The implications of Godel's theorem
| Abstract | In 1931 Kurt Gödel proved two theorems about the completeness and consistency of first-order arithmetic. Their implications for philosophy are profound. Many fashionable tenets are shown to be untenable: many traditional intuitions are vindicated by incontrovertible arguments | |||||||||
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Zofia Adamowicz & Teresa Bigorajska (2001). Existentially Closed Structures and Gödel's Second Incompleteness Theorem. Journal of Symbolic Logic 66 (1):349-356.
Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. Philosophia Mathematica 17 (2):208-219.
Andrzej Mostowski (1952/1982). Sentences Undecidable in Formalized Arithmetic: An Exposition of the Theory of Kurt Gödel. Greenwood Press.
N. Shankar (1994). Metamathematics, Machines, and Gödel's Proof. Cambridge University Press.
George Boolos (1995). Introductory Note to Kurt Gödel's ``Some Basic Theorems on the Foundations of Mathematics and Their Implications''. In Solomon Feferman (ed.), Kurt Gödel, Collected Works. Oxford University Press.
Mark Steiner (2001). Wittgenstein as His Own Worst Enemy: The Case of Gödel's Theorem. Philosophia Mathematica 9 (3):257-279.
Matthias Baaz (ed.) (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press.
Raymond M. Smullyan (1992). Gödel's Incompleteness Theorems. Oxford University Press.
Panu Raatikainen (2005). On the Philosophical Relevance of Gödel's Incompleteness Theorems. Revue Internationale de Philosophie 59 (4):513-534.
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