Skip to main content
Logicism Renewed

Book description

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Logicism, as put forward by Bertrand Russell, was predicated on a belief that all of mathematics can be deduced from a very small number of fundamental logical principles. In this volume, the twenty-third publication in the Lecture Notes in Logic series, Paul C. Gilmore revisits logicism in light of recent advances in mathematical logic and theoretical computer science. Gilmore addresses the need for languages which can be understood by both humans and computers and, using Intensional Type Theory (ITT), provides a unified basis for mathematics and computer science. This yields much simpler foundations for recursion theory and the semantics of computer programs than those currently provided by category theory.

Refine List
Actions for selected content:
Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Send to Kindle
  • Send to Dropbox
  • Send to Google Drive
  • Send content to

    To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to .

    To send content items to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

    Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

    Find out more about the Kindle Personal Document Service.

    Please be advised that item(s) you selected are not available.
    You are about to send

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
S., Abramsky, Dov M., Gabbay, and T.S.E., Maibaum (editors), Handbook of logic in computer science, background: Mathematical structures, vol. 1, Clarendon Press, Oxford, 1992.
S., Abramsky, Dov M., Gabbay, and T.S.E., Maibaum (editors), Handbook of logic in computer science, Semantic structures, vol. 3, Clarendon Press, Oxford, 1994.
Samson, Abramsky and Achim, Jung, Domain theory, In Abramsky et al. [2], pp. 1–168.
Harvey, Abramson and Veronica, Dahl, Logic grammars, Springer-Verlag, 1989.
Peter, Aczel, Non–well–founded sets, CSLI Lecture Notes, no. 14, CSLI, 1988.
James H., Andrews, A weakly-typed higher order logic with general lambda terms and y combinator, Proceedings, works in progress track, 15th international conference on theorem proving in higher order logics, no. CP- 2002-211736, NASA Conference Publication, 2002, pp. 1–11.
James H., Andrews, Cut elimination for a weakly-typed higher order logic, Technical Report 611, Department of Computer Science, University of Western Ontario, December 2003.
Peter B., Andrews, Resolution in type theory, The Journal of Symbolic Logic, vol. 36 (1971), pp. 414–432.
Peter B., Andrews, An introduction to mathematical logic and type theory: To truth through proof, Academic Press, 1986.
K.R., Apt and M.H., van Emden, Contributions to the theory of logic programming, Journal of the ACM, vol. 29 (1982), no. 3, pp. 841–862.
Alfred Jules, Ayer, Language, truth and logic, second ed., Victor Gollancz Ltd, 1950.
Maurice, JayBach, Aspecification of data structures with application to data base systems, Ph.D. thesis, Faculty of Pure Science, Columbia University, 1978.
H.P., Barendregt, The lambda calculus, its syntax and semantics, revised ed., North-Holland, 1985.
Jon, Barwise (editor), Handbook of mathematical logic, North Holland, 1977.
Jon, Barwise and John, Etchmendy, The liar: An exercise in truth and circularity, Oxford University Press, 1987.
Jon, Barwise and Lawrence, Moss, Vicious circles, CSLI, 1996.
Michael J., Beeson, Foundations of constructive mathematics, Springer-Verlag, 1980.
Paul, Benacerraf and Hilary, Putnam, Philosophy of mathematics, selected readings, Cambridge University Press, 1983, 2nd edition, 1st edition published by Prentice-Hall Inc., 1964.
E.W., Beth, Semantic entailment and formal derivability, Mededelingen de Koninklijke Nederlandse Akademie der Wetenschappen, Afdeeling Letterkunde, Nieuwe Reeks, vol. 18 (1955), no. 13, pp. 309–342.
E.W., Beth, Semantic construction of intuitionistic logic, Mededelingen de KoninklijkeNederlandse Akademie derWetenschappen, Afdeeling Letterkunde, Nieuwe Reeks, vol. 19 (1956), no. 11, pp. 357–388.
Michael Julian, Black, Naive semantic networks, Final Paper for Directed Studies in Computer Science, Dept of Computer Science, University of B.C., January 22,1985.
K.A., Bowen and R.A., Kowalski (editors), Fifth international logic programming conference, MIT Press, 1988.
Rudolf, Carnap, The logical syntax of language, Kegan Paul, Trench, Trubner and Co. Ltd, London, 1937, English translation by Amethe Smeaton of Logische Syntax der Sprache, 1934.
Rudolph, Carnap, Meaning and necessity, a study in semantics and modal logic, University of Chicago Press, 1947.
Noam, Chomsky, Language and problems of knowledge, MIT Press, 1988.
A., Church and J.B., Rosser, Some properties of conversion, Transactions of the American Mathematical Society, vol. 39 (1936), pp. 11–21.
Alonzo, Church, Schröder's anticipation of the simple theory of types, The Journal of Unified Science (Erkenntnis), vol. IX (1939), pp. 149–152.
Alonzo, Church, A formulation of the simple theory of types, The Journal of Symbolic Logic, vol. 5 (1940), pp. 56–68.
Alonzo, Church, The calculi of lambda conversion, Princeton University Press, 1941.
Alonzo, Church, A formulation of the logic of sense and denotation, Structure, method and meaning, essays in honor of Henry M. Sheffer (Horace M., Kallen, Paul, Henle and Susanne K., Langer, editors), The Liberal Arts Press, New York, 1951.
Alonzo, Church, Introduction to mathematical logic volume I, Princeton University Press, 1956.
Nino B., Cocchiarella, Logical investigations of predication and the problem of universals, Bibliopolis Press, Naples, 1986.
Nino B., Cocchiarella, Conceptual realism versus Quine on classes and higher-order logic, Synthese, vol. 90 (1992), pp. 379–436.
A., Colmerauer, H., Kanoui, P., Roussel, and R., Pasero, Un systeme de communication homme-machine en francais, Technical report, Groupe de Recherche en Intelligence Artificielle, Université d'Aix-Marseille, 1973.
Haskell B., Curry, Outline of a formalist philosophy of mathematics, North-Holland, 1951.
Haskell B., Curry, A theory of formal deducibility, Notre Dame Mathematical Lectures, No. 6, 1957.
Haskell B., Curry and Robert, Feys, Combinatory logic, North- Holland, 1958.
Martin, Davis (editor), The undecidable, basic papers on undecidable propositions, unsolvable problems and computable functions, Raven Press, Hewlett New York, 1965.
Keith, Devlin, The maths gene: How mathematical thinking evolved and why numbers are like gossip, Basic Books, 2000.
Keith, Devlin, The maths gene: Why everyone has it, but most people don't use it, Weidenfeld and Nicolson, 2000.
Gilles, Dowak, Amy, Felty, Hugo, Herbelin, Gerard, Huet, Chet, Murthy, Catherine, Parent, Christine, Paulin-Mohring, and Benjamin, Werner, The coq proof assistant user's guide, Rapport Techniques 154, INRIA, Rocquencourt, France, 1993.
William M., Farmer, A partial functions version of Church's simple theory of types, The Journal of Symbolic Logic, vol. 55 (1990), pp. 1269–1290.
S., Feferman, Categorical foundations and foundations of category theory, Logic, foundations of mathematics and computability theory (R.E., Butts and J., Hintikka, editors), D. Reidel, Dordrecht–Holland, 1977, pp. 149–169.
S., Feferman, Towards useful type-free theories, The Journal of Symbolic Logic, vol. 49 (1984), pp. 75–111.
S., Feferman, In the light of logic, Oxford University Press, 1998.
M.C., Fitting and R., Mendelsohn, First-order modal logic, Synthese Library, vol. 277, Kluwer Academic, 1998.
Melvin, Fitting, First-order logic and automated theorem proving, 2 ed., Springer-Verlag, 1996.
Melvin, Fitting, Types, tableaus, and Gödel's god, Kluwer Academic, 2000.
Gottlob, Frege, Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought, In van Heijenoort [147], A translation of a booklet of 1879.
Dov M., Gabbay, C.J., Hogger, and J.A., Robinson (editors), Handbook of logic in artificial intelligence and logic programming, logic programming, vol. 5, Clarendon Press, Oxford, 1998.
Peter, Geach and Max, Black (editors), Translations from the philosophical writings of Gottlob Frege, 2nd ed., Blackwell, Oxford, 1960.
Gerhard, Gentzen, Investigations of logical deductions, In Szabo [140], translation of a paper of 1935.
P.C., Gilmore, Attributes, sets, partial sets and identity, Logic and foundations of mathematics (D., van Dalen, J.G., Dijkman, S.C., Kleene, and A.S., Troelstra, editors), Wolters-Noordhoff Publishing, Groningen, 1968, pp. 53–69.
Paul C., Gilmore, An abstract computer with a Lisp-like machine language without a label operator, Computer programming and formal systems (P., Braffort and D., Hirschberg, editors), North-Holland, Amsterdam, 1963, pp. 71–86.
Paul C., Gilmore, A consistent naive set theory: Foundations for a formal theory of computation, IBM Research Report RC 3413, IBM Thomas J., Watson Research Laboratory, June 1971.
Paul C., Gilmore, Purely functional programs as recursions, IBM Research Report RC 4088, IBM Thomas J., Watson Research Laboratory, October 1972.
Paul C., Gilmore, Defining and computing many–valued functions, Parallel computers— parallel mathematics, Proceedings of the IMACS (AICA)-GI symposium, Technical University of Munich (M., Feilmeier, editor), 1977, pp. 17–23.
Paul C., Gilmore, Combining unrestricted abstraction with universal quantification, To h.b. curry: Essays on combinatorial logic, lambda calculus and formalism (J.P., Seldin and J.R., Hindley, editors), Academic Press, 1980, This is a revised version of [55], pp. 99–123.
Paul C., Gilmore, Natural deduction based set theories: A new resolution of the old paradoxes, The Journal of Symbolic Logic, vol. 51 (1986), pp. 393–411.
Paul C., Gilmore, A foundation for the entity relationship approach: How and why, Proceedings of the 6th entity relationship conference (S.T.March, editor), North-Holland, 1988, pp. 95–113.
Paul C., Gilmore, NaDSyL and some applications, Computational logic and proof theory, The Kurt Gödel colloquium (Georg, Gottlob, Alexander, Leitsch, and Daniele, Mundici, editors), Lecture Notes in Computer Science, vol. 1289, Springer-Verlag, 1997, pp. 153–166.
Paul C., Gilmore, An impredicative simple theory of types, Presented at the Fourteenth Workshop on Mathematical Foundations for Programming Systems, Queen Mary College, London, May 1998.
Paul C., Gilmore, An intensional type theory: Motivation and cut-elimination, The Journal of Symbolic Logic, vol. 66 (2001), pp. 383–400.
Paul C., Gilmore, A nominalist motivated intuitionist type theory: A foundation for recursive function theory, In preparation, 2005.
Paul C., Gilmore and George K., Tsiknis, A formalization of category theory in NaDSet, Theoretical Computer Science, vol. 111 (1993), pp. 211–253.
Paul C., Gilmore and George K., Tsiknis, Logical foundations for programming semantics, Theoretical Computer Science, vol. 111 (1993), pp. 253–290.
J.Y., Girard,, 1994, Letter to author, March 16, 1994.
Kurt, Gödel, The consistency of the continuum hypothesis, 1940.
Kurt, Gödel, On formally undecidable propositions of Principia Mathematica and related systems I, In van Heijenoort [147], translation of 1931 paper, pp. 596–616.
Nelson, Goodman and W.V., Quine, Steps toward a constructive nominalism, The Journal of Symbolic Logic, vol. 12 (1947), pp. 105–122.
Michael J.C., Gordon, The denotational description of programming languages, An introduction, Springer-Verlag, New York, Heidelberg, Berlin, 1979.
C.A., Gunter and D.S., Scott, Semantic domains, Handbook of theoretical computer science, Volume B: Formal models and semantics (Jan van, Leeuwen, editor), vol. B, MIT Press/Elsevier, 1990, pp. 633–674.
Leon, Henkin, The completeness in the first order functional calculus, The Journal of Symbolic Logic, vol. 14 (1949), pp. 150–166.
Leon, Henkin, Completeness in the theory of types, The Journal of Symbolic Logic, vol. 15 (1950), pp. 81–91.
Leon, Henkin, Some notes on nominalism, The Journal of Symbolic Logic, vol. 18 (1951), pp. 19–29.
Jacques, Herbrand, Investigations in proof theory: The properties of true propositions, In van Heijenoort [147], Translation of portion of PhD thesis, pp. 525–581.
Arend, Heyting, Die formalen Regeln der intuitionistischen Logik, Sitzungberichte der Preussischen Akademie der Wissenschafter, Physikalischmathematische Klasse, (1930), pp. 42–56.
D., Hilbert and P., Bernays, Grundlagen der Mathematik I, second ed., vol. 1, Springer-Verlag, 1968, The first edition was published in 1934.
D., Hilbert and P., Bernays, Grundlagen der Mathematik II, second ed., vol. 2, Springer-Verlag, 1970, The first edition was published in 1939.
Patricia, Hill and John, Lloyd, The Gödel programming language, MIT Press, 1994.
P.M., Hill and J., Gallagher, Meta-programming in logic programming, In Gabbay et al. [50], pp. 421–497.
J.R., Hindley, B., Lercher, and J.P., Seldin, Introduction to combinatory logic, Cambridge University Press, 1972.
R., Hindley, The principal type-scheme of an object in cobinatory logic, Transactions of the American Mathematical Society, vol. 146 (1969), pp. 29–65.
K.J.J., Hintikka, Form and content in quantification theory, Acta Philosophica Fennica, vol. 8 (1955), pp. 7–55.
Wilfred, Hodges, Logic, an introduction to elementary logic, Penguin Books Ltd, 1991, reprinting of book published by Pelican Books Ltd, 1977.
Alfred, Horn, On sentences which are true of direct unions of algebras, The Journal of Symbolic Logic, vol. 16 (1951), pp. 14–21.
Gregor, Kiczales, John, Lamping, Anurag, Mendhekar, Chris, Maeda, Cristina Videira, Lopes, Jean-Marc, Loingtier, and John, Irwin, Aspect-oriented programming, Proceedings of the European conference on object-oriented programming, vol. LNCS 1241, Springer-Verlag, 1997.
Stephen Cole, Kleene, Introduction to metamathematics, North- Holland, 1952.
R.A., Kowalski, Predicate logic as a programming language, Information Processing, vol. 74 (1974), pp. 569–574.
Saul A., Kripke, Semantical analysis of intuitionistic logic I, Formal systems and recursive functions, North-Holland, 1965, pp. 92–130.
J., Lambek, Are the traditional philosophies of mathematics really incompatible?, The Mathematical Intelligencer, vol. 16 (1994), pp. 56–62.
J., Lambek, Categorical logic, Encyclopedia of mathematics, Kluwer Academic, 1998, pp. 107–111.
J., Lambek and P.J., Scott, Introduction to higher order categorical logic, Cambridge University Press, 1994.
J.W., Lloyd, Foundations of logic programming, 2nd ed., Springer-Verlag, 1987.
S., MacLane, Categorical algebra and set-theoretical foundations, Axiomatic set theory, proceedings of a symposium in pure mathematics (Providence, R.I.), vol. XIII, American Mathematical Society, 1967, pp. 231–240.
P., Martin-Löf, Notes on constructive mathematics, Almqvist & Wiksell, Stockholm, 1970.
P., Martin-Löf, Intuitionistic type theory, Bibliopolis, Napoli, 1984.
J., McCarthy, Recursive functions of symbolic expressions and their computation by machine, Communications of the Association for Computing Machinery, vol. 3 (1960), pp. 184–195.
Bernard, Meltzer and Donald, Michie (editors), Machine intelligence 5, American Elsevier, 1970.
R., Milner, A theory of type polymorphism in programming languages, Journal Computing System Science, vol. 17 (1978), pp. 348–375.
R., Milner, A calculus of communicating systems, Lecture Notes in Computer Science, no. 92, Springer-Verlag, 1980.
R., Milner, Calculi for synchrony and asynchrony, Theoretical Computer Science, vol. 25 (1983), pp. 267–310.
Robin, Milner and Mads, Tofte, Co-induction in relational semantics, Theoretical Computer Science, vol. 87 (1991), pp. 209–220.
Richard, Montague, English as a formal language, In Thomason [143], pp. 188–221.
Richard, Montague, Syntactical treatment of modality, with corollaries on reflexion principles and finite axiomatization, In Thomason [143], pp. 286–302.
P.D., Mosses, Denotational semantics, In Gabbay et al. [50], pp. 499–590.
G., Nadathur and D., Miller, An overview of lambda prolog, In Bowen and Kowalski [22], pp. 810–827.
Gopalan, Nadathur and Dale, Miller, Higher-order logic programming, In Gabbay et al. [50], pp. 577–632.
Michael J., O'Donnell, Introduction: Logic and logic programming languages, In Gabbay et al. [50], pp. 1–67.
S., Owre, N., Shankar, and J.M., Rushby, The PVS specification language (beta release), Technical report, Computer Science Laboratory, SRI International, Menlo Park CA 94025, June 1993.
D., Park, Fixpoint, induction and proofs of program properties, In Meltzer and Michie [99], pp. 59–78.
Barbara H., Partee and Hermann L.W., Hendriks, Montague grammar, In van Benthem and ter Meulen [146].
L.C., Paulson, Logic and computation: Interactive proof with Cambridge LCF, Cambridge Tracts in Theoretical Computer Science, vol. 2, Cambridge University Press, 1990.
L.C., Paulson, Isabelle: A generic theorem prover, Lecture Notes in Computer Science, vol. 828, Springer Verlag, 1994.
Giuseppe, Peano, The principles of arithmetic, presented by a new method, In van Heijenoort [147], A reprinting of a 1889 paper, pp. 83–97.
F., Pfenning, Logic programming in the LF logical framework, Logical frameworks, Cambridge University Press, 1991, pp. 149–181.
I.C.C., Phillips, Recursion theory, In Abramsky et al. [1], pp. 79–187.
Axel, Poigné, Basic category theory, In Abramsky et al. [1], pp. 413–634.
Dag, Prawitz, Natural deduction, a proof-theoretical study, Stockholm Studies in Philosphy, vol. 3, Almquist and Wiksell, Stockholm, 1965.
Willard Van Orman, Quine, Mathematical logic, revised ed., Harvard University Press, 1951.
John C., Reynolds, Theories of programming languages, Cambridge University Press, 1998.
Abraham, Robinson, Non-standard analysis, North-Holland, 1966.
J.A., Robinson, A machine-oriented logic based on resolution, Journal of the Association for Computing Machinery, vol. 12 (1965), pp. 23–41.
John, Rushby, Formal methods and the certification of critical systems, Technical Report SRI-CSL-93-07, Computer Science Laboratory,Stanford Research Institute, November 1993.
Bertrand, Russell, Introduction to mathematical philosophy, George Allen and Unwin Ltd, London, 1919, Reprinted many times.
Bertrand, Russell, The principles of mathematics, second ed., George Allen and Unwin Ltd, London, 1937.
Jean E., Sammet, Programming languages: History and fundamentals, Prentic-Hall, Inc., 1969.
K., Schütte, Syntactical and semantical properties of simple type theory, The Journal of Symbolic Logic, vol. 25 (1960), pp. 305–326.
Dana, Scott, Mathematical concepts in programming language semantics, AFIPS conference proceedings, vol. 40, AFIPS press, 1972.
Wilfred, Sellars, Abstract entities, Review of Metaphysics, vol. 16 (1963), pp. 625–671.
Wilfred, Sellars, Classes as abstract entities and the Russell paradox, Review of Metaphysics, vol. 17 (1963), pp. 67–90.
Joseph R., Shoenfield, Axioms of set theory, In Barwise [14], pp. 321–344.
Thoralf, Skolem, Some remarks on axiomatized set theory, In van Heijenoort [147], An English translation of a 1922 paper, pp. 290–301.
R.M., Smullyan, First-order logic, Dover Press, New York, 1994, Revised Edition, first published by Springer-Verlag, Berlin, 1968.
J.F., Sowa, Conceptual structures: Information processing in mind and machine, Addison-Wesley, Reading, Mass., 1984.
J.M., Spivey, The Z notation: A reference manual, Prentice Hall, New York, 1992, Second Edition.
S.W.P., Steen, Mathematical logic, Cambridge University Press, 1972.
Leon, Sterling and Ehud, Shapiro, The art of Prolog, The M.I.T. Press, 1986.
Joseph E., Stoy, Denotational semantics: The Scott-Strachey approach to programming language theory, The MIT Press, 1977.
M.E., Szabo (editor), The collected papers of Gerhard Gentzen, North- Holland, 1969.
Alfred, Tarski, A lattice-theoretical fixpoint theorem and its applications, Pacific Journal of Mathematics, vol. 5 (1955), pp. 285–309.
Alfred, Tarski, The concept of truth in formalized languages, Logic, semantics, metamathematics, papers from 1923 to 1938, Oxford University Press, 1956, An English translation by J.H., Woodger of a paper of 1936., pp. 152–268.
Richmond H., Thomason (editor), Formal philosophy, selected papers of Richard Montague, Yale University Press, New Haven and London, 1974.
A.S., Troelstra, Aspects of constructive mathematics, In Barwise [14], pp. 973–1052.
A.M., Turing, On computable numbers, with an application to the Entsheidungsproblem, In Davis [38], reprinting of paper of 1936-37, pp. 115–153.
Johann van, Benthem and Alice ter, Meulen (editors), Handbook of logic and language, Elsevier, 1997.
Jean van, Heijenoort (editor), From Frege to Gödel, A source book in mathematical logic, 1879-1931, Harvard University Press, 1967.
Richard L., Wexelblat (editor), A history of programming languages, Academic Press, 1981.
Alfred North, Whitehead and Bertrand, Russell, Principia mathematica, vol. 1, Cambridge University Press, 1925, second edition.
Niklaus, Wirth, Algorithms + data structures = programs, Prentice- Hall, 1976.
Ernst, Zermelo, Investigations in the foundations of set theory, In van Heijenoort [147], translation of paper of 1908, pp. 199–215.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed