Download PDF by Copeland B.J., et al. (eds.): Computability: Turing, Goedel, Church, and beyond

By Copeland B.J., et al. (eds.)

ISBN-10: 0262018993

ISBN-13: 9780262018999

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Additional info for Computability: Turing, Goedel, Church, and beyond

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3. 6–1. 3. 9 The Post-War Turing on Learning Turing did not attempt to explain what he called the “activity of the intuition,” either in his 1939 paper nor the wartime letters to Newman. A human mathematician working according to the rules of a fixed logical system is in effect a proof-producing machine; and when intuition supplies the mathematician with some new means of proof, he or she becomes a different proof-producing machine, capable of a larger set of proofs. How does the mathematician achieve this transformation from one proof-finding machine to another?

Reprinted with English translation as “On formally undecidable propositions of Principia Mathematica and related systems I” in Gödel, Collected Works I, 144–195. Gödel, K. 1933. The present situation in the foundations of mathematics. In Gödel, Collected Works III, 45–53. Gödel, K. 1934. On undecidable propositions of formal mathematical systems. In Gödel, Collected Works I, 346–369. Gödel, K. 193?. Undecidable Diophantine propositions. In Gödel, Collected Works III, 164–175. Gödel, K. 1946. Remarks before the Princeton bicentennial conference on problems in mathematics.

V: Correspondence, H–Z, ed. S. Feferman, J. W. , W. Goldfarb, C. Parsons, and W. Sieg. Oxford: Clarendon Press. 32 B. Jack Copeland and Oron Shagrir Good, I. J. 1948. Early notes on electronic computers. Unpublished. University of Manchester National Archive for the History of Computing, MUC/Series 2/a4. , ed. 1988. The Universal Turing Machine: A Half-Century Survey. Oxford: Oxford University Press. Hilbert, D. 1902. Mathematical problems: Lecture delivered before the International Congress of Mathematicians at Paris in 1900.

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Computability: Turing, Goedel, Church, and beyond by Copeland B.J., et al. (eds.)


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