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Infinities, impossibilities, and the man in the white linen suit

iain.so

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Re: Infinities, impossibilities, and the man in the white linen suit

#51

Post by mwkaufma »

stavros wrote: post #48
mwkaufma wrote: post #43

Earlier quoted context omitted.

One might gently recommend reading the "Political and social views" section on Frege's wikipedia entry before hitching your hot-take wagon to that particular horse.

Why does him being a raging racist preclude him from being the greatest logician?

Given that the case for "greatest logician" can be made for at least a dozen candidates, picking the bigot is conspicuous - especially raised specifically in contrast to Gödel who literally had to flee the Nazis. "Show us your politics without telling."

Re: Infinities, impossibilities, and the man in the white linen suit

#52

Post by stavros »

mwkaufma wrote: post #51
stavros wrote: post #48

Earlier quoted context omitted.

Why does him being a raging racist preclude him from being the greatest logician?

Given that the case for "greatest logician" can be made for at least a dozen candidates, picking the bigot is conspicuous - especially raised specifically in contrast to Gödel who literally had to flee the Nazis. "Show us your politics without telling."

Ah, well, could be. I don't know enough about logicians to argue.

Re: Infinities, impossibilities, and the man in the white linen suit

#53

Post by cubefox »

mwkaufma wrote: post #43
cubefox wrote: post #17

> The greatest logician since Aristotle Not to diminish Gödel's work, but the greatest logician since Aristotle was clearly Gottlob Frege, the inventor of modern predicate logic.

One might gently recommend reading the "Political and social views" section on Frege's wikipedia entry before hitching your hot-take wagon to that particular horse.

> One might gently recommend reading the "Political and social views" section

This obviously changes absolutely nothing about his status as greatest logician since Aristotle.

By the way, he is also the person who could be, more appropriately than anyone else, called "father of analytic philosophy", since he strongly influenced Russel, Wittgenstein and Carnap, all themselves major figures of early analytic philosophy, and wrote influential analytic philosophy classics like "On Sense and Reference" more than 130 years ago.

Michael Dummett (who was, according to an obituary, "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality") marked Frege's 1884 book "The Foundations of Arithmetic" as the beginning of analytic philosophy.

Re: Infinities, impossibilities, and the man in the white linen suit

#54

Post by seanhunter »

skippyfish wrote: post #25
hardbass wrote: post #20

Earlier quoted context omitted.

I don't understand the point at all. Mathematical theorems like godel's incompleteness theorem or the halting problem are applicable to everything including the human brain. If they were a limitation to developing general intelligence then human beings wouldn't have existed.

> Godel's incompleteness theorem or the halting problem are applicable to everything including the human brain. Maybe. That's if you assume that the universe is a conventional computer. Far from settled and the alternative isn't necessarily just "God does it" - it might be that the universe is a "computer-plus", with some processes that produce results not computable by Turing means. It would be strange, but so is qu…

This line of thinking doesn’t really go anywhere. You can say “but what if ? Then doesn’t apply!”

Well great. Then where are you? You are precisely nowhere. You haven’t disproved the results in the system and you haven’t proved anything else.

Re: Infinities, impossibilities, and the man in the white linen suit

#55

Post by mwkaufma »

cubefox wrote: post #53
mwkaufma wrote: post #43

Earlier quoted context omitted.

One might gently recommend reading the "Political and social views" section on Frege's wikipedia entry before hitching your hot-take wagon to that particular horse.

> One might gently recommend reading the "Political and social views" section This obviously changes absolutely nothing about his status as greatest logician since Aristotle. By the way, he is also the person who could be, more appropriately than anyone else, called "father of analytic philosophy", since he strongly influenced Russel, Wittgenstein and Carnap, all themselves major figures of early analytic philosophy,…

"obviously" -- keep telling on yourself.

Re: Infinities, impossibilities, and the man in the white linen suit

#56

Post by cubefox »

mwkaufma wrote: post #55
cubefox wrote: post #53

Earlier quoted context omitted.

> One might gently recommend reading the "Political and social views" section This obviously changes absolutely nothing about his status as greatest logician since Aristotle. By the way, he is also the person who could be, more appropriately than anyone else, called "father of analytic philosophy", since he strongly influenced Russel, Wittgenstein and Carnap, all themselves major figures of early analytic philosophy,…

"obviously" -- keep telling on yourself.

Yes, I'm not committing the logical fallacy of confusing truth values and moral values.

Re: Infinities, impossibilities, and the man in the white linen suit

#57

Post by hardbass »

Diogenesian wrote: post #44
hardbass wrote: post #21

Earlier quoted context omitted.

The worse confusion they seem to have is they think mathematical theorems are only applicable to "computers". Mathematical theorems have no escape, they apply just as much to human brains as to computers. If these theorems were a blocker for developing general intelligence then how do humans exist.

Gödel believed the human brain used non-mathematical reasoning (i.e. inexpressible with a Turing machine) to derive the axioms and thus could "see outside" of any particular axiom schema. The Church-Turing thesis throws cold water on this: since the human body (including brain) is describable by a finite system of Schrödinger equations, and these equations can be solved numerically by a Turing machine, the human proc…

Some problem being too chaotic or computationally expensive to perform is a completely different thing that claiming something supernatural. And there is hardly any reason for computers to be confined to silicon digital logic, using coprocessors is a standard procedure, so whatever element if any which exhibits hypercomputation (which is highly doubtful as the universe barely even reaches even a small fraction of the possibilities of turing machines let alone beyond them) or otherwise more efficient classical computation, we can isolate the element and use it as a chip.

Re: Infinities, impossibilities, and the man in the white linen suit

#58

Post by mwkaufma »

cubefox wrote: post #56
mwkaufma wrote: post #55

Earlier quoted context omitted.

"obviously" -- keep telling on yourself.

Yes, I'm not committing the logical fallacy of confusing truth values and moral values.

No, just a much more mundane rhetorical bait-and-switch. Ranking the "greatest logician" is purely-subjective, not a truth-value. Barging in like the kool-aid-man to bellyache that Harper isn't applauding Frege in an article that has nothing to do with him, while dismissing with a wave of your hand the obvious reason that nobody does that. To put it in your debate-club lingo: that's begging the question.

Re: Infinities, impossibilities, and the man in the white linen suit

#59

Post by Diogenesian »

hardbass wrote: post #57
Diogenesian wrote: post #44

Earlier quoted context omitted.

Gödel believed the human brain used non-mathematical reasoning (i.e. inexpressible with a Turing machine) to derive the axioms and thus could "see outside" of any particular axiom schema. The Church-Turing thesis throws cold water on this: since the human body (including brain) is describable by a finite system of Schrödinger equations, and these equations can be solved numerically by a Turing machine, the human proc…

Some problem being too chaotic or computationally expensive to perform is a completely different thing that claiming something supernatural. And there is hardly any reason for computers to be confined to silicon digital logic, using coprocessors is a standard procedure, so whatever element if any which exhibits hypercomputation (which is highly doubtful as the universe barely even reaches even a small fraction of the…

To be clear the limitation here isn't silicon logic, it's theoretical logic (specifically general recursive functions). It sure seems like any possible computation can be expressed as a general recursive function, but that's a scientific thesis, not a mathematical theorem. As we have yet to formalize "define a physical system" it is possible that this task isn't actually expressible in 21st century mathematical logic. I suppose some custom hardware which doesn't use logic at all might help, but then Gödel's theorem wouldn't apply at all. (Likewise with modal logic.)

Re: Infinities, impossibilities, and the man in the white linen suit

#60

Post by My_Name »

"the sentence...is true but unprovable"

Personally, I would say that if it cannot be shown to be true or false, it cannot be said to be true (or false).

Asking that about that sentence is, to my mind, a category error, like asking what sound yellow makes.

I'm reminded of the episode of Star Trek (TOS) where they make a bunch of robots explode by saying "This sentence is false". Any reasonably written software deals with exceptions very easily.

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