
116On preservingLogica Universalis 1 (2): 295310. 2007.. This paper examines the underpinnings of the preservationist approach to characterizing inference relations. Starting with a critique of the ‘truthpreservation’ semantic paradigm, we discuss the merits of characterizing an inference relation in terms of preserving consistency. Finally we turn our attention to the generalization of consistency introduced in the early work of Jennings and Schotch, namely the concept of level.

113How Do Logics Explain?Australasian Journal of Philosophy 96 (1): 157167. 2018.Antiexceptionalists about logic maintain that it is continuous with the empirical sciences. Taking antiexceptionalism for granted, we argue that traditional approaches to explanation are inadequate in the case of logic. We argue that Andrea Woody's functional analysis of explanation is a better fit with logical practice and accounts better for the explanatory role of logical theories.

73Logical Pluralism and Logical FormLogique Et Analyse 61 (241): 2542. 2018.Disputes about logic are commonplace and undeniable. It is sometimes argued that these disputes are not genuine disagreements, but are rather merely verbal ones. Are advocates of different logics simply talking past each other? In this paper we argue that pluralists (and anyone who sees competing logics as genuine rivals), should reject the claim that real disagreement requires competing logics to assign the same meaning to logical connectives, or the same logical form to arguments. Along the wa…Read more

69Against logical generalismSynthese 118. forthcoming.The orthodox view of logic takes for granted the central importance of logical principles. Logic, and thus logical reasoning, is to be understood as a system of rules or principles with universal application. Let us call this orthodox view logical generalism. In this paper we argue that logical generalism, whether monist or pluralist, is wrong. We then outline an account of logical consequence in the absence of general logical principles, which we call logical particularism.

53Remarks on the Scott–Lindenbaum TheoremStudia Logica 102 (5): 10031020. 2014.In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of inference, familiar from Gentzen, in which one may consider multiple conclusions rather than single formulas. Scott used this idea to good effect in a number of projects including the axiomatization of manyvalued logics (of various kinds) and a reconsideration of the motivation of C.I. Lewis. Since he left the subject it has been vigorously…Read more

42Worlds and times: NS and the master argumentSynthese 181 (2): 295315. 2011.In the fourteenth century, Duns Scotus suggested that the proper analysis of modality required not just moments of time but also “moments of nature”. In making this suggestion, he broke with an influential view first presented by Diodorus in the early Hellenistic period, and might even be said to have been the inventor of “possible worlds”. In this essay we take Scotus’ suggestion seriously devising first a doubleindex logic and then introducing the temporal order. Finally, using the temporal o…Read more

24Getting the Most Out of InconsistencyJournal of Philosophical Logic 44 (5): 573592. 2015.In this paper we look at two classic methods of deriving consequences from inconsistent premises: RescherManor and SchotchJennings. The overall goal of the project is to confine the method of drawing consequences from inconsistent sets to those that do not require reference to any information outside of very general facts about the set of premises. Methods in belief revision often require imposing assumptions on premises, e.g., which are the important premises, how the premises relate in nonl…Read more

24Decidability of an Xstit LogicStudia Logica 102 (3): 577607. 2014.This paper presents proofs of completeness and decidability of a nontemporal fragment of an Xstit logic. This shows a distinction between the nontemporal fragments of Xstit logic and regular stit logic since the latter is undecidable. The proof of decidability is via the finite model property. The finite model property is shown to hold by constructing a filtration. However, the set that is used to filter the models isn’t simply closed under subformulas, it has more complex closure conditions. …Read more

23Level CompactnessNotre Dame Journal of Formal Logic 47 (4): 545555. 2006.The concept of compactness is a necessary condition of any system that is going to call itself a finitary method of proof. However, it can also apply to predicates of sets of formulas in general and in that manner it can be used in relation to level functions, a flavor of measure functions. In what follows we will tie these concepts of measure and compactness together and expand some concepts which appear in d'Entremont's master's thesis, "Inference and Level." We will also provide some applicat…Read more

18Reflecting rules: A note on generalizing the deduction theoremJournal of Applied Logic 13 (3): 188196. 2015.The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all socalled ‘derivable rules’ can be encoded into the object languag…Read more

147. Preserving Logical StructureIn Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic, University of Toronto Press. pp. 105144. 2009.In this paper Gillman Payette looks at various structural properties of the underlying logic X, and ascertains if these properties will hold of the forcing relation based on X. The structural properties are those that do not deal with particular connectives directly. These properties include the structural rules of inference, compactness, and compositionality among others. The presentation of the logic X is carried out in the style of algebraic logic; thus, a description of the resulting ‘forcin…Read more

76. Preserving What?In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic, University of Toronto Press. pp. 85104. 2009.In this essay Gillman Payette and Peter Schotch present an account of the key notions of level and forcing in much greater generality than has been managed in any of the early publications. In terms of this level of generality the hoary notion that correct inference is truthpreserving is carefully examined and found wanting. The authors suggest that consistency preservation is a far more natural approach, and one that can, furthermore, characterize an inference relation. But an examination of t…Read more

1Logical ParticularismIn Jeremy Wyatt, Nikolaj J. L. L. Pedersen & Nathan Kellen (eds.), Pluralisms in Truth and Logic, Palgrave Macmillan. pp. 277299. 2018.Logics—that is to say logical systems—are generally conceived of as describing the logical forms of arguments as well as endorsing cer tain principles or rules of inference specified in terms of these forms. From this perspective, a correct logic is a system which captures only (and perhaps all) of the correct principles, and good—i.e. logical— reasoning is reasoning which at the level of logical form conforms to the principles of a correct logic. In contrast, as logical particularists we rejec…Read more

,” “Shut up,” he explained. Essays in Honour of Peter K. Schotch (edited book)College Publications. 2016.
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Mathematics 
Areas of Interest
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