- School of Historical and Philosophical Studies - Research Publications
School of Historical and Philosophical Studies - Research Publications
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ItemNegation on the Australian PlanBerto, F ; Restall, G (SPRINGER, 2019-12)We present and defend the Australian Plan semantics for negation. This is a comprehensiveaccount,suitableforavarietyofdifferentlogics.Itisbasedontwoideas.The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilitiesbetweensuchpoints.WedefuseanumberofobjectionstothisPlan,raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.
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ItemNormal Proofs, Cut Free Derivations and Structural RulesRestall, G (Springer Netherlands, 2014)
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ItemFirst Degree Entailment, Symmetry and ParadoxRestall, G (Nicolaus Copernicus, 2017-03-01)Here is a puzzle, which I learned from Terence Parsons in his “True Contradictions” [8]. First Degree Entailment (fde) is a logic which allows for truth value gaps as well as truth value gluts. If you are agnostic between assigning paradoxical sentences gaps and gluts (and there seems to be no very good reason to prefer gaps over gluts or gluts over gaps if you’re happy with fde), then this looks no different, in effect, from assigning them a gap value? After all, on both views you end up with a theory that doesn’t commit you to the paradoxical sentence or its negation. How is the fde theory any different from the theory with gaps alone? In this paper, I will present a clear answer to this puzzle an answer that explains how being agnostic between gaps and gluts is a genuinely different position than admitting gaps alone, by using the formal notion of a bi-theory, and showing that while such positions might agree on what is to be accepted, they differ on what is to be rejected.
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ItemNo Preview AvailableReview of Advances in Proof-Theoretic SemanticsRESTALL, G (University of Notre Dame, 2016-05-15)
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ItemNo Preview AvailableFixed-Point Models for Theories of Properties and ClassesRESTALL, G (Victoria University of Wellington, 2017)There is a vibrant (but minority) community among philosophical logicians seeking to resolve the paradoxes of classes, properties and truth by way of adopting some non-classical logic in which trivialising paradoxical arguments are not valid. There is also a long tradition in theoretical computer science–going back to Dana Scott’s fixed point model construction for the untyped lambda-calculus–of models allowing for fixed points. In this paper, I will bring these traditions closer together, to show how these model constructions can shed light on what we could hope for in a non-trivial model of a theory for classes, properties or truth featuring fixed points.
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ItemPluralism and ProofsRestall, G (Kluwer Academic Publishers, 2014)Beall and Restall's Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical derivations to produce derivations for intuitionistic logic and for dual intuitionistic logic. The result is another way to understand the manner in which we can have different consequence relations in the same language. Furthermore, the proof-theoretic perspective gives us a different explanation of how the one concept of negation can have three different truth conditions, those in classical, intuitionistic and dual-intuitionistic models. © 2014 Springer Science+Business Media Dordrecht.
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ItemWhat are we to accept, and what are we to reject, while saving truth from paradox?Restall, G (SPRINGER, 2010-02)
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ItemOn t and u, and what they can doRestall, G (OXFORD UNIV PRESS, 2010-10)