66 found
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  1.  95
    Axiomatic Theories of Truth.Volker Halbach - 2008 - Stanford Encyclopedia of Philosophy.
    Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...)
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  2. Axiomatizing Kripke's Theory of Truth.Volker Halbach & Leon Horsten - 2006 - Journal of Symbolic Logic 71 (2):677 - 712.
    We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...)
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  3.  10
    On the Costs of Nonclassical Logic.Volker Halbach & Carlo Nicolai - forthcoming - Journal of Philosophical Logic:1-31.
    Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: of the system KF of Feferman formulated in classical logic, and the system PKF of Halbach and Horsten, formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the (...)
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  4.  56
    Disquotationalism and Infinite Conjunctions.Volker Halbach - 1999 - Mind 108 (429):1-22.
    According to the disquotationalist theory of truth, the Tarskian equivalences, conceived as axioms, yield all there is to say about truth. Several authors have claimed that the expression of infinite conjunctions and disjunctions is the only purpose of the disquotationalist truth predicate. The way in which infinite conjunctions can be expressed by an axiomatized truth predicate is explored and it is considered whether the disquotationalist truth predicate is adequate for this purpose.
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  5.  22
    Yablo Without Gödel.Volker Halbach & Shuoying Zhang - forthcoming - Analysis:anw062.
    We prove Yablo’s paradox without the diagonal lemma or the recursion theorem. Only a disquotation schema and axioms for a serial and transitive ordering are used in the proof. The consequences for the discussion on whether Yablo’s paradox is circular or involves self-reference are evaluated.
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  6.  36
    Axiomatizing Semantic Theories of Truth?Martin Fischer, Volker Halbach, Jönne Kriener & Johannes Stern - 2015 - Review of Symbolic Logic 8 (2):257-278.
    We discuss the interplay between the axiomatic and the semantic approach to truth. Often, semantic constructions have guided the development of axiomatic theories and certain axiomatic theories have been claimed to capture a semantic construction. We ask under which conditions an axiomatic theory captures a semantic construction. After discussing some potential criteria, we focus on the criterion of ℕ-categoricity and discuss its usefulness and limits.
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  7.  28
    Computational Structuralism.Volker Halbach & Leon Horsten - 2005 - Philosophia Mathematica 13 (2):174-186.
    According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by (nonstandard) models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations is isomorphic to the standard model of arithmetic. (...)
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  8.  70
    How Innocent is Deflationism?Volker Halbach - 2001 - Synthese 126 (1-2):167 - 194.
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  9.  84
    Possible-Worlds Semantics for Modal Notions Conceived as Predicates.Volker Halbach, Hannes Leitgeb & Philip Welch - 2003 - Journal of Philosophical Logic 32 (2):179-223.
    If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...)
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  10.  55
    A System of Complete and Consistent Truth.Volker Halbach - 1994 - Notre Dame Journal of Formal Logic 35 (1):311--27.
    To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation and conecessitation T and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is -inconsistent, but it can be approximated by models obtained by a kind of rule-of-revision semantics. Furthermore we prove that FS is equivalent to a system already studied by Friedman and Sheard and give an analysis (...)
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  11.  47
    Reducing Compositional to Disquotational Truth.Volker Halbach - 2009 - Review of Symbolic Logic 2 (4):786-798.
    Disquotational theories of truth, that is, theories of truth based on the T-sentences or similar equivalences as axioms are often thought to be deductively weak. This view is correct if the truth predicate is allowed to apply only to sentences not containing the truth predicate. By taking a slightly more liberal approach toward the paradoxes, I obtain a disquotational theory of truth that is proof theoretically as strong as compositional theories such as the Kripket probe the compositional axioms.
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  12.  65
    Reflections On Frege And Hilbert.Bernd Buldt, Volker Halbach & Reinhard Kahle - 2005 - Synthese 147 (1):1-2.
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  13.  44
    Conservative Theories of Classical Truth.Volker Halbach - 1999 - Studia Logica 62 (3):353-370.
    Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS of [2] are conservative over PA.
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  14. Norms for Theories of Reflexive Truth.Leon Horsten & Volker Halbach - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag.
     
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  15.  66
    How Not to State T-Sentences.Volker Halbach - 2006 - Analysis 66 (4):276–280.
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  16. The Logic Manual.Volker Halbach - 2010 - Oxford University Press.
    The Logic Manual is a clear and concise introduction to logic for beginning philosophy students.
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  17.  54
    On a Side Effect of Solving Fitch's Paradox by Typing Knowledge.Volker Halbach - 2008 - Analysis 68 (298):114-120.
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  18.  25
    Truth and Reduction.Volker Halbach - 2000 - Erkenntnis 53 (1-2):97-126.
    The proof-theoretic results on axiomatic theories oftruth obtained by different authors in recent years are surveyed.In particular, the theories of truth are related to subsystems ofsecond-order analysis. On the basis of these results, thesuitability of axiomatic theories of truth for ontologicalreduction is evaluated.
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  19. The Deflationists' Axioms for Truth.Volker Halbach & Leon Horsten - 2008 - In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. Oxford University Press.
     
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  20.  1
    Axiomatische Wahrheitstheorien.Volker Halbach - 1999 - Studia Logica 63 (1):138-140.
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  21.  65
    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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  22.  9
    Principles of Truth.Volker Halbach & Leon Horsten (eds.) - 2002 - Hänsel-Hohenhausen.
  23.  72
    Tarskian and Kripkean Truth.Volker Halbach - 1997 - Journal of Philosophical Logic 26 (1):69-80.
    A theory of the transfinite Tarskian hierarchy of languages is outlined and compared to a notion of partial truth by Kripke. It is shown that the hierarchy can be embedded into Kripke's minimal fixed point model. From this results on the expressive power of both approaches are obtained.
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  24.  4
    Coherence and Dynamics of Belief.Volker Halbach & Erik J. Olsson - 1999 - Erkenntnis 50.
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  25.  4
    How Not to State T-Sentences.Volker Halbach - 2006 - Analysis 66 (292):276-280.
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  26.  55
    Tarski Hierarchies.Volker Halbach - 1995 - Erkenntnis 43 (3):339 - 367.
    The general notions of object- and metalanguage are discussed and as a special case of this relation an arbitrary first order language with an infinite model is expanded by a predicate symbol T0 which is interpreted as truth predicate for . Then the expanded language is again augmented by a new truth predicate T1 for the whole language plus T0. This process is iterated into the transfinite to obtain the Tarskian hierarchy of languages. It is shown that there are natural (...)
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  27.  3
    On the Benefits of a Reduction of Modal Predicates to Modal Operators.Volker Halbach - 2009 - In Hieke Alexander & Leitgeb Hannes (eds.), Reduction, Abstraction, Analysis. Ontos Verlag. pp. 323--333.
  28.  20
    Self-Reference in Arithmetic I.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):671-691.
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  29.  7
    Modalized Disquotationalism.Volker Halbach - 2003 - In Leon Horsten & Volker Halbach (eds.), Principles of Truth. De Gruyter. pp. 75-102.
  30.  21
    Editorial Introduction.Volker Halbach - 2001 - Studia Logica 68 (1):3-20.
    I survey some important semantical and axiomatic theories of self-referential truth. Kripke's fixed-point theory, the revision theory of truth and appraoches involving fuzzy logic are the main examples of semantical theories. I look at axiomatic theories devised by Cantini, Feferman, Freidman and Sheard. Finally some applications of the theory of self-referential truth are considered.
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  31. Computational Structuralism &Dagger.Volker Halbach & Leon Horsten - 2005 - Philosophia Mathematica 13 (2):174-186.
    According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations is isomorphic to the standard model of arithmetic. On (...)
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  32.  1
    `Contemporary Methods for Investigating the Concept of Truth – An Introduction'.Leon Horsten & Volker Halbach - 2003 - In Leon Horsten & Volker Halbach (eds.), Principles of Truth. De Gruyter. pp. 11-36.
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  33.  1
    A System Of Complete And Consistent Truth.Volker Halbach - 1994 - Notre Dame Journal of Formal Logic 35 (3):311-327.
    To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation φ/Tφ and conecessitation T φ/φ and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is w-inconsistent, but it can be approximated by models obtained by a kind of rule-of-revision semantics. Furthermore we prove that FS is equivalent to a system already studied by Friedman and Sheard and give (...)
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  34.  9
    Self-Reference in Arithmetic II.Volker Halbach & Albert Visser - 2014 - Review of Symbolic Logic 7 (4):692-712.
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  35.  4
    How Innocent Is Deflationism?Volker Halbach - 2001 - Synthese 126 (1):167-194.
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  36.  16
    War Descartes Erkenntnistheoretischer Voluntarist?Volker Halbach - 2002 - Zeitschrift für Philosophische Forschung 56 (4):545 - 562.
    Nach Auffassung einiger Autoren wie Alvin Goldman und William Alston setzt normative Erkenntnistheorie einen erkenntnistheoretischen Voluntarismus voraus, der besagt, daß epistemische Verhaltensweisen wie Glauben, Urteilen, Urteilsenthaltung willentliche Handlungen sind. Normen können dann auf diese Verhaltensweisen einwirken, indem wir den Normen willentlich Folge leisten. Gegen diesen Voluntarismus spricht aber die Beobachtung, daß epistemische Verhaltensweisen in den meisten Fällen keine willentlichen Handlungen sind. Descartes' wurde von beiden genannten Autoren als ein typischer Vertreter eines normativen Ansatzes angesehen, der diesen unhaltbaren Voluntarismus voraussetzt. Ich (...)
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  37.  6
    Löwe Benedikt and Welch Philip. Set-Theoretic Absoluteness and the Revision Theory. Studia Logica, Vol. 68 (2001), Pp. 21–41. Löwe Benedikt. Revision Sequences and Computers with an Infinite Amount of Time. Journal of Logic and Computation, Vol. 11 (2001), Pp. 25–40. [REVIEW]Volker Halbach - 2003 - Bulletin of Symbolic Logic 9 (2):235-237.
  38.  10
    On Lehrer's Principle of Trustworthiness.Volker Halbach - 1999 - Erkenntnis 50 (2/3):259 - 272.
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  39. AG Burgess and JP Burgess, Truth.Volker Halbach - 2012 - Bulletin of Symbolic Logic 18 (2):271.
  40.  2
    Can We Grasp Consistency?Volker Halbach - 2003 - In Olsson Erik (ed.), The Epistemology of Keith Lehrer. Kluwer Academic Publishers. pp. 75--87.
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  41.  1
    Beklemishev Lev D.. Induction Rules, Reflection Principles, and Provably Recursive Functions. Annals of Pure and Applied Logic, Vol. 85 , Pp. 193–242. [REVIEW]Volker Halbach - 2002 - Bulletin of Symbolic Logic 8 (2):302-303.
  42.  6
    Review: Lev D. Beklemishev, Induction Rules, Reflection Principles, and Provably Recursive Functions. [REVIEW]Volker Halbach - 2002 - Bulletin of Symbolic Logic 8 (2):302-303.
  43.  8
    Editorial Overview.Volker Halbach & Erik J. Olsson - 1999 - Erkenntnis 50 (2-3):149-153.
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  44. Axiomatic Theories of Truth.Volker Halbach - 2011 - Cambridge University Press.
    At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on the (...)
     
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  45. Aksjomatyczne Teorie Prawdy.Volker Halbach - manuscript
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  46. Classical Symmetric Truth.Volker Halbach - 1997 - In Julian Nida-Rümelin & Georg Meggle (eds.), Analyomen 2, Volume I: Logic, Epistemology, Philosophy of Science. De Gruyter. pp. 87-92.
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  47. 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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  48. Induction Rules, Reflection Principles, and Provably Recursive Functions.Volker Halbach & Lev D. Beklemishev - 2002 - Bulletin of Symbolic Logic 8 (2):302.
  49. Kapitel II. Die Basistheorie.Volker Halbach - 1996 - In Axiomatische Wahrheitstheorien. De Gruyter. pp. 15-29.
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  50. Kapitel I. Grundlagen.Volker Halbach - 1996 - In Axiomatische Wahrheitstheorien. De Gruyter. pp. 1-14.
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