Confessions of an Apostate Mathematician [pdf]

https://web.math.princeton.edu/~nelson/papers/rome.pdf

by ukj • 7 years ago

3 6 7 years ago

web.math.princeton.edu

The conclusion of this essay is deeply stupid. The author uses formalism in the same way that he accuses Hilbert of doing, except that where Hilbert presumably remained a closet Platonist, the author is apparently some sort of nihilist. The comparison of mathematical propositions to sheet music is transparently inappropriate: for, if the latter truly denoted nothing, we would not continue to print endless volumes of it. Surely, even music that is absolutely nonrepresentational still has the virtue of being a pleasing or stimulating pattern of sound; so we should discard as just silly the notion that notion that, e.g., an existential quantifier is nothing more and nothing less than a backwards E printed on paper, and that the endless volumes of text containing the symbol are produced for no reason.

I am not a Platonist, nor a formalist, nor an intuitionist, but there is a completely coherent interpretation of mathematics, entirely fleshed out in my mind, which is none of these. I could summarize it here, but I’ve grown rather tired of broadcasting my ideas pseudonymously in random comment threads only to see them published a year or so later with no attribution (and why not; why cite a random commenter?). Whether you believe me or not when I say that there is another way, the nihilism in this essay can clearly be rejected as an abortive train of thought.

ukj3• 7 years ago

Elsewhere, Nelson has stated that despite the labels Mathematicians use to describe themselves (Platonist, Formalists, Intuitionist) they still seem to have the uncanny ability to agree on the correctness of any particular piece of work, despite their philosophical differences.

I am sure there is a lesson in there somewhere ;)

Biased hint: distributed consensus.

DATACOMMANDER3• 7 years ago

Yes, and that’s precisely what makes the nihilist position so silly. (I’m sure the author wouldn’t describe himself as a nihilist, but if the position presented in his essay isn’t nihilism, then what—other than a waste of the reader’s time—can we call it?)

Confessions of an Apostate Mathematician [pdf]

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