Kant and Math

One of the most fascinating areas within Kant’s perception of reality is his view on math. Although he believes that Geometry is an a priori science, on the subject of algebra, Kant writes, “We might, indeed, at first suppose that the proposition 7 + 5 = 12 is a merely analytic proposition, and follows by the principle of contradiction from the concept of a sum of 7 and 5. But if we look more closely we find that the concept of the sum of 7 and 5 contains nothing save the union of the two numbers into one, and in this no thought is being taken as to what the single number may be which combines both. The concept of 12 is by no means already thought in merely thinking this union of 7 and 5” (52-53). There algebra is a posteriori.

Kant’s argument relies on the assumption that no one would see the union of 7 and 5 as automatically being 12 in an a priori situation. However, I believe that it is possible to view this as a priori. I think that this is a situation where Kant is giving a subjective opinion. One that is not resolute and without valid contradictions.