- School of Historical and Philosophical Studies - Research Publications
School of Historical and Philosophical Studies - Research Publications
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ItemNo Preview AvailableGeometric Models for Relevant LogicsRestall, G ; Duntsch, I ; Mares, E (Springer International Publishing, 2022-01-01)Alasdair Urquhart’s work on models for relevant logics is distinctive in a number of different ways. One key theme, present in both his undecidability proof for the relevant logic R (Urquhart 1984) and his proof of the failure of interpolation in R (Urquhart 1993), is the use of techniques from geometry (Urquhart 2019). In this paper, inspired by Urquhart’s work, I explore ways to generate natural models of R+ from geometries, and different constraints that an accessibility relation in such a model might satisfy. I end by showing that a set of natural conditions on an accessibility relation, motivated by geometric considerations, is jointly unsatisfiable.
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ItemTruth-Tellers in Bradwardine’s Theory of TruthRestall, G ; Kann, C ; Loewe, B ; Rode, C ; Uckelman, SL (Peeters, 2018)
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ItemAssertion, Denial, Accepting, Rejecting, Symmetry and ParadoxRESTALL, G ; Caret, C ; Hjortland, O (Oxford University Press, 2015)Proponents of a dialethic or “truth-value glut” response to the paradoxes of self-reference argue that “truth-value gap” analyses of the paradoxes fall foul of the extended liar paradox: “this sentence is not true.” If we pay attention to the role of assertion and denial and the behaviour of negation in both “gap” and “glut” analyses, we see that the situation with these approaches has a pleasing symmetry: gap approaches take some denials to not be expressible by negation, and glut approaches take some negations to not express denials. But in the light of this symmetry, considerations against a gap view point to parallel considerations against a glut view. Those who find some reason to prefer one view over another (and this is almost everyone) must find some reason to break this symmetry.
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ItemDecorated Linear Order Types and the Theory of ConcatenationRESTALL, G ; Cacic, ; Pudlak, ; Urquhart, ; Visser, (Cambridge University Press, 2010)
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ItemProof Theory and Meaning: the context of deducibilityRESTALL, G (Cambridge University Press, 2010)
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ItemProofnets for S5: sequents and circuits for modal logicRESTALL, G ; Dimitracopoulos, C ; Newelski, L ; Normann, D ; Steel, J (Cambridge University Press, 2008)
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ItemTruth-makers, entailment and necessityRestall, G ; Lowe, EJ ; Rami, A (Acumen Publishing Limited, 2011-01-01)
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ItemMinimalists about truth can (and should) be epistemicists, and it helps if they are revision theorists tooRESTALL, GA ; BEALL, JC ; ARMOUR-GARB, B (Oxford University Press, 2005)
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ItemAlways moreRestall, G ; Pelis, M (COLLEGE PUBLICATIONS, 2010)
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ItemBarriers to ImplicationRESTALL, G ; Russell, ; Pigden, (Palgrave Macmillan, 2010)