The Bounds of Logic: A Generalized Viewpoint by Gila Sher

By Gila Sher

The Bounds of Logic provides a brand new philosophical idea of the scope and nature of common sense according to serious research of the rules underlying sleek Tarskian good judgment and encouraged through mathematical and linguistic developments.

Extracting vital philosophical rules from Tarski's early paintings in semantics, Sher questions no matter if those are absolutely learned via the traditional first-order procedure. the reply lays the root for a brand new, broader belief of common sense exemplified in different contemporary mathematical and linguistic writings. by means of as a rule characterizing logical phrases, Sher establishes a primary lead to semantics. Her improvement of the inspiration of logicality for quantifiers of many variables and her paintings on branching are of significant value, for linguistics.

Sher outlines the limits of the recent good judgment and issues out many of the philosophical ramifications of the hot view of common sense for such matters because the logicist thesis, ontological dedication, the function of arithmetic in good judgment, and the metaphysical underpinnings of good judgment. She proposes a "constructive" definition of logical phrases, reexamines and extends the concept of branching quantification, and discusses a number of linguistic matters and purposes.

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2 Does the advent of generalized quantifiers mark a genuine break­ through in modern logic? Has logic, in Russell's turn of expression. given thought new wings once again? Generalized quantifiers were first introduced as a "natural generaliza­ tion of the logical quantifiers" by A. Mostowski in his 1957 paper "On a Generalization of Quantifiers,,3. Mostowski conceived his generalized quantifiers semantically as functions from sets of objects in the universe of a model for first-order logic to the set of truth values.

Preface Whatever the fate of the particulars, one thing is certain. There is no going back to the view that logic is [standard] first-order logic. Jon Barwise, Model- Theoretic Logics When I went to Columbia University to study with Prof. Charles Parsons, I felt I was given a unique opportunity to work on "foundational" issues in logic. I was interested not so much in the controversies involving logicism, intuitionism, and formalism as in the ideas behind "core" logic: first-order Fregean, Russellian, Tarskian logic.

On the other hand, since empirical evidence is not given precedence, the proposals for linguistic applications are presented merely as theoretical hypotheses, and their empirical value is left for the linguist to judge. My search for new logical forms is prompted by interests on several levels. For one thing, it is a way of asking the general philosophical questions: What is logic? Why should logic take the form of standard mathematical logic? For another, it is an attempt to understand more deeply the fundamental principles of modern logic.

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The Bounds of Logic: A Generalized Viewpoint by Gila Sher
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