Confessions of an Apostate Mathematician [pdf](web.math.princeton.edu)
web.math.princeton.edu
Confessions of an Apostate Mathematician [pdf]
https://web.math.princeton.edu/~nelson/papers/rome.pdf
1 comments
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.
I am sure there is a lesson in there somewhere ;)
Biased hint: distributed consensus.
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?)
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.
All Mathematicians are human, not all humans are Mathematicians.
Humans look for (and find) meaning wherever they can.
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.
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 )
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 )
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.