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  1. Logical pluralism.Jc Beall & Greg Restall - 2000 - Australasian Journal of Philosophy 78 (4):475 – 493.
    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 (...)
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  2. Spandrels of truth.Jc Beall - 2010 - Bulletin of Symbolic Logic 16 (2):284-286.
  3. Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
    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 relation itself.
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  4.  59
    Formal Theories of Truth.Jc Beall, Michael Glanzberg & David Ripley - 2018 - Oxford: Oxford University Press. Edited by Michael Glanzberg & David Ripley.
    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.
  5. The simple argument for subclassical logic.Jc Beall - 2018 - Philosophical Issues 28 (1):30-54.
    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 and its (...)
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  6. Free of Detachment: Logic, Rationality, and Gluts.Jc Beall - 2013 - Noûs 49 (2):410-423.
  7. The law of non-contradiction : new philosophical essays.Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.) - 2004 - New York: Oxford University Press.
    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 inquiry into (...)
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  8. On the Ternary Relation and Conditionality.Jc Beall, Ross T. Brady, J. Michael Dunn, A. P. Hazen, Edwin D. Mares, Robert K. Meyer, Graham Priest, Greg Restall, David Ripley, John Slaney & Richard Sylvan - 2012 - Journal of Philosophical Logic 41 (3):595 - 612.
    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 of conditionality. We close by briefly discussing (...)
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  9.  95
    There is no Logical Negation: True, False, Both, and Neither.Jc Beall - 2017 - Australasian Journal of Logic 14 (1):Article no. 1.
    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.
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  10. Off-Topic: A New Interpretation of Weak-Kleene Logic.Jc Beall - 2016 - Australasian Journal of Logic 13 (6).
    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.
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  11. Complete Symposium on Jc Beall's Christ – A Contradiction: A Defense of Contradictory Christology.Jc Beall, Timothy Pawl, Thomas McCall, A. J. Cotnoir & Sara L. Uckelman - 2019 - Journal of Analytic Theology 7 (1):400-577.
    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’ other than what they are, (...)
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  12. God of the gaps: a neglected reply to God’s stone problem.Jc Beall & A. J. Cotnoir - 2017 - Analysis 77 (4):681-689.
    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.
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  13. Hegelian Conjunction, Hegelian Contradiction.Jc Beall & Elena Ficara - 2023 - History and Philosophy of Logic 44 (2):119-131.
    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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  14. Multiple-conclusion lp and default classicality.Jc Beall - 2011 - Review of Symbolic Logic 4 (2):326-336.
    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.
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  15. Shrieking against gluts: the solution to the 'just true' problem.Jc Beall - 2013 - Analysis 73 (3):438-445.
    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.
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  16.  82
    Lp+, k3+, fde+, and their 'classical collapse'.Jc Beall - 2013 - Review of Symbolic Logic 6 (4):742-754.
    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+.
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  17.  62
    (1 other version)Deflationism and Paradox.Jc Beall & Bradley P. Armour-Garb (eds.) - 2005 - Oxford, England: Oxford University Press.
    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 language, and anyone working on truth. Contributors (...)
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  18.  70
    A simple approach towards recapturing consistent theories in paraconsistent settings.Jc Beall - 2013 - Review of Symbolic Logic 6 (4):755-764.
    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, throughout, is arithmetic; but (...)
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  19. The Liar Paradox.JC Beall & Michael Glanzberg - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
    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 (...)
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  20.  14
    (2 other versions)Logic: The Basics.Jc Beall - 2010 - New York: Routledge.
    _Logic: The Basics_ is an accessible introduction to several core areas of logic. The first part of the book features a self-contained introduction to the standard topics in classical logic, such as: · mathematical preliminaries · propositional logic · quantified logic · English and standard ‘symbolic translations’ · tableau procedures. Alongside comprehensive coverage of the standard topics, this thoroughly revised second edition also introduces several philosophically important nonclassical logics, free logics, and modal logics, and gives the reader an idea of (...)
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  21. Nonclassical theories of truth.Jc Beall & David Ripley - 2018 - In Jc Beall & David Ripley (eds.), Oxford Handbook of Truth.
    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 that one may fruitfully turn from this essay to the more-detailed (...)
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  22. Heaps of gluts and Hyde-ing the sorites.JC Beall & Mark Colyvan - 2001 - Mind 110 (438):401--408.
    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].
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  23.  83
    A Note on Freedom from Detachment in the Logic of Paradox.Jc Beall, Thomas Forster & Jeremy Seligman - 2013 - Notre Dame Journal of Formal Logic 54 (1):15-20.
    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.
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  24. A Neglected Qua Solution to the Fundamental Problem of Christology.Jc Beall & Jared Henderson - 2019 - Faith and Philosophy 36 (2):157-172.
    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).
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  25.  93
    God, gluts and evil.Jc Beall - forthcoming - Analysis.
    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 evil? The unanimous view even among glut (...)
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  26. True and false–as if. Ch. 12 of G. Priest, Jc Beall and B. Armour-Garb.Jc Beall - 2004 - In Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The law of non-contradiction : new philosophical essays. New York: Oxford University Press.
     
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  27.  72
    On Williamson's new Quinean argument against nonclassical logic.Jc Beall - 2019 - Australasian Journal of Logic 16 (7):202-230.
    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 Quinean argument implicitly relies on Quine's conservatism principle. (...)
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  28.  77
    Finding Tolerance without Gluts.Jc Beall - 2014 - Mind 123 (491):791-811.
    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 (...)
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  29. From full blooded platonism to really full blooded platonism.Jc Beall - 1999 - Philosophia Mathematica 7 (3):322-325.
    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.
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  30. Why Priest's reassurance is not reassuring.Jc Beall - 2012 - Analysis 72 (3):517-525.
    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 a (...)
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  31.  69
    End of Inclosure.Jc Beall - 2014 - Mind 123 (491):829-849.
    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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  32.  29
    On Contradictory Christology: A Reply to Uckelman’s ‘Contradictions, Impossibility, and Triviality’.Jc Beall - 2019 - Journal of Analytic Theology 7 (1):560-577.
  33.  62
    (1 other version)Curry's Paradox.Lionel Shapiro & Jc Beall - 2017 - Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. CSLI Publications.
    “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 (...)
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  34. Future Contradictions.Jc Beall - 2012 - Australasian Journal of Philosophy 90 (3):547-557.
    A common and much-explored 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 simply to sketch (...)
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  35. Dialetheists against Pinocchio.Jc Beall - 2011 - Analysis 71 (4):689-691.
    This paper argues that, contrary to P. Eldridge-Smith, the so-called Pinocchio paradox affords no argument against ‘simply semantic dialetheism’.
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  36.  29
    Adding to Relevant Restricted Quantification.Jc Beall - 2011 - Australasian Journal of Logic 10:36-44.
    This paper presents, in a more general setting, a simple approach to ‘relevant restricted generalizations’ advanced in previous work. After reviewing some desiderata for restricted generalizations, I present the target route towards achieving the desiderata. An objection to the approach, due to David Ripley, is presented, followed by three brief replies, one from a dialetheic perspective and the others more general.
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  37.  69
    Strict-Choice Validities: A Note on a Familiar Pluralism.Jc Beall - 2014 - Erkenntnis 79 (S2):301-307.
    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 (...)
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  38.  49
    Not so deep inconsistency: a reply to Eklund.Jc Beall & Graham Priest - 2007 - Australasian Journal of Logic 5:74-84.
    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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  39. Vague Intensions: A Modest Marriage Proposal.Jc Beall - 2010 - In Richard Dietz & Sebastiano Moruzzi (eds.), Cuts and clouds: vagueness, its nature, and its logic. New York: Oxford University Press.
     
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  40.  68
    A Note on FDE “All the Way Up”.Jc Beall & Caleb Camrud - 2020 - Notre Dame Journal of Formal Logic 61 (2):283-296.
    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 Priest’s result to show (...)
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  41.  46
    The simple liar without bivalence?Jc Beall & OtÁvio Bueno - 2002 - Analysis 62 (1):22-26.
  42. Non-detachable validity and deflationism.Jc Beall - 2015 - In Colin R. Caret & Ole T. Hjortland (eds.), Foundations of Logical Consequence. Oxford, England: Oxford University Press.
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  43. Further remarks on truth and contradiction.Bradley Armour-Garb & JC Beall - 2002 - Philosophical Quarterly 52 (207):217-225.
    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 which arise out of familiar philosophical theorizing about truth.
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  44.  45
    On Contradictory Christology: Preliminary Remarks, Notation and Terminology.Jc Beall - 2019 - Journal of Analytic Theology 7 (1):434-439.
    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 (...)
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  45.  59
    Truth and the absence of fact.Jc Beall - 2003 - Australasian Journal of Philosophy 81 (3):437 – 439.
    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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  46.  21
    (1 other version)Where the Paths Meet: Remarks on Truth and Paradox.Jc Beall & Michael Glanzberg - 1981 - In Felicia Ackerman (ed.), Midwest Studies in Philosophy. Minneapolis: University of Minnesota Press. pp. 169–198.
    This chapter contains sections titled: Nature: Two Conceptions of Truth Background on Logic and Paradox Nature and Logic And Now Revenge References.
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  47. A Neglected Reply to Prior’s Dilemma.Jc Beall - 2012 - In James Maclaurin (ed.), Rationis Defensor: Essays in Honour of Colin Cheyne. Springer.
    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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  48.  27
    A Dilemma in Pawline Christology.Jc Beall - 2023 - Journal of Philosophical Theological Research 25 (3):55-62.
    A longstanding problem confronting Christian theology and its doctrine of incarnation is the apparent contradiction that it faces. For example, to be divine, in the relevant sense, is to have the limitlessness of God. To be human, in the relevant sense, is to have the limitations of humans. The incarnation (in the person of Jesus per Christian doctrine) is to be both divine and human. Many theologians and sympathetic philosophers have attempted to ‘consistentize’ (i.e., make consistent) incarnation. Timothy Pawl has (...)
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  49.  99
    The simple liar without bivalence?Jc Beall & Otávio Bueno - 2002 - Analysis 62 (1):22–26.
  50. From possible worlds to paraconsistency: on the inevitability of paraconsistent entailment.Jc Beall - 2022 - Asian Journal of Philosophy 1 (1):1-8.
    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.
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