School of Historical and Philosophical Studies - Research Publications
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ItemA Paraconsistent Model of Vagueness(OXFORD UNIV PRESS, 2010-10)
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ItemBridging the Modal Gap( 2010)
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ItemSECRECY IN CONSEQUENTIALISM: A DEFENCE OF ESOTERIC MORALITY(WILEY-BLACKWELL PUBLISHING, INC, 2010-03)Abstract Sidgwick's defence of esoteric morality has been heavily criticized, for example in Bernard Williams's condemnation of it as ‘Government House utilitarianism.’ It is also at odds with the idea of morality defended by Kant, Rawls, Bernard Gert, Brad Hooker, and T.M. Scanlon. Yet it does seem to be an implication of consequentialism that it is sometimes right to do in secret what it would not be right to do openly, or to advocate publicly. We defend Sidgwick on this issue, and show that accepting the possibility of esoteric morality makes it possible to explain why we should accept consequentialism, even while we may feel disapproval towards some of its implications.
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ItemExtensionality and Restriction in Naive Set Theory(Springer Science and Business Media LLC, 2010-02)
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ItemTRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY(Cambridge University Press (CUP), 2010-03)This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis.
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ItemHopes Fade For Saving Truth(CAMBRIDGE UNIV PRESS, 2010-01)
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ItemInclosures, Vagueness, and Self-Reference(University of Notre Dame, 2010-01-01)In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related issues— especially so called “higher order” vagueness.
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ItemWitchcraft, Relativism and the Problem of the Criterion(SPRINGER, 2010-01)
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ItemOn t and u, and what they can do(OXFORD UNIV PRESS, 2010-10)