The Bounds of Logic: A Generalized Viewpoint

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 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 foundation for a new, broader conception of logic exemplified in numerous recent mathematical and linguistic writings. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her development of the notion of logicality for quantifiers of many variables 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 underpinnings 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.