David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Mind 115 (459):567 - 605 (2006)
It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of the breakdown than do others. The paper concludes with some morals about the nature of validity and about a possible alternative to the idea that mathematical theories are indefinitely extensible.
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Citations of this work BETA
Elia Zardini (2013). Naive Modus Ponens. Journal of Philosophical Logic 42 (4):575-593.
J. Ketland (2012). Validity as a Primitive. Analysis 72 (3):421-430.
Cezary Cieśliński (2010). Truth, Conservativeness, and Provability. Mind 119 (474):409-422.
Kevin Scharp (2014). Truth, Revenge, and Internalizability. Erkenntnis 79 (S3):597-645.
Justin Bledin (2014). Logic Informed. Mind 123 (490):277-316.
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