Varieties of Logic
Stewart Shapiro
Abstract
This book challenges a longstanding view that logic is absolutely general, and topic neutral, by developing 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 some raging “debates” in the literature, such as that between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between advocates of higher-order logic and those who ... More
This book challenges a longstanding view that logic is absolutely general, and topic neutral, by developing 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 some raging “debates” in the literature, such as that between inferentialists and advocates of a truth-conditional, model-theoretic approach, and between advocates of higher-order logic and those who limit logic to first-order. This book then shows how different logics are appropriate for different mathematical theories. This immediately raises central questions concerning meaning, both of words and phrases like “valid” and “implies” and of the logical terminology itself, words like “or” and “not,” as they are used in rigorous mathematical deduction. Do those words have the same meaning, in different theories with different logics, or does the meaning shift from theory to theory? This book proposes that this question of meaning shift is itself context-sensitive; it depends on what is salient in a conversation comparing the theories. The result is a kind of contextualism concerning logic. This book also deals with questions concerning the logic of both formal and philosophical foundational studies, especially when the various theories under study do not have the same logic.
Keywords:
logic,
pluralism,
relativism,
contextualism,
validity,
logical consequence,
inferentialism,
model theory,
meaning,
foundations
Bibliographic Information
| Print publication date: 2014 |
Print ISBN-13: 9780199696529 |
| Published to Oxford Scholarship Online: September 2014 |
DOI:10.1093/acprof:oso/9780199696529.001.0001 |
