Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism free ebook download.

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Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism free ebook download

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Mathematics

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Author(s):	Jared Warren

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	0190086157
Pages:	408	OCR:		Quality:		ISBN13:
Uploader:	topron	Upload Date:	3/17/2022 11:04:09 AM

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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.
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Tags: Conventionalism Logical Mathematical Revitalizing Shadows Syntax

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