Earlier quoted context omitted.
>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.
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.
http://en.wikipedia.org/wiki/G%C3%B6del's_incompleteness_the...