•  48
    A 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
  •  40
    Tim Maudlin, Truth and Paradox: Solving the Riddles (review)
    Philosophical Review 116 (3): 478-481. 2007.
  •  50
    On Williamson's new Quinean argument against nonclassical logic
    Australasian 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
  •  100
    Complete Symposium on Jc Beall's Christ – A Contradiction: A Defense of Contradictory Christology
    with Timothy Pawl, Thomas McCall, A. J. Cotnoir, and Sara L. Uckelman
    Journal of Analytic Theology 7 (1): 400-577. 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
  •  44
    Is Yablo's paradox non-circular?
    Analysis 61 (3): 176-187. 2001.
  •  311
    A Neglected Qua Solution to the Fundamental Problem of Christology
    Faith and Philosophy 36 (2): 157-172. 2019.
    This paper advances and defends a new solution to the so-called fundamental problem in christology (the problem being the apparent contradiction entailed by the christian doctrine of divine incarnation).
  •  7
    Introductory Remarks
    The Monist 89 (1): 3-8. 2006.
  •  72
    Existential claims and platonism
    Philosophia Mathematica 9 (1): 80-86. 2001.
    This paper responds to Colin Cheyne's new anti-platonist argument according to which knowledge of existential claims—claims of the form such-tmd-so exist—requires a caused connection with the given such-and-so. If his arguments succeed then nobody can know, or even justifiably believe, that acausal entities exist, in which case (standard) platonism is untenable. I argue that Cheyne's anti-platonist argument fails
  •  118
    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
  •  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
  •  91
    The simple argument for subclassical logic
    Philosophical Issues 28 (1): 30-54. 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
  •  21
    True, false and paranormal
    Analysis 66 (2): 102-114. 2006.
  •  147
    Where the Paths Meet: Remarks on Truth and Paradox
    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
  •  48
    Truth and the absence of fact
    Australasian 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
  •  257
    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
  •  78
    There is no Logical Negation: True, False, Both, and Neither
    Australasian Journal of Logic 14 (1). 2017.
    In this paper I advance and defend a very simple position according to which logic is subclassical but is weaker than the leading subclassical-logic views have it.
  •  48
    Curry's Paradox
    Edward 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
  •  85
    Spandrels of truth
    Oxford University Press. 2009.
    In Spandrels of Truth, Beall concisely presents and defends a modest, so-called dialetheic theory of transparent truth
  •  105
    True, false and paranormal
    Analysis 66 (2). 2006.
  •  71
    Further remarks on truth and contradiction
    Philosophical Quarterly 52 (207): 217-225. 2002.
    We address an issue recently discussed by Graham Priest: whether the very nature of truth (understood as in correspondence theories) rules out true contradictions, and hence whether a correspondence-theoretic notion of truth rules against dialetheism. We argue that, notwithstanding appearances to the contrary, objections from within the correspondence theory do not stand in the way of dialetheism. We close by highlighting, but not attempting to resolve, two further challenges for dialetheism whi…Read more
  •  309
    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
  •  33
    The simple liar without bivalence?
    with Ot&Aacutevio Bueno
    Analysis 62 (1): 22-26. 2002.
  •  61
    This paper presents a new puzzle for certain positions in the theory of truth. The relevant positions can be stated in a language including a truth predicate T and an operation that takes sentences to names of those sentences; they are positions that take the T-schema A ↔ T to hold without restriction, for every sentence A in the language. As such, they must be based on a nonclassical logic, since paradoxes that cannot be handled classically will arise. The bestknown of these paradoxes is probab…Read more
  •  130
    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