The Universal Computer: The Road from Leibniz to Turing by Martin Davis

By Martin Davis

How do modern-day pcs practice this sort of big range of initiatives? Davis illustrates how the reply lies within the undeniable fact that pcs are primarily engines of common sense. Their and software program embodies recommendations constructed via logicians sugh as Gottfried Leibniz, Kurt Godel and Alan Turing.

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Of Lincoln, aged 1 4 years," and one P. W. B. took the trouble to write accusing G. B. of pla­ giarism. P. W. B. admitted that he was unable to provide a reference to the source from which he was accusing G. B. of copying, but regarded it as simply beyond belief that the work could have been produced by a BODLE TURNS GEORGE LOGIC INTO BODLE ALGEBRA 23 24 THE UNIVERSAL CO M P U T E R fourteen year old. The battle led to an exchange of several letters between G. B. and P. W. , all duly published in the Herald .

Not F. W & P. If W & P & H, then S. H. CON CLUSIONS: Not L . S. FRESE: FROM BREAKTHROUGH TO DESPAIR 51 Using the symbol --, to stand for "not" and the other symbols we've intro­ duced, this now becomes L�F --, f WA P WA PA H � S H •L s One final symbol should be mentioned: V standing for . . or The following table provides a summary of the symbols that have been intro­ duced: . --, v 1\ � v :3 . . not . . . or . . . and . . if . . , then . . every some At the end of the previous chapter, the sentence All failing students are either stupid or lazy was exhibited as an example whose logical structure would be missed by Boole's analysis.

Then . . every some At the end of the previous chapter, the sentence All failing students are either stupid or lazy was exhibited as an example whose logical structure would be missed by Boole's analysis. In Frege's logic, it is easy. Writing F(x ) for x is a failing student, S(x) for x is stupid, L(x) for x is lazy, the sentence can be expressed as (Vx)(F(x) � S(x) V L(x)) . 52 THE U N I VERSAL CO M P U T E R By now it should be clear that Frege was not just developing a mathe­ matical treatment of logic but also was actually creating a new language.

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