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

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  1. Michael Jubien (1977). Ontology and Mathematical Truth. 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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  2.  55
    Charles Sayward (2005). Steiner Versus Wittgenstein: Remarks on Differing Views of Mathematical Truth. 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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  3.  40
    Graham Priest (1983). An Anti-Realist Account of Mathematical Truth. 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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  4.  34
    David Fair (1984). Provability and Mathematical Truth. 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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  5.  2
    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.
    “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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  6.  62
    László Szabó, A Physicalist Account of Mathematical Truth.
    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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  7.  61
    Alan Weir, A Neo-Formalist Approach to Mathematical Truth.
    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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  8.  23
    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.
    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.  14
    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.
    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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  10. Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
  11. Bradley Armour‐Garb & James A. Woodbridge (2014). From Mathematical Fictionalism to Truth‐Theoretic Fictionalism. 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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  12. Phil Corkum (2012). Aristotle on Mathematical Truth. 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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  13.  63
    Laszlo E. Szabo, How Can Physics Account for Mathematical Truth?
    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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  14.  66
    G. B. Keene (1956). Analytic Statements and Mathematical Truth. 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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  15.  2
    Virginia Klenk (1990). What Mathematical Truth Need Not Be. In J. Dunn & A. Gupta (eds.), Truth or Consequences. Kluwer 197--208.
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  16. Hilary Putnam (1975). What is Mathematical Truth? In Mathematics, Matter and Method. Cambridge University Press 60--78.
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  17.  84
    Mark Balaguer (2001). A Theory of Mathematical Correctness and Mathematical Truth. Pacific Philosophical Quarterly 82 (2):87–114.
  18.  82
    Carl G. Hempel (1964). On the Nature of Mathematical Truth. In P. Benacerraf H. Putnam (ed.), Philosophy of Mathematics. Prentice-Hall 366--81.
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  19.  19
    Ann P. Lowry (1971). Whitehead and the Nature of Mathematical Truth. Process Studies 1 (2):114-123.
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  20. Paul Benacerraf (2003). What Mathematical Truth Could Not Be--1. In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press
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  21.  22
    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.
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  22.  70
    Richard Creath (1980). Benacerraf and Mathematical Truth. Philosophical Studies 37 (4):335 - 340.
  23.  2
    Otavio Bueno (2000). Empiricism, Mathematical Truth and Mathematical Knowledge. Poznan Studies in the Philosophy of the Sciences and the Humanities 71:219-242.
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  24.  21
    Gian-Carlo Rota (1991). The Concept of Mathematical Truth. Review of Metaphysics 44 (3):483 - 494.
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  25.  13
    Robert Hanna (2010). Mathematical Truth Regained. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer 147--181.
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  26.  7
    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.
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  27. Penelope Maddy (1996). The Legacy of Mathematical Truth. In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell 60--72.
     
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  28.  6
    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.
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  29. C. Liu (2000). Empiricism, Mathematical Truth and Mathematical Knowledge Commentary. Poznan Studies in the Philosophy of the Sciences and the Humanities 71:219-242.
     
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  30.  10
    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.
  31.  3
    Charles A. Baylis (1946). Review: C. G. Hempel, On the Nature of Mathematical Truth. [REVIEW] Journal of Symbolic Logic 11 (3):100-100.
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  32. Charles A. Baylis (1946). Hempel C. G.. On the Nature of Mathematical Truth. The American Mathematical Monthly, Vol. 52 , Pp. 543–556. Journal of Symbolic Logic 11 (3):100.
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  33. Max Black (1949). 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] Journal of Symbolic Logic 14 (3):184-185.
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  34. Judith Grabiner (2000). The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth by Paul Hoffman. [REVIEW] Isis: A Journal of the History of Science 91:804-805.
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  35. W. D. Hart (1987). Benacerraf Paul. Mathematical Truth. The Journal of Philosophy, Vol. 70 , Pp. 661–679.Jubien Michael. Ontology and Mathematical Truth. Noûs, Vol. 11 , Pp. 133–150.Kitcher Philip. The Plight of the Platonist. Noûs, Vol. 12 , Pp. 119–136. [REVIEW] Journal of Symbolic Logic 52 (2):552-554.
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  36. Elhanan Yakira (1990). What is a Mathematical Truth? In Spinoza and Leibniz. Studia Spinozana: An International and Interdisciplinary Series 6:73-101.
  37. P. B. Andrews (2002). An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Kluwer Academic Publishers.
    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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  38.  17
    Jean-Yves Béziau (2011). Truth as a Mathematical Object. Principia 14 (1):31-46.
    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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  39. John Hayden Woods (1974). Proof & Truth: Mathematical Logic for Non-Mathematicians. Martin.
     
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  40.  19
    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.
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  41.  30
    Emilia Anvarovna Taissina (2008). Philosophical Truth in Mathematical Terms and Literature Analogies. Proceedings of the Xxii World Congress of Philosophy 53:273-278.
    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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  42. Josué Antonio Nescolarde-Selva, Josep-Lluis Usó-Doménech & Hugh Gash (2015). A Logic-Mathematical Point of View of the Truth: Reality, Perception, and Language. Complexity 20 (4):58-67.
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  43.  13
    Melvin Fitting (1986). Notes on the Mathematical Aspects of Kripke's Theory of Truth. Notre Dame Journal of Formal Logic 27 (1):75-88.
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  44.  26
    Michael Hymers (2003). The Dignity of a Rule: Wittgenstein, Mathematical Norms, and Truth. Dialogue 42 (03):419-446.
    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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  45. Ian Mueller (2000). Mathematical Method and Philosophical Truth. Filozofski Vestnik 21 (1):131-155.
     
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  46.  1
    Gila Sher (2012). Truth and Knowledge in Logic and Mathematics. 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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  47.  1
    P. B. Andrews & Mitsuru Yasuhara (2003). REVIEWS-An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Bulletin of Symbolic Logic 9 (3):408.
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  48.  1
    George W. Patterson (1952). Abbott Wilton R.. Computing Logical Truth with the California Digital Computer. Mathematical Tables and Other Aids to Computation, Vol. 5 , Pp. 120–128. [REVIEW] Journal of Symbolic Logic 17 (4):280-281.
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  49. Sergio Galvan (2010). 12 The Emergence of the Intuition of Truth in Mathematical Thought. In Antonella Corradini & Timothy O'Connor (eds.), Emergence in Science and Philosophy. Routledge 6--233.
     
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  50.  10
    Niels Egmont Christensen (1965). A Non-Truth-Functional Interpretation of Mathematical Logic. Analysis 25 (Suppl-3):129 - 132.
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