Logic, Language, and Mathematics: Themes from the Philosophy of Crispin Wright

Cover
Logic, Language, and Mathematics: Themes from the Philosophy of Crispin Wright
Copyright
Dedication
Contents
Preface
Bio-bibliographic Note
	Books
	Editied Volumes
	Translation
	Festschriften
	Articles and Critical Stuides
		General Epistemology
		Relativism and Contextualism
		Realism and Truth
		Metasemantics
		Philosophy of Logic and Modality
		Philosophy of Mathematics (i)—General Issues
		Philosophy of Mathematics (ii)—Frege and Abstractionism
		Vagueness and the Sorites
		The Self and Self-knowledge
		Wittgenstein, Privacy, Rule-following
Notes on the Contributors
Part I: Frege and Neo-Logicism
	Chapter 1: Generality and Objectivity in Frege’s Foundations of Arithmetic
		Frege’s Desiderata
		The Problem of Apriority
		Separating the Logical from the Psychological
		The Solution to the Problem of Apriority
		Is Hume’s Principle Ad Hoc?
		Apriority and Foundational Security
		Frege Arithmetic and Hilbert’s Program
		Characterizing the Structure of the Natural Numbers
		References
	Chapter 2: A Logic for Frege’s Theorem
		1. Opening
		2. Predecession
		3. Ancestral Logic
		4. Schemata in Schematic Logic: A Digression
		5. Arché Logic
		7. Philosophical Considerations
		6. Frege’s Theorem
		Appendix
		References
	Chapter 3: Logicism and Logical Consequence
		1. Introduction
			Full Semantics
			Henkin Semantics
		2. Comparing (╞F) and (╞H) as Putative Definitions of Logical Consequence
		3. On Using L2K to Practise Arithmetic or Real Analysis
		4. Neo-Fregean Logicism
		References
	Chapter 4: Logicism and Second-Order Logic
		Editor’s Introduction
		1. Reductions of Arithmetic to Logic and Set Theory
		2. Some Objections to Logicism
		3. A Short Course in Second-Order Logic
		Postscript
		References
	Chapter 5: Solving the Caesar Problem—with Metaphysics
		1. Introduction
		2. Understanding a Definition
		3. Formalities
		4. The Proposal
		5. Three Questions
		6. Simple Perversity
		7. Polymorphous Perversity
		8. Brute Perversity
		9. Uniqueness
		10. Recap
		References
Part II: Vagueness
	Chapter 6. Vagueness and Intuitionistic Logic
		1. Wright’s Paradox of Sharp Boundaries
		2. Intuitionism as the Logic of Vagueness
		3. A Semantics for Vague Predicates that Validates Intuitionistic Logic
		4. The Sorites Revisited
		5. Problems for the Proposal
		References
	Chapter 7: Quandary and Intuitionism: Crispin Wright on Vagueness
		References
Part III: Logical Revisionism
	Chapter 8: Wright and Revisionism
		1. Background: Anti-Realism
		2. Background: Dummett’s Revisionary Argument(s)
		3. (Un)decidability: A First Try
		4. Reconstructing Dummett’s Revisionism: The Two-Step Naïve Revisionary Argument
		5. The One-Step Naïve Revisionary Argument
		6. The Rejection of the Naïve Arguments
		7. Wright’s Basic Revisionary Argument: Epistemic Ascent
		8. The Two-Step Revisionary Argument
		9. A Problem for Wright’s Basic Revisionary Argument
		10. Anti-Realism, Knowledge of Bivalence, and Knowledge of Excluded Middle
		11. The Awkward Wrinkle
		12. The Awkward Customer
		13. Concluding Remarks
		Appendix: Deductions
		References
	Chapter 9: Inferentialism, Logicism, Harmony,and a Counterpoint
		1. Introduction
			1.1 Sentence-Focused, Truth-Conditional Semantic
			1.2 Sequent-Focused, Inferential Semantics
		2. Inferentialism
			2.1 Brandom’s Inferentialism and the Choice of Logic
			2. 2 Other Noteworthy Points
		3. The Author’s Preferred Version of Inferentialism
		4. Constructive Logicism and Wright’s Neo-Fregean Logicism
		5. Inferentialist Accounts of the Meanings of Logical Operators
			5.1 Introduction and Elimination of Sentence-Forming Operators
			5.2 Introduction and Elimination of Term-Forming Operators
			5.3 Balance, or Equilibrium, between Introduction and Elimination Rules
		6. Explications of Balance
			6.1 Conservative Extension of Logical Fragments by New Operators
			6.2 Reduction Procedures (and Normalizability of Proofs)
			6.3 Harmony, by Reference to Strength of Conclusion and Weakness of Major Premise
		7. Earlier Formulations of Harmony
			7.1 The Formulation in Natural Logic
			7.2 The Formulation in Anti-Realism and Logic
			7.3 The Formulation in The Taming of the True
		8. Wright’s Tonkish Example
		9. The Revised Version of the Principle of Harmony
		10. On the Requirements of Full Use of Conditions and Rules
		11. Conclusion to the Discussion of Harmony
		References
Part IV: Metaphysical Possibility
	Chapter 10: CCCP
		1. Preliminary Remarks
		2. CCCP and Its Range of Application—Some Doubts about Its Applicability to Putative A Posteriori Necessities Aired and Answered
		3. Wright’s Examples
			SuperWright
			The Sceptical Mathematician
		4. A Possible Defence of Kripke’s Argument Rehearsed and Rejected
		5. Two Doubts about Wright’s Per Impossibile Model
		6. The Sceptical Mathematician Dissected, a Fresh Diagnosis, and an Alternative Model for Explaining Some Modal Illusions
		7. Some Stock-Taking
		8. The Complexities of Conceivability De Se, and another Route to Modal Illusion
		9. Concluding Remarks
		References
Replies: By Crispin Wright
Foreword
Replies to Part I: Frege and Logicism
	1. Frege’s Theorem
		1.1 Demopoulos
		1.2 The Epistemological Status of Hume’s Principle
		1.3 Justifying the Ontology
	2. Rendering unto Caesar . . .
		2.1 Prolegomena
		2.2 Three Proposals about the Latent Content of Good Abstractions
			2.2.1. Cross-World Import
			2.2.2 Sortals and Categories
			2.2.3 Real Definition
	3. (Neo-)Logicism and Higher-Order Logic
		3.1 Edwards
		3.2 Misgivings about the Logicality of Higher-order Logic
		3.3 Boolos
		3.4 Neutralism
		3.5 Heck
	References
Replies to Part II: Intuitionism and the Sorites
	1. The Basic Analogy
	2.. The Tolerance and ‘No Sharp Boundaries’Paradoxes
	3. Constraints on an Intuitionistic Solution
	4. Addressing Constraint 1: “The Basic RevisionaryArgument”
	5. One Objection to the Basic Revisionary Argument
	6. Two Further Objections
	7. Addressing Constraint 1: A Different Tack—Knowledge-Theoretic Semantics
	8. Addressing Constraint 1 (cont.): The Payoff
	9. Addressing Constraint 2
		9.1 Projective Error
		9.2 Inflated Normativity
		9.3 An Operator Shift?
		9.4 Irrelevant Truths
		9.5 Oversight of the Implications of Seamless Transition
	10. Addressing Constraint 3
	11. Rumfitt’s Semantics
	Coda: The ‘Forced March’ Paradox
	References
Replies to Part III: Logical Revisionism
	1. Tennant
	2. Why Care about Harmony?
	3. Another Puzzle
	4. Tennant’s Rogues’ Gallery
	5. Dummett on Indefinite Extensibility
	6. Shieh
	References
Reply to Part IV: The Epistemology of Metaphysical Possibility
	1. Kripke’s Challenge
		(i) Water is H₂O
		(ii) Hesperus is Phosphorus
	2. One Proposed Response
	3. Hale’s Objections and Countersuggestions
	4. A Different Response
	Coda
	References
Index Nominum
Index