Abstract for Field’s talk

There are strong pressures to restrict classical logic in connection with notions like truth (in “paradoxical constructions” such as Liar sentences), and to a lesser extent in connection with vagueness. But what is the non-classical logic to be like? A hitherto underappreciated problem is getting a logic that adequately deals with restricted quantification; the standard logics of vagueness, and previous work by myself and others on the logic of the paradoxes, all fail miserably on restricted quantification. About half the talk will be a review of some motivations for going non-classical on these problems; the rest will be on the special problems posed by restricted quantification, with a gesture toward a solution. (I do have a solution, available on my website for anyone interested (“Naive Truth and Restricted Quantification: Saving Truth a Whole Lot Better”), but it is rather technical and I won’t give very much detail about it in the lecture.)

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