One of the fundamental theses of this book is that logical consequence and logical truth are not simply given, but arise as conventions among the users of logic. Thus Syverson explains convention within a game-theoretic framework, as a kind of equilibrium between the strategies of players in a game where they share common knowledge of events—a revisiting of Lewis's Convention that argues that convention can be reasonably treated as coordination equilibria. Most strikingly, a realistic solution is provided for Gray's classic coordination problem, wherein two generals can only communicate with each other through unreliable means.

What is the source of logical and mathematical truth? This volume revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. In Shadows of Syntax, Jared Warren offers the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. He argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims. In Part I, Warren explains exactly what conventionalism amounts to and what linguistic conventions are. Part II develops an unrestricted inferentialist theory of the meanings of logical constants that leads to logical conventionalism. This conventionalist theory is elaborated in discussions of logical pluralism, the epistemology of logic, and of the influential objections that led to the historical demise of conventionalism. Part III aims to extend conventionalism from logic to mathematics. Unlike logic, mathematics involves both ontological commitments and a rich notion of truth that cannot be generated by any algorithmic process. To address these issues Warren develops conventionalist-friendly but independently plausible theories of both metaontology and mathematical truth. Finally, Part IV steps back to address big picture worries and meta-worries about conventionalism. This book develops and defends a unified theory of logic and mathematics according to which logical and mathematical truths are reflections of our linguistic rules, mere shadows of syntax.

The daring idea that convention - human decision - lies at the root both of necessary truths and much of empirical science reverberates through twentieth-century philosophy, constituting a revolution comparable to Kant's Copernican revolution. This book provides a comprehensive study of Conventionalism. Drawing a distinction between two conventionalist theses, the under-determination of science by empirical fact, and the linguistic account of necessity, Yemima Ben-Menahem traces the evolution of both ideas to their origins in Poincaré's geometric conventionalism. She argues that the radical extrapolations of Poincaré's ideas by later thinkers, including Wittgenstein, Quine, and Carnap, eventually led to the decline of conventionalism. This book provides a fresh perspective on twentieth-century philosophy. Many of the major themes of contemporary philosophy emerge in this book as arising from engagement with the challenge of conventionalism.

This wide-ranging collection of essays explores the nature of logic and the key issues and debates in the metaphysics of logic.

Rudolf Carnap's deflationary approach to ontology is once again attracting considerable interest and support. Eleven original essays by leading voices in metametaphysics deepen our understanding of Carnap's contributions to metaontology, and explore how his legacy can be mined for insights into the contemporary debate.

Henri Poincare (1854–1912) was one of the greatest mathematicians and philosophers of all time. He founded topology and made important contributions to theoretical physics. Yet despite his numerous achievements Poincare never constructed a systematic philosophy. In this book, Elie Zahar presents Poincare’s work for the first time as a unified system of thought.