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  1. In Contradiction: A Study of the Transconsistent.Graham Priest - 1987 - Dordrecht, Netherland: Oxford University Press.
    In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...)
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  • Remarks on the Foundations of Mathematics.Ludwig Wittgenstein - 1956 - Oxford: Macmillan.
    Wittgenstein's work remains, undeniably, now, that off one of those few philosophers who will be read by all future generations.
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  • A Survey of Mathematical Logic.Hao Wang - 1962 - Peking, China: Science Press North-Holland.
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  • Mathematical Platonism and Dummettian Anti‐Realism.John McDowell - 1989 - Dialectica 43 (1‐2):173-192.
    SummaryThe platonist, in affirming the principle of bivalence for sentences for which there is no decision procedure, disconnects their truth‐conditions from conditions that would enable us to prove them ‐ as if Goldbach's conjecture, say, might just happen to be true. According to Dummett, what has gone wrong here is that the meaning of the relevant sentences has been conceived so as to go beyond what could be learned in learning to use them, or displayed in using them competently. Dummett (...)
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  • On Some Standard Objections to Mathematical Conventionalism.Severin Schroeder - 2017 - Belgrade Philosophical Annual 30:83-98.
    According to Wittgenstein, mathematical propositions are rules of grammar, that is, conventions, or implications of conventions. So his position can be regarded as a form of conventionalism. However, mathematical conventionalism is widely thought to be untenable due to objections presented by Quine, Dummett and Crispin Wright. It has also been argued that only an implausibly radical form of conventionalism could withstand the critical implications of Wittgenstein’s rule-following considerations. In this article I discuss those objections to conventionalism and argue that none (...)
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  • Anti-Realism and Objectivity in Wittgenstein's Philosophy of Mathematics.Pïeranna Garavaso - 1991 - Philosophica 48.
    In the first section, I characterize realism and illustrate the sense in which Wittgenstein's account of mathematics is anti-realist. In the second section, I spell out the above notion of objectivity and show how and anti-realist account of truth, namely, Putnam's idealized rational acceptability, preserves objectivity. In the third section, I discuss the "majority argument" and illustrate how Wittgenstein's anti-realism can also account for the objectivity of mathematics. What Putnam's and Wittgenstein's anti-realisms ultimately show is that this notion of objectivity (...)
     
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  • Mathematics and Forms of Life.Severin Schroeder - 2015 - Nordic Wittgenstein Review 4:111-130.
    According to Wittgenstein, mathematics is embedded in, and partly constituting, a form of life. Hence, to imagine different, alternative forms of elementary mathematics, we should have to imagine different practices, different forms of life in which they could play a role. If we tried to imagine a radically different arithmetic we should think either of a strange world or of people acting and responding in very peculiar ways. If such was their practice, a calculus expressing the norms of representation they (...)
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  • One: Being an Investigation Into the Unity of Reality and of its Parts, Including the Singular Object Which is Nothingness.Graham Priest - 2014 - Oxford, England: Oxford University Press.
    Graham Priest presents an original exploration of questions concerning the one and the many. He covers a wide range of issues in metaphysics--unity, identity, grounding, mereology, universals, being, intentionality and nothingness--and draws on Western and Asian philosophy as well as paraconsistent logic to offer a radically new treatment of unity.
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  • Wittgenstein and the Vienna Circle: Conversations.Friedrich Waismann - 1979 - Rowman & Littlefield Publishers.
  • World‐Pictures and Wittgensteinian Certainty.Hiroshi Ohtani - 2018 - Metaphilosophy 49 (1-2):115-136.
    Although certainty is a fundamental notion in epistemology, it is less studied in contemporary analytic epistemology than other important notions such as knowledge or justification. This paper focuses on Wittgensteinian certainty, according to which the very basic dimension of our epistemic practices, the elements of our world-pictures, are objectively certain, in that we cannot legitimately doubt them. The aim of the paper is to offer the best philosophical way to clarify Wittgensteinian certainty, in a way that is consonant with Wittgenstein's (...)
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  • Philosophical Pictures About Mathematics: Wittgenstein and Contradiction.Hiroshi Ohtani - 2018 - Synthese 195 (5):2039-2063.
    In the scholarship on Wittgenstein’s later philosophy of mathematics, the dominant interpretation is a theoretical one that ascribes to Wittgenstein some type of ‘ism’ such as radical verificationism or anti-realism. Essentially, he is supposed to provide a positive account of our mathematical practice based on some basic assertions. However, I claim that he should not be read in terms of any ‘ism’ but instead should be read as examining philosophical pictures in the sense of unclear conceptions. The contrast here is (...)
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  • Wittgenstein on Pure and Applied Mathematics.Ryan Dawson - 2014 - Synthese 191 (17):4131-4148.
    Some interpreters have ascribed to Wittgenstein the view that mathematical statements must have an application to extra-mathematical reality in order to have use and so any statements lacking extra-mathematical applicability are not meaningful (and hence not bona fide mathematical statements). Pure mathematics is then a mere signgame of questionable objectivity, undeserving of the name mathematics. These readings bring to light that, on Wittgenstein’s offered picture of mathematical statements as rules of description, it can be difficult to see the role of (...)
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  • Radical Anti-Realism, Wittgenstein and the Length of Proofs.Mathieu Marion - 2009 - Synthese 171 (3):419 - 432.
    After sketching an argument for radical anti-realism that does not appeal to human limitations but polynomial-time computability in its definition of feasibility, I revisit an argument by Wittgenstein on the surveyability of proofs, and then examine the consequences of its application to the notion of canonical proof in contemporary proof-theoretical-semantics.
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  • Monism: The One True Logic.Stephen Read - 2006 - In D. de Vidi & T. Kenyon (eds.), A Logical Approach to Philosophy: Essays in Memory of Graham Solomon. Springer.
    Logical pluralism is the claim that different accounts of validity can be equally correct. Beall and Restall have recently defended this position. Validity is a matter of truth-preservation over cases, they say: the conclusion should be true in every case in which the premises are true. Each logic specifies a class of cases, but differs over which cases should be considered. I show that this account of logic is incoherent. Validity indeed is truth-preservation, provided this is properly understood. Once understood, (...)
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  • Wittgenstein, Anti-Realism and Mathematical Propositions.Jacques Bouveresse - 1992 - Grazer Philosophische Studien 42 (1):133-160.
    Wittgenstein is generally supposed to have abandoned in the 1930's a realistic conception of the meaning of mathematical propositions, founded on the idea of tmth-conditions which could in certain cases transcend any possibility of verification, for a realistic one, where the idea of truth-conditions is replaced by that of conditions of justification of assertability. It is argued that for Wittgenstein mathematical propositions, which are, as he says, "grammatical" propositions, have a meaning and a role which differ to a much greater (...)
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  • Wittgenstein on Philosophy of Logic and Mathematics.Juliet Floyd - 2004 - Graduate Faculty Philosophy Journal 25 (2):227-287.
    A survey of Wittgenstein's writings on logic and mathematics; an analytical bibliography of contemporary articles on rule-following, social constructivism, Wittgenstein, Godel, and constructivism is appended. Various historical accounts of the nature of mathematical knowledge glossed over the effects of linguistic expression on our understanding of its status and content. Initially Wittgenstein rejected Frege's and Russell's logicism, aiming to operationalize the notions of logical consequence, necessity and sense. Vienna positivists took this to place analysis of meaning at the heart of philosophy, (...)
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  • Wittgenstein, Anti-Realism and Mathematical Propositions.Jacques Bouveresse - 1992 - Grazer Philosophische Studien 42 (1):133-160.
    Wittgenstein is generally supposed to have abandoned in the 1930's a realistic conception of the meaning of mathematical propositions, founded on the idea of tmth-conditions which could in certain cases transcend any possibility of verification, for a realistic one, where the idea of truth-conditions is replaced by that of conditions of justification of assertability. It is argued that for Wittgenstein mathematical propositions, which are, as he says, "grammatical" propositions, have a meaning and a role which differ to a much greater (...)
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  • Beyond the Limits of Thought.Graham Priest - 1999 - Philosophical Quarterly 49 (194):121-125.
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  • Beyond the Limits of Thought.Graham Priest - 1995 - Philosophy 71 (276):308-310.
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  • Realism, Anti-Realism, Quietism: Wittgenstein's Stance.Pasquale Frascolla - 2014 - Grazer Philosophiseche Studien 89 (1):11-21.
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  • Wittgenstein on the Contradictions in Logic and in the Foundations of Mathematics.Z. A. Sokuler - 1988 - Philosophia Mathematica (1):21-28.
  • Fifty Years of Parainconsistent Logics.Jerzy Perzanowski - 1999 - Logic and Logical Philosophy 7:21-24.
  • Wittgenstein, Philosophy and Logic.Ilham Dilman - 1970 - Analysis 31 (2):33 - 42.
    This article is concerned to say something about what the study of logic meant to wittgenstein. It is concerned to bring out why the kind of questions wittgenstein raised about logic and mathematics cannot be pursued in a purely formal and abstract manner-As russell pursued them to a very large extent. It tries to understand the prominence wittgenstein gave to a study of these questions in his philosophical investigations and to appreciate the sense in which he regarded a study of (...)
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  • Can Contradictions Be True?Timothy Smiley & Graham Priest - 1993 - Aristotelian Society Supplementary Volume 67 (1):17 - 54.
  • Paraconsistent Logic.David Ripley - 2015 - Journal of Philosophical Logic 44 (6):771-780.
    In some logics, anything whatsoever follows from a contradiction; call these logics explosive. Paraconsistent logics are logics that are not explosive. Paraconsistent logics have a long and fruitful history, and no doubt a long and fruitful future. To give some sense of the situation, I’ll spend Section 1 exploring exactly what it takes for a logic to be paraconsistent. It will emerge that there is considerable open texture to the idea. In Section 2, I’ll give some examples of techniques for (...)
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  • A Survey of Mathematical Logic.Hao Wang - 1965 - Journal of Symbolic Logic 30 (2):249-250.
     
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  • On Wittgenstein's Philosophy of Mathematics.James Conant - 1997 - Proceedings of the Aristotelian Society 97 (2):195–222.
  • Wittgenstein on Mathematics.Michael Potter - 2011 - In Marie McGinn & Oskari Kuusela (eds.), The Oxford Handbook of Wittgenstein. Oxford University Press.
     
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  • Can Contradictions Be True?Timothy Smiley & Graham Priest - 1993 - Proceedings of the Aristotelian Society, Supplementary Volumes 67:17-54.
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  • Wittgenstein on Contradiction and the Philosophy of Paraconsistent Logic.Diego Marconi - 1984 - History of Philosophy Quarterly 1 (3):333 - 352.
  • Was Wittgenstein Really an Anti-Realist About Mathematics?Hilary Putnam - 2001 - In Timothy McCarthy & Sean C. Stidd (eds.), Wittgenstein in America. Oxford University Press. pp. 140--194.
     
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  • I Wittgenstein.James Conant - unknown
    The document before you is by a member of a fanatical sect of heretical Ludwig scholars. Through a twist of fate it has fallen into my hands. I hesitate to make it public, since its circulation may do more harm than good. What speaks against publication is that it has the power to corrupt young minds. I do not take a light view of the dangers it poses in this regard. What speaks in favor of publication is the fact that (...)
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