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  1. Tatiana Arrigoni (2011). V = L and Intuitive Plausibility in Set Theory. A Case Study. 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. Francesco Berto (2009). The Gödel Paradox and Wittgenstein's Reasons. 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. Cezary Cieśliński (2015). Typed and Untyped Disquotational Truth. In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Netherlands
    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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  4. Cezary Cieśliński (2015). The Innocence of Truth. 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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  5. Cezary Cieśliński (2011). T-Equivalences for Positive Sentences. 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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  6. Cezary Cieśliński (2010). Deflationary Truth and Pathologies. 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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  7. Justin Clarke-Doane, Flawless Disagreement in Mathematics.
    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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  8. Roy T. Cook (2003). Review of J. Mayberry, The Foundations of Mathematics in the Theory of Sets. [REVIEW] British Journal for the Philosophy of Science 54 (2):347-352.
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  9. Farzad Didehvar, Consistency Problem and “Unexpected Hanging Problem”.
  10. Giambattista Formica (2013). Da Hilbert a von Neumann: La Svolta Pragmatica Nell'assiomatica. Carocci.
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  11. Kentaro Fujimoto (2010). Relative Truth Definability of Axiomatic Truth Theories. 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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  12. Kurt Gödel (1964). What is Cantor's Continuum Problem (1964 Version). In P. Benacerraf H. Putnam (ed.), Journal of Symbolic Logic. Prentice-Hall 116-117.
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  13. Luca Incurvati (forthcoming). Can the Cumulative Hierarchy Be Categorically Characterized? Logique Et Analyse.
    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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  14. T. Kubalica (2008). The Importance of Truth in the Thought of Bruno Bauch. Kwartalnik Filozoficzny 36 (3):63-81.
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  15. 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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  16. Vann Mcgee (2001). Truth by Default. 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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  17. Toby Meadows (2015). Naive Infinitism: The Case for an Inconsistency Approach to Infinite Collections. 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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  18. Pierluigi Miraglia (2000). Finite Mathematics and the Justification of the Axiom of Choicet. 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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  19. Charles Parsons (1998). Hao Wang as Philosopher and Interpreter of Gödel. 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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  20. Lydia Patton (2014). Hilbert's Objectivity. 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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  21. D. Schlimm (2013). Axioms in Mathematical Practice. 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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