>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.

Define 'precise'. :P

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

Ok but you're jumping down the rabbit hole to quickly. Physicists assume spherical cows, early mathematicians assumed only integers, why can't Rand assume that "self" is the thoughts and actions encased in one's skin? It is a good jump off point and a lot of useful philosophies can be derived from there. Sure they eventually break down once you push the definitions hard enough, but that just means the model needs to be refined. Newtonian Physics needed to be refined as well, that didn't mean it should have been scrapped.

I think there's an important difference here. Early mathematicians started with an exact definition that turned out to be incorrect (ie., that all numbers could be represented as either integers or the ratio of integers).

The refinement you're talking about here isn't so much a matter of modifying an incorrect but exact definition as it is clarifying an irrefutable but ambiguous definition.

That said, maybe something could come of this if you truly got to the very basic building blocks. For instance, an integer is just a definition - an exact one, but a definition nonetheless. So we can define a rational number as the ratio of two integers, and then build a refutable hypothesis from it - that all numbers are either integers or the ratio of integers.

I have serious doubts as to whether "self interest" could ever be defined as precisely as an integer, though.

Actually, there already is stuff that's far more refined (and empirically true) than Ayn Rand. It's called evolutionary psychology. Unfortunately, understanding it leaves one feeling rather unedified. It's like realizing that you've been a pawn in somebody else's game, and will continue to be one until your life ends. With Ayn Rand fans, this kind of message doesn't seem to be in demand.

Saying that evolutionary psychology is more true than Ayn Rand is damning with awfully faint praise.

Any good links/more info on evolutionary psychology?

Steven Pinker's papers and books, although you have probably already encountered those.

"Self" and "interested" never appear in isolation in the above example, so we can only speculate on their precise interpretations when used in isolation. However, the compound concept "self-interested" has a well-defined meaning, even in casual, every-day conversations.

Calling into question the meaning of "self-interested" is merely a filibuster.

I couldn't disagree more. "Self interested" absolutely does not have a well understood meaning in casual, every-day conversations. It's one of the most ambiguous terms out there.

Try this out: at a dinner party (one that you don't care if you're invited back), declare that "all people act out of self-interest, ultimately."

Odds are good that two people will disagree quite vehemently about this, and at the core will be a fundamental disagreement about what it means to be "self-interested".