81 found
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  1. A Set of Axioms for Logic.Theodore Hailperin - 1944 - Journal of Symbolic Logic 9 (1):1-19.
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  2.  9
    Sentential Probability Logic.Theodore Hailperin - 2000 - Studia Logica 64 (3):405-408.
  3. Quantification Theory and Empty Individual-Domains.Theodore Hailperin - 1953 - Journal of Symbolic Logic 18 (3):197-200.
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  4.  23
    Probability Logic.Theodore Hailperin - 1984 - Notre Dame Journal of Formal Logic 25 (3):198-212.
  5.  27
    Kenneth Harris and Branden Fitelson/Comments on Some Completeness Theorems of Urquhart and Méndez & Salto 51–55 Dominic Gregory/Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actu. [REVIEW]Theodore Hailperin & Ontologically Neutral Logic - 2001 - Journal of Philosophical Logic 30 (1):617-618.
    The paper begins with a more carefully stated version of ontologically neutral logic, originally introduced in. A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.
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  6.  2
    [Omnibus Review].Theodore Hailperin - 1967 - Journal of Symbolic Logic 32 (2):252-252.
  7.  5
    A Set of Axioms for Logic.Theodore Hailperin - 1944 - Journal of Symbolic Logic 9 (3):73-74.
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  8.  21
    Herbrand Semantics, the Potential Infinite, and Ontology-Free Logic.Theodore Hailperin - 1992 - History and Philosophy of Logic 13 (1):69-90.
    This paper investigates the ontological presuppositions of quantifier logic. It is seen that the actual infinite, although present in the usual completeness proofs, is not needed for a proper semantic foundation. Additionally, quantifier logic can be given an adequate formulation in which neither the notion of individual nor that of a predicate appears.
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  9.  10
    Logics Without Existence Assumptions.Theodore Hailperin - 1968 - Journal of Symbolic Logic 37 (2):424-424.
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  10.  79
    Probability Semantics for Quantifier Logic.Theodore Hailperin - 2000 - Journal of Philosophical Logic 29 (2):207-239.
    By supplying propositional calculus with a probability semantics we showed, in our 1996, that finite stochastic problems can be treated by logic-theoretic means equally as well as by the usual set-theoretic ones. In the present paper we continue the investigation to further the use of logical notions in probability theory. It is shown that quantifier logic, when supplied with a probability semantics, is capable of treating stochastic problems involving countably many trials.
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  11.  13
    Algebraical Logic 1685–1900.Theodore Hailperin - 2004 - In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic. Elsevier. pp. 3--323.
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  12.  43
    The Development of Probability Logic From Leibniz to Maccoll.Theodore Hailperin - 1988 - History and Philosophy of Logic 9 (2):131-191.
    The introduction has a brief statement, sufficient for the purpose of this paper, which describes in general terms the notion of probability logic on which the paper is based. Contributions made in the eighteenth century by Leibniz, Jacob Bernoulli and Lambert, and in the nineteenth century by Bolzano, De Morgan, Boole, Peirce and MacColl are critically examined from a contemporary point of view. Historicity is maintained by liberal quotations from the original sources accompanied by interpretive explanation. Concluding the paper is (...)
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  13.  32
    Ontologically Neutral Logic.Theodore Hailperin - 1997 - History and Philosophy of Logic 18 (4):185-200.
    An elaboration in detail of the contention made in an earlier paper 1 that quantifier logic can be given an adequate formulation in which neither the notion of an individual nor that of a predicate appears. The logic is compatible with either an infinitistic or non-infinitistic completeness theorem.
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  14.  3
    Quantification Theory and Empty Individual Domains.Theodore Hailperin - 1955 - Journal of Symbolic Logic 20 (3):284-284.
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  15.  34
    Probability Logic and Combining Evidence.Theodore Hailperin - 2006 - History and Philosophy of Logic 27 (3):249-269.
    In Hailperin 1996 , in addition to its formal development of Probability Logic, there are many sections devoted to historical origins, illustrative examples, and discussion of related work by other authors. Here selected portions of its formal treatment are summarized and then used as a basis for a probability logic treatment of combining evidence.
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  16. Remarks on Identity and Description in First-Order Axiom Systems.Theodore Hailperin - 1954 - Journal of Symbolic Logic 19 (1):14-20.
  17.  38
    An Incorrect Theorem.Theodore Hailperin - 1965 - Journal of Symbolic Logic 30 (1):27.
  18.  31
    A Theory of Restricted Quantification I.Theodore Hailperin - 1957 - Journal of Symbolic Logic 22 (1):19-35.
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  19.  38
    Quantifier Probability Logic and the Confirmation Paradox.Theodore Hailperin - 2007 - History and Philosophy of Logic 28 (1):83-100.
    Exhumation and study of the 1945 paradox of confirmation brings out the defect of its formulation. In the context of quantifier conditional-probability logic it is shown that a repair can be accomplished if the truth-functional conditional used in the statement of the paradox is replaced with a connective that is appropriate to the probabilistic context. Description of the quantifier probability logic involved in the resolution of the paradox is presented in stages. Careful distinction is maintained between a formal logic language (...)
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  20.  8
    Distributive Normal Forms in the Calculus of Predicates.Theodore Hailperin - 1955 - Journal of Symbolic Logic 20 (1):75-76.
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  21.  10
    Boole's Logic and Probability a Critical Exposition From the Standpoint of Contemporary Algebra, Logic, and Probability Theory.Theodore Hailperin - 1976
  22.  7
    Boole's Logic and Probability. A Critical Exposition From the Standpoint of Contemporary Algebra, Logic and Probability Theory.N. T. Gridgeman & Theodore Hailperin - 1988 - Journal of Symbolic Logic 53 (4):1253.
  23.  30
    A Complete Set of Axioms for Logical Formulas Invalid in Some Finite Domain.Theodore Hailperin - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (6):84-96.
  24.  4
    Distributive Normal Forms in the Calculus of Predicates.Theodore Hailperin - 1955 - Journal of Symbolic Logic 20 (2):164-164.
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  25.  42
    Karel Lambert. Notes on “E!“: II. Philosophical Studies , Vol. 12 , Pp. 1–5.Theodore Hailperin - 1967 - Journal of Symbolic Logic 32 (2):251.
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  26.  38
    George Boole. Selected Manuscripts on Logic and its Philosophy. Edited by Ivor Grattan-Guinness and Gérard Bornet. Science Networks Historical Studies, Vol. 20. Birkhäuser Verlag, Basel, Boston, and Berlin, 1997, Lxiv + 236 Pp. - Ivor Grattan-Guinness. Boole's Quest for the Foundations of His Logic. Therein, Pp. Xiii–Xlvii. - Gérard Bornet. Boole's Psychologism as a Reception Problem. Therein, Pp. Xlvii–Lviii. [REVIEW]Theodore Hailperin - 1998 - Journal of Symbolic Logic 63 (1):332-333.
  27.  26
    John T. Kearns. Quantifiers and Universal Validity. Logique Et Analyse, N.S. Vol. 9 , Pp. 298–309. - George Goe. A Reconstruction of Formal Logic. Notre Dame Journal of Formal Logic, Vol. 7 , Pp. 129–157. - George Goe. Corrections to My Paper “A Reconstruction of Formal Logic.”Notre Dame Journal of Formal Logic, Vol. 7 , P. 158. [REVIEW]Theodore Hailperin - 1968 - Journal of Symbolic Logic 33 (1):137-138.
  28.  24
    Max Beberman and Herbert E. Vaughan. High School Mathematics. Course 2. Plane Geometry with Appendices on Logic and Solid Geometry. D. C. Heath and Company, Boston, Englewood, Chicago, San Francisco, Atlanta, Dallas, London, and Toronto, 1965, Xi + 584 Pp. - Max Beberman and Herbert E. Vaughan. High School Mathematics. Course 2. Plane Geometry with Appendices on Logic and Solid Geometry. Teacher's Edition. D. C. Heath and Company, Boston, Englewood, Chicago, San Francisco, Atlanta, Dallas, London, and Toronto, 1965, 608 Pp. [REVIEW]Theodore Hailperin - 1966 - Journal of Symbolic Logic 31 (4):672-673.
  29.  2
    A Theory of Restricted Quantification.Theodore Hailperin - 1960 - Journal of Symbolic Logic 25 (2):175-176.
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  30.  22
    Karel Lambert. Notes on E! III: A Theory of Descriptions. Philosophical Studies , Vol. 13 , Pp. 51–59. - Jaakko Hintikka. Definite Descriptions and Self-Identity.Philosophical Studies , Vol. 15 , Pp. 5–7. - Karel Lambert. Notes on E! IV. Philosophical Studies , Vol. 15 , Pp. 85–88. , P. 48.) - Karel Lambert. Definite Descriptions and Self-Identity. II. Philosophical Studies , Vol. 15 , Vol. 17 , Pp. 35–43. [REVIEW]Theodore Hailperin - 1967 - Journal of Symbolic Logic 32 (2):252.
  31.  22
    Rolf Schock. Contributions to Syntax, Semantics, and the Philosophy of Science. Notre Dame Journal of Formal Logic, Vol. 5 No. 4 , Pp. 241–289. [REVIEW]Theodore Hailperin - 1972 - Journal of Symbolic Logic 37 (2):423.
  32.  11
    A Theory of Restricted Quantification II.Theodore Hailperin - 1957 - Journal of Symbolic Logic 22 (2):113-129.
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  33.  21
    Max Beberman and Herbert E. Vaughan. High School Mathematics. Course 1. Revised Edition of XXX 401. D. C. Heath and Company, Boston1964, Ix + 598 Pp. - Max Beberman and Herbert E. Vaughan. High School Mathematics. Course 1. Teacher's Edition. Revised Edition of XXX 401. D. C Heath and Company, Boston1964, Pages Irregularly Numbered. [REVIEW]Theodore Hailperin - 1966 - Journal of Symbolic Logic 31 (1):111-112.
  34.  15
    Boole's Abandoned Propositional Logic.Theodore Hailperin - 1984 - History and Philosophy of Logic 5 (1):39-48.
    The approach used by Boole in Mathematical analysis of logic to develop propositional logic was based on the idea of ?cases? or ?conjunctures of circumstances?. But this was dropped in Laws of thought in favor of one which Boole considered to be more satisfactory, that of using the notion of ?time for which a proposition is true?. We show that, when suitable clarifications and corrections are made, the earlier approach? which accords with modern logic in eschewing the extraneous notion of (...)
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  35.  20
    Leon Henkin, W. Norman Smith, Verne J. Varineau, Michael J. Walsh. Retracing Elementary Mathematics. The Macmillan Company, New York1962, Xviii + 418 Pp. [REVIEW]Theodore Hailperin - 1964 - Journal of Symbolic Logic 29 (4):209.
  36.  19
    David Pager. An Emendation of the Axiom System of Hilbert and Ackermann for the Restricted Calculus of Predicates. The Journal of Symbolic Logic, Vol. 27 No. 2 , Pp. 131–138. [REVIEW]Theodore Hailperin - 1969 - Journal of Symbolic Logic 34 (3):520-520.
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  37.  18
    William H. Halberstadt. An Introduction to Modern Logic. An Elementary Textbook of Symbolic Logic. Harper & Brothers, New York1960, Xii + 221 Pp. [REVIEW]Theodore Hailperin - 1964 - Journal of Symbolic Logic 29 (1):43.
  38.  17
    Hubert H. Schneider. Semantics of the Predicate Calculus with Identity and the Validity in the Empty Individual-Domain. Portugaliae Mathematica, Vol. 17 , Pp. 85–96. - Hubert H. Schneider. A Syntactical Characterization of the Predicate Calculus with Identity and the Validity in All Individual-Domains. Portugaliae Mathematica, Vol 20 , Pp. 105–117. [REVIEW]Theodore Hailperin - 1965 - Journal of Symbolic Logic 30 (3):385-386.
  39. Review: John T. Kearns, Quantifiers and Universal Validity; George Goe, A Reconstruction of Formal Logic; George Goe, Corrections to My Paper "A Reconstruction of Formal Logic.". [REVIEW]Theodore Hailperin - 1968 - Journal of Symbolic Logic 33 (1):137-138.
  40. Review: Max Beberman, Herbert E. Vaughan, High School Mathematics. Course 1. [REVIEW]Theodore Hailperin - 1966 - Journal of Symbolic Logic 31 (1):111-112.
  41.  15
    C. C. Chang and H. Jerome Keisler. An Improved Prenex Nomal Form. The Journal of Symbolic Logic, Vol. 27 No. 3 , Pp. 317–326.Theodore Hailperin - 1968 - Journal of Symbolic Logic 33 (3):479.
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  42.  15
    H. Leblanc and R. H. Thomason. Completeness Theorems for Some Presupposition-Free Logics. Fundamenta Mathematicae, Vol. 62 No. 2 , Pp. 125–164. [REVIEW]Theodore Hailperin - 1972 - Journal of Symbolic Logic 37 (2):424-425.
  43.  14
    B. H. Arnold. Logic and Boolean Algebra. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962, Viii + 144 Pp. [REVIEW]Theodore Hailperin - 1964 - Journal of Symbolic Logic 29 (2):95-96.
  44.  45
    Logic Semantics with the Potential Infinite.Theodore Hailperin - 2010 - History and Philosophy of Logic 31 (2):145-159.
    A form of quantification logic referred to by the author in earlier papers as being 'ontologically neutral' still made use of the actual infinite in its semantics. Here it is shown that one can have, if one desires, a formal logic that refers in its semantics only to the potential infinite. Included are two new quantifiers generalizing the sentential connectives, equivalence and non-equivalence. There are thus new avenues opening up for exploration in both quantification logic and semantics of the infinite.
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  45.  43
    Foundations of Probability in Mathematical Logic.Theodore Hailperin - 1937 - Philosophy of Science 4 (1):125-150.
    It is the purpose of this paper to present a theory of probability derived from two-valued logic—the logic of which an aspect is given in Part I, Section A, of Principia Mathematica. The symbolic system of Mr. Keynes, given in his Treatise on Probability, will be shown to be a part of our system. We have, however, little if anything in common with his philosophical analysis; a definition of Keynes’ fundamental probability relation, free from psychological or material reference, will be (...)
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  46.  20
    Review: Nicholas Rescher, Definitions of "Existence."; Karel Lambert, Notes on "E!". [REVIEW]Theodore Hailperin - 1967 - Journal of Symbolic Logic 32 (2):251-251.
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  47.  36
    Potential Infinite Models and Ontologically Neutral Logic.Theodore Hailperin - 2001 - Journal of Philosophical Logic 30 (1):79-96.
    The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.
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  48.  17
    A Form of Herbrand's Theorem.Theodore Hailperin - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (7-12):107-120.
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  49.  28
    Probability Logic and Borel's Denumerable Probability.Theodore Hailperin - 2008 - History and Philosophy of Logic 29 (3):307-307.
    Borel's concept of denumerable probability is described by means of three of his illustrative problems and their solution. These problems are then reformulated in contemporary terms and solved from the viewpoint of probability logic. A section compares Kolmogorov set-theoretic probability with probability logic. The concluding section describes a highly adverse criticism of Borel's conception for its not using something like Kolmogorov theory (introduced two decades later) and, in support of Borel, this criticism is countered from the standpoint of quantifier probability (...)
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  50.  14
    Review: K. Jaakko, J. Hintikka, Distributive Normal Forms in the Calculus of Predicates. [REVIEW]Theodore Hailperin - 1955 - Journal of Symbolic Logic 20 (2):164-164.
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