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  1. V = L and Intuitive Plausibility in Set Theory. A Case Study.Tatiana Arrigoni - 2011 - Bulletin of Symbolic Logic 17 (3):337-360.
    What counts as an intuitively plausible set theoretic content (notion, axiom or theorem) has been a matter of much debate in contemporary philosophy of mathematics. In this paper I develop a critical appraisal of the issue. I analyze first R. B. Jensen's positions on the epistemic status of the axiom of constructibility. I then formulate and discuss a view of intuitiveness in set theory that assumes it to hinge basically on mathematical success. At the same time, I present accounts of (...)
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  2. The Gödel Paradox and Wittgenstein's Reasons.Francesco Berto - 2009 - Philosophia Mathematica 17 (2):208-219.
    An interpretation of Wittgenstein’s much criticized remarks on Gödel’s First Incompleteness Theorem is provided in the light of paraconsistent arithmetic: in taking Gödel’s proof as a paradoxical derivation, Wittgenstein was drawing the consequences of his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. It is shown that the features of paraconsistent arithmetics match (...)
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  3. On Deductionism.Dan Bruiger - manuscript
    Deductionism assimilates nature to conceptual artifacts (models, equations), and tacitly holds that real physical systems are such artifacts. Some physical concepts represent properties of deductive systems rather than of nature. Properties of mathematical or deductive systems can thereby sometimes falsely be ascribed to natural systems.
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  4. The Kinds of Truth of Geometry Theorems.Michael Bulmer, Desmond Fearnley-Sander & Tim Stokes - 2001 - In Jürgen Richter-Gebert & Dongming Wang (eds.), LNCS: Lecture Notes In Computer Science. Springer Verlag. pp. 129-142.
    Proof by refutation of a geometry theorem that is not universally true produces a Gröbner basis whose elements, called side polynomials, may be used to give inequations that can be added to the hypotheses to give a valid theorem. We show that (in a certain sense) all possible subsidiary conditions are implied by those obtained from the basis; that what we call the kind of truth of the theorem may be derived from the basis; and that the side polynomials may (...)
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  5. Minimalism and the Generalisation Problem: On Horwich’s Second Solution.Cezary Cieśliński - forthcoming - Synthese:1-25.
    Disquotational theories of truth are often criticised for being too weak to prove interesting generalisations about truth. In this paper we will propose a certain formal theory to serve as a framework for a solution of the generalisation problem. In contrast with Horwich’s original proposal, our framework will eschew psychological notions altogether, replacing them with the epistemic notion of believability. The aim will be to explain why someone who accepts a given disquotational truth theory Th, should also accept various generalisations (...)
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  6. The Epistemic Lightness of Truth: Deflationism and its Logic.Cezary Cieśliński - 2017 - Cambridge University Press.
    This book analyses and defends the deflationist claim that there is nothing deep about our notion of truth. According to this view, truth is a 'light' and innocent concept, devoid of any essence which could be revealed by scientific inquiry. Cezary Cieśliński considers this claim in light of recent formal results on axiomatic truth theories, which are crucial for understanding and evaluating the philosophical thesis of the innocence of truth. Providing an up-to-date discussion and original perspectives on this central and (...)
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  7. The Innocence of Truth.Cezary Cieśliński - 2015 - Dialectica 69 (1):61-85.
    One of the popular explications of the deflationary tenet of ‘thinness’ of truth is the conservativeness demand: the declaration that a deflationary truth theory should be conservative over its base. This paper contains a critical discussion and assessment of this demand. We ask and answer the question of whether conservativity forms a part of deflationary doctrines.
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  8. Typed and Untyped Disquotational Truth.Cezary Cieśliński - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag.
    We present an overview of typed and untyped disquotational truth theories with the emphasis on their (non)conservativity over the base theory of syntax. Two types of conservativity are discussed: syntactic and semantic. We observe in particular that TB—one of the most basic disquotational theories—is not semantically conservative over its base; we show also that an untyped disquotational theory PTB is a syntactically conservative extension of Peano Arithmetic.
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  9. T-Equivalences for Positive Sentences.Cezary Cieśliński - 2011 - Review of Symbolic Logic 4 (2):319-325.
    Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.
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  10. Deflationary Truth and Pathologies.Cezary Cieśliński - 2010 - Journal of Philosophical Logic 39 (3):325-337.
    By a classical result of Kotlarski, Krajewski and Lachlan, pathological satisfaction classes can be constructed for countable, recursively saturated models of Peano arithmetic. In this paper we consider the question of whether the pathology can be eliminated; we ask in effect what generalities involving the notion of truth can be obtained in a deflationary truth theory (a theory of truth which is conservative over its base). It is shown that the answer depends on the notion of pathology we adopt. It (...)
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  11. Flawless Disagreement in Mathematics.Justin Clarke-Doane - unknown
    A disagrees with B with respect to a proposition, p, flawlessly just in case A believes p and B believes not-p, or vice versa, though neither A nor B is guilty of a cognitive shortcoming – i.e. roughly, neither A nor B is being irrational, lacking evidence relevant to p, conceptually incompetent, insufficiently imaginative, etc.
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  12. Review of J. Mayberry, The Foundations of Mathematics in the Theory of Sets[REVIEW]Roy T. Cook - 2003 - British Journal for the Philosophy of Science 54 (2):347-352.
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  13. Consistency Problem and “Unexpected Hanging Problem”.Farzad Didehvar - unknown
  14. Da Hilbert a von Neumann: La Svolta Pragmatica Nell'assiomatica.Giambattista Formica - 2013 - Carocci.
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  15. Relative Truth Definability of Axiomatic Truth Theories.Kentaro Fujimoto - 2010 - Bulletin of Symbolic Logic 16 (3):305-344.
    The present paper suggests relative truth definability as a tool for comparing conceptual aspects of axiomatic theories of truth and gives an overview of recent developments of axiomatic theories of truth in the light of it. We also show several new proof-theoretic results via relative truth definability including a complete answer to the conjecture raised by Feferman in [13].
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  16. What is Cantor's Continuum Problem (1964 Version).Kurt Gödel - 1964 - In P. Benacerraf H. Putnam (ed.), Journal of Symbolic Logic. Prentice-Hall. pp. 116-117.
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  17. On Truth and Instrumentalisation.Chris Henry - 2016 - London Journal of Critical Thought 1:5-15.
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  18. Can the Cumulative Hierarchy Be Categorically Characterized?Luca Incurvati - 2016 - Logique Et Analyse 59 (236):367-387.
    Mathematical realists have long invoked the categoricity of axiomatizations of arithmetic and analysis to explain how we manage to fix the intended meaning of their respective vocabulary. Can this strategy be extended to set theory? Although traditional wisdom recommends a negative answer to this question, Vann McGee (1997) has offered a proof that purports to show otherwise. I argue that one of the two key assumptions on which the proof rests deprives McGee's result of the significance he and the realist (...)
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  19. The Importance of Truth in the Thought of Bruno Bauch.T. Kubalica - 2008 - Kwartalnik Filozoficzny 36 (3):63-81.
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  20. Benacerraf's Dilemma and Informal Mathematics.Gregory Lavers - 2009 - 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. Truth by Default.Vann Mcgee - 2001 - Philosophia Mathematica 9 (1):5-20.
    There is no preferred reduction of number theory to set theory. Nonetheless, we confidently accept axioms obtained by substituting formulas from the language of set theory into the induction axiom schema. This is only possible, it is argued, because our acceptance of the induction axioms depends solely on the meanings of aritlunetical and logical terms, which is only possible if our 'intended models' of number theory are standard. Similarly, our acceptance of the second-order natural deduction rules depends solely on the (...)
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  22. Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections.Toby Meadows - 2015 - Notre Dame Journal of Formal Logic 56 (1):191-212.
    This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limited impact on everyday (...)
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  23. Finite Mathematics and the Justification of the Axiom of Choicet.Pierluigi Miraglia - 2000 - Philosophia Mathematica 8 (1):9-25.
    I discuss a difficulty concerning the justification of the Axiom of Choice in terms of such informal notions such as that of iterative set. A recent attempt to solve the difficulty is by S. Lavine, who claims in his Understanding the Infinite that the axioms of set theory receive intuitive justification from their being self-evidently true in Fin(ZFC), a finite counterpart of set theory. I argue that Lavine's explanatory attempt fails when it comes to AC: in this respect Fin(ZFC) is (...)
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  24. Provably True Sentences Across Axiomatizations of Kripke’s Theory of Truth.Carlo Nicolai - forthcoming - Studia Logica:1-30.
    We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...)
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  25. Minimal Type Theory (MTT).Pete Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  26. Hao Wang as Philosopher and Interpreter of Gödel.Charles Parsons - 1998 - Philosophia Mathematica 6 (1):3-24.
    The paper undertakes to characterize Hao Wang's style, convictions, and method as a philosopher, centering on his most important philosophical work From Mathematics to Philosophy, 1974. The descriptive character of Wang's characteristic method is emphasized. Some specific achievements are discussed: his analyses of the concept of set, his discussion, in connection with setting forth Gödel's views, of minds and machines, and his concept of ‘analytic empiricism’ used to criticize Carnap and Quine. Wang's work as interpreter of Gödel's thought and the (...)
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  27. Hilbert's Objectivity.Lydia Patton - 2014 - Historia Mathematica 41 (2):188-203.
    Detlefsen (1986) reads Hilbert's program as a sophisticated defense of instrumentalism, but Feferman (1998) has it that Hilbert's program leaves significant ontological questions unanswered. One such question is of the reference of individual number terms. Hilbert's use of admittedly "meaningless" signs for numbers and formulae appears to impair his ability to establish the reference of mathematical terms and the content of mathematical propositions (Weyl (1949); Kitcher (1976)). The paper traces the history and context of Hilbert's reasoning about signs, which illuminates (...)
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  28. Axioms in Mathematical Practice.D. Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
    On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...)
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  29. Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
    Hilbert’s program was an ambitious and wide-ranging project in the philosophy and foundations of mathematics. In order to “dispose of the foundational questions in mathematics once and for all,” Hilbert proposed a two-pronged approach in 1921: first, classical mathematics should be formalized in axiomatic systems; second, using only restricted, “finitary” means, one should give proofs of the consistency of these axiomatic systems. Although Gödel’s incompleteness theorems show that the program as originally conceived cannot be carried out, it had many partial (...)
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  30. Numbers and Functions in Hilbert's Finitism.Richard Zach - 1998 - Taiwanese Journal for History and Philosophy of Science 10:33-60.