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QuoteRef: godeK_1931
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ThesaHelp:
references g-h
Topic:
limitations of formalism
Topic:
Godel's incompleteness theorem
Topic:
Liar's paradox and Russell's paradox
Topic:
mathematics as a formal system
Topic:
Turing machine
Group:
formalism
Reference
Godel, K., "On formally undecidable propositions of Principia mathematica and related systems I", Monatshefte fur Mathematik und Physik, 38, pp. 173-198, 1931. Google
Other Reference
page numbers from p. 592-617 in J. van Heijenoort, From Frege to Godel, Cambridge Massachusetts: Harvard University Press, 1967, translated by the editor
596 ;;Quote: although Principia mathematica and Zermelo-Fraenkel set theory formalize all of mathematics, they contain simple, undecidable problems
598 ;;Quote: gives Godel's sentence; it is true because it is unprovable in the system PM
598+;;Quote: Godel's sentence is similar to the Liar's paradox and Richard's antimony
614 ;;Quote: the consistency of a recursive consistent class of formulas is not provable in the system
616 ;;Quote: formal systems or formalisms are the same as Turing machines
616+;;Quote: can not prove the consistency of any consistent formal system that contains a certain amount of number theory
ThesaHelp: references g-h (299 items)
Topic: limitations of formalism (92 items)
Topic: Godel's incompleteness theorem (19 items)
Topic: Liar's paradox and Russell's paradox (25 items)
Topic: mathematics as a formal system (30 items)
Topic: Turing machine (30 items)
Group: formalism (9 topics, 473 quotes)