One gathers the impression from what is here, that Kant's not terribly compelling, or plausible, whatever his historical importance. I think this is debatable.
About the claim that is made here, that Frege was the first to point out that geometry is not synthetic a priori. Well, this implies that indeed, geometry is not synthetic a priori. However, Some believe that Frege was wrong. I'll note that I'm also reading, here, about how this position 'was given a boost by Einstein's relativity..' That is to say, that Einstein's relativity
is a reason to think that geometry is not synthetic a priori. But how is it that this follows?
Also, one might believe the assertion, or not, that pure geometry--which consists only of deductive inferences--is analytic, and empirical geometry--which deals with what space is like in the real world--is known a posteriori.
I really would want to know Kant's reply, about this notion of 'what space is like in
the real world'. Also, this notion that pure geometry consists only of deductive inference.
I disagree. In fact, I disapprove. The 'terms' lists the definition of analytic, and I would hope that at the very very least, one might glean from the Critique of Pure Reason & Prolegomena that geometry is not analytic, and why. Kant is talking about why 7 + 5 = 12 is not analytic. One may ask, what Kant would make of nonEuclidean geometry, of the sort that is used in the General Theory of Relativity. And, I'll provide an answer -- he'd say that it is synthetic a priori judgment (what else?).
I suppose that there are those who might wish to reject or modify Kant's theories, but I want to just be clear that the notion that synthetic judgments that can be known a priori, do actually consistute mathematics, is not made impossible to believe because of Einstein and Frege. In brief, about Einstein, I take the statement that 'space is very different from what we had assumed' to be an interpretation of the General Theory of Relativity, and not the General Theory of Relativity itself. Especially, to the degree that any of this is taken to be relevant to what Kant has to say about space. Kant is not peddling some assumption about what space is, that contradicts Einstein. I might allow that there is some equivocation here, involving
multiple meanings of the word 'space'. Certainly, I'd say that Newton's idea of space is wrong, if Einstein is right. But Kant goes to some (apparently wasted) effort to distinguish his position from Newton's. Anyways, I hope this is enough to raise a doubt about what we supposedly have learned of 'pop'-Kant.