MIT Press (1991)

Gila Sher
University of California, San Diego
The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications.
Keywords Logic  Definition of Logical Terms (Constants)  Logical Consequence  Tarski  Generalized Quantifiers  Branching Quantifiers  Criterion of Logicality  Mathematics and Logic  Semantics
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Reprint years 1991
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ISBN(s) 0262193116   0262193116   9780262193115
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Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
Truth and Objectivity.Crispin Wright - 1992 - Harvard University Press.

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