Re: __?__

[Vaughan Pratt <pratt@cs.stanford.edu>]

On 12/14/2011 1:35 PM, Eduardo J. Dubuc wrote:
> Is the following nonsense ?
>
> http://arxiv.org/abs/1112.2141

The concluding paragraph of the conclusion, on page 37, reads as follows.

"Kurt Gödel provided innovative but convoluted proofs of some normal 
properties of a simple recurrence relation, accompanied by spectacular 
misinterpretations. Gödel’s incompleteness conjectures have beguiled 
generations of readers lost in the sea of his complex proofs; his 
unwarranted conclusions have smashed mathematical reason against the 
petrified relics of ancient misunderstandings. But other thinkers have 
seen more clearly; most importantly George Boole, whose brilliant 
synthesis of algebra and logic has shown the way to modern computer 
science. Perhaps it is time to raise the lamp in Boole’s lighthouse, and 
to let the beacon of unified mathematics and logic guide a renewed quest 
for the rational understanding of our world."

Let's go through this point by point.

1.  "...convoluted proofs..."  Gödel's 1931 paper was 25 pages. 
Norman's is 48.  Sounds like a pot calling the kettle black.

2.  "Gödel’s incompleteness conjectures have beguiled generations of 
readers lost in the sea of his complex proofs..."  Evidently Norman is 
one of those readers, since he appears to have mistaken a legitimate 
proof for a conjecture.

3.  "But other thinkers have seen more clearly; most importantly George 
Boole, whose brilliant synthesis of algebra and logic has shown the way 
to modern computer science."  Since Boole's book predated Gödel's proof 
by 77 years, Norman's implication would seem to be that logicians 
including Gödel had failed to grasp Boole's deep insights throughout 
that period, and furthermore throughout the following 80 years up to the 
present, obliging Norman to bring them to light.

Similar logic would show that Newton invented quantum mechanics on the 
basis of his corpuscular theory of light.

If there is any legitimate point in Norman's article, it would be along 
the lines of Kripke's semantics of the liar paradox (to which Haim 
Gaifman had a nice follow-up).  Norman may well have rediscovered 
Kripke's insight, but in that case he should either discuss the 
connection or explain why his references make a reference to Kripke 
unnecessary.  Boole himself is not sufficient for that purpose because 
arithmetic mod 2 did not occur to him as a model of his axioms.

Vaughan Pratt


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