ThesaHelp: references gh
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. 173198, 1931.
Google
Other Reference
page numbers from p. 592617 in J. van Heijenoort, From Frege to Godel, Cambridge Massachusetts: Harvard University Press, 1967, translated by the editor
Quotations
596 ;;Quote: although Principia mathematica and ZermeloFraenkel 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

Related Topics
ThesaHelp: references gh (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)
