The Bounds of Logic

Presents a philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying Tarskian logic and inspired by mathematical and linguistic developments. Using ideas from Tarski's work in semantics, Sher lays the foundation for a broader conception of logic.

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"The Bounds of Logic" presents a philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying Tarskian logic and inspired by mathematical and linguistic developments. 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 foundations for a broader conception of logic exemplified in numerous recent mathematical and linguistic writings. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. 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 underpinnings of logic. She proposes a "constructive" definition of logical terms, re-examines and extends the notion of branching quantification, and discusses various linguistic issues and applications.