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.
HardcoverOut of Print ISBN: 9780262193115 196 pp. | 6.1 in x 9.1 in
This is an outstanding piece of work. From central considerations of philosophical logic, it draws out implications, through the study of quantification, for logic, mathematics, and linguistics. It is extremely well-organized and argued.
University of California
In this book Gila Sher asks which of the operations of the type of the quantifiers should be recognized as belonging to logic, and why. Drawing upon sources in model theory and the semantics of natural language, she extends our understanding of these questions and offers a deep explication of the distinction between logical and non-logical concepts. This is a work to be recommended for its contributions to linguistics, to logic, and to philosophy.
Professor of Philosophy, MIT
This book provides an extremely lucid and thorough discussion of the most fundamental features of modern approaches to quantification. Starting from Mostowski's and Tarski's seminal work, Sher develops a general notion of 'logicality' that serves as a criterion for distinguishing logical terms. Linguists interested in the empirical import of Generalized Quantifiers and branching quantification will find this terrific book indispensible.
Professor, Linguistics, University of Maryland
Gila Sher brings to bear on issues about generalizations of logic a more systematic philosophical perspective than has been worked out up to now. She defends a very interesting 'maximalist' characterization of logic terms, which arises naturally from an investigation of generalizations of quantifiers. This investigation will be of interest to logicians and linguists as well as philosophers.
Professor of Philosophy, Harvard University