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Truth, Conservativeness, and Provability

Mind 119 (474):409-422 (2010)

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  1. Bounded Induction and Satisfaction Classes.Henryk Kotlarski - 1986 - Mathematical Logic Quarterly 32 (31-34):531-544.
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  • Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Mathematical Logic Quarterly 35 (2):97-130.
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  • Truth.Paul Horwich - 1999 - In Meaning. Oxford University Press. pp. 261-272.
    What is truth. Paul Horwich advocates the controversial theory of minimalism, that is that the nature of truth is entirely captured in the trivial fact that each proposition specifies its own condition for being true, and that truth is therefore an entirely mundane and unpuzzling concept. The first edition of Truth, published in 1980, established itself as the best account of minimalism and as an excellent introduction to the debate for students. For this new edition, Horwich has refined and developed (...)
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  • Proof and Truth: Through Thick and Thin.Stewart Shapiro - 1998 - Journal of Philosophy 95 (10):493-521.
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  • Proof and Truth.Stewart Shapiro - 1998 - Journal of Philosophy 95 (10):493-521.
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  • Truth and the Unprovability of Consistency.H. Field - 2006 - Mind 115 (459):567-606.
    It might be thought that we could argue for the consistency of a mathematical theory T within T, by giving an inductive argument that all theorems of T are true and inferring consistency. By Gödel's second incompleteness theorem any such argument must break down, but just how it breaks down depends on the kind of theory of truth that is built into T. The paper surveys the possibilities, and suggests that some theories of truth give far more intuitive diagnoses of (...)
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  • Conservativeness and Translation-Dependent T-Schemes.Jeffrey Ketland - 2000 - Analysis 60 (4):319-328.
    Certain translational T-schemes of the form True « f, where f can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.
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  • Conservativeness and Translation-Dependent T-Schemes.Jeffrey Ketland - 2000 - Analysis 60 (4):319–328.
    Certain translational T-schemes of the form True(“f”) « f(f), where f(f) can be almost any translation you like of f, will be a conservative extension of Peano arithmetic. I have an inkling that this means something philosophically, but I don’t understand my own inkling.
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  • Truth.Paul Horwich - 1998 - Clarendon Press.
    Paul Horwich gives the definitive exposition of a prominent philosophical theory about truth, `minimalism'. His theory has attracted much attention since the first edition of Truth in 1990; he has now developed, refined, and updated his treatment of the subject, while preserving the distinctive format of the book. This revised edition appears simultaneously with a new companion volume, Meaning; the two books demystify central philosophical issues, and will be essential reading for all who work on the philosophy of language.
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  • How Innocent Is Deflationism?Volker Halbach - 2001 - Synthese 126 (1):167-194.
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  • Deflationism and Tarski’s Paradise.Jeffrey Ketland - 1999 - Mind 108 (429):69-94.
    Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called (...)
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  • Deflationism and the Gödel Phenomena: Reply to Ketland.Neil Tennant - 2005 - Mind 114 (453):89-96.
    I am not a deflationist. I believe that truth and falsity are substantial. The truth of a proposition consists in its having a constructive proof, or truthmaker. The falsity of a proposition consists in its having a constructive disproof, or falsitymaker. Such proofs and disproofs will need to be given modulo acceptable premisses. The choice of these premisses will depend on the discourse in question.
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  • Deflationism and the Gödel Phenomena.Neil Tennant - 2002 - Mind 111 (443):551-582.
    consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non-trivial fashion. The extended methods of formal proof must capture the essentials of the so-called ‘semantical argument’ for the truth of the Gödel sentence. We are concerned to show that the (...)
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  • Construction of Satisfaction Classes for Nonstandard Models.Henryk Kotlarski, Stanislav Krajewski & Alistair H. Lachlan - 1981 - Canadian Mathematical Bulletin 24 (1):283--93.
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  • Full Satisfaction Classes: A Survey.Henryk Kotlarski - 1991 - Notre Dame Journal of Formal Logic 32 (4):573-579.
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  • Deflationism and the Godel Phenomena.N. Tennant - 2002 - Mind 111 (443):551-582.
    Any consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non-trivial fashion. The extended methods of formal proof must capture the essentials of the so-called 'semantical argument' for the truth of the Gödel sentence. We are concerned to show that (...)
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  • Disquotational Truth and Analyticity.Volker Halbach - 2001 - Journal of Symbolic Logic 66 (4):1959-1973.
    The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences, yet not in the scope of negation, the system with the reflection (...)
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  • Notes on Formal Theories of Truth.Andrea Cantini - 1989 - Zeitshrift für Mathematische Logik Und Grundlagen der Mathematik 35 (1):97--130.
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  • Deflationism and the Gödel Phenomena: Reply to Tennant.Jeffrey Ketland - 2005 - Mind 114 (453):75-88.
    Any (1-)consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a nontrivial fashion. The extended methods of formal proof must capture the essentials of the so-called 'semantical argument' for the truth of the Gödel sentence. We are concerned to show that (...)
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  • A Guide to Truth Predicates in the Modern Era.Michael Sheard - 1994 - Journal of Symbolic Logic 59 (3):1032-1054.
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  • Disquotational Truth and Analyticity.Volker Halbach - 2001 - Journal of Symbolic Logic 66 (4):1959-1973.
    The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences, yet not in the scope of negation, the system with the reflection (...)
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