Results for 'mathematical truth'

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  1. Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
  2.  25
    Mathematical Truth.Paul Benacerraf, Michael Jubien & Philip Kitcher - 1987 - Journal of Symbolic Logic 52 (2):552-554.
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  3. Mathematics: Truth and Fiction? Review of Mark Balaguer's Platonism and Anti-Platonism in Mathematics.Mark Colyvan & Edward N. Zalta - 1999 - Philosophia Mathematica 7 (3):336-349.
    Mark Balaguer’s project in this book is extremely ambitious; he sets out to defend both platonism and fictionalism about mathematical entities. Moreover, Balaguer argues that at the end of the day, platonism and fictionalism are on an equal footing. Not content to leave the matter there, however, he advances the anti-metaphysical conclusion that there is no fact of the matter about the existence of mathematical objects.1 Despite the ambitious nature of this project, for the most part Balaguer does (...)
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  4. What is Mathematical Truth?Hilary Putnam - 1975 - In Mathematics, Matter and Method. Cambridge University Press. pp. 60--78.
  5.  87
    Why Pure Mathematical Truths Are Metaphysically Necessary: A Set-Theoretic Explanation.Hannes Leitgeb - 2020 - Synthese 197 (7):3113-3120.
    Pure mathematical truths are commonly thought to be metaphysically necessary. Assuming the truth of pure mathematics as currently pursued, and presupposing that set theory serves as a foundation of pure mathematics, this article aims to provide a metaphysical explanation of why pure mathematics is metaphysically necessary.
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  6. A Theory of Mathematical Correctness and Mathematical Truth.Mark Balaguer - 2001 - Pacific Philosophical Quarterly 82 (2):87–114.
    A theory of objective mathematical correctness is developed. The theory is consistent with both mathematical realism and mathematical anti-realism, and versions of realism and anti-realism are developed that dovetail with the theory of correctness. It is argued that these are the best versions of realism and anti-realism and that the theory of correctness behind them is true. Along the way, it is shown that, contrary to the traditional wisdom, the question of whether undecidable sentences like the continuum (...)
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  7. Are Mathematical Truths Synthetic a Priori?Jaakko Hintikka - 1968 - Journal of Philosophy 65 (20):640-651.
  8. Aristotle on Mathematical Truth.Phil Corkum - 2012 - British Journal for the History of Philosophy 20 (6):1057-1076.
    Both literalism, the view that mathematical objects simply exist in the empirical world, and fictionalism, the view that mathematical objects do not exist but are rather harmless fictions, have been both ascribed to Aristotle. The ascription of literalism to Aristotle, however, commits Aristotle to the unattractive view that mathematics studies but a small fragment of the physical world; and there is evidence that Aristotle would deny the literalist position that mathematical objects are perceivable. The ascription of fictionalism (...)
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  9. Ontology and Mathematical Truth.Michael Jubien - 1977 - Noûs 11 (2):133-150.
    The main goal of this paper is to urge that the normal platonistic account of mathematical truth is unsatisfactory even if pure abstract entities are assumed to exist (in a non-Question-Begging way). It is argued that the task of delineating an interpretation of a formal mathematical theory among pure abstract entities is not one that can be accomplished. An important effect of this conclusion on the question of the ontological commitments of informal mathematical theories is discussed. (...)
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  10.  20
    The Benacerraf Problem of Mathematical Truth and Knowledge.Eileen S. Nutting - 2022 - Internet Encyclopedia of Philosophy.
    The Benacerraf Problem of Mathematical Truth and Knowledge Before philosophical theorizing, people tend to believe that most of the claims generally accepted in mathematics—claims like “2+3=5” and “there are infinitely many prime numbers”—are true, and that people know many of them. Even after philosophical theorizing, most people remain committed to mathematical truth and mathematical knowledge. … Continue reading The Benacerraf Problem of Mathematical Truth and Knowledge →.
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  11.  16
    Empiricism, Mathematical Truth and Mathematical Knowledge.Otavio Bueno - 2000 - Poznan Studies in the Philosophy of the Sciences and the Humanities 71:219-242.
  12. On the Nature of Mathematical Truth.Carl G. Hempel - 1945 - In P. Benacerraf H. Putnam (ed.), Philosophy of Mathematics. Prentice-Hall. pp. 366--81.
  13. What Mathematical Truth Could Not Be--1.Paul Benacerraf - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.
     
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  14.  22
    Mathematical Truth Regained.Robert Hanna - 2010 - In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. pp. 147--181.
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  15. Empiricism, Mathematical Truth and Mathematical Knowledge Commentary.C. Liu - 2000 - Poznan Studies in the Philosophy of the Sciences and the Humanities 71:219-242.
  16.  10
    What Mathematical Truth Need Not Be.Virginia Klenk - 1990 - In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer Academic Publishers. pp. 197--208.
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  17.  61
    The Concept of Mathematical Truth.Gian-Carlo Rota - 1991 - Review of Metaphysics 44 (3):483 - 494.
    LIKE ARTISTS WHO FAIL TO GIVE an accurate description of how they work, like scientists who believe in unrealistic philosophies of science, mathematicians subscribe to a concept of mathematical truth that runs contrary to the truth.
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  18.  99
    Does The Necessity of Mathematical Truths Imply Their Apriority?Mark McEvoy - 2013 - Pacific Philosophical Quarterly 94 (4):431-445.
    It is sometimes argued that mathematical knowledge must be a priori, since mathematical truths are necessary, and experience tells us only what is true, not what must be true. This argument can be undermined either by showing that experience can yield knowledge of the necessity of some truths, or by arguing that mathematical theorems are contingent. Recent work by Albert Casullo and Timothy Williamson argues (or can be used to argue) the first of these lines; W. V. (...)
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  19.  85
    Analytic Statements and Mathematical Truth.G. B. Keene - 1955 - Analysis 16 (4):86 - 90.
    Mathematically, Truths have been said to be analytic. Leibniz tried to prove this in a way criticized by frege. The author states: "it is the purpose of this note to exhibit the full force of frege's criticism." frege also attempted to prove the same thing, But concludes the author, In his attempt, Has not "found universal acceptance among mathematical logicians." he finds the value in frege's analysis to be the fact of his attempt at proof and the need for (...)
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  20.  87
    Provability and Mathematical Truth.David Fair - 1984 - Synthese 61 (3):363 - 385.
    An insight, Central to platonism, That the objects of pure mathematics exist "in some sense" is probably essential to any adequate account of mathematical truth, Mathematical language, And the objectivity of the mathematical enterprise. Yet a platonistic ontology makes how we can come to know anything about mathematical objects and how we use them a dark mystery. In this paper I propose a framework for reconciling a representation-Relative provability theory of mathematical truth with (...)
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  21. Benacerraf and Mathematical Truth.Richard Creath - 1980 - Philosophical Studies 37 (4):335 - 340.
  22. What is a Mathematical Truth? In Spinoza and Leibniz.Elhanan Yakira - 1990 - Studia Spinozana: An International and Interdisciplinary Series 6:73-101.
  23. The Legacy of Mathematical Truth.Penelope Maddy - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 60--72.
     
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  24. Descartes on Mathematical Truths: Coherence and Correspondence in the Refutation of Skepticism.Marcelo De Araujo - 2006 - History of Philosophy Quarterly 23 (4):319.
  25.  72
    A Physicalist Account of Mathematical Truth.László Szabó - manuscript
    Realists, Platonists and intuitionists jointly believe that mathematical concepts and propositions have meanings, and when we formalize the language of mathematics, these meanings are meant to be reflected in a more precise and more concise form. According to the formalist understanding of mathematics (at least, according to the radical version of formalism I am proposing here) the truth, on the contrary, is that a mathematical object has no meaning; we have marks and rules governing how these marks (...)
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  26.  29
    Paul Benacerraf. Mathematical Truth. The Journal of Philosophy, Vol. 70 , Pp. 661–679. - Michael Jubien. Ontology and Mathematical Truth. Noûs, Vol. 11 , Pp. 133–150. - Philip Kitcher. The Plight of the Platonist. Noûs, Vol. 12 , Pp. 119–136. [REVIEW]W. D. Hart - 1987 - Journal of Symbolic Logic 52 (2):552-554.
  27.  75
    Divine Will and Mathematical Truth: Gassendi and Descartes on the Status of the Eternal Truths.Rene Descartes - 1995 - In Roger Ariew & Marjorie Glicksman Grene (eds.), Descartes and His Contemporaries: Meditations, Objections, and Replies. University of Chicago Press. pp. 145.
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  28. Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth.E. Szabo´ La´Szlo´ - 2003 - International Studies in the Philosophy of Science 17 (2):117-125.
    This article is a brief formulation of a radical thesis. We start with the formalist doctrine that mathematical objects have no meanings; we have marks and rules governing how these marks can be combined. That's all. Then I go further by arguing that the signs of a formal system of mathematics should be considered as physical objects, and the formal operations as physical processes. The rules of the formal operations are or can be expressed in terms of the laws (...)
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  29. Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth.Charles Sayward - 2005 - Theoria 20 (3):347-352.
    Mark Steiner criticizes some remarks Wittgenstein makes about Gödel. Steiner takes Wittgenstein to be disputing a mathematical result. The paper argues that Wittgenstein does no such thing. The contrast between the realist and the demonstrativist concerning mathematical truth is examined. Wittgenstein is held to side with neither camp. Rather, his point is that a realist argument is inconclusive.
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  30. Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth.Charles Sayward - 2005 - Theoria 20 (3):347-352.
    Mark Steiner criticizes some remarks Wittgenstein makes about Gödel. Steiner takes Wittgenstein to be disputing a mathematical result. The paper argues that Wittgenstein does no such thing. The contrast between the realist and the demonstrativist concerning mathematical truth is examined. Wittgenstein is held to side with neither camp. Rather, his point is that a realist argument is inconclusive.
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  31. Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics.Markus Pantsar - 2009 - Dissertation, University of Helsinki
    One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be (...)
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  32. “Deus Fons Veritatis”: The Subject and its Freedom. The Ontic Foundation of Mathematical Truth. A Biographical-Theoretical Interview with Gaspare Polizzi.Imre Toth - 2009 - Iris. European Journal of Philosophy and Public Debate 1 (1):29-80.
    “Deus fons veritatis”: the Subject and its Freedom. The Ontic Foundation of Mathematical Truth is the title of Gaspare Polizzi’s long biographical-theoretical interview with Imre Toth. The interview is divided into eight parts. The first part describes the historical and cultural context in which Toth was formed. A Jew by birth, during the Second World War Toth became a communist and a partisan, enduring prison, torture, and internment in a concentration camp from 1940 until 6 June 1944. In (...)
     
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  33.  11
    Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth.Charles Sayward - 2005 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (3):347-352.
    Mark Steiner criticizes some remarks Wittgenstein makes about Gödel. Steiner takes Wittgenstein to be disputing a mathematical result. The paper argues that Wittgenstein does no such thing. The contrast between the realist and the demonstrativist concerning mathematical truth is examined. Wittgenstein is held to side with neither camp. Rather, his point is that a realist argument is inconclusive.
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  34.  5
    Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth.Charles Sayward - 2010 - Theoria 20 (3):347-352.
    Mark Steiner criticizes some remarks Wittgenstein makes about Gödel. Steiner takes Wittgenstein to be disputing a mathematical result. The paper argues that Wittgenstein does no such thing. The contrast between the realist and the demonstrativist concerning mathematical truth is examined. Wittgenstein is held to side with neither camp. Rather, his point is that a realist argument is inconclusive.
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  35.  84
    How Can Physics Account for Mathematical Truth?Laszlo E. Szabo - unknown
    If physicalism is true, everything is physical. In other words, everything supervenes on, or is necessitated by, the physical. Accordingly, if there are logical/mathematical facts, they must be necessitated by the physical facts of the world. In this paper, I will sketch the first steps of a physicalist philosophy of mathematics; that is, how physicalism can account for logical and mathematical facts. We will proceed as follows. First we will clarify what logical/mathematical facts actually are. Then, we (...)
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  36. From Mathematical Fictionalism to Truth‐Theoretic Fictionalism.Bradley Armour-Garb & James A. Woodbridge - 2014 - Philosophy and Phenomenological Research 88 (1):93-118.
    We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.
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  37.  69
    An Anti-Realist Account of Mathematical Truth.Graham Priest - 1983 - Synthese 57 (1):49 - 65.
    The paper gives a semantics for naive (inconsistent) set theory in terms of substitutional quantification. Soundness is proved in an appendix. In the light of this construction, Several philosophical issues are discussed, Including mathematical necessity and the set theoretic paradoxes. Most importantly, It is argued, These semantics allow for a nominalist account of mathematical truth not committed to the existence of a domain of abstract entities.
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  38.  84
    A Neo-Formalist Approach to Mathematical Truth.Alan Weir - manuscript
    I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results (...)
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  39.  59
    Truth Through Proof: A Formalist Foundation for Mathematics.Alan Weir - 2010 - Oxford, England: Oxford University Press.
    Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Alan Weir aims to develop a more satisfactory successor to game formalism utilising a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance.
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  40.  3
    A Neo-Formalist Approach to Mathematical Truth.Alan Weir - 1998 - The Paideia Archive: Twentieth World Congress of Philosophy 34:41-47.
    I outline a variant on the formalist approach to mathematics which rejects textbook formalism's highly counterintuitive denial that mathematical theorems express truths while still avoiding ontological commitment to a realm of abstract objects. The key idea is to distinguish the sense of a sentence from its explanatory truth conditions. I then look at various problems with the neo-formalist approach, in particular at the status of the notion of proof in a formal calculus and at problems which Gödelian results (...)
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  41.  32
    Whitehead and the Nature of Mathematical Truth.Ann P. Lowry - 1971 - Process Studies 1 (2):114-123.
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  42.  19
    Review: C. G. Hempel, On the Nature of Mathematical Truth[REVIEW]Charles A. Baylis - 1946 - Journal of Symbolic Logic 11 (3):100-100.
  43.  13
    Hempel C. G.. On the Nature of Mathematical Truth. The American Mathematical Monthly, Vol. 52 , Pp. 543–556.Charles A. Baylis - 1946 - Journal of Symbolic Logic 11 (3):100-100.
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    Readings in Philosophical Analysis. Selected and Edited by Feigl Herbert and Sellars Wilfrid. Appleton-Century-Crofts, Inc., New York, 1949, X + 626 Pp.Quine W. V.. Designation and Existence, Pp. 44–51.Tarski Alfred. The Semantic Conception of Truth, Pp. 52–84.Frege Gottlob. On Sense and Nominatum, Pp. 85–102.Russell Bertrand. On Denoting, Pp. 103–115.Nagel Ernest. Logic Without Ontology, Pp. 191–210.Hempel Carl G.. On the Nature of Mathematical Truth, Pp. 222–237.Carnap Rudolf. The Two Concepts of Probability, Pp. 330–348.Chisholm Roderick M.. The Contrary-to-Fact Conditional, Pp. 482–497. [REVIEW]Max Black - 1949 - Journal of Symbolic Logic 14 (3):184-185.
  45.  21
    A Note on Philip Kitcher's Analysis of Mathematical Truth.Thomas M. Norton-Smith - 1991 - Notre Dame Journal of Formal Logic 33 (1):136-139.
  46.  19
    The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth. Paul Hoffman.Judith V. Grabiner - 2000 - Isis 91 (4):804-805.
  47.  6
    The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth by Paul Hoffman. [REVIEW]Judith Grabiner - 2000 - Isis 91:804-805.
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  48. Truth and Proof: The Platonism of Mathematics.W. W. Tait - 1986 - Synthese 69 (3):341 - 370.
  49.  35
    Truth and Knowledge in Logic and Mathematics.Gila Sher - 2012 - The Logica Yearbook 2011:289-304.
    Logic and mathematics are abstract disciplines par excellence. What is the nature of truth and knowledge in these disciplines? In this paper I investigate the possibility of a new approach to this question. The underlying idea is that knowledge qua knowledge, including logical and mathematical knowledge, has a dual grounding in mind and reality, and the standard of truth applicable to all knowledge is a correspondence standard. This applies to logic and mathematics as much as to other (...)
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  50. Truth in Mathematics.Harold Garth Dales & Gianluigi Oliveri (eds.) - 1998 - Oxford, England: Oxford University Press, Usa.
    general, abstract situation. On the other side, I know that graduate students and all mathematicians sometimes falter because their intuitive, ..
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