Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism

Description

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. Title Page Copyright Page Dedication Contents Preface Acknowledgments Introduction Part I The Philosophical Background 1 What Is Conventionalism? 2 Linguistic Conventions Part II Revitalizing Logical Conventionalism 3 Unrestricted Logical Inferentialism 4 Logical Conventionalism 5 Alternative Conventions, Alternative Logics 6 The Epistemology of Logic 7 The Very Idea of Truth by Convention Part III Revitalizing Mathematical Conventionalism 8 From Logic to Mathematics 9 Metaontology, Existence, and Reference 10 Mathematical Determinacy 11 Truth, Paradoxes, Freedom, Applications, and Knowledge 12 Metamathematics versus Conventionalism Part IV Reflections 13 Old Slogans, New Dogmas 14 The Facts of the Matter Bibliography Name Index Subject Index