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Profile: Greg Restall (University of Melbourne)
  1. Logical Pluralism.Jc Beall & Greg Restall - 2005 - Oxford University Press.
    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. 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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  3.  74
    Assertion, Denial and Non-Classical Theories.Greg Restall - 2013 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Springer. pp. 81--99.
    In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...)
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  4. Truthmakers, Entailment and Necessity.Greg Restall - 1996 - Australasian Journal of Philosophy 74 (2):331 – 340.
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  5.  33
    Pluralism and Proofs.Greg Restall - 2014 - Erkenntnis 79 (S2):279-291.
    Beall and Restall’s Logical Pluralism (2006) characterises pluralism about logical consequence in terms of the different ways cases can be selected in the analysis of logical consequence as preservation of truth over a class of cases. This is not the only way to understand or to motivate pluralism about logical consequence. Here, I will examine pluralism about logical consequence in terms of different standards of proof. We will focus on sequent derivations for classical logic, imposing two different restrictions on classical (...)
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  6. Moral Fictionalism Versus the Rest.Daniel Nolan, Greg Restall & Caroline West - 2004 - Australasian Journal of Philosophy 83 (3):307 – 330.
    In this paper we introduce a distinct metaethical position, fictionalism about morality. We clarify and defend the position, showing that it is a way to save the 'moral phenomena' while agreeing that there is no genuine objective prescriptivity to be described by moral terms. In particular, we distinguish moral fictionalism from moral quasi-realism, and we show that fictionalism possesses the virtues of quasi-realism about morality, but avoids its vices.
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  7. On the Ternary Relation and Conditionality.Jc Beall, Ross Brady, J. Michael Dunn, A. P. Hazen, Edwin 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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  8.  67
    Multiple Conclusions.Greg Restall - 2005 - In Petr Hájek, Luis Valdés-Villanueva & Dag Westerståhl (eds.), Logic, Methodology and Philosophy of Science. College Publications.
    Our topic is the notion of logical consequence: the link between premises and conclusions, the glue that holds together deductively valid argument. How can we understand this relation between premises and conclusions? It seems that any account begs questions. Painting with very broad brushtrokes, we can sketch the landscape of disagreement like this: “Realists” prefer an analysis of logical consequence in terms of the preservation of truth [29]. “Anti-realists” take this to be unhelpful and o:er alternative analyses. Some, like Dummett, (...)
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  9.  51
    An Introduction to Substructural Logics.Greg Restall - 2000 - Routledge.
    This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both (...)
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  10.  94
    Relevant Restricted Quantification.J. C. Beall, Ross T. Brady, A. P. Hazen, Graham Priest & Greg Restall - 2006 - Journal of Philosophical Logic 35 (6):587-598.
    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.
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  11. Ways Things Can't Be.Greg Restall - 1997 - Notre Dame Journal of Formal Logic 38 (4):583-596.
    Paraconsistent logics are often semantically motivated by considering "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of meanings to inconsistent believers. In this paper I show that we can understand paraconsistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) believe that things are like each of the worlds in the set. I show that this account gives a sound and complete semantics (...)
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  12.  53
    Logical Consequence.JC Beall & Greg Restall - unknown
    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 (...)
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  13.  61
    A Cut-Free Sequent System for Two-Dimensional Modal Logic, and Why It Matters.Greg Restall - 2012 - Annals of Pure and Applied Logic 163 (11):1611-1623.
    The two-dimensional modal logic of Davies and Humberstone [3] is an important aid to our understanding the relationship between actuality, necessity and a priori knowability. I show how a cut-free hypersequent calculus for 2D modal logic not only captures the logic precisely, but may be used to address issues in the epistemology and metaphysics of our modal concepts. I will explain how the use of our concepts motivates the inference rules of the sequent calculus, and then show that the completeness (...)
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  14. Carnap's Tolerance, Meaning, and Logical Pluralism.Greg Restall - 2002 - Journal of Philosophy 99 (8):426 - 443.
    In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism.
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  15.  78
    Truth Values and Proof Theory.Greg Restall - 2009 - Studia Logica 92 (2):241-264.
    I present an account of truth values for classical logic, intuitionistic logic, and the modal logic S5, in which truth values are not a fundamental category from which the logic is defined, but rather, an idealisation of more fundamental logical features in the proof theory for each system. The result is not a new set of semantic structures, but a new understanding of how the existing semantic structures may be understood in terms of a more fundamental notion of logical consequence.
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  16. Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
     
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  17.  69
    Not Every Truth Can Be Known (at Least, Not All at Once).Greg Restall - 2009 - In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press. pp. 339--354.
    According to the “knowability thesis,” every truth is knowable. Fitch’s paradox refutes the knowability thesis by showing that if we are not omniscient, then not only are some truths not known, but there are some truths that are not knowable. In this paper, I propose a weakening of the knowability thesis (which I call the “conjunctive knowability thesis”) to the e:ect that for every truth p there is a collection of truths such that (i) each of them is knowable and (...)
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  18.  31
    On Priest on Nonmonotonic and Inductive Logic.Greg Restall - 2016 - Thought: A Journal of Philosophy 5 (2):119-124.
    Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending this choice of logic in the face of the criticism that this logic is not truth preserving, Priest argued that requirement is too much to ask: since LPm is a nonmonotonic logic, it necessarily fails to preserve truth. In this article, I show that this assumption (...)
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  19.  32
    How to Be Really Contraction Free.Greg Restall - 1993 - Studia Logica 52 (3):381 - 391.
    A logic is said to be contraction free if the rule from A→(A→B) to A→B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be robustly contraction free if (...)
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  20.  26
    Negation in Relevant Logics (How I Stopped Worrying and Learned to Love the Routley Star).Greg Restall - 1999 - In Dov M. Gabbay & Heinrich Wansing (eds.), What is Negation? Kluwer Academic Publishers. pp. 53-76.
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  21.  61
    Proofnets for S5: Sequents and Circuits for Modal Logic.Greg Restall - 2007 - In C. Dimitracopoulos, L. Newelski & D. Normann (eds.), Logic Colloquium 2005. Cambridge: Cambridge University Press. pp. 151-172.
    In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated in terms (...)
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  22.  82
    One Way to Face Facts.Greg Restall - 2004 - Philosophical Quarterly 54 (216):420–426.
    Stephen Neale presents, in Facing Facts (Oxford: Clarendon Press, 2001), one convenient package containing his reasoned complaints against theories of facts and non-extensional connectives. The slingshot is a powerful argument (or better, it is a powerful family of arguments) which constrains theories of facts, propositions and non-extensional connectives by showing that some of these theories are rendered trivial. This book is the best place to find the state of the art on the slingshot and its implications for logic, language and (...)
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  23.  71
    Relevant and Substructural Logics.Greg Restall - unknown
    This essay is structured around the bifurcation between proofs and models: The first section discusses Proof Theory of relevant and substructural logics, and the second covers the Model Theory of these logics. This order is a natural one for a history of relevant and substructural logics, because much of the initial work — especially in the Anderson–Belnap tradition of relevant logics — started by developing proof theory. The model theory of relevant logic came some time later. As we will see, (...)
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  24.  74
    Information Flow and Relevant Logics.Greg Restall - 1996 - In Jerry Seligman & Dag Westerståhl (eds.), Logic, Language and Computation. CSLI Publications, Stanford. pp. 463–477.
  25. Łukasiewicz, Supervaluations and the Future.Greg Restall - 2005 - Logic and Philosophy of Science 3:1-10.
    A B S T R AC T: In this paper I consider an interpretation of future contingents which motivates a unification of a Łukasiewicz-style logic with the more classical supervaluational semantics. This in turn motivates a new non-classical logic modelling what is “made true by history up until now. ” I give a simple Hilbert-style proof theory, and a soundness and completeness argument for the proof theory with respect to the intended models.
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  26.  30
    Routes to Triviality.Susan Rogerson & Greg Restall - 2004 - Journal of Philosophical Logic 33 (4):421-436.
    It is known that a number of inference principles can be used to trivialise the axioms of naïve comprehension - the axioms underlying the naïve theory of sets. In this paper we systematise and extend these known results, to provide a number of general classes of axioms responsible for trivialising naïve comprehension.
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  27. Defending Logical Pluralism.JC Beall & Greg Restall - unknown
    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.
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  28.  19
    A Note on Naive Set Theory in ${Rm LP}$.Greg Restall - 1992 - Notre Dame Journal of Formal Logic 33 (3):422-432.
  29. Using Peer Instruction to Teach Philosophy, Logic, and Critical Thinking.Sam Butchart, Toby Handfield & Greg Restall - 2009 - Teaching Philosophy 32 (1):1-40.
    Peer Instruction is a simple and effective technique you can use to make lectures more interactive, more engaging, and more effective learning experiences. Although well known in science and mathematics, the technique appears to be little known in the humanities. In this paper, we explain how Peer Instruction can be applied in philosophy lectures. We report the results from our own experience of using Peer Instruction in undergraduate courses in philosophy, formal logic, and critical thinking. We have consistently found it (...)
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  30.  41
    Displaying and Deciding Substructural Logics 1: Logics with Contraposition.Greg Restall - 1998 - Journal of Philosophical Logic 27 (2):179-216.
    Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic. However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.
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  31.  23
    Normal Proofs, Cut Free Derivations and Structural Rules.Greg Restall - 2014 - Studia Logica 102 (6):1143-1166.
    Different natural deduction proof systems for intuitionistic and classical logic —and related logical systems—differ in fundamental properties while sharing significant family resemblances. These differences become quite stark when it comes to the structural rules of contraction and weakening. In this paper, I show how Gentzen and Jaśkowski’s natural deduction systems differ in fine structure. I also motivate directed proof nets as another natural deduction system which shares some of the design features of Genzen and Jaśkowski’s systems, but which differs again (...)
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  32.  57
    Four-Valued Semantics for Relevant Logics (and Some of Their Rivals).Greg Restall - 1995 - Journal of Philosophical Logic 24 (2):139 - 160.
    This paper gives an outline of three different approaches to the four-valued semantics for relevant logics (and other non-classical logics in their vicinity). The first approach borrows from the 'Australian Plan' semantics, which uses a unary operator '⋆' for the evaluation of negation. This approach can model anything that the two-valued account can, but at the cost of relying on insights from the Australian Plan. The second approach is natural, well motivated, independent of the Australian Plan, and it provides a (...)
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  33.  27
    Simplified Semantics for Relevant Logics (and Some of Their Rivals).Greg Restall - 1993 - Journal of Philosophical Logic 22 (5):481 - 511.
    This paper continues the work of Priest and Sylvan in Simplified Semantics for Basic Relevant Logics, a paper on the simplified semantics of relevant logics, such as B⁺ and B. We show that the simplified semantics can also be used for a large number of extensions of the positive base logic B⁺, and then add the dualising '*' operator to model negation. This semantics is then used to give conservative extension results for Boolean negation.
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  34. A Participatory Model of the Atonement.Tim Bayne & Greg Restall - 2009 - In Yujin Nagasawa & Erik J. Wielenberg (eds.), New Waves in Philosophy of Religion. Palgrave-Macmillan. pp. 150.
    In this paper we develop a participatory model of the Christian doctrine of the atonement, according to which the atonement involves participating in the death and resurrection of Christ. In part one we argue that current models of the atonement—exemplary, penal, substitutionary and merit models—are unsatisfactory. The central problem with these models is that they assume a purely deontic conception of sin and, as a result, they fail to address sin as a relational and ontological problem. In part two we (...)
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  35. New Waves in Philosophical Logic.Greg Restall & Gillian Kay Russell (eds.) - 2012 - Palgrave-Macmillan.
    Machine generated contents note: -- Series Editors' PrefaceAcknowledgementsNotes on ContributorsHow Things Are Elsewhere; W. Schwarz Information Change and First-Order Dynamic Logic; B.Kooi Interpreting and Applying Proof Theories for Modal Logic; F.Poggiolesi & G.Restall The Logic(s) of Modal Knowledge; D.Cohnitz On Probabilistically Closed Languages; H.Leitgeb Dogmatism, Probability and Logical Uncertainty; B.Weatherson & D.Jehle Skepticism about Reasoning; S.Roush, K.Allen & I.HerbertLessons in Philosophy of Logic from Medieval Obligations; C.D.Novaes How to Rule Out Things with Words: Strong Paraconsistency and the Algebra of Exclusion; (...)
     
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  36.  29
    What Are We to Accept, and What Are We to Reject, While Saving Truth From Paradox? [REVIEW]Greg Restall - 2010 - Philosophical Studies 147 (3):433 - 443.
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  37. Logic: An Introduction.Greg Restall - 2005 - Routledge.
    Propositional logic -- Propositions and arguments -- Connectives and argument forms -- Truth tables -- Trees -- Vagueness and bivalence -- Conditionality -- Natural deduction -- Predicate logic -- Predicates, names, and quantifiers -- Models for predicate logic -- Trees for predicate logic -- Identity and functions -- Definite descriptions -- Some things do not exist -- What is a predicate? -- What is logic?
     
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  38.  31
    Logics, Situations and Channels.Greg Restall - unknown
    The notion of that information is relative to a context is important in many different ways. The idea that the context is small — that is, not necessarily a consistent and complete possible world — plays a role not only in situation theory, but it is also an enlightening perspective from which to view other areas, such as modal logics, relevant logics, categorial grammar and much more. In this article we will consider these areas, and focus then on one further (...)
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  39.  50
    Paraconsistent logics!Greg Restall - 1997 - Bulletin of the Section of Logic 26 (3):156-163.
    In this note I respond to Hartley Slater's argument 12 to the e ect that there is no such thing as paraconsistent logic. Slater's argument trades on the notion of contradictoriness in the attempt to show that the negation of paraconsistent logics is merely a subcontrary forming operator and not one which forms contradictories. I will show that Slater's argument fails, for two distinct reasons. Firstly, the argument does not consider the position of non-dialethic paraconsistency which rejects the possible truth (...)
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  40.  15
    Arithmetic and Truth in Lukasiewicz's Infinitely Valued Logic.Greg Restall - 1992 - Logique Et Analyse 139 (140):303-312.
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  41. Envelopes and Indifference.Graham Priest & Greg Restall - unknown
    Consider this situation: Here are two envelopes. You have one of them. Each envelope contains some quantity of money, which can be of any positive real magnitude. One contains twice the amount of money that the other contains, but you do not know which one. You can keep the money in your envelope, whose numerical value you do not know at this stage, or you can exchange envelopes and have the money in the other. You wish to maximise your money. (...)
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  42.  47
    Barriers to Implication.Greg Restall - unknown
    Implication barrier theses deny that one can derive sentences of one type from sentences of another. Hume’s Law is an implication barrier thesis; it denies that one can derive an ‘ought’ (a normative sentence) from an ‘is’ (a descriptive sentence). Though Hume’s Law is controversial, some barrier theses are philosophical platitudes; in his Lectures on Logical Atomism, Bertrand Russell claims: You can never arrive at a general proposition by inference particular propositions alone. You will always have to have at least (...)
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  43.  14
    Modalities in Substructural Logics.Greg Restall - 1992 - Logique Et Analyse 35:303-321.
  44.  95
    Logical Pluralism and the Preservation of Warrant.Greg Restall - 2004 - In S. Rahman (ed.), Logic, Epistemology, and the Unity of Science. Dordrecht: Kluwer Academic Publishers. pp. 163--173.
  45.  64
    Substructural Logics.Greg Restall - forthcoming - Stanford Encyclopedia of Philosophy.
    summary of work in relevant in the Anderson– tradition.]; Mares Troestra, Anne, 1992, Lectures on , CSLI Publications [A quick, easy-to.
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  46.  70
    Curry's Revenge: The Costs of Non-Classical Solutions to the Paradoxes of Self-Reference.Greg Restall - 2007 - In J. C. Beall (ed.), Revenge of the Liar: New Essays on the Paradox. Oxford University Press.
    The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell’s paradox and their cousins pose enormous difficulties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as motivating a non-classical theory of logical consequence. Similar logical principles are used in each of the paradoxical inferences. If one (...)
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  47.  24
    Minimalists About Truth Can (and Should) Be Epistemicists, and It Helps If They Are Revision Theorists Too.Greg Restall - 2005 - In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. Clarendon Press.
  48.  35
    Proof Theory and Meaning: The Context of Deducibility.Greg Restall - 2010 - In F. Delon, U. Kohlenbach, P. Maddy & F. Stephan (eds.), Logic Colloquium 2007. Cambridge: Cambridge University Press. pp. 204-219.
  49.  90
    Modelling Truthmaking.Greg Restall - 2000 - Logique Et Analyse 43 (169-170):211-230.
    According to one tradition in realist philosophy, 'truthmaking' amounts to necessitation. That is, an object x is a truthmaker for the claim A if x exists, and the existence of x necessitates the truth of A. I argued in my paper "Truthmakers, Entailment and Necessity" [14], that if we wish to use this account of truthmaking, we ought understand the entailment connective "=>" in such a claim as a relevant entailment, in the tradition of Anderson and Belnap and their co-workers (...)
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  50.  52
    Assertion, Denial, Commitment, Entitlement, and Incompatibility (and Some Consequence).Greg Restall - 2008 - Studies in Logic:1.
    In this short paper, I compare and contrast the kind of symmetric treatment of negation favoured in different ways by Huw Price (in “Why ‘Not’?”) and by me (in “Multiple Conclusions”) with Robert Brandom’s analysis of scorekeeping in terms of commitment, entitlement and incompatibility. Both kinds of account are what Brandom calls a normative pragmatics. They are both semantic anti-realist accounts of meaning in the significance of vocabulary is explained in terms of our rule-governed (normative) practice (pragmatics). These accounts differ (...)
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