You may enjoy the following exchange between two philosophers and one mathematician.
Bertrand Russell, speaking of Godel’s incompleteness theorem, wrote:
It made me glad that I was no longer working at mathematical logic. If a given set of axioms leads to a contradiction, it is clear that at least one of the axioms must be false.
Wittgenstein dismissed the theorem as trickery:
Mathematics cannot be incomplete; any more than a sense can be incomplete. Whatever I can understand, I must completely understand.
Godel replied:
Russell evidently misinterprets my result; however, he does so in a very interesting manner… In contradistinction Wittgenstein… advances a completely trivial and uninteresting misinterpretation.
According to Gleick (in The Information), the only person who understood Godel’s theorem when Godel first presented it was another mathematician, Neumann Janos, who moved to the USA and began presenting it wherever he went, by then calling himself John von Neumann.
The soundtrack for Godel’s incompleteness theorem should be, I think, the last couple minutes of ‘Ludus’ from Tabula Rasa by Arvo Part.
I’ve been wondering why von Neumann didn’t do much work in the foundations of mathematics. (It seems like something he should have been very interested in.) Your comment made me do some searching. It turns out:
John von Neumann was a vain and brilliant man, well used to putting his stamp on a mathematical subject by sheer force of intellect. He had devoted considerable effort to the problem of the consistency of arithmetic, and in his presentation at the Konigsberg symposium, had even come forward as an advocate for Hilbert’s program. Seeing at once the profound implications of Godel’s achievement, he had taken it one step further—proving the unprovability of consistency, only to find that Godel had anticipated him. That was enough. Although full of admiration for Godel—he’d even lectured on his work—von Neumann vowed never to have anything more to do with logic. He is said to have boasted that after Godel, he simply never read another paper on logic. Logic had humiliated him, and von Neumann was not used to being humiliated. Even so, the vow proved impossible to keep, for von Neumann’s need for powerful computational machinery eventually forced him to return to logic.
ETA: Am I the only one who fantasizes about cloning a few dozen individuals from von Neumann’s DNA, teaching them rationality, and setting them to work on FAI? There must be some Everett branches where that is being done, right?
Am I the only one who fantasizes about cloning a few dozen individuals from von Neumann’s DNA, teaching them rationality, and setting them to work on FAI?
von Neumann wanted to nuke the Eastern Bloc countries. He would probably ahve been more interested in a commie-killing AI.
Russell evidently misinterprets my result; however, he does so in a very interesting manner… In contradistinction Wittgenstein… advances a completely trivial and uninteresting misinterpretation.
You may enjoy the following exchange between two philosophers and one mathematician.
Bertrand Russell, speaking of Godel’s incompleteness theorem, wrote:
Wittgenstein dismissed the theorem as trickery:
Godel replied:
According to Gleick (in The Information), the only person who understood Godel’s theorem when Godel first presented it was another mathematician, Neumann Janos, who moved to the USA and began presenting it wherever he went, by then calling himself John von Neumann.
The soundtrack for Godel’s incompleteness theorem should be, I think, the last couple minutes of ‘Ludus’ from Tabula Rasa by Arvo Part.
I’ve been wondering why von Neumann didn’t do much work in the foundations of mathematics. (It seems like something he should have been very interested in.) Your comment made me do some searching. It turns out:
ETA: Am I the only one who fantasizes about cloning a few dozen individuals from von Neumann’s DNA, teaching them rationality, and setting them to work on FAI? There must be some Everett branches where that is being done, right?
We’d need to inoculate the clones against vanity, it appears.
Interesting story. Thanks for sharing your findings.
von Neumann wanted to nuke the Eastern Bloc countries. He would probably ahve been more interested in a commie-killing AI.
Well spoken! :)