Search results for 'mathematical truth' (try it on Scholar)

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  1. Markus Pantsar (2009). Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics. Dissertation, University of Helsinkiscore: 122.0
    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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  2. Bradley Armour‐Garb & James A. Woodbridge (2014). From Mathematical Fictionalism to Truth‐Theoretic Fictionalism. Philosophy and Phenomenological Research 88 (1):93-118.score: 120.0
    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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  3. Michael Jubien (1977). Ontology and Mathematical Truth. Noûs 11 (2):133-150.score: 120.0
    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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  4. Graham Priest (1983). An Anti-Realist Account of Mathematical Truth. Synthese 57 (1):49 - 65.score: 120.0
    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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  5. Charles Sayward (2005). Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth. Theoria 20 (3):347-352.score: 120.0
    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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  6. David Fair (1984). Provability and Mathematical Truth. Synthese 61 (3):363 - 385.score: 120.0
    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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  7. Imre Toth (2009). “Deus Fons Veritatis”: The Subject and its Freedom. The Ontic Foundation of Mathematical Truth. A Biographical-Theoretical Interview with Gaspare Polizzi. Iris 1 (1):29-80.score: 120.0
    “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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  8. La´Szlo´ E. Szabo´ (2003). Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth. International Studies in the Philosophy of Science 17 (2):117-125.score: 118.0
    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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  9. Alan Weir, A Neo-Formalist Approach to Mathematical Truth.score: 114.0
    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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  10. László Szabó, A Physicalist Account of Mathematical Truth.score: 114.0
    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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  11. László E. Szabó (2003). Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth. International Studies in the Philosophy of Science 17 (2):117 – 125.score: 114.0
    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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  12. G. B. Keene (1956). Analytic Statements and Mathematical Truth. Analysis 16 (4):86 - 90.score: 104.0
    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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  13. Andrea Cantini (1996). Logical Frameworks for Truth and Abstraction: An Axiomatic Study. Elsevier Science B.V..score: 102.0
    This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as type-free or self-referential . These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) (...)
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  14. Laszlo E. Szabo, How Can Physics Account for Mathematical Truth?score: 102.0
    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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  15. Phil Corkum (2012). Aristotle on Mathematical Truth. British Journal for the History of Philosophy 20 (6):1057-1076.score: 100.0
    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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  16. Virginia Klenk (1990). What Mathematical Truth Need Not Be. In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer. 197--208.score: 96.0
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  17. Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.score: 94.0
  18. Esther Ramharter (2006). Making Sense of Questions in Logic and Mathematics: Mill Vs. Carnap. Prolegomena 5 (2):209-218.score: 92.0
    Whether mathematical truths are syntactical (as Rudolf Carnap claimed) or empirical (as Mill actually never claimed, though Carnap claimed that he did) might seem merely an academic topic. However, it becomes a practical concern as soon as we consider the role of questions. For if we inquire as to the truth of a mathematical statement, this question must be (in a certain respect) meaningless for Carnap, as its truth or falsity is certain in advance due to (...)
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  19. Carl G. Hempel (1964). On the Nature of Mathematical Truth. In P. Benacerraf H. Putnam (ed.), Philosophy of Mathematics. Prentice-Hall. 366--81.score: 92.0
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  20. Hilary Putnam (1975). What is Mathematical Truth? In Mathematics, Matter and Method. Cambridge University Press. 60--78.score: 92.0
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  21. Robert Hanna (2010). Mathematical Truth Regained. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. 147--181.score: 92.0
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  22. Paul Benacerraf (2003). What Mathematical Truth Could Not Be--1. In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.score: 92.0
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  23. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.score: 90.0
    This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation (...)
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  24. Mark Balaguer (2001). A Theory of Mathematical Correctness and Mathematical Truth. Pacific Philosophical Quarterly 82 (2):87–114.score: 90.0
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  25. Richard Creath (1980). Benacerraf and Mathematical Truth. Philosophical Studies 37 (4):335 - 340.score: 90.0
  26. Jessica Carter (2013). Handling Mathematical Objects: Representations and Context. Synthese 190 (17):3983-3999.score: 90.0
    This article takes as a starting point the current popular anti realist position, Fictionalism, with the intent to compare it with actual mathematical practice. Fictionalism claims that mathematical statements do purport to be about mathematical objects, and that mathematical statements are not true. Considering these claims in the light of mathematical practice leads to questions about how mathematical objects are handled, and how we prove that certain statements hold. Based on a case study on (...)
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  27. Gian-Carlo Rota (1991). The Concept of Mathematical Truth. Review of Metaphysics 44 (3):483 - 494.score: 90.0
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  28. Thomas M. Norton-Smith (1991). A Note on Philip Kitcher's Analysis of Mathematical Truth. Notre Dame Journal of Formal Logic 33 (1):136-139.score: 90.0
  29. Rene Descartes (1995). Divine Will and Mathematical Truth: Gassendi and Descartes on the Status of the Eternal Truths. In Roger Ariew & Marjorie Glicksman Grene (eds.), Descartes and His Contemporaries: Meditations, Objections, and Replies. University of Chicago Press. 145.score: 90.0
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  30. W. D. Hart (1987). Review: Paul Benacerraf, Mathematical Truth; Michael Jubien, Ontology and Mathematical Truth; Philip Kitcher, The Plight of the Platonist. [REVIEW] Journal of Symbolic Logic 52 (2):552-554.score: 90.0
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  31. Charles A. Baylis (1946). Review: C. G. Hempel, On the Nature of Mathematical Truth. [REVIEW] Journal of Symbolic Logic 11 (3):100-100.score: 90.0
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  32. la´ Szlo´ E. Szabo´ (2003). Formal Systems as Physical Objects: A Physicalist Account of Mathematical Truth. International Studies in the Philosophy of Science 17 (2):117-125.score: 90.0
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  33. Otavio Bueno (2000). Empiricism, Mathematical Truth and Mathematical Knowledge. Poznan Studies in the Philosophy of the Sciences and the Humanities 71:219-242.score: 90.0
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  34. C. Liu (2000). Empiricism, Mathematical Truth and Mathematical Knowledge Commentary. Poznan Studies in the Philosophy of the Sciences and the Humanities 71:219-242.score: 90.0
     
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  35. Ann P. Lowry (1971). Whitehead and the Nature of Mathematical Truth. Process Studies 1 (2):114-123.score: 90.0
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  36. Penelope Maddy (1996). The Legacy of Mathematical Truth. In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. 60--72.score: 90.0
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  37. Elhanan Yakira (1990). What is a Mathematical Truth? In Spinoza and Leibniz. Studia Spinozana: An International and Interdisciplinary Series 6:73-101.score: 90.0
  38. Charles Sayward (1990). Four Views of Arithmetical Truth. Philosophical Quarterly 40 (159):155-168.score: 84.0
    Four views of arithmetical truth are distinguished: the classical view, the provability view, the extended provability view, the criterial view. The main problem with the first is the ontology it requires one to accept. Two anti-realist views are the two provability views. The first of these is judged to be preferable. However, it requires a non-trivial account of the provability of axioms. The criterial view is gotten from remarks Wittgenstein makes in Tractatus 6.2-6.22 . It is judged to be (...)
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  39. Jean-Yves Béziau (2011). Truth as a Mathematical Object. Principia 14 (1):31-46.score: 84.0
    Neste artigo, discutimos em que sentido a verdade é considerada como um objeto matemático na lógica proposicional. Depois de esclarecer como este conceito é usado na lógica clássica, através das noções de tabela de verdade, de função de verdade, de bivaloração, examinamos algumas generalizações desse conceito nas lógicas não clássicas: semânticas matriciais multi-valoradas com três ou quatro valores, semântica bivalente não veritativa, semânticas dos mundos possiveis de Kripke. DOI:10.5007/1808-1711.2010v14n1p31.
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  40. Hartry Field (1998). Which Undecidable Mathematical Sentences Have Determinate Truth Values. In H. G. Dales & Gianluigi Oliveri (eds.), Truth in Mathematics. Oxford University Press, Usa. 291--310.score: 84.0
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  41. John Hayden Woods (1974). Proof & Truth: Mathematical Logic for Non-Mathematicians. Martin.score: 84.0
     
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  42. Roger Wertheimer (1999). How Mathematics Isn't Logic. Ratio 12 (3):279–295.score: 78.0
    If logical truth is necessitated by sheer syntax, mathematics is categorially unlike logic even if all mathematics derives from definitions and logical principles. This contrast gets obscured by the plausibility of the Synonym Substitution Principle implicit in conceptions of analyticity: synonym substitution cannot alter sentence sense. The Principle obviously fails with intercepting: nonuniform term substitution in logical sentences. 'Televisions are televisions' and 'TVs are televisions' neither sound alike nor are used interchangeably. Interception synonymy gets assumed because logical sentences and (...)
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  43. Emilia Anvarovna Taissina (2008). Philosophical Truth in Mathematical Terms and Literature Analogies. Proceedings of the Xxii World Congress of Philosophy 53:273-278.score: 78.0
    The article is based upon the following starting position. In this post-modern time, it seems that no scholar in Europe supports what is called “Enlightenment Project” with its naïve objectivism and Correspondence Theory of Truth1, - though not being really hostile, just strongly skeptical about it. No old-fasioned “classical” academical texts; only His Majesty Discourse as chain of interpretations and reinterpretations. What was called objectivity “proved to be” intersubjectivity; what was called Object (in Latin and German and Russian tradition) now (...)
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  44. Luca Incurvati (2008). Too Naturalist and Not Naturalist Enough: Reply to Horsten. Erkenntnis 69 (2):261 - 274.score: 74.0
    Leon Horsten has recently claimed that the class of mathematical truths coincides with the class of theorems of ZFC. I argue that the naturalistic character of Horsten’s proposal undermines his contention that this claim constitutes an analogue of a thesis that Daniel Isaacson has advanced for PA. I argue, moreover, that Horsten’s defence of his claim against an obvious objection makes use of a distinction which is not available to him given his naturalistic approach. I suggest a way out (...)
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  45. Michael Hymers (2003). The Dignity of a Rule: Wittgenstein, Mathematical Norms, and Truth. Dialogue 42 (03):419-446.score: 74.0
    Paul Boghossian (1996; 1998)argues that Wittgenstein suffered from a "confusion" (1996, 377) if he thought that he could treat propositions of logic and mathematics both as rules and as being true as a matter of convention. He also suggests that such "rule-prescriptivism" (377) about math and logic leads to a vicious regress (1998). Focusing on Wittgenstein's normativism about mathematics, I argue that neither of these claims is true.
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  46. Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.score: 72.0
    Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative (...)
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  47. Melvin Fitting (1986). Notes on the Mathematical Aspects of Kripke's Theory of Truth. Notre Dame Journal of Formal Logic 27 (1):75-88.score: 72.0
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  48. Niels Egmont Christensen (1965). A Non-Truth-Functional Interpretation of Mathematical Logic. Analysis 25 (Suppl-3):129 - 132.score: 72.0
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  49. Alan Weir (2010). Truth Through Proof: A Formalist Foundation for Mathematics. OUP Oxford.score: 72.0
    Truth Through Proof defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. 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. This framework allows for sentences whose truth-conditions are not representational, which are made true or (...)
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  50. Comments on Charles Parsons (2012). Correct Provided the Mathematical Axioms of the Metalanguage Are True–and That Proviso Uses the Very Notion of Truth That Some People Claim Tarski Completely Explained for Us! Why Do I Say This? Well, Remember That Tarski's Criterion of Adequacy is That All the T-Sentences Must Be Theorems of the Metalanguage. If the Metalanguage is Incorrect and It Can Be Incorrect With. In Maria Baghramian (ed.), Reading Putnam. Routledge.score: 72.0
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