| Description |
1 online resource |
| Contents |
Introduction -- Prologue -- Part I. Monism vs. Pluralism -- 1. Conceptions of Logical Consequence -- 1.1 Tarski on logical consequence -- 1.2 Accounts of logical consequence -- 1.3 Philonian consequence -- 1.4 The necessity of logic -- 1.5 The formality of logic -- 1.6 'The intuitive concept of consequence' -- 2. What Is Monism? -- 2.1 Defining monism-a first pass -- 2.1.1 A scheme -- 2.1.2 Admissible formalizations -- 2.1.3 Admissible logics -- 2.1.4 A true logic -- 2.1.5 The one true logic -- 2.2 Epistemics -- Appendix: the least true logic -- 3. Against Pluralism -- 3.1 Extensionally divergent formalizations -- 3.2 Horses for courses: languages and domains -- 3.2.1 Horses for courses: interlinguistic -- 3.2.2 Horses for courses: intralinguistic -- 3.3 Pluralism proper -- 3.3.1 Beall and Restall's modest pluralism -- 3.3.2 Shapiro's eclectic pluralism -- 3.4 Beall and Restall's modest pluralism -- 3.4.1 The 'settled core' of consequence -- 3.5 Shapiro's eclectic pluralism -- 3.5.1 SIA as a test case for pluralism -- 3.6 Metalogical reasoning -- 3.7 Logical nihilism -- 3.8 A problem for logical pluralism -- 3.8.1 All true logics -- 3.8.2 The single correct metalogic -- 3.8.3 Some arbitrary true logic -- 3.8.4 Each true logic -- 3.8.5 Summary -- 3.9 Two further issues -- 3.9.1 Non-deductive reasoning -- 3.9.2 A problem for monism? -- 3.10 Conclusion -- Appendix: metalogical meaning variance -- PART II. The logos hypothesis -- 4. The Lâ#x88;#x9E;Gâ#x88;#x9E;S Hypothesis -- 4.1 Introduction -- 4.2 Type and sort -- 4.3 The Lâ#x88;#x9E;Gâ#x88;#x9E;S Hypothesis -- 4.4 Back to origins -- 4.5 Top-down and bottom-up arguments -- 4.6 Pure FTTâ#x88;#x9E;â#x88;#x9E; defined -- 4.7 Semantics for pure FTTâ#x88;#x9E;â#x88;#x9E; -- 4.8 What are the formulas of pure FTTâ#x88;#x9E;â#x88;#x9E;? -- 5. Beyond the Finitary -- 5.1 Generalized quantifiers -- 5.2 The concurrence argument for FOL -- 5.3 Beyond FOL: 'there are infinitely many' -- 5.3.1 The finitude objection -- 5.3.2 The mathematical validity objection -- 5.3.3 The finite-description objection -- 5.3.4 The indeterminacy objection -- 5.3.5 Diagnosis -- 5.4 Generalization: 'there are ̧Â#x9D;Å#x93;... many' -- 5.5 Beyond SOL: infinitary conjunction -- 5.5.1 Superhumans -- 5.5.2 Generalization -- 5.6 Beyond SOL: cardinality quantifiers -- 5.7 Conclusion -- Appendix: technical results -- 6. Isomorphism Invariance -- 6.1 Introduction -- 6.2 Form as schematic -- 6.2.1 MacFarlane on formality -- 6.2.2 Form as normative -- 6.2.3 Form as topic-neutral -- 6.2.4 Form as abstraction -- 6.4 A necessary condition on OTL -- 6.5 Miscellaneous comments -- 6.6 McGee's Theorem -- 6.6.1 Isomorphism invariance -- 6.6.2 Relations -- 6.6.3 Caveats -- 6.6.4 Isomorphism-invariant relations -- 7. Towards the One True Logic -- 7.1 The logic's type -- 7.2 Theory of models -- 7.3 Mathematical consequences? -- Appendix: the generalized quantifier 'most' -- PART III. OBJECTIONS -- 8. The Heterogeneity Objection -- 8.1 Introduction -- 8.2 Uniform-isomorphism invariance -- 8.3 Feferman's invariantism -- 8.4 Bonnay's invariantism -- 8.5 Conclusion -- 9. The Overgeneration Objection -- 9.1 Introduction -- 9.2 Sensitivity -- 9.3 CH is logically true -- 9.4 CH is determinate -- 9.5 CH is epistemically determined -- 9.6 CH and neutrality -- 9.6.1 Dialectical neutrality -- 9.6.2 Informational neutrality -- 9.7 CH is logically expressible -- 9.8 Identity -- 9.9 Conclusion -- Appendix: logical notions -- 10. The Absoluteness Objection -- 10.1 The absoluteness objection -- 10.2 Meaning-theoretic motivations -- 10.3 Anti-realist motivations -- 10.4 Independence motivations -- 10.5 Conclusion -- 11. The Intensional Objection -- 11.1 Unicorn negation -- 11.2 Modal responses -- 11.3 Biting the bullet -- 11.4 An open question -- 11.5 Conclusion -- Conclusion -- Bibliography -- Index |
| Summary |
Logical monism is the claim that there is a single correct logic, the 'one true logic' of our title. The view has evident appeal, as it reflects assumptions made in ordinary reasoning as well as in mathematics, the sciences, and the law. In all these spheres, we tend to believe that there are determinate facts about the validity of arguments. Despite its evident appeal, however, logical monism must meet two challenges. The first is the challenge from logical pluralism, according to which there is more than one correct logic. The second challenge is to determine which form of logical monism is the correct one. One True Logic is the first monograph to explicitly articulate a version of logical monism and defend it against the first challenge. It provides a critical overview of the monism vs pluralism debate and argues for the former. It also responds to the second challenge by defending a particular monism, based on a highly infinitary logic. It breaks new ground on a number of fronts and unifies disparate discussions in the philosophical and logical literature. In particular, it generalizes the Tarski-Sher criterion of logicality, provides a novel defence of this generalization, offers a clear new argument for the logicality of infinitary logic and replies to recent pluralist arguments |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based on online resource; title from home page (Oxford Academic, viewed August 4, 2023) |
| Subject |
Logic.
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Monism.
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History & Philosophy.
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MATHEMATICS.
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Logic.
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PHILOSOPHY.
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Language.
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Logic
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Monism
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| Genre/Form |
Electronic books
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| Form |
Electronic book
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| Author |
Paseau, Alexander, author.
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| ISBN |
9780192565242 |
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0192565249 |
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9780191868214 |
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0191868213 |
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