Shadows of Syntax: Revitalizing Logical and Mathematical ConventionalismWhat 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. |
Contents
PART II REVITALIZING LOGICAL CONVENTIONALISM | 53 |
PART III REVITALIZING MATHEMATICAL CONVENTIONALISM | 195 |
PART IV REFLECTIONS | 319 |
349 | |
Other editions - View all
Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism Jared Warren Limited preview - 2020 |
Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism Jared Warren Limited preview - 2020 |
Common terms and phrases
accept according actual allow already answer applied approach argued argument arithmetic assume assumption basic rules called Carnap chapter claims classical completely concept concerns conclusion connectives consider consistency conventionalism conventionalist defined definition determinate developed directly discussion dispositions distinction English epistemic equivalence example existence explained expression extension fact false follow formal fully give given idea important inference inference rules inferentialism inferentialist instance interpretation involves issue kind language lead least linguistic logic and mathematics logical truth mathematical matter meaning metaphysical metasemantic natural noted notion objects particular perhaps philosophical pluralism possible practice predicate premises principle problem proof provable prove quantifier question reason rejection relevant requires role rules seems semantic sense sentence similar simply standard structural syntactic Syntax theorem theory things translation trivial true understanding unrestricted inferentialism validity worries