[forgotmylastone]

>I can tell you what an integer is, what a square root is, and what a ratio is, and as a result, I can (by looking it up in a book and typing in the text, heh heh) prove that the square root of 2 can't be expressed as the ratio of two integers.

Not without words you can't.

[geebee]

sure, but these words have precise definitions. Paul alluded to this when he wrote "in fact, it would not be a bad definition of math to call it the study of terms that have precise meanings".

"Ratio", "Square Root", and "Integer" have precise definitions, whereas "self interest" is imprecise.

[euccastro]

Define 'precise'. :P

http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_the...