Shadows of Syntax

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 Epistemology of Logic

This chapter shows that unrestricted inferentialism/conventionalism leads to a naturalistically satisfying account of our a priori knowledge of logical validity. The chapter first lays the groundwork by discussing the general question of what conditions arguments need to meet in order to lead to knowledge of their conclusions. Following Boghossian, the chapter then argues that inferentialism/conventionalism is particularly well posed to allow rule-circular arguments to lead to a priori knowledge of the validity of our basic rules. Restricted inferentialists were often forced to complicate and sometimes abandon their accounts of logical knowledge in the face of bad company. By contrast, unrestricted inferentialism has no problem at all with bad company. All told, conventionalism gives a naturalistic account of our a priori knowledge of logic.

Inferentialism and the Epistemology of Logic

This essay attempts to clarify the project of explaining the possibility of ‘blind reasoning’—namely, of basic logical inferences to which we are entitled without our having an explicit justification for them. The role played by inferentialism in this project is examined and objections made to inferentialism by Paolo Casalegno and Timothy Williamson are answered. Casalegno proposes a recipe for formulating a counterexample to any proposed constitutive inferential role by imaging a subject who understands the logical constant in question but fails to have the capacity to make the inference in question; Williamson’s recipe turns on imagining an expert who continues to understand the constant in question while having developed sophisticated considerations for refusing to make it. It’s argued that neither recipe succeeds.

Closing Reflections1

In these brief comments, the author discusses the origins of his interest in the epistemology, why he has always found inferentialist accounts of it implausible, and why the similarities between the epistemology of logic and the epistemology of other domains have always been salient to him. There is also a brief account of the asymmetry between the role of internalism in Boghossian’s epistemology and the role of externalism in the author’s epistemology. Finally, there are some reflections on the ways in which we can hope to improve the shaky methodology of traditional epistemology, for example by making more use of formal methods and the findings of experimental psychology.

The Epistemology of Logic-Based Therapy

This article describes some core elements of Logic-Based Therapy and Consultation and examines some of their epistemic properties.