The Boundary Stones of Thought An Essay in the Philosophy of Logic 1st Edition by Ian Rumfitt 019105335X 9780191053351
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ISBN 10: 019105335X
ISBN 13: 9780191053351
Author: Ian Rumfitt
The Boundary Stones of Thought seeks to defend classical logic from a number of attacks of a broadly anti-realist character. Ian Rumfitt is sympathetic to many of the premisses underlying these attacks. Indeed, he regards some of them as effective challenges to certain principles of classical semantics, notably the Principle of Bivalence. He argues, though, that they are ineffective against classical logic itself. The book starts by considering the general problem of how conflicts over logical laws may be rationally discussed and adjudicated. This leads to a consideration of the nature of logic: Rumfitt identifies the particular features that mark out logical consequence from other consequence relations, and he advances a new argument for the ancient thesis that there is a modal element in the notion of logical consequence. He develops a theory of that modal element in terms of perhaps incomplete possibilities, rather than fully determinate possible worlds. Some prima facie powerful arguments against the validity of certain classical logical laws are then analysed in the light of this account of logic. Throughout, care is taken to separate lines of anti-classical argument that, although distinct, are often run together or confused. The analysis yields, as by-products, semantic theories for a number of problematical areas of discourse. These areas include our talk about sub-atomic particles, about the infinite, about infinitesimals, about sets, and vague discourse. Rumfitt concludes by defending his stance of accepting classical logic while rejecting Bivalence, against Aristotle’s argument that a classical logician is committed to Bivalence. The ultimate aim is to liberate classical logic from the dead hand of classical semantics.
The Boundary Stones of Thought An Essay in the Philosophy of Logic 1st Table of contents:
1. Introduction
1.1 Disputes Over Logical Laws
1.2 The Scope of This Book, and the Nature of Disputes Over Basic Logical Laws
1.3 The Argument of the Present Book
Part I The Nature of Logic
2. Logical Laws
2.1 Consequence
2.2 Inference and Deduction
2.3 The Varieties of Deduction and of Implication Relations
2.4 Implications and Possibilities
2.5 The Role of Logic
2.6 Knowledge by Deduction
3. Logical Necessity
3.1 Logical Consequence Redux
3.2 The Controversy Over Logical Necessity
3.3 Notions of Necessity
3.4 Logical Necessity versus Apriority and Metaphysical Necessity
3.5 Logical and Metaphysical Necessity: The Paradox Resolved
Part II Five Attacks on Classical Logic
4. The Argument of Dummett’s ‘Truth’
4.1 The Argument against Classical Logic in Dummett’s ‘Truth’
4.2 The Exclusionary Theory of Conceptual Content
4.3 Where the Argument of ‘Truth’ Fails
4.4 Exclusion and Truth
4.5 An Exclusionary Semantics for the Language of the Propositional Calculus
4.6 The Choice of Logic within an Exclusionary Semantics
5. The Verificationist Attack on Classical Logic
5.1 The Strong Verificationist Attack on Classical Logic
5.2 How to Be a Strong Verificationist
5.3 A Renewed Threat to Classical Logic
5.4 Why One Should Not Be a Strong Verificationist
5.5 Dubious Grounds: McDowell’s Challenge to Classical Logic
6. Possibilities
6.1 Moderate Modal Realism and Possible Worlds
6.2 Reasons for Seeking an Unworldly Theory
6.3 Previous Unworldly Theories
6.4 The Structure of the Space of Possibilities; Truth-Ground Semantics
6.5 Distribution and Quantum Mechanics
6.6 Distribution and Regularity
7. Challenges from the Infinite and from the Infinitesimal
7.1 The Semantics and Logic of Negation
7.2 Statements With and Without Backs
7.3 The Intuitionists on Infinity
7.4 A Consolation Prize for the Intuitionist: Smooth Infinitesimal Analysis
7.5 Logic and Metaphysics
8. The Challenge from Vagueness
8.1 The Paradox of the Heap
8.2 Intuitionism as the Logic of Vagueness
8.3 A Semantics for Vague Predicates that Validates Intuitionistic Logic
8.4 Paradigms and Poles
8.5 A Semantics for Polar Predicates that Validates Classical Logic
8.6 The Sorites Revisited
8.7 Vagueness and Distribution
9. On the Use of Classical Logic in Set Theory
9.1 What is Mathematics About?
9.2 Attempts to Attain Categoricity
9.3 The Iterative Conception of Sets, and the Threat to Classical Logic
9.4 Attempts to Justify Classical Logic under the Iterative Conception
9.5 Classical Logic Justified via a Negative Translation
9.6 Classical Logic in Set Theories Weaker than ZF
9.7 ‘As Far as Possible’ versus ‘As Far as Necessary’
10. Conclusion
10.1 The Simple and Revised Arguments for Bivalence
10.2 Where the Arguments Go Wrong
10.3 Classical Logic versus Classical Semantics
References
Index
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