man, sometimes i love reading paul graham:
Outside of math there's a limit to how far you can push words; in fact, it would not be a bad definition of math to call it the study of terms that have precise meanings.
but sometimes..
[4] Philosophy is like math's ne'er-do-well brother. It was born when Plato and Aristotle looked at the works of their predecessors and said in effect "why can't you be more like your brother?" Russell was still saying the same thing 2300 years later.
Math is the precise half of the most abstract ideas, and philosophy the imprecise half. It's probably inevitable that philosophy will suffer by comparison, because there's no lower bound to its precision. Bad math is merely boring, whereas bad philosophy is nonsense. And yet there are some good ideas in the imprecise half.
ouch. i may have said similar things myself, but usually when i'm angry or trying to exhibit wry wit. myself, i tend to take the historical perspective and view math as a subset of philosophy.
it has an added bonus, too: if mathematics is philosophy, then there is no reason why it should be useful, except to prepare the mind for other processes of thought. if it is useful, fine, but that's not why we do it.
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