Varieties of LogicLogical 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, perhapsbetter, 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-theoreticapproach, and between those who advocate higher-order logic and those who insist that logic is first-order. Shapiro 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 anon-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 questionsabout 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. |
Contents
Relativism Pluralism Tolerance | 1 |
Varieties of Pluralism and Relativism for Logic | 17 |
Structure An Eclectic Perspective | 63 |
We Mean What We Say But What Do We Mean? | 88 |
Meaning and Context | 126 |
Theory and Metatheory Logic and Metalogic I Philosophical and Foundational Studies | 163 |
Theory and Metatheory Logic and Metalogic II Metatheoretic Perspective | 182 |
Recapitulation and Conclusion | 205 |
210 | |
221 | |
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Common terms and phrases
argue argument forms arithmetic articulated axioms Beall and Restall claim classical logic classicist concerning logic conclusion connectives and quantifiers context of assessment context-sensitive course deductive system different logics different meanings different theories dispute eclectic orientation epistemic ex falso quodlibet example excluded middle first-order logic folk-relative folk-relativism formal language framework given HA+CT Hilbertian holds indexical contextualism intuitionistic analysis intuitionistic logic intuitionistic theories invalid invoke Kripke least legitimate logical consequence logical particles logical terminology logical terms logician mathematical theories mathematicians matter meaning-shift meta-theory modal model theory model-theoretic monistic natural language natural number negation nilsquare non-logical notion of consequence notion of logical paraconsistent logics Peano arithmetic perhaps perspective philosophical pluralism predicate present proof-theoretic propositions question Quine real numbers relation relative relativism relevance logics Restall's second-order semantics sentence set theory Shapiro smooth infinitesimal analysis sort statement structures Tarski theorem thesis True Logic truth truth-value valid variable various Waismann words