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62Finding Tolerance without GlutsMind 123 (491): 791-811. 2014.Weber, Colyvan, and Priest have advanced glutty approaches to the sorites, on which the truth about the penumbral region of a soritical series is inconsistent. The major benefit of a glut-based approach is maintaining the truth of all sorites premisses while none the less avoiding, in a principled fashion, the absurdity of the sorites conclusion. I agree that this is a major virtue of the target glutty approach; however, I think that it can be had without gluts. If correct, this result weighs he…Read more
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62Strict-Choice Validities: A Note on a Familiar PluralismErkenntnis 79 (S2): 301-307. 2014.My aim here is a modest one: to note another example in which the theory of validity and the theory of ‘inference’ naturally come apart. The setting is multiple-conclusion logic. At least on one philosophy of multiple-conclusion logic, there are very clear examples of where logic qua validity and logic qua normative guide to inference are essentially different things. On the given conception, logic tells us only what follows from what, what our ‘choices’ are given a set of premises; it is simply…Read more
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58A simple approach towards recapturing consistent theories in paraconsistent settingsReview of Symbolic Logic 6 (4): 755-764. 2013.I believe that, for reasons elaborated elsewhere (Beall, 2009; Priest, 2006a, 2006b), the logic LP (Asenjo, 1966; Asenjo & Tamburino, 1975; Priest, 1979) is roughly right as far as logic goes.1 But logic cannot go everywhere; we need to provide nonlogical axioms to specify our (axiomatic) theories. This is uncontroversial, but it has also been the source of discomfort for LP-based theorists, particularly with respect to true mathematical theories which we take to be consistent. My example, throu…Read more
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56Review of Paradox and Paraconsistency (review)Notre Dame Philosophical Reviews. 2003.When physicists disagree as to whose theory is right, they can (if we radically idealize) form an experiment whose results will settle the difference. When logicians disagree, there seems to be no possibility of resolution in this manner. In Paradox and Paraconsistency John Woods presents a picture of disagreement among logicians, mathematicians, and other “abstract scientists” and points to some methods for resolving such disagreement. Our review begins with (very) short sketches of the chapter…Read more
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55Curry's ParadoxEdward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. CSLI Publications. 2017.“Curry’s paradox”, as the term is used by philosophers today, refers to a wide variety of paradoxes of self-reference or circularity that trace their modern ancestry to Curry (1942b) and Löb (1955). The common characteristic of these so-called Curry paradoxes is the way they exploit a notion of implication, entailment or consequence, either in the form of a connective or in the form of a predicate. Curry’s paradox arises in a number of different domains. Like Russell’s paradox, it can take the f…Read more
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54Eco-Logical Lives: The Philosophical Lives of Richard Routley/sylvan and Val Routley/plumwood, by Dominic Hyde: Cambridge: The White Horse Press, 2014, viii + 265, £60.00 (review)Australasian Journal of Philosophy 93 (3): 619-621. 2015.
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54On Williamson's new Quinean argument against nonclassical logicAustralasian Journal of Logic 16 (7): 202-230. 2019.In "Semantic paradoxes and abductive methodology", Williamson presents a new Quinean argument based on central ingredients of common pragmatism about theory choice (including logical theory, as is common). What makes it new is that, in addition to avoiding Quine's unfortunate charge of mere terminological squabble, Williamson's argument explicitly rejects at least for purposes of the argument Quine's key conservatism premise. In this paper I do two things. First, I argue that Williamson's new Qu…Read more
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53A Note on FDE “All the Way Up”Notre Dame Journal of Formal Logic 61 (2): 283-296. 2020.A very natural and philosophically important subclassical logic is FDE. This account of logical consequence can be seen as going beyond the standard two-valued account to a four-valued account. A natural question arises: What account of logical consequence arises from considering further combinations of such values? A partial answer was given by Priest in 2014; Shramko and Wansing had also given a partial result some years earlier, although in a different context. In this note we generalize Prie…Read more
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51End of InclosureMind 123 (491): 829-849. 2014.This paper briefly defends theses in Beall 2014 against objections advanced in Weber et al. 2014. The second part of the paper both defends and fortifies an objection to the ‘inclosure’ argument for glut theory, spelling an end to the inclosure strategy (or at least its application to the sorites)
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50Trivializing sentences and the promise of semantic completenessAnalysis 75 (4): 573-584. 2015.This paper challenges defenders/advocates of the semantic-completeness route towards gluts to explain, in simple and plausible terms, why the ‘trivializer paradox’, framed in terms of closure relatives on theories, fails to undermine their argument.
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50Truth and the absence of factAustralasian Journal of Philosophy 81 (3). 2003.Book Information Truth and the Absence of Fact. By Hartry Field. Clarendon Press. Oxford. 2001. Pp. xi + 401. Hardback, 45.00, US$65.00. Paperback, 16.99, $24.95
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50Is the observable world consistent?Australasian Journal of Philosophy 78 (1). 2000.This Article does not have an abstract
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48Review of G. Priest, Towards Non-Being: The Logic and Metaphysics of Intentionality (review)Notre Dame Philosophical Reviews 2006 (9). 2006.
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47Not so deep inconsistency: a reply to EklundAustralasian Journal of Logic 5 74-84. 2007.In his “Deep Inconsistency?” Eklund attacks arguments to the effect that some contradictions are true, and especially those based on the liar paradox, to be found in Priest’ In Contradiction. The point of this paper is to evaluate his case.
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46God, gluts and evilAnalysis. forthcoming.Traditional monotheism appears to many to involve contradiction in basic 'omni' properties (e.g. omnipotence and too-heavy stones, etc.). A glut-theoretic account of such problems treats them as gluts (dual to familiar truth-value gaps): 'omnipotence' is both true of and false of God. Many philosophers, glut theorists and otherwise, acknowledge that such a glut-theoretic account of at least some traditional omni-god problems is natural, at least in the abstract. But what about the problem of evi…Read more
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45Tim Maudlin, Truth and Paradox: Solving the Riddles (review)Philosophical Review 116 (3): 478-481. 2007.
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44Mancosu (ed.), The Philosophy of Mathematical Practice (review)Australasian Journal of Philosophy 88 (2): 376-376. 2010.This Article does not have an abstract
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41Formal Theories of TruthOxford University Press. 2018.Three leading philosopher-logicians present a clear and concise overview of formal theories of truth, explaining key logical techniques. Truth is as central topic in philosophy: formal theories study the connections between truth and logic, including the intriguing challenges presented by paradoxes like the Liar.
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41Algebraic methods in philosophical logicAustralasian Journal of Philosophy 81 (3). 2003.Book Information Algebraic Methods in Philosophical Logic. By J. Michael Dunn and Gary Hardegree. Clarendon Press. Oxford. 2001. Pp. xv + 470. 60.50.
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39Possibilities and paradox: an introduction to modal and many-valued logicOxford University Press. 2003.Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience…Read more
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38Understanding truthAustralasian Journal of Philosophy 79 (2). 2001.Book Information Understanding Truth. By Soames Scott. Oxford University Press. New York. 1999. Pp. ix + 268. Cloth
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36Review of Roy Sorensen, Vagueness and Contradiction (review)Notre Dame Philosophical Reviews 2002 (8). 2002.
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31On Contradictory Christology: A Reply to Cotnoir’s ‘On the Role of Logic’Journal of Analytic Theology 7 (1): 529-543. 2019.ㅤ
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31On Contradictory Christology: Preliminary Remarks, Notation and TerminologyJournal of Analytic Theology 7 (1): 434-439. 2019.The following are some preliminary remarks that will set the stage for my individual replies to Timothy Pawl, Thomas McCall, A. J. Cotnoir, and Sara L. Uckelman’s responses to my paper ‘Christ – A Contradiction’. In that paper I advance and defend a contradictory Christology which solves the fundamental ‘problem’ of Christology by holding that Christ is a contradictory being: it is true that Christ is mutable and it is false that Christ is mutable; it is true that Christ is immutable and it is f…Read more
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30Review of Stewart Shapiro (ed.), The Oxford Handbook of Philosophy of Mathematics and Logic (review)Notre Dame Philosophical Reviews 2005 (9). 2005.
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30TruthAustralasian Journal of Philosophy 79 (2). 2001.Book Information Truth. Truth Enrique Villanueva Atascadero, CA Ridgeview Publishing Company 1997 i + 446 Edited by Enrique Villanueva . Ridgeview Publishing Company. Atascadero, CA. Pp. i + 446.
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28A Neglected Reply to Prior’s DilemmaIn James Maclaurin (ed.), Rationis Defensor, . 2012.This paper offers a novel reply to Prior’s dilemma (for the Is/Ought principle), advocating a so-called Weak Kleene framework motivated by two not uncommon thoughts in the debate, namely, that ought statements are identified as those that use ‘ought’, and that ought statements are ‘funny’ in ways that is statements aren’t (e.g., perhaps sometimes being ‘gappy’ with respect to truth and falsity).
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