TimS comments on Rationality Quotes March 2012 - Less Wrong

4 Post author: Thomas 03 March 2012 08:04AM

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Comment author: TimS 02 March 2012 06:43:02PM 1 point [-]

Hmm, I'll have to think about the derivation of zero, the irrational numbers, etc.

I should also point out that many, if not all, of these discoveries (or "inventions") either arose as a solution to a scientific problem (f.ex. Calculus), or were found to have a useful scientific application after the fact (f.ex. imaginary numbers). How can this be, if mathematics is entirely "non-empirical"

The motivation for derivation of mathematical facts is different from the ability to derive them. I don't why the Cartesian skeptic would want to invent calculus. I'm only saying it would be possible. It wouldn't be possible if mathematics was not independent of empirical facts (because the Cartesian skeptic is isolated from all empirical facts except the skeptic's own existence).

Comment author: Bugmaster 02 March 2012 06:50:24PM *  1 point [-]

I don't why the Cartesian skeptic would want to invent calculus. I'm only saying it would be possible.

My point is that we humans are not ideal Cartesian skeptics. We live in a universe which, at the very least, appears to be largely independent of our minds (though of course our minds are parts of it). And in this universe, a vast majority of mathematical concepts have practical applications. Some were invented with applications in mind, while others were found to have such applications after their discovery. How could this be, if math is entirely non-empirical ? That is, how do you explain the fact that math is so useful to science and engineering ?

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