David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Analysis 69 (2):233-239 (2009)
According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the principles involved in this argument – when applied to our maximal mathematical theory – are unsound. This paper defends the received view by showing that there is a way of seeing the truth of the Goedel sentence which is immune to Field's strategy.
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References found in this work BETA
Hartry Field (1994). Are Our Logical and Mathematical Concepts Highly Indeterminate? Midwest Studies in Philosophy 19 (1):391-429.
Volker Halbach & Leon Horsten (2006). Axiomatizing Kripke's Theory of Truth. Journal of Symbolic Logic 71 (2):677 - 712.
Jeffrey Ketland (1999). Deflationism and Tarski's Paradise. Mind 108 (429):69-94.
Jeffrey Ketland (2005). Deflationism and the Gödel Phenomena: Reply to Tennant. Mind 114 (453):75-88.
Neil Tennant (2002). Deflationism and the Gödel Phenomena. Mind 111 (443):551-582.
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