The Boundary Stones of Thought: An Essay in the Philosophy of Logic

Hardcover | April 22, 2015

byIan Rumfitt

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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 classicalsemantics, 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, andhe 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 againstthe 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 acceptingclassical 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.

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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 classicalsemantics, notably the Principle of Bivalenc...

Ian Rumfitt studied philosophy at Balliol College, Oxford and at Princeton University. He has taught the subject at Keele University, the University of Michigan at Ann Arbor, University College, Oxford (where he was a Tutorial Fellow for seven years), and at Birkbeck College, London (where he was Professor of Philosophy from 2005 unti...
Format:HardcoverDimensions:368 pages, 9.21 × 6.14 × 1 inPublished:April 22, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198733631

ISBN - 13:9780198733638

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Table of Contents

1. IntroductionPART ONE: THE NATURE OF LOGIC2. Logical laws3. Logical necessityPART TWO: FIVE ATTACKS ON CLASSICAL LOGIC4. The argument of Dummett's 'Truth'5. The verificationist attack on classical logic6. Possibilities7. Challenges from the infinite and from the infinitesimal8. The challenge from vagueness9. On the use of classical logic in set theory10. ConclusionBibliographyIndex