Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Why Philosophers Should Care About Computational Complexity

scottaaronson.com

Post reply on HN
Print view View original

21–30 of 38 posts

Re: Why Philosophers Should Care About Computational Complexity

#21

Post by yason »

I've always considered philosophy as a sort of the mind's struggle for its own life. The introspective mind somehow can't validate itself without somehow having the absolute last say about something.

Given this track, a philosophical mind will produce a lot of thoughts, models, and theories of how anything that already exists could exist in the first place. That is itself an interesting mind-game that in some cases might even produce an insight that is applicable to something real, but generally that's where it should stay.

The mind can't think itself into existence, even if it wants to believe it can.

If it does the result bears resemblance to as if someone would try to describe forest but only be allowed to draw straight lines in one color. At best it could be exemplary line art, at worst it's just ridiculous and childish and most people will turn the other way.

Re: Why Philosophers Should Care About Computational Complexity

#22

Post by ionfish »

jerf wrote: post #9
strlen wrote: post #4

They already do. Incompleteness Theorem ("some logical statements are true but are unprovable", e.g., "this program will terminate" for some arbitrary programs a.k.a. the Halting Problem) is one of the most significant achievements in logic. Here's philosophers' take on Kurt Godel: http://plato.stanford.edu/entries/goedel/ I am, however, curious as to how other problems in computational complexity figure in philosoph…

I haven't read the paper, but here's one example I've seen. Assume for the moment that the universe is closed, complete (there is nothing but our universe), and deterministic under the hood. Obviously, nobody in the universe has free will, right? Because it's all closed and all outcomes are predetermined. But maybe that's not a useful definition of free will. The conventional, fuzzy definition of free will has an omn…

Your suggestion confuses an epistemic limitation with a metaphysical one. Just because no one knows what we're going to do next doesn't mean there isn't a fact of the matter about it.

While the idea of God looking down on us from on high is a compelling story, if you take God away but leave determinism it doesn't do anything to resolve the problem: our actions are still pre-determined and cannot be changed.

Of course, whether or not that makes us free is a further question. A compatibilist [1] would claim that we are.

[1] http://plato.stanford.edu/entries/compatibilism/

Re: Why Philosophers Should Care About Computational Complexity

#23

Post by p4bl0 »

It seems nobody has mentionned Gregory Chaitin[1] yet, and in my opinion it's kind of mandatory when discussing this very topic. So now it's done :-). I like his work a lot. His not really working on this subject anymore (now he's developping a new field called metabiology which is also fascinating but not very relevant here) but he used to work on Algorithmic Information Theory and he wrote a lot of books and essays (you can find almost everything on his webpage) on the subject we're discussing here. _The Limits of Mathematics_[2] might be the most relevant to Hacker News users.

[1] http://www.cs.umaine.edu/~chaitin/ [2] http://news.ycombinator.com/item?id=1725936

Re: Why Philosophers Should Care About Computational Complexity

#24

Post by bumbledraven »

p4bl0 wrote: post #23

It seems nobody has mentionned Gregory Chaitin[1] yet, and in my opinion it's kind of mandatory when discussing this very topic. So now it's done :-). I like his work a lot. His not really working on this subject anymore (now he's developping a new field called metabiology which is also fascinating but not very relevant here) but he used to work on Algorithmic Information Theory and he wrote a lot of books and essays…

It seems nobody has mentionned Gregory Chaitin[1] yet

With good reason. The logician Torkel Franzen said it well in "Gödel's Theorem: An Incomplete Guide" [Chapter 8, p 148]: ``Chaitin's claim to have discovered "the amazing fact that some mathematical statements are true for no reason" has no apparent content, but seems rather to be based on the general associations surrounding the word "random".''

Re: Why Philosophers Should Care About Computational Complexity

#25

Post by yters »

ionfish wrote: post #22
jerf wrote: post #9

Earlier quoted context omitted.

I haven't read the paper, but here's one example I've seen. Assume for the moment that the universe is closed, complete (there is nothing but our universe), and deterministic under the hood. Obviously, nobody in the universe has free will, right? Because it's all closed and all outcomes are predetermined. But maybe that's not a useful definition of free will. The conventional, fuzzy definition of free will has an omn…

Your suggestion confuses an epistemic limitation with a metaphysical one. Just because no one knows what we're going to do next doesn't mean there isn't a fact of the matter about it. While the idea of God looking down on us from on high is a compelling story, if you take God away but leave determinism it doesn't do anything to resolve the problem: our actions are still pre-determined and cannot be changed. Of course…

Compatibilism is just one of those "answers" that defines away the problem. "Oh, if we just say that free will is determined then problem solved! I'm a genius!"

Also, FWIW omniscience is not logically incompatible with free will.

Re: Why Philosophers Should Care About Computational Complexity

#28

Post by ionfish »

yters wrote: post #25
ionfish wrote: post #22

Earlier quoted context omitted.

Your suggestion confuses an epistemic limitation with a metaphysical one. Just because no one knows what we're going to do next doesn't mean there isn't a fact of the matter about it. While the idea of God looking down on us from on high is a compelling story, if you take God away but leave determinism it doesn't do anything to resolve the problem: our actions are still pre-determined and cannot be changed. Of course…

Compatibilism is just one of those "answers" that defines away the problem. "Oh, if we just say that free will is determined then problem solved! I'm a genius!" Also, FWIW omniscience is not logically incompatible with free will.

I think that's a bit unfair to the compatibilist position. Ultimately an account of free will should include a definition of the concept, and an explanation of how it figures into our intuitions about particular cases. In particular it should explain situations in which the given definition conflicts with our intuitions, and obviously determinism is a big part of that.

The incompatibilist argument is at heart very straightforward: free will is incompatible with determinism; determinism is true; therefore free will does not exist. When pressed on the second premise, the incompatibilist can further assert that indeterminism is incompatible with free will, and that determinism and indeterminism exhaust the possibilities (this is just an instance of the law of the excluded middle). Therefore regardless of which one of them holds, free will does not exist.

However, even this argument requires a definition of free will, in order to demonstrate its incompatibility with (in)determinism. It thus suffers from the same 'problem' that you allege compatibilism does: the compatibilist can simply say that the incompatibilist is defining the problem into existence.

I'm curious to know what you think an answer which didn't suffer from the problem you outline would look like.

Re: Why Philosophers Should Care About Computational Complexity

#29

Post by Jach »

strlen wrote: post #4

They already do. Incompleteness Theorem ("some logical statements are true but are unprovable", e.g., "this program will terminate" for some arbitrary programs a.k.a. the Halting Problem) is one of the most significant achievements in logic. Here's philosophers' take on Kurt Godel: http://plato.stanford.edu/entries/goedel/ I am, however, curious as to how other problems in computational complexity figure in philosoph…

The incompleteness theorem has an interesting "workaround": http://stirling-westrup-tt.blogspot.com/2011/07/tt-ns-2823-u...

Re: Why Philosophers Should Care About Computational Complexity

#30

Post by jerf »

ionfish wrote: post #22
jerf wrote: post #9

Earlier quoted context omitted.

I haven't read the paper, but here's one example I've seen. Assume for the moment that the universe is closed, complete (there is nothing but our universe), and deterministic under the hood. Obviously, nobody in the universe has free will, right? Because it's all closed and all outcomes are predetermined. But maybe that's not a useful definition of free will. The conventional, fuzzy definition of free will has an omn…

Your suggestion confuses an epistemic limitation with a metaphysical one. Just because no one knows what we're going to do next doesn't mean there isn't a fact of the matter about it. While the idea of God looking down on us from on high is a compelling story, if you take God away but leave determinism it doesn't do anything to resolve the problem: our actions are still pre-determined and cannot be changed. Of course…

"Confuses" is one way to read it. "Shines a spotlight on the intersection of" would be a somewhat friendlier way to read it. Is a fact that can't be known, even in theory, even a sensibly a "fact"? I deny your implicit claim that that isn't an interesting question because the answer is transparently obvious.

Epistemology becomes much richer when fed with mathematical proofs of statements like this, and some older snap answers at least have to be reconsidered.

Post reply on HN