Friday, May 16, 2008

KANT: HOW IS PURE MATHEMATICS? SECTION 7

"All mathematical cognition has this peculiarity: it must first exhibit its concept in intuition, and do so a priori, in an intution that it is not empirical but pure. Without this mathematics cannot take a single step, hence its judgements are always intuitive; whereas philosophy must be satisfied with discursive judgements from mere concepts, and though it may illustrate its apodeictic doctrines through intuitions, can never derive them from it"

I think that here Kant is saying that math shows it concepts as an instinct and something that you should already know. It is not something that can be proven it is something that is pure and comes naturally. He also compares philosophy to math saying that philosophy has many ideas and proceeds to a conclusion through reason instead of intuition.

I don't understand because math really doesn't come naturally unless you learn it. For example, when you learn 2+2=4. You may know this now and when someone asks you this the answer comes naturally to know because you know it but at first you did not know it and someone had to teach it to you so it really isn't natural.

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