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Sunday, 17 February 2019


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When you wake up, Gödel will still be a dead 'German'! One of those intellectuals who left so much political and social wreckage in his wake.

Wait! If I can sneak this one in under the deadline, I'll suggest you take to bed with you D.R. Hofstadter's incandescently brilliant Gödel, Escher, Bach: An Eternal Golden Braid, which will offer you firsthand evidence for Emerson's dictum that “The mind, once stretched by a new idea, never returns to its original dimensions.”

You think his loophole on the US Constitution is tricky, wait til you get to his Incompleteness Theorems - and yes, there are two of them!


Just seen Whiters comment - you wind-up merchant!

Ref Malcolm, yes, GEB EGB is brilliant. The very best teaching writing I've ever read.

But, but, but!!!

Hofstadter's conclusion on Godel's discoveries was diametrically wrong and opposite to Godel's.

Being an extremist materialist - mechanist, to be exact - Hofstadter couldn't bear the thought that there was truth and form beyond the reach of the most powerful logical system knowable to man, that of the Turing machine. This was the very discovery of Godel's incompleteness theorems. And the astonishing implications of that discovery: that for those truths and forms to exist, as Godel's proved they do, they do so in a system more powerful than man's brain and the Turing machine. We can only know of that system's existence and that there is truth and form within it, as per Godel's proofs, but we and our most powerful Turing machine tool can know nothing more of it and them.

What had been instinctively known to man since he had a brain was now proven by his most powerful machine tool in 1931.

So Hofstadter became a Godel denier, twisting and turning to excuse the Turing machine and man's mind's ignorance and limitation, insisting beyond reason, logic, and Godel's own proof that there was nothing more than a Turing machine, and we are just a meat version thereof.

Of the pre-Godel reasoners and philosophers whose instinct was right, Berkeley described us and all the material things we perceive and conceive of as not material at all, but rather all are the thoughts of God - we are but less powerful systems running inside a more powerful system.

From Godel and Berkeley one can really put materialism in its place, Berkeley again ...

"I do not argue against the existence of any one thing that we can apprehend, either by sense or reflection. That the things I see with mine eyes and touch with my hands do exist, really exist, I make not the least question. The only thing whose existence we deny, is that which philosophers call matter or corporeal substance. And in doing of this, there is no damage done to the rest of mankind, who, I dare say, will never miss it."

Of Hofstadter's contemporaries who understood Godel authentically you need to read: JR Lucas, "On the Freedom of the Will."

Hofstadter devotes nearly a whole chapter in GEB EGB of panicky rejection of JR Lucas, with some choice academic-on-academic bitchiness, if I remember rightly!

Great stuff.



It has been a long time -- over thirty years -- since I read GEB, and what has stayed with me, for the most part, is the virtuosic playfulness with which Hofstadter illustrated his theme of self-reference, and crept up on Gödel's Theorem. I know that Hofstadter is an ally of Daniel Dennett's in a model of consciousness that I did for a while, in my own early infatuation with absolute scientific materialism, find seductive and appealing -- but I got over it quite some time ago.

If I remember correctly, Hofstadter's assault on Lucas was based on a boiled-down version of the "Church-Turing thesis", which he represented as saying that anything a brain can do, no matter how seemingly intuitive or even magical, rests ultimately on a computable substrate.

Lucas had argued that Gödel's theorem meant that a mechanistic model of the mind had to be false. Hofstadter replied (quite unconvincingly if you ask me) that Lucas's objection only applied to the substrate -- to the lowest, most computational, level of the brain -- and that somehow the real magic, the very sort of stuff that Gödel proved that formal systems couldn't manage, could still emerge at higher levels of mind.

Meh. I think he's palming the card here (or having his cake and eating it too, or something). But the book is still brilliant, and it was a real eye-opener for me when I read it in my early thirties.

So: you are a Berkelian idealist? I can't say I'd describe myself as one, but as I think Yogi Berra once said, "It's tough to make doxastic commitments, especially about ontology."

(I'll refrain from kicking any rocks, anyway.)

"If I remember correctly, Hofstadter's assault on Lucas was based on a boiled-down version of the "Church-Turing thesis", which he represented as saying that anything a brain can do, no matter how seemingly intuitive or even magical, rests ultimately on a computable substrate."

JR Lucas would've agreed with that, when considering only the limited corporeal, material substrate of the "brain" as perceived by us.

But what about all the rest of the truths and forms that extend the "brain" into the greater "mind", these truths and forms being proven to exist by G in his Incompleteness theorems yet also proven to be beyond the reach of logical enquiry to discover the truth state or the formula of the form? And these extra-brain truths and forms being causal in the mind means that no Turing machine is ever going to model a mind and thus predict human behaviour.

If I remember rightly, Hofstadter's panicky rejection of JR Lucas was to adopt the second of the two possibilities which were the outcome of the Incompleteness theorems:


(1) Truth and form exists but the truth state and formulas thereof are unknowable to a Turing machine, or,

(2) Numbers are bullshit because they involve a logical contradiction in their axioms.

Hofstadter chose (2) in order to deny (1).

Imagine that! An academic in the field of mathematics, logic, and science denying the credibility of numbers! How fearful of the discovered limits of his profession, nay, discovery of the falsehood of his lifelong faith and raison d'etre, must he be to be a mathematician who denies numbers?!

But he did, and merely shrugged his shoulders and said, "So be it, numbers have a contradiction in their definition but I will still continue to work with them and hold them true. But I will not accept there is truth and form greater than a Turing machine and the logical tools of my trade and lifelong faith in materialism."

Wow. I mean, woooooow!

Just wait til the mainstream gets a hold of that whopper. It'll make the hockey stick "Hide the decline" look like a child's fib.


"Alice laughed. "There's no use trying," she said: 'one can't believe impossible things.'

'I daresay you haven't had much practice,' said the Queen. 'When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast."

- Lewis Carroll, who was also a mathematician, logician and Anglican deacon to boot!

Alice in Wonderland - published 1865.

Godel's Incompleteness Theorems - published 1931.

How's about dwelling on Keynes's old adage for a moment, eh Bob? "When the facts change, I change my mind. What do you do, sir?"



'The General Theory of Employment, Interest and Money' - published 1936. Pythagorean theorem - circa 500 bc. When people are right, they're right.

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