{"product_id":"varieties-of-logic-paperback","title":"Varieties of Logic - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eStewart Shapiro\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003eLogical 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 \u003cem\u003eVarieties of Logic\u003c\/em\u003e, 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eA 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. \u003cp\u003e\u003c\/p\u003eThe 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. \u003cp\u003e\u003c\/p\u003eLogic 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.\u003cbr\u003e\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cbr\u003eStewart Shapiro, \u003cem\u003eOhio State University\u003c\/em\u003e, \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003eStewart Shapiro received an MA in mathematics in 1975, and a PhD in philosophy in 1978, both from the State University of New York at Buffalo. He is currently the O'Donnell Professor of Philosophy at the Ohio State University. He specializes in philosophy of mathematics, logic, philosophy of logic, and philosophy of language, with a recent interest in semantics, and is the author of \u003cem\u003eFoundations without foundationalism: a case for second-order logic\u003c\/em\u003e (OUP, 1991), \u003cem\u003ePhilosophy of mathematics: structure and ontology\u003c\/em\u003e (OUP, 1997), \u003cem\u003eVagueness in context\u003c\/em\u003e (OUP, 2006), and a textbook in the philosophy of mathematics, \u003cem\u003eThinking about mathematics: the philosophy of mathematics\u003c\/em\u003e (OUP, 2000).\u003cbr\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 240\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.6 x 8.4 x 5.4 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e August 16, 2020\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47540207190237,"sku":"9780198822691","price":72.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0811\/9867\/8237\/files\/d0tIbjR4N3hlQmV3eGR5V3ZUTXBBZz09.webp?v=1772578054","url":"https:\/\/handfulofbooks.com\/products\/varieties-of-logic-paperback","provider":"Handful of Books","version":"1.0","type":"link"}