feb 11, 2012

i think i just finally understood why godel became a platonist. it always sort of bugged me. platonism is sort of.....insane. i sort of wrote it off as ptsd or something. lots of geniuses sort of lose it...

it's sort of intuitive to think of numbers as human constructions. abstractions, perhaps, but things that came from our own imagination. to think number has an independent existence from human thought seems sort of insane, although i've had to contemplate it when reading up on pythagoreanism. i've flirted with it, but have always rejected it. maybe the abstraction exists independently of physical existence, but that's what an abstraction *is*. where would this universe of numbers exist? it's crazy talk.

but, if there are true statements that exist outside of arithmetic then this means that the way we understand numbers is, in fact, a model of something that has an outside existence. just like the way that we understand the universe with physics is a model while the universe has an existence outside of that model.

so, if number theory is an incomplete model of something that exists without it, if number has an independent existence outside of the minds of human beings....well that's what the pythagoreans thought and what plato accepted.

yeah. ok. got it. still creates more questions than it answers, though...

what we call 'mathematics' is itself a model, a model of how numbers behave.

(edit: what that means is that what godel really did is debunk this entire line of thinking that centers around kant.

i don't think that's well understood.)