In this paper, I have two different purposes. The first one is destructive. I will show that it's not a good idea to have a theory of truth that is consistent but inconsistent. In order to bring out this point, it is useful to consider a particular case: FS (Friedman-Sheard). This theory proves the McGee's Sentence: "Not all iterated applications of the truth predicate to my name are true". Then, althought FS is not inconsistent, it turns out to be inconsistent. But in first-order case inconsistency implies that this theory of truth has not standard model. So, in theories of truth without standard models, the introduction of the truth-predicate to a first order theory does not maintain the standard ontology. The higher-order case is even worst. In second order theories with standard semantic the same introduction produces a theory that doesn't have a model. So, if an inconsistent theory of truth is bad, an unsatisfiable theory is really bad. The second propose is constructive. If we disarm the supertheory FS and adopt the sequence of theories FS0, FS1, FS2, FS3, … , the serie has the same virtues of FS without its disgusting consequences. So, my view recovers the best of FS without generating an omega-inconsistent theory. The price is to adopt a series of theories that extend indefinitely, abandoning the attempt to unify into a single theory for truth predicate of arithmetic

Monday, June 20, 12 – 13:30 p.m.,

Hartry Field (NYU)
Validity and the Epistemic 'Ought'

Venue: LCLI Seminar Room

Abstract

To be distributed soon