•  745
    Heaps of gluts and Hyde-ing the sorites
    with Mark Colyvan
    Mind 110 (438): 401--408. 2001.
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  •  591
    Looking for contradictions
    Australasian Journal of Philosophy 79 (4). 2001.
    This Article does not have an abstract
  •  272
    On the Ternary Relation and Conditionality
    with Ross T. Brady, J. Michael Dunn, A. P. Hazen, Edwin D. Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney, and Richard Sylvan
    Journal of Philosophical Logic 41 (3). 2012.
    One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer 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
  •  252
    Two Flavors of Curry’s Paradox
    Journal of Philosophy 110 (3): 143-165. 2013.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity…Read more
  •  224
    The Liar Paradox
    with Michael Glanzberg
    In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Csli Publications. 2010.
    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!
  •  223
    Logical Pluralism
    with Greg Restall
    Oxford University Press. 2005.
    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
  •  219
    Defending logical pluralism
    with Greg Restall
    In Logical Consequence: Rival Approaches, Hermes. pp. 1-22. 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.
  •  210
    Logical pluralism
    with Greg Restall
    Australasian 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
  •  169
    The Law of Non-Contradiction : New Philosophical Essays (edited book)
    with Graham Priest and Bradley P. Armour-Garb
    Oxford University Press. 2004.
    The Law of Non-Contradiction - 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. Twenty-three 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
  •  163
    Analetheism and dialetheism
    with D. Ripley
    Analysis 64 (1): 30-35. 2004.
  •  158
    On truthmakers for negative truths
    Australasian Journal of Philosophy 78 (2). 2000.
    This Article does not have an abstract
  •  158
    A Neglected Qua Solution to the Fundamental Problem of Christology
    Faith and Philosophy 36 (2): 157-172. 2019.
    We advance a neglected QUA solution to the fundamental problem of Christology. Our chief aim is to put the view on the theological table, leaving future debate to tell its ultimate fate. After presenting the view we measure it against standard problems that confront extant QUA views and also against objections peculiar to the proposed view.
  •  153
    The story goes that Epimenides, a Cretan, used to claim that all Cretans are always liars. Whether he knew it or not, this claim is odd. It is easy to see it is odd by asking if it is true or false. If it is true, then all Cretans, including Epimenides, are always liars, in which case what he said must be false. Thus, if what he says is true, it is false. Conversely, suppose what Epimenides said is false. Then some Cretan at some time speaks truly. This might not tell us anything about Epimenide…Read more
  •  151
    Logical Consequence
    with Greg Restall and Gil Sagi
    Stanford 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
  •  150
    Nonclassical theories of truth
    with David Ripley
    In 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 victory-through-sacrifice policy: sacrifice details in exchange for clarity of big-picture ideas. This policy results in our giving all-too-brief treatment to certain topics that have dominated discussion in the non-classical-logic area of truth studies. (This is particularly so of the ‘suitable conditoinal’ issue: §4.3.) Still, we present enough representative ideas t…Read more
  •  141
    Future Contradictions
    Australasian Journal of Philosophy 90 (3): 547-557. 2012.
    A common and much-explored thought is ?ukasiewicz'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
  •  140
    Can u do that?
    with G. Priest and Z. Weber
    Analysis 71 (2): 280-285. 2011.
    In his ‘On t and u and what they can do’, Greg Restall presents an apparent problem for a handful of well-known non-classical solutions to paradoxes like the liar. In this article, we argue that there is a problem only if classical logic – or classical-enough logic – is presupposed. 1. Background Many have thought that invoking non-classical logic – in particular, a paracomplete or paraconsistent logic – is the correct response to the liar and related paradoxes. At the most basic level, the targ…Read more
  •  132
    Where the Paths Meet: Remarks on Truth and Paradox &ast
    Midwest Studies in Philosophy 32 (1): 169-198. 2008.
    The study of truth is often seen as running on two separate paths: the nature path and the logic path. The former concerns metaphysical questions about the ‘nature’, if any, of truth. The latter concerns itself largely with logic, particularly logical issues arising from the truth-theoretic paradoxes. Where, if at all, do these two paths meet? It may seem, and it is all too often assumed, that they do not meet, or at best touch in only incidental ways. It is often assumed that work on the metaph…Read more
  •  128
    Relevant Restricted Quantification
    with Ross T. Brady, A. P. Hazen, Graham Priest, and Greg Restall
    Journal of Philosophical Logic 35 (6): 587-598. 2006.
    The paper reviews a number of approaches for handling restricted quantification in relevant logic, and proposes a novel one. This proceeds by introducing a novel kind of enthymematic conditional
  •  121
    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 glut-theoretic 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
  •  118
    Curry's paradox, so named for its discoverer, namely Haskell B. Curry, is a paradox within the family of so-called paradoxes of self-reference (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 T-schema) and naive set theory (unrestricted axiom of abstraction), respectively. If one accepts naive truth theory (or naive set theory), then Curry's …Read more
  •  113
  •  108
    Revenge of the Liar: New Essays on the Paradox (edited book)
    Oxford University Press. 2007.
    The Liar paradox raises foundational questions about logic, language, and truth (and semantic notions in general). A simple Liar sentence like 'This sentence is false' appears to be both true and false if it is either true or false. For if the sentence is true, then what it says is the case; but what it says is that it is false, hence it must be false. On the other hand, if the statement is false, then it is true, since it says (only) that it is false. How, then, should we classify Liar senten…Read more
  •  106
    On the identity theory of truth
    Philosophy 75 (1): 127-130. 2000.
    According to the so-called 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
  •  100
    Why Priest's reassurance is not reassuring
    Analysis 72 (3): 517-525. 2012.
    In the service of paraconsistent (indeed, ‘dialetheic’) theories, Graham Priest has long advanced a non-monotonic 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
  •  98
    From full blooded platonism to really full blooded platonism
    Philosophia Mathematica 7 (3): 322-325. 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
  •  98
    Dialetheists against Pinocchio
    Analysis 71 (4): 689-691. 2011.
    This paper argues that, contrary to P. Eldridge-Smith, the so-called Pinocchio paradox affords no argument against ‘simply semantic dialetheism’