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Truth is one of the oldest and most central topics in philosophy. Formal theories explore the connections between truth and logic, and they address truth-theoretic paradoxes such as the Liar. Three leading philosopher-logicians now present a concise overview of the main issues and ideas in formal theories of truth. Beall, Glanzberg, and Ripley explain key logical techniques on which such formal theories rely, providing the formal and logical background needed to develop formal theories of truth. They examine the most important truth-theoretic paradoxes, including the Liar paradoxes. They explore approaches that keep principles of truth simple while relying on nonclassical logic; approaches that preserve classical logic but do so by complicating the principles of truth; and approaches based on substructural logics that change the shape of the target consequence relation itself. Finally, inconsistency and revision theories are reviewed, and contrasted with the approaches previously discussed. For any reader who has a basic grounding in logic, this book offers an ideal guide to formal theories of truth.
Metasemantics comprises new work on the philosophical foundations of linguistic semantics, by a diverse group of established and emerging experts in the philosophy of language, metaphysics, and the theory of content. The science of semantics aspires to systematically specify the meanings of linguistic expressions in context. The paradigmatic metasemantic question is accordingly: what more basic or fundamental features of the world metaphysically determine these semantic facts? Efforts to answer this question inevitably raise others. Where are the boundaries of semantics? What is the essence of the meaning relation? Which framework should we use for semantic theorizing? What are the intrinsic...
Pure inductive logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years plus the main contributions of the authors and their collaborators over the last decade to present a comprehensive account of the discipline within a single unified context. The exposition is structured around the traditional bases of rationality, such as avoiding Dutch Books, respecting symmetry and ignoring irrelevant information. The authors uncover further rationality concepts, both in the unary and in the newly emerging polyadic languages, such as conformity, spectrum exchangeability, similarity and language invariance. For logicians with a mathematical grounding, this book provides a complete self-contained course on the subject, taking the reader from the basics up to the most recent developments. It is also a useful reference for a wider audience from philosophy and computer science.
Ten specially written essays define the term 'constructivism' and ask crucial questions about the foundation of morality.
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterly fundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that arithmetic follows, purely logically, from a near definition. As Crispin Wright was the first to mak...
Many philosophers assume that to be a responsible agent is to be an apt target of responses like blame and praise. But what do these responses consist of, precisely? And do they really belong together, simply negative and positive symmetrical counterparts of each other? While there has been a lot of philosophical work on the nature of blame over the past 15 years--yielding multiple conflicting theories--there has been little on the nature of praise. Indeed, those few who have investigated praise--including both philosophers and psychologists--have concluded that it is quite different in some respects than blame, and that the two in fact may not be symmetrical counterparts at all. In this boo...
This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.
This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory of singularities is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the si...
This book contains twelve chapters by leading and up-and-coming philosophers on metaepistemology, that is, on the nature, existence and authority of epistemic facts. One of the central divides in metaepistemology is between epistemic realists and epistemic anti-realists. Epistemic realists think that epistemic facts (such as the fact that you ought to believe what your evidence supports) exist independently of human judgements and practices, and that they have authority over our judgements and practices. Epistemic anti-realists think that, if epistemic facts exist at all, they are grounded in human judgements and practices, and gain any authority they have from our judgements and practices. This book considers both epistemic realist and anti-realist perspectives, as well as perspectives that 'transcend' the realism/anti-realism dichotomy. As such, it constitutes the 'state of the art' with regard to metaepistemology, and will shape the debate in years to come.