Lectures on the Philosophy of Mathematics by Joel David Hamkins;

Author:Joel David Hamkins;
Language: eng
Format: epub
Tags: Philosophy of mathematics; numbers; Frege; Russell; Cantor; Dedekind; platonism; realism; logicism; structuralism; formalism; intuitionism; type theorism; fictionalism; categoricity; geometry; Euclid; constructability; rigour; infinity; uncountability; transfinite; computability; Turing; halting problem; undecidability; Hilbert Program; Gödel incompleteness theorems; set theory; large cardinals; Zermelo; multiverse.
Publisher: MIT Press

She distinguishes moral mathematical truth from elegance, saying that,

An elegant proof is often a clever trick, a piece of magic…, the sort of proof that drives you mad when you’re trying to understand something precisely because it’s so clever that it doesn’t explain anything at all. (p. 13)

And she distinguishes it from constructive proof and from explanatory proof, and from a host of other kinds of proof as well. Ultimately, however, she offers no positive full account of the term, even though she is quite right that this word is widely used by mathematicians. What does it mean?

I am a mathematical moralist. I am more interested in moral truth than provable truth. But nevertheless I am a law-abiding mathematician. I grit my teeth and grudgingly chug through writing a proof even though I already know the result is true, and will not be any more convinced of its truth when I’ve written the proof. If only I could find a mathematical system in which moral truth and provable truth were always equivalent. Then I’d never have to prove anything again. (p. 17–18)

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