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  1. Theodore Hailperin (2011). Logic Semantics with the Potential Infinite. 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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  2. Theodore Hailperin (2008). Probability Logic and Borel's Denumerable Probability. 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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  3. Theodore Hailperin (2007). Quantifier Probability Logic and the Confirmation Paradox. 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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  4. Theodore Hailperin (2006). Probability Logic and Combining Evidence. 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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  5. Theodore Hailperin (2004). Algebraical Logic 1685–1900. In Dov M. Gabbay, John Woods & Akihiro Kanamori (eds.), Handbook of the History of Logic. Elsevier. 3--323.
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  6. Theodore Hailperin (2001). Potential Infinite Models and Ontologically Neutral Logic. 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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  7. Theodore Hailperin & Ontologically Neutral Logic (2001). 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] Journal of Philosophical Logic 30:617-618.
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  8. Theodore Hailperin (2000). Probability Semantics for Quantifier Logic. 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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  9. Theodore Hailperin (1998). Boole George. Selected Manuscripts on Logic and its Philosophy. Edited by Grattan-Guinness Ivor and Bornet Gérard. Science Networks Historical Studies, Vol. 20. Birkhäuser Verlag, Basel, Boston, and Berlin, 1997, Lxiv+ 236 Pp. Grattan-Guinness Ivor. Boole's Quest for the Foundations of His Logic. Therein, Pp. Xiii–Xlvii. Bornet Gérard. Boole's Psychologism as a Reception Problem. Therein, Pp. Xlvii–Lviii. [REVIEW] Journal of Symbolic Logic 63 (1):332-333.
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  10. Theodore Hailperin (1998). Review: George Boole, Ivor Grattan-Guinness, Gerard Bornet, Selected Manuscripts on Logic and Its Philosophy. [REVIEW] Journal of Symbolic Logic 63 (1):332-333.
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  11. Theodore Hailperin (1997). Beberman Max and Vaughan Herbert E.. High School Mathematics. Course 2. Plane Geometry with Appendices on Logic and Solid Geometry. DC Heath and Company, Boston, Englewood, Chicago, San Francisco, Atlanta, Dallas, London, and Toronto, 1965, Xi+ 584 Pp. Beberman Max and Vaughan Herbert E.. High School Mathematics. Course 2. Plane Geometry with Appendices on Logic and Solid Geometry. Teacher's Edition. DC Heath and Company, Boston, Englewood, Chicago, San Francisco, Atlanta, Dallas, London, and Toronto ... [REVIEW] Journal of Symbolic Logic 31 (4):672-673.
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  12. Theodore Hailperin (1997). Ontologically Neutral Logic. 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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  13. Theodore Hailperin (1996). Beberman Max and Vaughan Herbert E.. High School Mathematics. Course 1. Revised Edition of XXX 401 (10–13). DC Heath and Company, Boston 1964, Ix+ 598 Pp. Beberman Max and Vaughan Herbert E.. High School Mathematics. Course 1. Teacher's Edition. Revised Edition of XXX 401 (14–17). D. C Heath and Company, Boston 1964, Pages Irregularly Numbered.(The Pages of the Students' Edition Are Reproduced with Their Same Numbers, and with Most Pages, Added Material for the Teacher is Inserted on Extra Pages.). [REVIEW] Journal of Symbolic Logic 31 (1):111-112.
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  14. Theodore Hailperin (1992). Herbrand Semantics, the Potential Infinite, and Ontology-Free Logic. 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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  15. Theodore Hailperin (1991). Probability Logic in the Twentieth Century. History and Philosophy of Logic 12 (1):71-110.
    This essay describes a variety of contributions which relate to the connection of probability with logic. Some are grand attempts at providing a logical foundation for probability and inductive inference. Others are concerned with probabilistic inference or, more generally, with the transmittance of probability through the structure (logical syntax) of language. In this latter context probability is considered as a semantic notion playing the same role as does truth value in conventional logic. At the conclusion of the essay two fully (...)
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  16. Theodore Hailperin (1988). The Development of Probability Logic From Leibniz to Maccoll. 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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  17. Theodore Hailperin (1987). Infinite Truth-Functional Logic. Notre Dame Journal of Formal Logic 29 (1):28-33.
  18. Theodore Hailperin (1984). Review: G. C. Smith, The Boole-De Morgan Correspondence 1842-1864. [REVIEW] Journal of Symbolic Logic 49 (2):657-659.
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  19. Theodore Hailperin (1984). Boole's Abandoned Propositional Logic. 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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  20. Theodore Hailperin (1984). Probability Logic. Notre Dame Journal of Formal Logic 25 (3):198-212.
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  21. Theodore Hailperin (1972). Review: H. Leblanc, R. H. Thomason, Completeness Theorems for Some Presupposition-Free Logics. [REVIEW] Journal of Symbolic Logic 37 (2):424-425.
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  22. Theodore Hailperin (1972). Review: Rolf Schock, Contributions to Syntax, Semantics, and the Philosophy of Science. [REVIEW] Journal of Symbolic Logic 37 (2):423-423.
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  23. Theodore Hailperin (1972). Review: Rolf Schock, Logics Without Existence Assumptions. [REVIEW] Journal of Symbolic Logic 37 (2):424-424.
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  24. Theodore Hailperin (1969). A Form of Herbrand's Theorem. Mathematical Logic Quarterly 15 (7‐12):107-120.
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  25. Theodore Hailperin (1969). Review: David Pager, An Emendation of the Axiom System of Hilbert and Ackermann for the Restricted Calculus of Predicates. [REVIEW] Journal of Symbolic Logic 34 (3):520-520.
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  26. Theodore Hailperin (1968). Review: C. C. Chang, H. Jerome Keisler, An Improved Prenex Normal Form. [REVIEW] Journal of Symbolic Logic 33 (3):479-479.
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  27. Theodore Hailperin (1968). 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] Journal of Symbolic Logic 33 (1):137-138.
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  28. Theodore Hailperin (1967). [Omnibus Review]. Journal of Symbolic Logic 32 (2):252-252.
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  29. Theodore Hailperin (1967). Review: Nicholas Rescher, Definitions of "Existence."; Karel Lambert, Notes on "E!". [REVIEW] Journal of Symbolic Logic 32 (2):251-251.
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  30. Theodore Hailperin (1966). Review: Max Beberman, Herbert E. Vaughan, High School Mathematics. Course 2. Plane Geometry with Appendices on Logic and Solid Geometry. [REVIEW] Journal of Symbolic Logic 31 (4):672-673.
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  31. Theodore Hailperin (1966). Review: Max Beberman, Herbert E. Vaughan, High School Mathematics. Course 1. [REVIEW] Journal of Symbolic Logic 31 (1):111-112.
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  32. Theodore Hailperin (1965). An Incorrect Theorem. Journal of Symbolic Logic 30 (1):27.
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  33. Theodore Hailperin (1965). Review: Hubert H. Schneider, Portugatiae Mathematica:Semantics of the Predicate Calculus with Identity and the Validity in the Empty Individual-Domain; Hubert H. Schneider, Portugatiae Mathematica:A Syntactical Characterization of the Predicate Calculus with Identity and the Validity in All Individual-Domains. [REVIEW] Journal of Symbolic Logic 30 (3):385-386.
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  34. Theodore Hailperin (1964). Review: B. H. Arnold, Logic and Boolean Algebra. [REVIEW] Journal of Symbolic Logic 29 (2):95-96.
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  35. Theodore Hailperin (1964). Review: Leon Henkin, W. Norman Smith, Verne J. Varineau, Michael J. Walsh, Retracing Elementary Mathematics. [REVIEW] Journal of Symbolic Logic 29 (4):209-209.
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  36. Theodore Hailperin (1964). Review: Leon Henkin, Mathematical Induction. [REVIEW] Journal of Symbolic Logic 29 (4):209-209.
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  37. Theodore Hailperin (1964). Review: William H. Halberstadt, An Introduction to Modern Logic. An Elementary Textbook of Symbolic Logic. [REVIEW] Journal of Symbolic Logic 29 (1):43-43.
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  38. Theodore Hailperin (1961). A Complete Set of Axioms for Logical Formulas Invalid in Some Finite Domain. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (6):84-96.
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  39. Theodore Hailperin (1960). Corrections to a Theory of Restricted Quantification. Journal of Symbolic Logic 25 (1):54-56.
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  40. Theodore Hailperin (1960). Review: Gunter Asser, Karl Schroter, Axiomatisierung der K-zahlig Allgemeingultigen Ausdrucke des Stufenkalkuls. [REVIEW] Journal of Symbolic Logic 25 (2):176-176.
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  41. Theodore Hailperin (1959). Review: Daya, Symmetry, Transitivity and Reflexivity; S. Bhattacharyya, Symmetry, Transitivity and Reflexivity. [REVIEW] Journal of Symbolic Logic 24 (2):185-186.
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  42. Theodore Hailperin (1959). Review: Marcel Boll, La Logique Dite Propositionnelle Et la Commutation. [REVIEW] Journal of Symbolic Logic 24 (3):256-256.
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  43. Hugues Leblanc & Theodore Hailperin (1959). Nondesignating Singular Terms. Philosophical Review 68 (2):239-243.
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  44. Theodore Hailperin (1958). Review: Ingebrigt Johansson, Sur le Concept de "le" (Ou de "ce qui") dans le Calcul Affirmatif et dans les Calculs Intuitionnistes; R. Feys, Ingebright Johansson, Discussion: Sur le Concept de "le" (Ou de "ce qui") dans le Calcul Affirmatif et dans les Calculs Intuitionnistes. [REVIEW] Journal of Symbolic Logic 23 (3):346-346.
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  45. Theodore Hailperin (1957). A Theory of Restricted Quantification I. Journal of Symbolic Logic 22 (1):19-35.
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  46. Theodore Hailperin (1957). A Theory of Restricted Quantification II. Journal of Symbolic Logic 22 (2):113-129.
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  47. Theodore Hailperin (1955). Review: K. Jaakko, J. Hintikka, Distributive Normal Forms in the Calculus of Predicates. [REVIEW] Journal of Symbolic Logic 20 (2):164-164.
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  48. Theodore Hailperin (1954). Remarks on Identity and Description in First-Order Axiom Systems. Journal of Symbolic Logic 19 (1):14-20.
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  49. Theodore Hailperin (1953). Quantification Theory and Empty Individual-Domains. Journal of Symbolic Logic 18 (3):197-200.
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  50. Theodore Hailperin (1950). Review: Hao Wang, A Formal System of Logic. [REVIEW] Journal of Symbolic Logic 15 (3):228-229.
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