lukeprog comments on Less Wrong Rationality and Mainstream Philosophy - Less Wrong

106 Post author: lukeprog 20 March 2011 08:28PM

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Comment author: Eliezer_Yudkowsky 21 March 2011 07:55:02PM 9 points [-]

When I wrote the post I didn't know that what you meant by "reductionist-grade naturalistic cognitive philosophy" was only the very narrow thing of dissolving philosophical problems to cognitive algorithms.

No, it's more than that, but only things of that level are useful philosophy. Other things are not philosophy or more like background intros.

Amy just arrived and I've got to start book-writing, but I'll take one example from this list, the first one, so that I'm not picking and choosing; later if I've got a moment I'll do some others, in the order listed.

  • Predicate logic.

Funny you should mention that.

There is this incredibly toxic view of predicate logic that I first encountered in Good Old-Fashioned AI. And then this entirely different, highly useful and precise view of the uses and bounds of logic that I encountered when I started studying mathematical logic and learned about things like model theory.

Now considering that philosophers of the sort I inveighed against in "against modal logic" seem to talk and think like the GOFAI people and not like the model-theoretic people, I'm guessing that the GOFAI people made the terrible, horrible, no good, very bad mistake of getting their views of logic from the descendants of Bertrand Russell who still called themselves "philosophers" instead of those descendants who considered themselves part of the thriving edifice of mathematics.

Anyway. If you and I agree that philosophy is an extremely sick field, that there is no standardized repository of the good stuff, that it would be a desperate and terrible mistake for anyone to start their life studying philosophy before they had learned a lot of cognitive science and math and AI algorithms and plain old material science as explained by non-philosophers, and that it's not worth my time to read through philosophy to pick out the good stuff even if there are a few small nuggets of goodness or competent people buried here and there, then I'm not sure we disagree on much - except this post sort of did seem to suggest that people ought to run out and read philosophy-qua-philosophy as written by professional philosophers, rather than this being a terrible mistake.

Will try to get to some of the other items, in order, later.

Comment author: lukeprog 14 May 2011 03:14:06AM 11 points [-]

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.

Comment author: Wei_Dai 14 May 2011 08:22:07AM *  12 points [-]

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?

Comment author: lukeprog 14 May 2011 08:35:19AM 2 points [-]

We'd need to inoculate the clones against vanity, it appears.

Interesting story. Thanks for sharing your findings.

Comment author: wedrifid 14 May 2011 07:02:26AM -1 points [-]

Russell evidently misinterprets my result; however, he does so in a very interesting manner... In contradistinction Wittgenstein... advances a completely trivial and uninteresting misinterpretation.

Well spoken! :)

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