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.
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.
Of course, since this is a community blog, we can have it both ways. Those of us interested in philosophy can go out and read (and/or write) lots of it, and we’ll chuck the good stuff this way. No need for anyone to miss out.
There is this incredibly toxic view of predicate logic that I first encountered in Good Old-Fashioned AI.
I’d be curious to know what that “toxic view” was. My GOFAI academic advisor back in grad school swore by predicate logic. The only argument against that I ever heard was that proving or disproving something is undecidable (in theory) and frequently intractible (in practice).
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.
Model theory as opposed to proof theory? What is it you think is great about 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.
I have no idea what you are saying here. That “Against Modal Logic” posting, and some of your commentary following it strike me as one of your most bizarre and incomprehensible pieces of writing at OB. Looking at the karma and comments suggests that I am not alone in this assessment.
Somehow, you have picked up a very strange notion of what modal logic is all about. The whole field of hardware and software verification is based on modal logics. Modal logics largely solve the undecidability and intractability problems the bedeviled GOFAI approaches to these problems using predicate logic. Temporal logics are modal. Epistemic and game-theoretic logics are modal.
Or maybe it is just the philosophical approaches to modal logic that offended you. The classical modal logic of necessity and possibility. The puzzles over the Barcan formulas when you try to combine modality and quantification. Or maybe something bizarre involving zombies or Goedel/Anselm ontological proofs.
Whatever it was that poisoned your mind against modal logic, I hope it isn’t contagious.
Modal logic is something that everyone should be exposed to, if they are exposed to logic at all. A classic introductory text: Robert Goldblatt: Logics of Time and Computation (pdf) is now available free online. I just got the current standard text from the library. It—Blackburn et al.: Modal Logic (textbook) - is also very good. And the standard reference work—Blackburn et al.: Handbook of Modal Logic—is outstanding (and available for less than $150 as Borders continues to go out of business :)
That is entirely possible. A five star review at the Amazon link you provided calls this “The classic work on the metaphysics of modality”. Another review there says:
Plantinga’s Nature of Necessity is a philosophical masterpiece. Although there are a number of good books in analytic philosophy dealing with modality (the concepts of necessity and possibility), this one is of sufficient clarity and breadth that even non-philosophers will benefit from it. Modal logic may seem like a fairly arcane subject to outsiders, but this book exhibits both its intrinsic interest and its general importance.
Yet among the literally thousands of references in the three books I linked, Platinga is not even mentioned. A fact which pretty much demonstrates that modal logic has left mainstream philosophy behind. Modal logic (in the sense I am promoting) is a branch of logic, not a branch of metaphysics.
I didn’t say in my original post that people should run out and start reading mainstream philosophy. If that’s what people got from it, then I’ll add some clarifications to my original post.
Instead, I said that mainstream philosophy has some useful things to offer, and shouldn’t be ignored. Which I think you agree with if you’ve benefited from the work of Bostrom and Dennett (including, via Drescher) and so on. But maybe you still disagree with it, for reasons that are forthcoming in your response to my other examples of mainstream philosophy contributions useful to Less Wrong.
But yeah, don’t let me keep you from your book!
As for predicate logic, I’ll have to take your word on that. I’ll ‘downgrade it’ in my list above.
If that’s what people got from it, then I’ll add some clarifications to my original.
FWIW, what I got from your original post was not “LW readers should all go out and start reading mainstream philosophy,” but rather “LW is part of a mainstream philosophical lineage, whether its members want to acknowledge that or not.”
I’m part of Roger Bacon’s lineage too, and not ashamed of it either, but time passes and things improve and then there’s not much point in looking back.
Meh. Historical context can help put things in perspective. You’ve done that plenty of times in your own posts on Less Wrong. Again, you seem to be holding my post to a different standard of usefulness than your own posts. But like I said, I don’t recommend anybody actually read Quine.
Oftentimes you simply can’t understand what some theorem or experiment was for without at least knowing about its historical context. Take something as basic as calculus: if you’ve never heard the slightest thing about classical mechanics, what possible meaning could a derivative, integral, or differential equation have to you?
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.
it’s more than that, but only things of that level are useful philosophy. Other things are not philosophy or more like background intros.
I’m not sure what “of that level” (of dissolving-to-algorithm) means, but I think I’ve demonstrated that quite a lot of useful stuff comes from mainstream philosophy, and indeed that a lot of mainstream philosophy is already being used by yourself and Less Wrong.
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.
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! :)
Of course, since this is a community blog, we can have it both ways. Those of us interested in philosophy can go out and read (and/or write) lots of it, and we’ll chuck the good stuff this way. No need for anyone to miss out.
Exactly. Like I did with my statistical prediction rules post.
I’d be curious to know what that “toxic view” was. My GOFAI academic advisor back in grad school swore by predicate logic. The only argument against that I ever heard was that proving or disproving something is undecidable (in theory) and frequently intractible (in practice).
Model theory as opposed to proof theory? What is it you think is great about model theory?
I have no idea what you are saying here. That “Against Modal Logic” posting, and some of your commentary following it strike me as one of your most bizarre and incomprehensible pieces of writing at OB. Looking at the karma and comments suggests that I am not alone in this assessment.
Somehow, you have picked up a very strange notion of what modal logic is all about. The whole field of hardware and software verification is based on modal logics. Modal logics largely solve the undecidability and intractability problems the bedeviled GOFAI approaches to these problems using predicate logic. Temporal logics are modal. Epistemic and game-theoretic logics are modal.
Or maybe it is just the philosophical approaches to modal logic that offended you. The classical modal logic of necessity and possibility. The puzzles over the Barcan formulas when you try to combine modality and quantification. Or maybe something bizarre involving zombies or Goedel/Anselm ontological proofs.
Whatever it was that poisoned your mind against modal logic, I hope it isn’t contagious. Modal logic is something that everyone should be exposed to, if they are exposed to logic at all. A classic introductory text: Robert Goldblatt: Logics of Time and Computation (pdf) is now available free online. I just got the current standard text from the library. It—Blackburn et al.: Modal Logic (textbook) - is also very good. And the standard reference work—Blackburn et al.: Handbook of Modal Logic—is outstanding (and available for less than $150 as Borders continues to go out of business :)
Reading Plantinga could poison almost anybody’s opinion of modal logic. :)
That is entirely possible. A five star review at the Amazon link you provided calls this “The classic work on the metaphysics of modality”. Another review there says:
Yet among the literally thousands of references in the three books I linked, Platinga is not even mentioned. A fact which pretty much demonstrates that modal logic has left mainstream philosophy behind. Modal logic (in the sense I am promoting) is a branch of logic, not a branch of metaphysics.
Yeah, we don’t disagree much on all those points.
I didn’t say in my original post that people should run out and start reading mainstream philosophy. If that’s what people got from it, then I’ll add some clarifications to my original post.
Instead, I said that mainstream philosophy has some useful things to offer, and shouldn’t be ignored. Which I think you agree with if you’ve benefited from the work of Bostrom and Dennett (including, via Drescher) and so on. But maybe you still disagree with it, for reasons that are forthcoming in your response to my other examples of mainstream philosophy contributions useful to Less Wrong.
But yeah, don’t let me keep you from your book!
As for predicate logic, I’ll have to take your word on that. I’ll ‘downgrade it’ in my list above.
FWIW, what I got from your original post was not “LW readers should all go out and start reading mainstream philosophy,” but rather “LW is part of a mainstream philosophical lineage, whether its members want to acknowledge that or not.”
Thanks for sharing. That too. :)
I’m part of Roger Bacon’s lineage too, and not ashamed of it either, but time passes and things improve and then there’s not much point in looking back.
Meh. Historical context can help put things in perspective. You’ve done that plenty of times in your own posts on Less Wrong. Again, you seem to be holding my post to a different standard of usefulness than your own posts. But like I said, I don’t recommend anybody actually read Quine.
Oftentimes you simply can’t understand what some theorem or experiment was for without at least knowing about its historical context. Take something as basic as calculus: if you’ve never heard the slightest thing about classical mechanics, what possible meaning could a derivative, integral, or differential equation have to you?
Does human nature improve, too?
What’s “human nature”?
Something that probably hasn’t changed much over the history of philosophy.
I’d very much like to see a post explaining that.
I’m not sure what “of that level” (of dissolving-to-algorithm) means, but I think I’ve demonstrated that quite a lot of useful stuff comes from mainstream philosophy, and indeed that a lot of mainstream philosophy is already being used by yourself and Less Wrong.