In his “Deep Inconsistency?” Eklund attacks arguments to the effect that some contradictions are true, and especially those based on the liar paradox, to be found in Priest’ In Contradiction. The point of this paper is to evaluate his case.

Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.

Dan Sperber, Deirdre Wilson; IX*—Loose Talk, Proceedings of the Aristotelian Society, Volume 86, Issue 1, 1 June 1986, Pages 153–172, https://doi.org/10.1093/ar.

This paper shows how to conservatively extend classical logic with a transparent truth predicate, in the face of the paradoxes that arise as a consequence. All classical inferences are preserved, and indeed extended to the full (truth—involving) vocabulary. However, not all classical metainferences are preserved; in particular, the resulting logical system is nontransitive. Some limits on this nontransitivity are adumbrated, and two proof systems are presented and shown to be sound and complete. (One proof system allows for Cut—elimination, but the (...) other does not.). (shrink)

In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues—especially so called "higher order" vagueness.

In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...) volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)

Philosophers from Hume, Kant, and Wittgenstein to the recent realists and antirealists have sought to answer the question, What are concepts? This book provides a detailed, systematic, and accessible introduction to an original philosophical theory of concepts that Christopher Peacocke has developed in recent years to explain facts about the nature of thought, including its systematic character, its relations to truth and reference, and its normative dimension. Particular concepts are also treated within the general framework: perceptual concepts, logical concepts, and (...) the concept of belief are discussed in detail. The general theory is further applied in answering the question of how the ontology of concepts can be of use in classifying mental states, and in discussing the proper relation between philosophical and psychological theories of concepts. Finally, the theory of concepts is used to motivate a nonverificationist theory of the limits of intelligible thought. Peacocke treats content as broad rather than narrow, and his account is nonreductive and non-Quinean. Yet Peacocke also argues for an interactive relationship between philosophical and psychological theories of concepts, and he plots many connections with work in cognitive psychology. (shrink)

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

In my “Deep Inconsistency”, I compared my meaning-inconsistency view on the liar with Graham Priest’s dialetheist view, using my view to help cast doubt on Priest’s arguments for his view. Jc Beall and Priest have recently published a reply to my article. I here respond to their criticisms. In addition, I compare the meaning–inconsistency view with Anil Gupta and Nuel Belnap’s revision theory of truth, and discuss how best to deal with the strengthened liar.

(Beall ed. The Revenge of the Liar, forthcoming from Oxford University Press) > The main presentation of my approach to the semantic paradoxes. I take them to show that understanding a natural language is sharing a cognitive relation to a logically false semantic theory with other speakers.