Does truth equal provability in the maximal theory?

Analysis 69 (2):233-239 (2009)
Abstract
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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DOI 10.1093/analys/anp007
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Axiomatizing Kripke's Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.

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