Confessions of an Apostate Mathematician [pdf]

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.