Mathematical realism, anti-realism.

Soo, I want to ask, what is the rational position? Is my position of math being just a concept silly?

Here are a reason to think your position is flawed: we could all change our minds and make 2+2 = 5. So for instance, right now I have two keys to doors in the philosophy department, one key to my apartment, and one key to my care on my keychain. If we group these keys into two groups of two and then add them together, this gives us four keys. If math is just a human construct, though, it could give us five keys. That seems like an incorrect description of math. Surely there have to be four keys any time there are two keys and two other keys.

Here is another reason to think your position is flawed: the laws of physics involve numbers. So for instance, the Planck constant is 6.62606957(29)×10−34 J.s. If math is just a human creation, then before we created math, the Planck constant didn't exist, or something. The laws of physics didn't exist before we invented the math it takes to describe them. The sentence "the Planck constant is equal to 6.62606957(29)×10−34 " wasn't true or false before humans invented numbers - it was simply meaningless. But surely the Planck constant has been 6.62etc. for far longer than humans have been around.

Here is another reason to think numbers are more than just things we made up: there does not seem to be much variation between numbers among cultures, even cultures that have been isolated from each other. In fact there is no variation, as far as I know - some cultures lack (or lacked) certain concepts, but, in terms of the concepts that each culture shares, all of these concepts agree, and all cultures have the same concept for (for instance) one and two. There are no cultures where you can add one and one and get three.

For more information see these articles:

http://plato.stanford.edu/entries/platonism-mathematics/

http://plato.stanford.edu/entries/fictionalism-mathematics/

http://plato.stanford.edu/entries/naturalism-mathematics/

http://plato.stanford.edu/entries/nominalism-mathematics/

http://plato.stanford.edu/entries/mathphil-indis/

/r/askphilosophy Thread