•  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
  •  25
    Review of J. W. Garson, Modal Logic for Philosophers (review)
    Notre Dame Philosophical Reviews 2007 (6). 2007.
  •  66
    Multiple-conclusion lp and default classicality
    Review of Symbolic Logic 4 (2): 326-336. 2011.
    Philosophical applications of familiar paracomplete and paraconsistent logics often rely on an idea of . With respect to the paraconsistent logic LP (the dual of Strong Kleene or K3), such is standardly cashed out via an LP-based nonmonotonic logic due to Priest (1991, 2006a). In this paper, I offer an alternative approach via a monotonic multiple-conclusion version of LP
  •  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
  •  12
    Minimalism, gaps, and the Holton conditional
    Analysis 60 (4): 340-351. 2000.
  •  120
    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
  •  591
    Looking for contradictions
    Australasian Journal of Philosophy 79 (4). 2001.
    This Article does not have an abstract
  •  52
    Logic: the Basics is an accessible introduction to the core philosophy topic of standard logic. Focussing on traditional Classical Logic the book deals with topics such as mathematical preliminaries, propositional logic, monadic quantified logic, polyadic quantified logic, and English and standard ‘symbolic transitions’. With exercises and sample answers throughout this thoroughly revised new edition not only comprehensively covers the core topics at introductory level but also gives the reader …Read more
  •  42
    Finding Tolerance without Gluts
    Mind 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
  •  45
    Lp+, k3+, fde+, and their 'classical collapse'
    Review of Symbolic Logic 6 (4): 742-754. 2013.
    This paper is a sequel to Beall (2011), in which I both give and discuss the philosophical import of a result for the propositional (multiple-conclusion) logic LP+. Feedback on such ideas prompted a spelling out of the first-order case. My aim in this paper is to do just that: namely, explicitly record the first-order result(s), including the collapse results for K3+ and FDE+
  •  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
  •  745
    Heaps of gluts and Hyde-ing the sorites
    with Mark Colyvan
    Mind 110 (438): 401--408. 2001.
    JSTOR is a not-for-profit 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]
  •  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
  •  4
    Formal Theories of Truth
    Oxford 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.
  •  2
    Liars and Heaps: New Essays on the Semantics of Paradox (edited book)
    Oxford University Press. 2003.
    Semantic and soritical paradoxes challenge entrenched, fundamental principles about language - principles about truth, denotation, quantification, and, among others, 'tolerance'. Study of the paradoxes helps us determine which logical principles are correct. So it is that they serve not only as a topic of philosophical inquiry but also as a constraint on such inquiry: they often dictate the semantic and logical limits of discourse in general. Sixteen specially written essays by leading figures i…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!
  •  40
    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
  •  28
    End of Inclosure
    Mind 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)
  •  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
  •  90
    Minimalism and the dialetheic challenge
    Australasian Journal of Philosophy 81 (3). 2003.
    Minimalists, following Horwich, claim that all that can be said about truth is comprised by all and only the nonparadoxical instances of (E) p is true iff p. It is, accordingly, standard in the literature on truth and paradox to ask how the minimalist will restrict (E) so as to rule out paradox-inducing sentences (alternatively: propositions). In this paper, we consider a prior question: On what grounds does the minimalist restrict (E) so as to rule out paradox-inducing sentences and, thereby, a…Read more
  •  73
    Deflationism and Paradox (edited book)
    with Bradley P. Armour-Garb
    Oxford University Press. 2005.
    Deflationist accounts of truth are widely held in contemporary philosophy: they seek to show that truth is a dispensable concept with no metaphysical depth. However, logical paradoxes present problems for deflationists that their work has struggled to overcome. In this volume of fourteen original essays, a distinguished team of contributors explore the extent to which, if at all, deflationism can accommodate paradox. The volume will be of interest to philosophers of logic, philosophers of langua…Read more
  •  49
    A Note on Freedom from Detachment in the Logic of Paradox
    with Thomas Forster and Jeremy Seligman
    Notre Dame Journal of Formal Logic 54 (1): 15-20. 2013.
    We shed light on an old problem by showing that the logic LP cannot define a binary connective $\odot$ obeying detachment in the sense that every valuation satisfying $\varphi$ and $(\varphi\odot\psi)$ also satisfies $\psi$ , except trivially. We derive this as a corollary of a more general result concerning variable sharing
  •  139
    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
  •  34
    Algebraic methods in philosophical logic
    Australasian 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.
  •  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’
  •  28
    A Neglected Reply to Prior’s Dilemma
    In 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).