Over the last two decades, William Lycan’s work on the semantics of conditionals has been distinguished by his careful attention to the connection between syntax and semantics, and more generally by his impeccable methodology. Lycan takes compositionality seriously, so he requires that the meaning of compound expressions like ‘even if’ be a combination of the constituent expressions, here ‘even’ and ‘if’. After reading his work, it’s hard to take seriously work that does not share this methodology.

This is a defense and extension of Stephen Yablo's claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form 'None of these subsequent sentences are true' generates the same instability in assigning truth values. I argue Yablo's technique of substituting infinity for self-reference applies to all so-called 'self-referential' paradoxes. A representative sample is provided which includes counterparts of the preface paradox, Pseudo-Scotus's validity paradox, the Knower, and other enigmas of the genre. I (...) rebut objections that Yablo's paradox is not a genuine liar by constructing a sequence of liars that blend into Yablo's paradox. I rebut objections that Yablo's liar has hidden self-reference with a distinction between attributive and referential self-reference and appeals to Gregory Chaitin's algorithmic information theory. The paper concludes with comments on the mystique of self-reference. (shrink)

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)

One of the few points of agreement to be found in mainstream responses to the logical and semantic problems generated by vagueness is the view that if any modification of classical logic and semantics is required at all then it will only be such as to admit underdetermined reference and truth-value gaps. Logics of vagueness including many valued logics, fuzzy logics, and supervaluation logics all provide responses in accord with this view. The thought that an adequate response might require the (...) recognition of cases of overdetermination and truth value gluts has few supporters. This imbalance lacks justification. As it happens, Jaskowski's paraconsistent discussive logic-a logic which admits truth value gluts-can be defended by reflecting on similarities between it and the popular supervaluationist analysis of vagueness already in the philosophical literature. A simple dualisation of supervaluation semantics results in a paraconsistent logic of vagueness based on what has been termed subvaluational semantics. (shrink)

In this book, Stephen Read sets out to rescue logic from its undeserved reputation as an inflexible, dogmatic discipline by demonstrating that its technicalities and processes are founded on assumptions which are themselves amenable to philosophical investigation. He examines the fundamental principles of consequence, logical truth and correct inference within the context of logic, and shows that the principles by which we delineate consequences are themselves not guaranteed free from error. Central to the notion of truth is the beguiling issue (...) of paradox. Its philosophical value, Read shows, lies in exposing the invalid assumption on which the paradox is built. Thinking About Logic also discusses logical puzzles which introduce questions relating to language, the world, and their relationship. (shrink)

This book contends that insufficient attention has been paid to the syntax of conditionals, as investigated by linguists.

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 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. (shrink)

Much recent work aimed at extending model-theoretic semantics has been formulated in response to specific needs, and little effort has been made in the direction of a truly "general" generalization. This work is an attempt to overcome these limitations. The unifying view is that semantics must account for the main relationships between languages and models in a uniform fashion, regardless of the specific conditions that may be imposed upon either notion. And the upshot is a general framework within which a (...) large variety of semantic theories naturally fall and from which the semantics of a wide class of logics can be obtained as special cases. ;The presentation is organized in two parts. In the first, a suitably general notion of a language is introduced along with a correspondingly general notion of a model, allowing for the possibility that the interpretation of some expressions be incomplete or inconsistent. The notion of a valuation is then systematically characterized by exploiting the idea that the value of an expression on a given model is always a function of the values it takes on the various ways of filling in the gaps and/or weeding out the gluts in the model. This account is shown to be grounded on some fundamental properties of the lattice of all admissible models, and may be viewed as a generalization of the method of super-valuations. ;The second part investigates the major properties of the resulting semantic apparatus. In particular, it is shown that the notion of logical validity as applied to single expressions is rather standard, and in fact reduces to the corresponding classical notion when this is available. Thus, gaps and gluts can be explained away as local phenomena that do not metastasize throughout the framework. However, with regard to the more comprehensive relation of entailment between expressions, the general picture is more intricate, as the notion of argument validity appears to escape the control of recursively specifiable systems. To shed light on this picture, a cost-benefit analysis of the proposed framework is offered in the concluding part. (shrink)