially, but are never challenged in practice, simply because there is no point.
- Why is it not possible for me to doubt that I have never been on the moon? And how could I try to doubt it? First and foremost, the supposition that perhaps I have been there would strike me as idle. Nothing would follow from it, nothing be explained by it. It would not tie in with anything in my life. When I say “Nothing speaks for, everything against it,” this presupposes a principle of speaking for and against. That is, I must be able to say what would speak for it.