
Confessions of an Apostate Mathematician [pdf] - ukj
https://web.math.princeton.edu/~nelson/papers/rome.pdf
======
DATACOMMANDER
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.

~~~
ukj
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.

~~~
DATACOMMANDER
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?)

~~~
ukj
To call him a nihilist based on his views of Mathematics is a bit too
reductionist, I think?

All Mathematicians are human, not all humans are Mathematicians.

Humans look for (and find) meaning wherever they can.

~~~
DATACOMMANDER
The position presented in the essay is _mathematical_ nihilism. I make no
comment on him or on his general philosophy, which I thought was obvious from
context.

~~~
ukj
It was also obvious from the essay that his Mathematical nihilism didn't
extend to computation.

So it kind of begs the question: What does Mathematics mean to a Computer
Scientist?

Least we forget that Ed Nelson was a strong proponent of Ultrafinitism (
[https://en.wikipedia.org/wiki/Ultrafinitism](https://en.wikipedia.org/wiki/Ultrafinitism)
)

