Varieties of Logic

Nonfiction, Religion & Spirituality, Philosophy, Logic, Reference & Language, Language Arts
Cover of the book Varieties of Logic by Stewart Shapiro, OUP Oxford
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Stewart Shapiro ISBN: 9780191053863
Publisher: OUP Oxford Publication: September 4, 2014
Imprint: OUP Oxford Language: English
Author: Stewart Shapiro
ISBN: 9780191053863
Publisher: OUP Oxford
Publication: September 4, 2014
Imprint: OUP Oxford
Language: English

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like 'valid' and 'logical consequence' are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the 'debates' in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Logical pluralism is the view that different logics are equally appropriate, or equally correct. Logical relativism is a pluralism according to which validity and logical consequence are relative to something. In Varieties of Logic, Stewart Shapiro develops several ways in which one can be a pluralist or relativist about logic. One of these is an extended argument that words and phrases like 'valid' and 'logical consequence' are polysemous or, perhaps better, are cluster concepts. The notions can be sharpened in various ways. This explains away the 'debates' in the literature between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between those who advocate higher-order logic and those who insist that logic is first-order. A significant kind of pluralism flows from an orientation toward mathematics that emerged toward the end of the nineteenth century, and continues to dominate the field today. The theme is that consistency is the only legitimate criterion for a theory. Logical pluralism arises when one considers a number of interesting and important mathematical theories that invoke a non-classical logic, and are rendered inconsistent, and trivial, if classical logic is imposed. So validity is relative to a theory or structure. The perspective raises a host of important questions about meaning. The most significant of these concern the semantic content of logical terminology, words like 'or', 'not', and 'for all', as they occur in rigorous mathematical deduction. Does the intuitionistic 'not', for example, have the same meaning as its classical counterpart? Shapiro examines the major arguments on the issue, on both sides, and finds them all wanting. He then articulates and defends a thesis that the question of meaning-shift is itself context-sensitive and, indeed, interest-relative. He relates the issue to some prominent considerations concerning open texture, vagueness, and verbal disputes. Logic is ubiquitous. Whenever there is deductive reasoning, there is logic. So there are questions about logical pluralism that are analogous to standard questions about global relativism. The most pressing of these concerns foundational studies, wherein one compares theories, sometimes with different logics, and where one figures out what follows from what in a given logic. Shapiro shows that the issues are not problematic, and that is usually easy to keep track of the logic being used and the one mentioned.

More books from OUP Oxford

Cover of the book Tax By Design by Stewart Shapiro
Cover of the book Muhammad: A Very Short Introduction by Stewart Shapiro
Cover of the book Letters of Ralph Vaughan Williams, 1895-1958 by Stewart Shapiro
Cover of the book Chesterton and the Romance of Orthodoxy by Stewart Shapiro
Cover of the book The Judicial House of Lords by Stewart Shapiro
Cover of the book The Oxford Handbook of Synesthesia by Stewart Shapiro
Cover of the book Demosthenes the Orator by Stewart Shapiro
Cover of the book Home: A Very Short Introduction by Stewart Shapiro
Cover of the book Compassion by Stewart Shapiro
Cover of the book Think: A Compelling Introduction to Philosophy by Stewart Shapiro
Cover of the book Herder by Stewart Shapiro
Cover of the book International Criminal Procedure by Stewart Shapiro
Cover of the book Alcohol: No Ordinary Commodity by Stewart Shapiro
Cover of the book Work, Worklessness, and the Political Economy of Health by Stewart Shapiro
Cover of the book Process, Action, and Experience by Stewart Shapiro
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy