Graduate studies at Western
Mind 115 (459):567 - 605 (2006)
|Abstract||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|
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Configure|
Similar books and articles
Scott Aikin (2009). A Consistency Challenge for Moral and Religious Beliefs. Teaching Philosophy 32 (2):127-151.
Anthony S. Gillies (2001). A New Solution to Moore's Paradox. Philosophical Studies 105 (3):237-250.
Enrico Martino (2006). Fictional Propositions and the Unprovability of Consistency. Grazer Philosophische Studien 72 (1):201-210.
Ryan Christensen (2011). Theories and Theories of Truth. Metaphysica 12 (1):31-43.
George Boolos (1979). The Unprovability of Consistency: An Essay in Modal Logic. Cambridge University Press.
Richard Tieszen (1994). Mathematical Realism and Gödel's Incompleteness Theorems. Philosophia Mathematica 2 (3):177-201.
Andrew Bacon (2013). A New Conditional for Naive Truth Theory. Notre Dame Journal of Formal Logic 54 (1):87-104.
Jan Woleński (2010). Truth and Consistency. Axiomathes 20 (2-3):347-355.
Added to index2009-01-28
Total downloads33 ( #41,965 of 729,377 )
Recent downloads (6 months)1 ( #61,087 of 729,377 )
How can I increase my downloads?