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  1. Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
  2. J. P. Burgess (2005). Neil Tennant. The Taming of the True. Oxford: Clarendon Press, 1997. Pp. Xviii + 466. ISBN 0-19-823717-0 (Cloth), 0-19-925160-6 (Paper). [REVIEW] Philosophia Mathematica 13 (2):202-215.
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  3. Andrea Cantini (1996). Logical Frameworks for Truth and Abstraction: An Axiomatic Study. Elsevier Science B.V..
    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) these (...)
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  4. Arkadiusz Chrudzimski (2009). Catégories formelles, nombres et conceptualisme. La première philosophie de l’arithmétique de Husserl. Philosophiques 36 (2):427-445.
    Résumé -/- Dans son premier livre (Philosophie de l’arithmétique 1891), Husserl élabore une très intéressante philosophie des mathématiques. Les concepts mathématiques sont interprétés comme des concepts de « deuxième ordre » auxquels on accède par une réflexion sur nos opérations mentales de numération. Il s’ensuit que la vérité de la proposition : « il y a trois pommes sur la table » ne consiste pas dans une relation mythique quelconque avec la réalité extérieure au psychique (où le nombre trois doit (...)
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  5. 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 also faces a (...)
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  6. Richard Creath (1980). Benacerraf and Mathematical Truth. Philosophical Studies 37 (4):335 - 340.
  7. H. G. Dales & Gianluigi Oliveri (eds.) (1998). Truth in Mathematics. 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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  8. Steven M. Duncan, Platonism by the Numbers.
    In this paper, I defend traditional Platonic mathematical realism from its contemporary detractors, arguing that numbers, understood as abstract, non-physical objects of rational intuition, are indispensable for the act of counting.
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  9. 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 platonism's valid insights. Besides helping to clarify (...)
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  10. Juliet Floyd (1995). On Saying What You Really Want to Say: Wittgenstein, Gödel and the Trisection of the Angle. In Jaakko Hintikka (ed.), From Dedekind to Gödel: The Foundations of Mathematics in the Early Twentieth Century, Synthese Library Vol. 251 (Kluwer Academic Publishers. 373-426.
  11. P. Garavaso (2013). Hilary Putnam's Consistency Objection Against Wittgenstein's Conventionalism in Mathematics. Philosophia Mathematica 21 (3):279-296.
    Hilary Putnam first published the consistency objection against Ludwig Wittgenstein’s account of mathematics in 1979. In 1983, Putnam and Benacerraf raised this objection against all conventionalist accounts of mathematics. I discuss the 1979 version and the scenario argument, which supports the key premise of the objection. The wide applicability of this objection is not apparent; I thus raise it against an imaginary axiomatic theory T similar to Peano arithmetic in all relevant aspects. I argue that a conventionalist can explain the (...)
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  12. Robert Hanna (2010). Mathematical Truth Regained. In Mirja Hartimo (ed.), Phenomenology and Mathematics. Springer. 147--181.
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  13. James Hawthorne (1996). Mathematical Instrumentalism Meets the Conjunction Objection. Journal of Philosophical Logic 25 (4):363-397.
    Scientific realists often appeal to some version of the conjunction objection to argue that scientific instrumentalism fails to do justice to the full empirical import of scientific theories. Whereas the conjunction objection provides a powerful critique of scientific instrumentalism, I will show that mathematical instnrunentalism escapes the conjunction objection unscathed.
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  14. Philip Hugly & Charles Sayward (1989). Can There Be a Proof That an Unprovable Sentence of Arithmetic is True? Dialectica 43 (43):289-292.
    Various authors of logic texts are cited who either suggest or explicitly state that the Gödel incompleteness result shows that some unprovable sentence of arithmetic is true. Against this, the paper argues that the matter is one of philosophical controversy, that it is not a mathematical or logical issue.
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  15. 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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  16. Luca Incurvati (2009). Does Truth Equal Provability in the Maximal Theory? Analysis 69 (2):233-239.
    According to the received view, formalism – interpreted as the thesis that mathematical truth does not outrun the consequences of our maximal mathematical theory – has been refuted by Goedel's theorem. In support of this claim, proponents of the received view usually invoke an informal argument for the truth of the Goedel sentence, an argument which is supposed to reconstruct our reasoning in seeing its truth. Against this, Field has argued in a series of papers that the principles involved in (...)
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  17. Luca Incurvati (2008). Too Naturalist and Not Naturalist Enough: Reply to Horsten. Erkenntnis 69 (2):261 - 274.
    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 of (...)
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  18. Rognvaldur Ingthorsson (2006). Truthmakers Without Truth. Metaphysica 7 (2):53–71.
    It is often taken for granted that truth is mind-independent, i.e. that, necessarily, if the world is objectively speaking in a certain way, then it is true that it is that way, independently of anyone thinking that it is that way. I argue that proponents of correspondence-truth, in particular immanent realists, should not take the mind-independence of truth for granted. The assumption that the mind-independent features of the world, i.e. ‘facts’, determine the truth of propositions, does not entail that truth (...)
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  19. Jeffrey Ketland & Panu Raatikainen, Truth and Provability Again.
    Lucas and Redhead ([2007]) announce that they will defend the views of Redhead ([2004]) against the argument by Panu Raatikainen ([2005]). They certainly re-state the main claims of Redhead ([2004]), but they do not give any real arguments in their favour, and do not provide anything that would save Redhead’s argument from the serious problems pointed out in (Raatikainen [2005]). Instead, Lucas and Redhead make a number of seemingly irrelevant points, perhaps indicating a failure to understand the logico-mathematical points at (...)
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  20. Gregory Lavers (2009). Benacerraf's Dilemma and Informal Mathematics. Review of Symbolic Logic 2 (4):769-785.
    This paper puts forward and defends an account of mathematical truth, and in particular an account of the truth of mathematical axioms. The proposal attempts to be completely nonrevisionist. In this connection, it seeks to satisfy simultaneously both horns of Benacerrafs work on informal rigour. Kreisel defends the view that axioms are arrived at by a rigorous examination of our informal notions, as opposed to being stipulated or arrived at by trial and error. This view is then supplemented by a (...)
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  21. 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.
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  22. Markus Pantsar (2009). Truth, Proof and Gödelian Arguments: A Defence of Tarskian Truth in Mathematics. 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 established to (...)
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  23. 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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  24. Panu Raatikainen (2004). Conceptions of Truth in Intuitionism. History and Philosophy of Logic 25 (2):131--45.
    Intuitionism’s disagreement with classical logic is standardly based on its specific understanding of truth. But different intuitionists have actually explicated the notion of truth in fundamentally different ways. These are considered systematically and separately, and evaluated critically. It is argued that each account faces difficult problems. They all either have implausible consequences or are viciously circular.
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  25. Esther Ramharter (2006). Making Sense of Questions in Logic and Mathematics: Mill Vs. Carnap. Prolegomena 5 (2):209-218.
    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 its purely syntactical (or (...)
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  26. Charles Sayward (2001). On Some Much Maligned Remarks of Wittgenstein on Gödel. Philosophical Investigations 24 (3):262–270.
    In "Remarks on the Foundations of Mathematics" Wittgenstein discusses an argument that goes from Gödel’s incompleteness result to the conclusion that some truths of mathematics are unprovable. Wittgenstein takes issue with this argument. Wittgenstein’s remarks in this connection have received very negative reaction from some very prominent people, for example, Gödel and Dummett. The paper is a defense of what Wittgenstein has to say about the argument in question.
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  27. Charles Sayward (1990). Four Views of Arithmetical Truth. Philosophical Quarterly 40 (159):155-168.
    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 the (...)
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  28. 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 can be combined. (...)
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  29. 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 will discuss how (...)
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  30. 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 of (...)
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  31. 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 of (...)
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