[geebee]

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.