On 12/14/2011 1:35 PM, Eduardo J. Dubuc wrote:
Is the following nonsense ?
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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]