My new God is Gödel

No, no, Gödel's not some character from Star Wars or one of those interminable Norse-based operas that Wagner composed, no, he was, er, well, sort of . . . a thinker, I suppose.  To be more accurate, he was a thinker on the abstruse subjects of logic and mathematics.  These twins and all their problems and contradictions were thought to have been licked into shape by Bertrand Russell and A. N. Whitehead in their monumental three-volume book Principia Mathematica (PM).  In so far as I understand it - yeeeees quite! - the pair of them reckoned that they had reduced every possible statement into a logical mathematical code of such rigor that henceforth there could be no confusions in reasoning.  For example, the liar's paradox, 'this statement is false', was dealt with and, so to speak, the logic-tight doors of reasoning were slammed shut with no untidy bits left outside!

And then along came quiet, shy, nervous Kurt Gödel blinking behind his black-framed specs and, in effect, pointed at Russell and told him his flies were undone!  There was, he discovered, an untidy bit left outside of Russell's reasoning and no amount of logical jiggery-pokery would make it go away.  Gödel's work became known as 'the incompleteness theorem' and I find it deeply comforting. 

Personally, as I have grown older, I have become more and more suspicious of those people, particularly swots of various kinds, who claim to have the final and complete answer to everything, and Principia Mathematica was supposed to have been the Absolute and Forever Answer to Absolutely Everything!  I can't debate with these great thinkers - and Russell and Whitehead were certainly very great thinkers - on their terms because I'm not brainy enough so you could describe my scepticism concerning their theories as being based on hunch - or perhaps a better word is 'faith' - and perhaps a better image is of a caveman clinging to his totem pole!  I still remember the thrill I experienced some years ago when I learned that at the sub-atomic level of matter, 'titchy thingies', that is, all the 'titchy thingies' that make up the 'things' we see about us, behave in a totally different and bizarre way such that their actions cannot be predicted with complete certainty.

'SoD' (Son of Duff) has been banging on about Gödel for years but I never quite took it in.  I think I learn better from reading words rather than listening to them so thanks are due, again, to James Gleik and his marvellous book The Information.

 

 

Related articles

Deconstructing Godel

What is Gödel's Theorem?

Roots of Conflict: Godel & Morality

Introduction to MetaGödel

Incompleteness in the natural world

Comments

[Up2L8]

Mr.D;
"learn better from reading words rather than listening to them

Certainly holds true with myself. Have yet to listen to a speech in its entirety (more than 5 minutes) from the lofty one. The written word being more digestive (decipherable?) than the oral version.

[David Duff]

Yes, and also whilst 'listening' in conversation mode we are all guilty of thinking about what we are going to say next which does not aid concentration. And, boy, do you need concentration for this Gödel stuff!

[Lawrence Duff]

Have you read the JR Lucas book yet?

SoD

[Lawrence Duff]

Good wiki write-up to put you in the mood.

His work is the DNA of freedom; John Stuart Mill, Hayek, Popper et al, the mere creatures formed from it. Great and righteous they all are, but one and all they are down-stream from Lucas's proofs and arguments, his arguments being so fundamentally rooted in the irrefutable logic of Godel's proof.

And where in God's green and pleasant land did this gentleman choose to retire himself? Dorset! Spooky,

SoD

[David Duff]

Thanks, SoD, the Lucas book awaits but first I must finish Gleik (who has at least given me an intro), and then I just have to read Keegan's "American Civil War" otherwise JK will beat me up and DM will give me a hundred lines!

Oh, and all the best people retire to Dorset, or at least, South Somerset!

[dearieme]

"learn better from reading words rather than listening to them": when I was young I was told that in lectures the male students learnt best from what was written, the female from what was said.

P.S. How nice to see that Gödel is becoming fashionable again.

[David Duff]

Well, if I signal approval, DM, then the man's home and dry!

[dearieme]

You are the very model of a modern Blether-General.

[Dom]

I'd like to recommend "godel's proof", by earnest nagel.

[David Duff]

Thanks a million, Dom, I only manage two and a half paragraphs of a pdf version I found and already, at 8.45 in the morning, I have a headache!

The essence of your comment is correct, DM, but the rank is wrong - I only made corporal!

[Andrew Duffin]

Is this Gödel as in "Gödel, Escher, Bach"?

Now there's an addition to your reading list, D!

If you ever read and understand it all, please do a post about it because you'll be the first person I've ever "met" who has done so.

It's a fun read, though: Achilles and the Tortoise indeed.

[David Duff]

Yes, Andrew, that's the fella' and I'm happy to say that I think 'SoD' has my old copy which I don't think I ever finished - well, actually, I know I didn't!

However, what I do have is 'SoD's copy of "I Am a Strange Loop" by Douglas Hofstadter and after blowing the dust off it I see from the old bookmark still inside that I reached page 67!

Not even 'E' for Effort!

[Paul Minter]

Hello there, David. I'm a little late to the party on this post and see that Andrew Duffin has beaten me to it, as far as mentioning the Douglas Hofstadter book is concerned. I read it many years ago, still have it and occasionally dip into it; I particularly liked the explanations about the musical forms of Bach, Pachelbel etc.

However, as far as Godël is concerned, I think that his work much influenced that of Alan Turing.

[David Duff]

Hello, Paul, and I'm sorry but I had to rescue you from the Spam Bin - bloody-bloody TypePad!

I don't know about Turing but he has certainly influenced 'SoD' (Son of Duff) who never stops spouting off about him. He has given me a copy of a book entitled "Freedom of the Will" by J. R. Lucas who is, apparently, a Godelian disciple. I haven't read it yet but I was struck by this random sentence I chanced upon: "We cannot reduce reason to rules, or mind to matter. And therefore we cannot take a completely materialist or determinist view of the universe ..." That chimes with me.

[Paul Minter]

I'm getting used to TypePad consigning me to the spam bin! Thanks for rescuing me so promptly!

I don't know if you've read it, but there is a good biography of Alan Turing by Andrew Hodges, which I read a few years ago. Another 'hero' of mine is Paul Dirac; I've yet to read his biography, 'The Strangest Man' by Graham Farmelo, but am looking forward to it, after I've finished my Wilbur Smith tale of ancient Egypt 'River God'!

Must get back to the baseball now (watching on ESPN America) - the only sport I follow avidly now, for some strange reason.

[Lawrence Duff]

Your quote from Lucas "We cannot reduce reason to rules, or mind to matter..." illustrates the contrast between Lucas and Hofstadter's conclusions from Gödel's proof: Hofstadter understands Gödel to mean precisely that we are in fact reducible to a Turing machine / neural network / strange loop (delete as applicable) implemented in carbon!

Their dispute is bitter; Hofstadter quotes Lucas extensively in GEB and attacks him with the vicious bitchiness that only academics can manage - unequaled even by Luvvies.

I find it stunning that anyone can possibly conclude that we are Turing machines / neural networks / strange loops or any other analytical contraption after the Godel penny drops; to do so seems to have missed point so completely as to be diametrically opposite to what follows from the proof.

There's a beautifully succinct sum-up in Lucas's Wiki: -

Quote
(1961) began a lengthy and heated debate over the implications of Gödel's incompleteness theorems for the anthropic mechanism thesis, by arguing that:
1.Determinism ↔ For any human h there exists at least one (deterministic) logical system L(h) which reliably predicts h's actions in all circumstances.
2.For any logical system L a sufficiently skilled mathematical logician (equipped with a sufficiently powerful computer if necessary) can construct some statements T(L) which are true but unprovable in L. (This follows from Gödel's first theorem.)
3.If a human m is a sufficiently skillful mathematical logician (equipped with a sufficiently powerful computer if necessary) then if m is given L(m), he or she can construct T(L(m)) and
4.Determine that they are true--which L(m) cannot do.
5.Hence L(m) does not reliably predict m's actions in all circumstances.
6.Hence m has free will.
7.It is implausible that the qualitative difference between mathematical logicians and the rest of the population is such that the former have free will and the latter do not.
Unquote

What part of "I am not a Turing machine / neural network / strange loop" doesn't anyone understand after that?

The materialists / mechanists have been slain by Gödel and Lucas. What started with Socrates geeing up Aristotle and Plato for a two thousand year dispute, with Aristotle probably having had the upper hand, swung conclusively the other way from 1931. Out of fashion Gödel might be, but when the full realization dawns on mankind, which like all the great ideas, Christianity, Liberalism, even Marxism, might take some time, the world will be changed, imho, more so than any ism or ity that preceded it.

SoD

[David Duff]

Oh God, my head's hurting! I'm off shopping so I will return later.

Paul, don't take your incarceration in the Spam Box personally - you were sharing it with 'SoD' this morning!

[David Duff]

'SoD', somewhere around 4,5, and 6 above, you lost me!