<biography, history of philosophy> Czech logician and mathematician (1906-1978). By applying an arithmetical method to the syntactical study of formalized logical languages, Goedel demonstrated in "Ueber formal unentscheidbare Saetze der Principia Mathematica und vervadter Systeme" ("On formally undecidable propositions of Principia Mathematica and related systems") (1931) that any consistent formal system powerful enough to contain arithmetic must contain at least one proposition whose truth or falsity cannot be proven within the system. It follows further that the consistency of a formal system cannot be evaluated from within the system itself. These discoveries brought an abrupt end to hopes for the purely-syntactical logicization of arithmetic. Goedel's own reflections on the significance of his work may be found in "The modern development of the foundations of mathematics in the light of philosophy" (1961). Recommended Reading: G–del's Proof (NYU, 1983); S. G. Shanker, Goedel's Theorem in Focus (Routledge, 1988); Raymond M. Smullyan, Forever Undecided: A Puzzle Guide to Goedel (Oxford, 1988); Raymond M. Smullyan, Goedel's Incompleteness Theorems (Oxford, 1992); and John L. Casti and Werner Depauli, Goedel: A Life of Logic, the Mind, and Mathematics (Perseus, 2000).
[A Dictionary of Philosophical Terms and Names]
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