Terms and Questions

Stewart Shapiro

in Foundations without Foundationalism

Published in print March 2000 | ISBN: 9780198250296
Published online November 2003 | e-ISBN: 9780191598388 | DOI:
 Terms and Questions

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A logic consists of a formal language, a deductive system and/or a model‐theoretic semantics. A formal language is a mathematical model of a natural language, focusing attention on features relevant to inference. A deductive system is a model of the practice of correctly inferring conclusions from premises; and model‐theoretic semantics is a model of the ways that sentences are about objects, and the ways that sentences can be true or false. These models can be good or bad, depending on the underlying purpose of the enterprise. On the view developed here, there is no question of finding the ‘correct’ or ‘true’ model. Different purposes suggest different models. The role of properties or sets in the semantics of second‐order logic is treated, marking the distinction between the logical conception of set and the iterative conception of set.

Keywords: deduction; formal language; inference; logic; mathematics; model theory; property; semantics; set; truth

Chapter.  11262 words. 

Subjects: Philosophy of Mathematics and Logic

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