On Intuition Kant's notion of intuition has had a profound impact on all those who have come after.

For those who don't have any idea, namely my intro to philosophy students since we covered this topic in intro to ethics last week, a brief recap follows.

Acording to Kant"[However] a mode of knowledge may relate to objects, intuition is that through which is in immediate relation to them ... But intuition takes place only in so far as the object is given to us " (CPR A 19/ B33 or p. 65 of the Kemp Smith translation of the Critique of Pure Reason).

In other words, intuition is the most primitive way in which the world appears to us before we start to apply concepts to it. We can't avoid making conceptual applications, because that's how we think about and come to understand the world. But even at the level of intuition, we don't perceive the world as it is, but only as it can be perceived by people. The content of intuitions always have certain relations to each other, namely temporal succession and spatial arrangement, but we have no way of knowing whether or not those relations reflect the actual way things are (in-themselves) or is just how they have to represented for us to make any sense of them.

Since our immediate representations (yes, being both immediate and a re-presentation, is at best an unfortunate way of putting it) are always arranged according to these two sorts of relations, we can make certain definite and informative conclusions about how every representation will be arranged. For Kant, these are geometry (the study of spatial relation) and arithmetic (since the integers are, initially a representation of temporal succession.) The fact that we can perceive the passage of time allows us to see that 7 + 5 =12. If you can get this far, the derivation of arithmetic from succession shouldn't be too much of a jump. I find it amusing that while many people would observe that the order of experience in time seems to be the foundation for our sense of rhythm, Kant makes it the foundation of arithmetic. Of course, it could be both.

Kant's notion of intuition has had profound impact on subsequent generations of philosophers. The important thing that they all have in common is that intuition is not a set of unexplained facts or an extra sort of perception over and above the ordinary senses. Most intuitionist accept a stronger requirement for proof then the contrasting non-intuitionists.

Mathematical intuitionism. A twentieth century school of mathematics founded by L. E. J Brouwer. The intuitionist limits mathematical proofs to "constructions in intuition". By this, they mean that the truths of mathematics are dependent on the formal conditions of experience and any conclusions that can not be carried out on these conditions are suspect. So, for instance, indirect proofs, those that depend on deriving a contradiction from the negation of the desire conclusions are ruled out. (Roughly "If A is false, B must be true and B must be false. Thus A must be true.") This is a very strong restriction. They call the formal aspects of experience intuition because Kant did, though their positions with regard to the rules derivable from space and, more importantly, time are quite different.

Ethical intutionism. This is a twentieth century school of thought famously associated with G. E. Moore, H. A, Prichard and A.C. Ewing. Pritchard claims, quite literally, that we know moral truths in the same way that we know that 7 x 4 = 28. Prichard doesn't seem to think that one could prove that 7 x 4 = 28 in any meaningful way. The only support one might have for this fact is "doing the sum". Moral philosophy was founded, he thought on a similar error, "... the mistake of supposing the possbility of proving what can only be apprehended directly by an act of moral thinking." (Prichard)

Now its not as immediately obvious that substituting direct apprehension for rational proof produces a stronger restrition on moral reasoning in the same way it does for mathematical reasoning. It all depends of course on what theory of moral reasoning these intutionists are to be compared. By making "good" a sort of logical primitive (a move famously associated with G. E. Moore), intuitionists remove arguments which seek to eliminate normative terms in favor of some other sort of vocabulary (the naturalistic fallacy). In particular, ethical intuitionism is generally contrasted with emotivism, the position that moral propositions are really expressions of imperative commands presumably motivated by the dispositions of the speaker. So the emotivist rules out arguments based on this sort of maneuvur.

What is perhaps more disturbing is the way that while we are usually able to acknowledge that some people are just better at doing arithmetic than others, we're not so willing to acknowledge that some people are just better at deriving moral conclusions.


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