Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism

by Jared Warren

Overview

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.

Product Details

ISBN-13:	9780190086152
Publisher:	Oxford University Press
Publication date:	08/03/2020
Pages:	408
Product dimensions:	6.00(w) x 9.30(h) x 1.30(d)

About the Author

Jared Warren is Assistant Professor of philosophy at Stanford University. He has published papers in metaphysics, epistemology, mind and language, metaphilosophy, and the philosophy of logic and mathematics.

Table of Contents

I. The Philosophical Background
1. What is Conventionalism
2. Linguistic Conventions

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

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

IV. Reflections
13. Old Slogans, New Dogmas
14. The Facts of the Matter

Editorial Reviews

"Philosophers of science, mathematics, and logic, including those educated to regard conventionalism as an early-20th-century curiosity, need to add this groundbreaking work to their reading lists. Summing Up: Essential. Upper-division undergraduates through faculty." — L. C. Archie, CHOICE

"Conventionalism about mathematics claims the same for mathematical truth. Conventionalism was popular among the logical positivists, with Carnap...His outstanding new book, Shadows of Syntax, builds upon these articles to provide the most sophisticated development of the conventionalist viewpoint that I have seen. Warren wrestles throughout with Quine's criticisms, contending that they are not nearly as powerful as is commonly supposed. Written in lucid, vibrant prose, this consistently gripping book offers numerous meaty arguments and ingenious gambits that merit sustained reflection...Shadows of Syntax is one of the most thought-provoking books that I have read in a long time. You should grapple with it yourself. You may come away more persuaded than I was. You will surely find it stimulating." — Michael Rescorla, History and Philosophy of Logic

From the Publisher