Saving Truth From Paradox

by Hartry Field

Saving Truth from Paradox is an ambitious investigation into paradoxes of truth and related issues, with occasional forays into notions such as vagueness, the nature of validity, and the incompleteness theorems. Hartry Field presents a new approach to the paradoxes and provides a systematic and detailed account of the main competing approaches.

Part One examines Tarski's, Kripke's, and Lukasiewicz's theories of truth, and discusses validity and soundness, and vagueness. Part Two considers a wide range of attempts to resolve the paradoxes within classical logic. In Part Three Field turns to non-classical theories of truth that that restrict excluded middle. He shows that there are theories of this sort in which the conditionals obey many of the classical laws, and that all the semantic paradoxes (not just the simplest ones) can be handled consistently with the naive theory of truth. In Part Four, these theories are extended to the property-theoretic paradoxes and to various other paradoxes, and some issues about the understanding of the notion of validity are addressed. Extended paradoxes, involving the notion of determinate truth, are treated very thoroughly, and a number of different arguments that the theories lead to "revenge problems" are addressed. Finally, Part Five deals with dialetheic approaches to the
approaches which, instead of restricting excluded middle, accept certain contradictions but alter classical logic so as to keep them confined to a relatively remote part of the language. Advocates of dialetheic theories have argued them to be better than theories that restrict excluded middle, for instance over issues related to the incompleteness theorems and in avoiding revenge problems. Field argues that dialetheists' claims on behalf of their theories are quite unfounded, and indeed that on some of these issues all current versions of dialetheism do substantially worse than the best theories that restrict excluded middle.

Genres: Philosophy, Logic

Hardcover

First published March 6, 2008

About the author

HARTRY FIELD (B.A., Wisconsin; M.A., Ph. D. Harvard), Silver Professor of Philosophy, specializes in metaphysics, philosophy of mathematics, philosophy of logic, and philosophy of science. He has had fellowships from the National Science Foundation, the National Endowment for the Humanities, and the Guggenheim Foundation. He is the author of Science Without Numbers (Blackwell 1980), which won the Lakatos Prize, of Realism, Mathematics and Modality (Blackwell 1989), and of Truth and the Absence of Fact (Oxford 2001). Current interests include objectivity and indeterminacy, a priori knowledge, causation, and the semantic and set-theoretic paradoxes.

Reviews

[Henry · Rating 5 out of 5]

Excluded middle believers will NEVER recover

[Joshua Stein · Rating 4 out of 5]

Field's Saving Truth from Paradox is, and should be, a long and challenging read. Even for those familiar with the background literature in logic and philosophy of math, the coverage that he gives to a wide number of theories of truth and their treatment of paradoxes can require some serious digestion, but overall it makes for a cool and satisfying read.

This is, like so many of the things that I post links to, not a book for the uninitiated. Field doesn't even pretend to be writing for those outside of philosophical logic, nor should he. The material is of serious interest within that field, and not of much interest outside of it. For those who are interested in the material and proficient enough to get a lot out of it, it is a very good piece of writing and I strongly recommend it.