Jon Culp asks a very important question, a fully satisfactory reply to which is, unfortunately, beyond my abilities to supply. Here is what he says:
“Bob, can you tell me, how can someone be a Kantian after the advent of non-Euclidean geometry, relativity theory, and quantum mechanics, each of which undoes some of the supposedly a priori elements of his philosophy? I'm not implying that you *are* a Kantian, but perhaps you could enlighten me.”
First let me give a simple answer, which is rather superficial. It never occurred to Kant that Euclid’s Elements and Newton’s Principia were not the last word in mathematics and physics. The arguments he gives in the Aesthetic, even if they are in their own terms totally successful, only prove that there is some mathematics of space that can be known a priori to be universal and necessary. He never makes the slightest effort to derive the axioms of Geometry from the arguments of the Aesthetic.
Similarly, the argument he begins in the Analytic of Concepts and [on my interpretation] brings to a close in the Second Analogy only shows, even if it succeeds, that there is a science of nature the fundamental principle of which [the Causal Maxim] can be established with necessity a priori. The most that that demonstration shows is that the science of nature is a closed system, presumably compatible with Relativity and Quantum Mechanics, or String Theory, or whatever other theories of nature physicists come up with. Now in fact Kant wrote a book called Metaphysical Foundations of Natural Science in which he does actually try to pull Newtonian physics out of the conclusions of the Critique, but it is a flop, as you might expect.
So, at that superficial level, Kant is safe from Jon Culp’s question. But that does not at all address the much deeper questions to which Kant, it seems to me, has no real answers. Among these are:
1. Once we attain some sophistication about axiomatised systems, and understand that there can be many alternative geometries or algebras, none of which has any greater claim to being rooted in mind-dependent forms of intuition than any other, what are we to make of such systems?
2. What is the relationship between the fundamental principle of physics [the Causal Maxim, in some form or other] and the endlessly many particular physical laws derived from experimental observation and theory construction [the Problem of Induction, as it is called in some iterations]?
Kant really has nothing interesting or important to say about these questions, alas, and in fact seems not even to have recognized their possibility.
Well, that is a bit of a letdown, I am afraid, but there it is. By the way, I do not consider myself a Kantian. I do consider myself a Marxist, but that is another story entirely.