Graduate studies at Western
Journal of Philosophical Logic 32 (2):139-177 (2003)
|Abstract||The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema "True( ) ↔ A", and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in "ordinary" contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True( ) with A within the language. The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are "defective". We can in fact define a hierarchy of "defectiveness" predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes ("revenge problems") involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various "levels of defectiveness" can all be made coherent together within a single object language|
|Keywords||conditionals Curry paradox determinateness Liar paradox truth|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Joachim Bromand (2002). Why Paraconsistent Logic Can Only Tell Half the Truth. Mind 111 (444):741-749.
Greg Restall (2007). Curry's Revenge: The Costs of Non-Classical Solutions to the Paradoxes of Self-Reference. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
Alexandre Billon (2011). My Own Truth ---Pathologies of Self-Reference and Relative Truth. In Rahman Shahid, Primiero Giuseppe & Marion Mathieu (eds.), Logic, Epistemology, and the Unity of Science, Vol. 23. springer.
Jason Zarri (2010). A Dilemma for Dialetheism. The Dualist 15 (Spring):21-31.
Kevin Scharp (2013). Truth, the Liar, and Relativism. Philosophical Review 122 (3):427-510.
J. C. Beall (ed.) (2007). Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
Hartry Field (2007). Solving the Paradoxes, Escaping Revenge. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
Thomas Hofweber (2007). Validity, Paradox, and the Ideal of Deductive Logic. In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
Laurence Goldstein (2009). A Consistent Way with Paradox. Philosophical Studies 144 (3):377 - 389.
Added to index2009-01-28
Total downloads28 ( #49,847 of 723,067 )
Recent downloads (6 months)2 ( #36,863 of 723,067 )
How can I increase my downloads?