Por Hartry Field (New York University).

Abstract: Lukasiewicz continuum-valued logic has been popular in dealing with vagueness, and prominent logicians (e.g. Thoralf Skolem and C. C. Chang) have been very interested in its application to the semantic, property-theoretic and set-theoretic paradoxes. But it isn’t ultimately workable for either. This talk will sketch how to generalize it to make it work (not for set theory, because of extensionality, but for truth and properties, and also for vagueness). The resulting theory is more powerful than Kripke's in that it treats conditionals and restricted (as well as unrestricted) quantifiers. I’ll avoid technical details, but give enough of the idea so that those technically inclined shouldn’t have much problem filling them in. There will also be a bit of discussion of why we need two kinds of conditionals.