Truth And Paradox
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Truth and Paradox
Truth and Paradox offers a comprehensive account of truth values and the norms governing claims about truth, based on a new approach to logic and semantics. Since the seminal work of Tarski in the mid-twentieth century, the Liar paradox and other related paradoxes have stood in the way of a precise philosophical account of truth. Tim Maudlin draws on analogies from mathematical physics to explicate the origin of classical truth-value gaps, and to provide an account of truth that avoids any hierarchy of languages or of truth predicates. He also closely investigates our reasoning about truth, including apparently unobjectionable reasoning about the paradoxical sentences. The fallacies in that reasoning are located not in any inferences concerning truth, but in the foundations of standard logic. Blocking the paradoxical arguments requires emendation of classical logic, and the requisite emendations call into question the existence of any a priori logical truths. Maudlin also includes a discussion of facts and factuality, most particularly the question of whether there are any facts about truth. All philosophers interested in logic and language will find this a stimulating read.
Truth and Paradox
Truth and Paradox offers a comprehensive account of truth values and the norms governing claims about truth, based on a new approach to logic and semantics. Since the seminal work of Tarski in the mid-twentieth century, the Liar paradox and other related paradoxes have stood in the way of a precise philosophical account of truth. Tim Maudlin draws on analogies from mathematical physics to explicate the origin of classical truth-value gaps, and to provide an account of truth that avoids any hierarchy of languages or of truth predicates. He also closely investigates our reasoning about truth, including apparently unobjectionable reasoning about the paradoxical sentences. The fallacies in that reasoning are located not in any inferences concerning truth, but in the foundations of standard logic. Blocking the paradoxical arguments requires emendation of classical logic, and the requisite emendations call into question the existence of any a priori logical truths. Maudlin also includes a discussion of facts and factuality, most particularly the question of whether there are any facts about truth. All philosophers interested in logic and language will find this a stimulating read.
Saving Truth From Paradox
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 Gödel 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 paradoxes: 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.