QUOTE(Ray @ Mar 12 2009, 10:24 AM) [snapback]539266[/snapback]
And if so, what's the reasoning behind that, poppa Liam? TELL ME A STORY!
Well, you would be inclined to accept that every right-angled triangle abides by Pythagoras' law, right? So now let's imagine a universe made only of triangles, and no humans. P's theorem would still be true, even if no one noticed it or brought it up, but it would still be present in the universe, governing the lengths of all the sides of the countless triangles. It merely fell to a human observer to notice that intrinsic property and take the time to write it down.
QUOTE(Ray @ Mar 12 2009, 10:24 AM) [snapback]539266[/snapback]
Nah, it's just painfully interesting to think about the possibilities there, and what we attribute these intrinsic universal rules. Dare I say the "G" word? Or is there simply more math that explains the other math?
You wouldn't be the first antirealist about maths if you so chose. I've got a whole VERY INTERESTING book on the subject. One argument I can think of off the top of my head goes something like: you can have two things, but you can never have two. There's no such thing as "a two" outside of our minds, but we go along blindly thinking that two is something that exists in the world. In fact it doesn't. Naturally you can apply this thinking to pretty much all facets of maths but you only need to prove that numbers don't really exist to effectively cut the balls off any logical mathematical thinking.
Personally, maths is one of those things that's out there in some form or another. The only thing we invented is the system of language and symbols which enables us to understand the chaos. There's a theory that describes the idea of a "convenient lie"; that is, we have no real knowledge of what we mean by "maths" in the greater scheme of things, but the language and concepts we use now - however inferior - do their job well enough for us to live our lives. Make of that what you will: depressingly resigned to our own ignorance, or is a lie truly enough for us to not worry about it any more?