
784Heaps of gluts and Hydeing the soritesMind 110 (438): 401408. 2001.JSTOR is a notforprofit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected].

638Looking for contradictionsAustralasian Journal of Philosophy 79 (4). 2001.This Article does not have an abstract

399Logical pluralismAustralasian Journal of Philosophy 78 (4). 2000.Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a position which h…Read more

379A Neglected Qua Solution to the Fundamental Problem of ChristologyFaith and Philosophy 36 (2): 157172. 2019.This paper advances and defends a new solution to the socalled fundamental problem in christology (the problem being the apparent contradiction entailed by the christian doctrine of divine incarnation).

343Two Flavors of Curry’s ParadoxJournal of Philosophy 110 (3): 143165. 2013.In this paper, we distinguish two versions of Curry's paradox: cCurry, the standard conditionalCurry paradox, and vCurry, a validityinvolving version of Curry's paradox that isn’t automatically solved by solving ccurry. A uniﬁed treatment of curry paradox thus calls for a uniﬁed treatment of both cCurry and vCurry. If, as is often thought, cCurry paradox is to be solved via nonclassical logic, then vCurry may require a lesson about the structure—indeed, the substructure—of the validity…Read more

327On mixed inferences and pluralism about truth predicatesPhilosophical Quarterly 50 (200): 380382. 2000.

290On the Ternary Relation and ConditionalityJournal of Philosophical Logic 41 (3). 2012.One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the RoutleyMeyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions o…Read more

277The law of noncontradiction : new philosophical essays (edited book)Oxford University Press. 2004.The Law of NonContradiction  that no contradiction can be true  has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twentythree of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced…Read more

270Defending logical pluralismIn Bryson Brown & John Woods (eds.), Logical Consequence: Rival Approaches, Hermes. pp. 122. 2001.We are pluralists about logical consequence [1]. We hold that there is more than one sense in which arguments may be deductively valid, that these senses are equally good, and equally deserving of the name deductive validity. Our pluralism starts with our analysis of consequence. This analysis of consequence is not idiosyncratic. We agree with Richard Jeffrey, and with many other philosophers of logic about how logical consequence is to be defined. To quote Jeffrey.

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231Logical ConsequenceStanford Encyclopedia of Philosophy. 2019.A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich will enrol…Read more

215From possible worlds to paraconsistency: on the inevitability of paraconsistent entailmentAsian Journal of Philosophy 1 (1): 18. 2022.A very common twofold view in contemporary philosophy is that classical logic is the correct view of logical consequence and that possibility conforms to classical logic in the sense that ‘possible worlds’ — whatever else they may be — are closed under classical logic. These two views are assumed in this paper. My aim in this paper is to show that a very natural ‘paraconsistent’ consequence relation is involved in the given view of possible worlds and logical consequence.

198On truthmakers for negative truthsAustralasian Journal of Philosophy 78 (2). 2000.This Article does not have an abstract

188Nonclassical theories of truthIn Jc Beall & David Ripley (eds.), Oxford Handbook of Truth, . 2018.This chapter attempts to give a brief overview of nonclassical (logic) theories of truth. Due to space limitations, we follow a victorythroughsacrifice policy: sacrifice details in exchange for clarity of bigpicture ideas. This policy results in our giving alltoobrief treatment to certain topics that have dominated discussion in the nonclassicallogic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas t…Read more

186God of the gaps: a neglected reply to God’s stone problemAnalysis 77 (4): 681689. 2017.Traditional monotheism has long faced logical puzzles. We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed logic but an appendix is offered as a brief review.

175Shrieking against gluts: the solution to the 'just true' problemAnalysis 73 (3): 438445. 2013.This paper applies what I call the shrieking method (a refined version of an idea with roots in Priest's work) to one of – if not the – issues confronting gluttheoretic approaches to paradox (viz., the problem of ‘just true’ or, what comes to the same, ‘just false’). The paper serves as a challenge to formulate a problem of ‘just true’ that isn't solved by shrieking (as advanced in this paper), if such a problem be thought to exist

167Curry's paradox, so named for its discoverer, namely Haskell B. Curry, is a paradox within the family of socalled paradoxes of selfreference (or paradoxes of circularity). Like the liar paradox (e.g., ‘this sentence is false’) and Russell's paradox , Curry's paradox challenges familiar naive theories, including naive truth theory (unrestricted Tschema) and naive set theory (unrestricted axiom of abstraction), respectively. If one accepts naive truth theory (or naive set theory), then Curry's …Read more

166On the identity theory of truthPhilosophy 75 (1): 127130. 2000.According to the socalled identity theory of truth. A proposition is true if the given proposition is identical to some fact. But with which fact must a proposition be identical if it is to be true? This question, according to some philosophers (notably Stewart Candlish), raises serious problems for the identity theory of truth. The worry is that the identity must specify the "right fact" if it is to be an acceptable theory. The current paper aims to help the identity theory by dissolving the a…Read more

160Future ContradictionsAustralasian Journal of Philosophy 90 (3): 547557. 2012.A common and muchexplored thought is Łukasiewicz's idea that the future is ‘indeterminate’—i.e., ‘gappy’ with respect to some claims—and that such indeterminacy bleeds back into the present in the form of gappy ‘future contingent’ claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future—one which is ‘glutty’ with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simpl…Read more

140Dialetheists against PinocchioAnalysis 71 (4): 689691. 2011.This paper argues that, contrary to P. EldridgeSmith, the socalled Pinocchio paradox affords no argument against ‘simply semantic dialetheism’

135Why Priest's reassurance is not reassuringAnalysis 72 (3): 517525. 2012.In the service of paraconsistent (indeed, ‘dialetheic’) theories, Graham Priest has long advanced a nonmonotonic logic (viz., MiLP) as our ‘universal logic’ (at least for standard connectives), one that enjoys the familiar logic LP (for ‘logic of paradox’) as its monotonic core (Priest, G. In Contradiction , 2nd edn. Oxford: Oxford University Press. First printed by Martinus Nijhoff in 1987: Chs. 16 and 19). In this article, I show that MiLP faces a dilemma: either it is (plainly) unsuitable as…Read more

134From full blooded platonism to really full blooded platonismPhilosophia Mathematica 7 (3): 322325. 1999.Mark Balaguer argues for full blooded platonism (FBP), and argues that FBP alone can solve Benacerraf's familiar epistemic challenge. I note that if FBP really can solve Benacerraf's epistemic challenge, then FBP is not alone in its capacity so to solve; RFBP—really full blooded platonism—can do the trick just as well, where RFBP differs from FBP by allowing entities from inconsistent mathematics. I also argue briefly that there is positive reason for endorsing RFBP

132The Liar ParadoxIn Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab. 2014.The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. As we (viz., the authors) have said it, presumably with the intention of you believing it when it is not true, it is a lie. But then it is true!

132Can deflationists be dialetheists?Journal of Philosophical Logic 30 (6): 593608. 2001.Philosophical work on truth covers two streams of inquiry, one concerning the nature (if any) of truth, the other concerning truthrelated paradox, especially the Liar. For the most part these streams have proceeded fairly independently of each other. In his "Deflationary Truth and the Liar" (JPL 28:455488, 1999) Keith Simmons argues that the two streams bear on one another in an important way; specifically, the Liar poses a greater problem for deflationary conceptions of truth than it does for…Read more

125Complete Symposium on Jc Beall's Christ – A Contradiction: A Defense of Contradictory ChristologyJournal of Analytic Theology 7 (1): 400577. 2019.The fundamental problem of Christology is the apparent contradiction of Christ as recorded at Chalcedon. Christ is human and Christ is divine. Being divine entails being immutable. Being human entails being mutable. Were Christ two different persons there’d be no apparent contradiction. But Chalcedon rules as much out. Were Christ only partly human or only partly divine there’d be no apparent contradiction. But Chalcedon rules as much out. Were the very meaning of ‘mutable’ and/or ‘immutable’ ot…Read more

124Fitch's proof, verificationism, and the knower paradoxAustralasian Journal of Philosophy 78 (2). 2000.I have argued that without an adequate solution to the knower paradox Fitch's Proof is or at least ought to beineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and any honest, n…Read more

120OffTopic: A New Interpretation of WeakKleene LogicAustralasian Journal of Logic 13 (6). 2016.This paper offers a new and very simple alternative to Bochvar's well known nonsense  or meaninglessness  interpretation of Weak Kleene logic. To help orient discussion I begin by reviewing the familiar Strong Kleene logic and its standard interpretation; I then review Weak Kleene logic and the standard interpretation. While I note a common worry about the Bochvar interpretation my aim is only to give an alternative  and I think very elegant  interpretation, not necessarily a replacement…Read more

114The simple argument for subclassical logicPhilosophical Issues 28 (1): 3054. 2018.This paper presents a simple but, by my lights, effective argument for a subclassical account of logic—an account according to which logical consequence is (properly) weaker than the standard, so‐called classical account. Alas, the vast bulk of the paper is setup. Because of the many conflicting uses of ‘logic’ the paper begins, following a disclaimer on logic and inference, by fixing the sense of ‘logic’ in question, and then proceeds to rehearse both the target subclassical account of logic an…Read more

110Hegelian Conjunction, Hegelian ContradictionHistory and Philosophy of Logic 44 (2): 119131. 2023.1. In both Benedetto Croce's and Hegel's own terminology, dialectics can be understood as dottrina degli opposti (the doctrine of the opposites – Lehre der Gegensätze).1 In the dialectical process,...
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