To start, let me rehearse Kant’s basic move in explaining our knowledge of the world. Most of us will accept that there are some things we can learn only through experience (like how many donkeys are now in my yard) and some things that are simply true by definition (like anyone with an uncle has a parent with a sibling). Set those aside for now as unproblematic. Kant was interested in a class of statements that are sort of a mix between the two. Take, for example, the fact that any square drawn within a circle will have less area than that of the circle. It has that “true by definition” sort of feel to it, but it isn’t simply true by definition. To see its truth, you need to check it out in your own mind’s eye (“pure intuition,” Kant called it, meaning sense experience unpolluted by anything your physical eye is actually taking in). Call this class of truths “apriori synthetic” facts.
Kant was the first to draw our attention to apriori synthetic truths, and he thought they included many extremely important truths: like the whole of geometry, and the whole of arithmetic, and some super-basic facts about what has to happen in the physical world: that every event has a cause, that when there’s an action, there’s an equal/opposite reaction, and that no event is causally isolated. Indeed, the apriori synthetic truths serve as the foundation for our knowledge of the world.
Now why should it be true that these facts are both known to us through pure intuition, and basic to the fabric of the cosmos? For that is a very nifty coincidence. It could be luck, or God. But Kant’s answer was that the human mind’s own inherent structure makes these truths available to itself through pure intuition, and also puts our experience into a kind of structure so that anything we could possibly experience will fulfill those apriori synthetic truths. They are our operating system, so to speak, regulating both our thinking and all the data that comes our way.
Very cool idea, right? So why did anyone give up on it? It’s hard to give a brief answer to this. I’ll try to write more about this later, but in the end, my view is that Philosophy suffered from a tragic sequence of ideological entanglements. It first had a torrid affair with voluptuous German Idealism; then bounced back from that relationship into a much safer one with Prudish Positivism; then was hit by two buses marked “WWI” and “WWII”, and lost its memory; and finally old Philosophy settled down into a tame relationship with its cousin, Scientific Naturalism. Through all that, the early childhood romance with Kantianism was just sort of forgotten.
There are some solid, worthier reasons not to be satisfied with Kantianism, at least in the form that Kant expressed it. They have to do with the discovery of non-Euclidean geometries and (perhaps) with quantum physics (depending on how you interpret both it and what Kant said about the purest laws of science). And there were some philosophers, the neo-kantians, who tried to repair the old man’s theory; but they too were caught up in various ways with the tragic sequence I described.
But it seems to me that a neo-neo-kantianism is both possible and attractive. This lesson was taught to me a little while ago when I sat in on a physics course. The professor started at one end of the whiteboard with some results we already knew. Then he did a whole bunch of math from that end of the board to the other, and ended up with a predicted consequence. And it turned out that the consequence was verified by experiment, with great precision. Now that is frankly amazing. To ask Kant’s question once again: why should it be that nature knows it has to obey the sorts of mathematical principles we find ourselves bound to think are true?
One might try to say that we learned math from nature in the first place. (That’s naturalism.) But this seems to me quite implausible. For, as I have dabbled in math and number theory, nothing about it seems rooted in empirical discovery at all: it is purely conceptual. Moreover, if you come across a real mathematician who tries to think through to the philosophical foundation of what s/he is doing (and such persons are quite rare), you will have found a platonist. It’s just not natural to think of math as natural. And we know that mathematical truths are not simply the derived consequences of some basic rules mathematicians established at some convention: we have Gödel to thank for teaching us that can’t be right. For any set of rules, there are mathematical truths that cannot be proven by that set – and we can prove that.
So we are left with a spooky coherence between how we have to think and how the world has to be. Why not go Kantian? But this time, we will attribute a different structure to the human mind. It’s hard to say just what that structure is, except to say it is whatever it is that makes math true. Call it MATH, a structure existing among concepts, ordering them and determining how they can be distinguished or combined. I think it may well be that MATH both determines our thinking and the thinking of any intellect; and if it does, then it may well also constrain the data structures in which we try to squeeze the booming and buzzing confusion of our sense experience.
Now MATH is not anything whose existence can be confirmed or denied through efforts in cognitive psychology. For, if MATH exists, any attempt at cognitive psychology must necessarily presuppose it. Thus it would be genuinely apriori, but also synthetic, inasmuch as MATH is not simply true by definition.
So there you have it, my friends: my own neo-kantianism. I cannot lay any claims to its originality, since it may well be close to something Carnap was flirting with in his Logical Construction of the World, but that project got tangled up with a host of other ideological moves I’d rather not make.
Huenemanniac 
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