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Philosophy - Logic & Philosophy of Language | The Realism-Antirealism Debate in the Age of Alternative Logics

The Realism-Antirealism Debate in the Age of Alternative Logics

Rahman, Shahid, Primiero, Giuseppe, Marion, Mathieu (Eds.)

2012, XVI, 348 p.

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  • The first work on the Realism-Antirealism debate in the Age of Alternative Logics
  • Large variety of different new topics are undertaken from the viewpoint of the well-known distinction `realism vs. antirealism'
  • Shows the most recent developments in philosophical logic

The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference.

The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view.

Content Level » Research

Keywords » Alternative Logics - Alternative logics - Anti-realism - Antirealism - Cantorian set theory - Explicit epistemic Logic - Frege - Frege-Tarski - Intuitionistic Logic - Jaakko Hintikka - Michael Dummet - Philosophy of Logic - Tarski

Related subjects » Logic & Philosophy of Language - Philosophy - Theoretical Computer Science

Table of contents 

Preface.- Acknowledgements.- List of Contributors.- Contents.- On When a Disjunction is Informative; Patrick Allo.- 1. Pluralism about Consequence and Content.- 2. Situated and Worldly Content.- 3. Factual and Constraining Content.- 4. Modelling Content.- 5. Three Objections Revisited.- References.- My own truth; Alexandre Billon.- 1. Introduction.- 2. The Truth-Teller is context-sensitive.- 3. The Truth-Teller is relative.- 4. Other pathologies of self-reference.- 4.1 The Liar.- 4.2 Other semantic pathologies.- 4.3 Immunity to revenge problems.- 5. Dissolutions, cassations and resolutions.- References.- Which Logic for the Radical Anti-Realist?; Denis Bonnay; Mikail Cozic.- 1. Introduction.- 2. From anti-realism to substructural logic.- 3. Life without structural rules.- 4.The anti-realist justification of substructural logic.- 5. A way out for radical anti-realism?.- 6. Conclusion.- References.- Moore’s Paradox as an argument against anti-realism; Jon Cogburn.- 1. Introduction.- 2. Moorean validity and proof theoretic semantics.- 3. On the inadvisability of biting the bullet.- 4. A new restriction strategy.- 5. Is antirealism a Moorean Validity? Reflections on Fitch’s proof and Dummett’s program.- 6. Further reflections on Fitch’s proof.- 7. Berkeley and Davidson’s use of Moorean validities.-References.- The Neutrality of Truth in the debate Realism vs. Anti-Realism; Maria J. Frapolli.- 1. Introduction.- 2. Truth.- 3. Realism and Antirealism.- 4. The prosentential view.- 5. The syntactic function of the truth predicate.- 6.The pragmatic function of the truth predicate.- 7. Epistemology and metaphysics.- References.- Modalities without worlds; Reinhard Kahle.- 1. Modal logic.- 2. Possible Worlds Semantics.- 3. The role of semantics.- 4. Criticism of modal logic .- 5. An alternative analysis of modalities: Possibility.- 5.1 Possibility as independence.- 5.2 Epistemic possibility.- 5.3 The future.- 5.4 Ontological modesty.- 5.5  A cross check.- 6. An alternative analysis of modalities: Necessity.- 6.1 Necessity as binary relation.- 6.2 Variety of alternatives.- 6.3 Unary necessity.- 6.4 The normative nature of unary necessity.- 7. The temporal aspect.- 7.1 The dynamics of the axiom system.- 7.2 Nested modalities.- 8. Conclusion.- References.-  Antirealism, meaning and truth-conditional semantics; Neil Kennedy.- 1. Introduction.- 2. Dummett’s antirealism.- 3. Harmony and classical logic.- 4. Antirealist meaning and holism.- 5. The disputed class.- 6. The obtaining of Truth conditions.- 7. By way of conclusion.- References.- Game Semantics and the Manifestation Thesis; Mathieu Marion.- 1. Rethinking the Anti-Realist Challenge.- 2. Towards a Renewal.- 3. The the Manifestation Argument and the Manifestation Thesis.- 4. Concluding Remarks.- References.- Conservativeness and Eliminability for Anti-Realistic Definitions; Francesca Poggiolesi.- 1. Realistic Conservativeness and Eliminability.- 2. Anti-Realistic Definitions and Sequent Calculus.- 3. Anti-realistic Conservativeness.- 4. Anti-Realistic Eliminability.- 5. Logical Variant of the Sequent Calculus.- 6. The Modal Case.- 7. Anti-realistic definitions in past attempts..- References.- Realism, Antirealism, and Paraconsistency; Graham Priest.- 1. Introduction.- 2. Classical vs Intuitionist Logic.- 3. The Logic of Constructible Negation.- 4.Paraconsistency.- 5. Quantified Intuitionist Logic.- 6. Quantified Logics of Constructible Negation.- 7. Conclusion.-  References.- Type-theoretical Dynamics; Giuseppe Primiero.- 1. Introduction.- 2. Conditions for type-theoretical Dynamics.-  3. Belief Revision.- 4. Belief Merging.- 5. Some Remarks.- 5.1 Admitting Beliefs.- 5.2 Degrees of Belief.- References.- Negation in the Logic of First Degree Entailment and Tonk: A Dialogical Study; Shahid Rahman.- 1. Introduction.- 2. Dialogical Logic and Meaning.- 2.1 Local Meaning.- 2.2 Global Meaning.- 2.3 Play level, Strategic Level and Tonk-like-Operators.- 3. The Dialogical Meaning of Negation and the Logic of First Degree Entailment.- The Logic of First-Degree Entailment.- 3.1 Hintikka’s Trees for Enquiry Games and FDE-Negation.- 3.2 Micheal Dunn’s relational semantics for FDE.- 3.3 A Dialogical Study of FDE-Negation.- Switch of Choices. Is Duality-Negation a Tonk-Like Operator?.- Dual Negation and Dual Dialogical-Contexts.- The conditional in Dual Contexts.- Appendices.- Appendix 1. Note on symmetric and asymmetric versions of the E-Rule.- Appendix 2. The disjunctive property and the symmetric rule for intuitionistic logic.- Appendix 3. Examples.- Appendix 4. Soundness and completeness of Hintikka-trees* for Enquiry Games in relation to M. Dunn’s relational semantics for FDE.- References.- Necessary Truth and Proof; Stephen Read.- 1. Truthmaker Realism.- 2. Incompleteness.- 3. Anti-realism.- 4. Logical Pluralism.- 5. Contingency.- References.- Anti-Realist Classical Logic and Realist Mathematics; Greg Restall.- 1. Introduction.- 2. Logic.- 3. Mathematical Practice and Mathematical Theories.- 4. Consequences of the View.- 5. Miscellaneous Concluding Remarks.-  References.- A Tale of two Anti-Realisms; Sanford Shieh.- 1. Epistemological Anti-Realism.- 2. The Bivalence Argument.- 3. Conceptual Anti-Realism.- 4. The Rejection of the Bivalence Argument.- 5. Proof-Theoretic Validity.- References.- A Double Diamond of Judgement; Goran Sundholm.- 1. Introduction.- 2.Judgement and inference: the traditional picture.- 3. The great Bohemian: unary judgement.- 4. Brentano and an alternative unary approach.- 5. Frege’s judgement: truth applied to function/argument structure.- 6. Cambridge truth-making.- 7. Constructivist alternative: Proofs of propositions.- References.- Stable Philosophical Systems and Radical Anti-Realism; Joseph Vidal-Rosset..- 1. Philosophical systems and philosophy of logic.- 1.1 Vuillemin’s classification.- 1.2 What is a stable philosophical system?.- 2. A case of philosophical dispute: Strict Finitism vs.Intuitionism.- 2.1 The contemporary strict finitist argument.- 2.2 Linear Logic and Radical Anti-Realism.- 2.3 The feasibility criteria: polynomial time computability.- 3. Conclusion: laziness or heroism?.- References.- Two Diamonds Are More Than One; Elia Zardini.- 1. Introduction and Overview.- 2. The Paradox of Knowability and the Restriction Strategy.- 3. A New Threat of Collapse of Feasible Knowability on Actual Knowledge.- 4.Transitivity, Factivity, and the Relativity of Accessibility.- 5. Epistemic Possibility of Knowledge and Feasible Knowability.- 6. Conclusion.- References.-

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