Online research in philosophy

Zeno''s paradoxes of motion and the semantic paradoxes of the Liar have long been thought to have metaphorical affinities. There are, in fact, isomorphisms between variations of Zeno''s paradoxes and variations of the Liar paradox in infinite-valued logic. Representing these paradoxes in dynamical systems theory reveals fractal images and provides other geometric ways of visualizing and conceptualizing the paradoxes.

One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth.

I propose a solution to the aletheic paradoxes on which truth predicates are assessment-sensitive. Truth is not an antecedently plausible topic for a semantic relativist treatment; nevertheless, the aletheic paradoxes give us good reason to think that truth is an inconsistent concept, and there are good reasons to think that semantic relativism is appropriate for inconsistent concepts, especially those that display what I call empirical inconsistency. Thus, I show that a promising version of the best approach to the paradoxes is an application of semantic relativism to truth itself—arguing from results about the paradoxes and general considerations about language use to aletheic assessment-sensitivity. The paper is divided into three parts, the first on the aletheic paradoxes, the second on semantic relativism, and the third on assessment-sensitivity with respect to truth predicates. The first contains an overview of my preferred approach to the paradoxes, which entails that truth is an inconsistent concept that that should be replaced (for certain purposes) by a team of consistent concepts that can do its work without causing troubling paradoxes. The second part provides an overview of semantic relativism and its rivals. The third considers which treatment is most appropriate for inconsistent concepts in general and truth in particular. In it, I propose an assessment-sensitivity view of truth, discuss some prominent objections to semantic relativism, and review some issues that arise for approaches to the aletheic paradoxes.

This book is about one of the most baffling of all paradoxes--the famous Liar paradox. Suppose we say: "We are lying now." Then if we are lying, we are telling the truth; and if we are telling the truth we are lying. This paradox is more than an intriguing puzzle, since it involves the concept of truth. Thus any coherent theory of truth must deal with the Liar. Keith Simmons discusses the solutions proposed by medieval philosophers and offers his own solutions and in the process assesses other contemporary attempts to solve the paradox. Unlike such attempts, Simmons' "singularity" solution does not abandon classical semantics and does not appeal to the kind of hierarchical view found in Barwise's and Etchemendy's The Liar. Moreover, Simmons' solution resolves the vexing problem of semantic universality--the problem of whether there are semantic concepts beyond the expressive reach of a natural language such as English.

The aim of this paper is to show that Graham Priest's dialetheic account of semantic paradoxes and the paraconsistent logics employed cannot achieve semantic universality. Dialetheism therefore fails as a solution to semantic paradoxes for the same reason that consistent approaches did. It will be demonstrated that if dialetheism can express its own semantic principles, a strengthened liar paradox will result, which renders dialetheism trivial. In particular, the argument is not invalidated by relational valuations, which were brought into paraconsistent logic in order to avoid strengthened liar paradoxes.

Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures in the field offer new thoughts and arguments about the paradoxes.

In Beyond the Limits of Thought [2002], Graham Priest argues that logical and semantic paradoxes have the same underlying structure (which he calls the Inclosure Schema ). He also argues that, in conjunction with the Principle of Uniform Solution (same kind of paradox, same kind of solution), this is sufficient to 'sink virtually all orthodox solutions to the paradoxes', because the orthodox solutions to the paradoxes are not uniform. I argue that Priest fails to provide a non-question-begging method to 'sink virtually all orthodox solutions', and that the Inclosure Schema cannot be the structure that underlies the Liar paradox. Moreover, Ramsey was right in thinking that logical and semantic paradoxes are paradoxes of different kinds.

Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..

A number of philosophers have argued that the key to understanding the semantic paradoxes is to recognize that truth is essentially relative to context. All of these philosophers have been motivated by the idea that once a liar sentence has been uttered we can ‘step back’ and, from the point of view of a different context, judge that the liar sentence is true. This paper argues that this ‘stepping back’ idea is a mistake that results from failing to relativize truth to context in the first place. Moreover, context-relative liar sentences, such as ‘This sentence is not true in any context’ present a paradox even after truth has been relativized to context. Nonetheless, the relativization of truth to context may offer us the means to avoid paradox, if we can justifiably deny that a sentence about a context can be true in the very context it is about.

In this essay (for undergraduates) I introduce three of the famous semantic paradoxes: the Liar, Grelling’s, and the No-No. Collectively, they seem to show that the notion of truth is highly paradoxical, perhaps even contradictory. They seem to show that the concept of truth is a bit akin to the concept of a married bachelor—it just makes no sense at all. But in order to really understand those paradoxes one needs to be very comfortable thinking about how lots of interesting sentences talk about not dogs or cats or elections or baseball but sentences. That is, we need to get familiar analyzing sentences that talk about sentences.