Skip to main content



Since Frege’s predicate logical transcription of Aristotelian categorical logic, the standard semantics of Aristotelian logic considers terms as standing for sets of individuals. From a philosophical standpoint, this extensional model poses problems: There exist serious doubts that Aristotle’s terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this question—they looked at terms as standing for concepts (“Begriffe”). In 1972, Corcoran presented a formal system for Aristotelian logic containing a calculus of natural deduction, while, with respect to semantics, he still made use of an extensional interpretation. In this paper we deal with a simple intensional semantics for Corcoran’s syntax—intensional in the sense that no individuals are needed for the construction of a complete Tarski model of Aristotelian syntax. Instead, we view concepts as containing or excluding other, “higher” concepts—corresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcoran’s work, furnishing his formal syntax with an adequate semantics which is free from presuppositions which have entered into modern interpretations of Aristotle’s theory via predicate logic.

Corresponding author
Hide All
Arnauld A. (1861). The Port Royal Logic. Translated from the French. Edinburgh, UK: James Gordon.
Boger G. (1998). Completion, reduction and analysis: Three proof-theoretic processes in Aristotle’s Prior Analytics. History and Philosophy of Logic, 19, 187226.
Code A. (1986). Aristotle: Essence and accident. In Grandy R. E., and Warner R., editors. Philosophical Grounds of Rationality. Oxford: Clarendon Press, pp. 411440.
Corcoran J., editor. (1972a). Ancient Logic and Its Modern Interpretation. Dordrecht, Holland/Boston, MA: D. Reidel Publishing Company.
Corcoran J. (1972b). Completeness of an ancient logic. Journal of Symbolic Logic, 37(4), 696702.
Corcoran J. (1974). Aristotle’s natural deduction system. In Corcoran J., editor. Ancient Logic and Its Modern Interpretation. Dordrecht, Holland: Reidel, pp. 85131.
Ebbinghaus K. (1964). Ein formales Modell der Syllogistik des Aristoteles. Number 9 in Hypomnemata. Göttingen, Germany: Vandenhoeck & Rupprecht.
Emilsson E. (2009). Porphyry. In Zalta E. N., editor. The Stanford Encyclopedia of Philosophy (Summer 2009 edition).
Frege G. (1967). Concept script, a formal language of pure thought modelled upon that of arithmetic. In vanHeijenoort J., editor, From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931. Cambridge, MA: Harvard University Press. Translation by S. Bauer-Mengelberg of ‘Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens’, Halle a. S.: Louis Nebert, 1879.
Frisch J. C. (1969). Extension and Comprehension in Logic. New York: Philosophical Library.
Glashoff K. (2002). On Leibniz’ characteristic numbers. Studia Leibnitiana, 34, 161.
Glashoff K. (2005). Aristotelian syntax from a computational-combinatorial point of view. Journal of Logic and Computation, 15(6), 949973.
Kant I. (1836). Metaphysical Works of the Celebrated Immanuel Kant. London: W. Simpkin and R. Marshall.
Kant I. (1991). Schriften zur Metaphysik und Logik, Volume 2 of Werkausgabe Band VI. Frankfurt am Main, Germany: Suhrkamp.
Leibniz G. W. (1999). Elementa calculi. In Sämtliche Schriften und Briefe IV, 1677-1690. Darmstadt/Leipzig/Berlin: Akademie-Verlag, pp. 195205.
Lukasiewicz J. (1957). Aristotle’s Syllogistic (second edition). Oxford: Clarendon Press.
Lyons J. (1977). Semantics: Volume 1. Cambridge: Cambridge University Press.
Maldonado A. M. (1998). Completitud de dos Cálculos Lógicos de Leibniz. Theso di grado, Departamento de Mathematicas, Universidad de Los Andes, Bogota.
Martin J. N. (1997). Aristotle’s natural deduction reconsidered. History and Philosophy of Logic, 18, 115.
Nedzynski T. G. (1979). Quantification, domains of discourse, and existence. Notre Dame Journal of Formal Logic, XX(1), 130140.
Porphyry. (1975). Isagoge. Trans. Warren Edward. Toronto, Ontario, Canada: The Pontifical Institute of Medieaeval Studies.
Quine W. v. O. (1951). Two dogmas of empiricism. The Philosophical Review, 60, 2043.
Smiley T. (1973). What is a syllogism? Journal of Philosophical Logic, 2, 136154.
Smith R. (1983). An ecthetic syllogistic. Notre Dame Journal of Formal Logic 24, 224232.
Tolley C. (2007). Kant’s conception of logic (Immanuel Kant). PhD Thesis, The University of Chicago.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 12 *
Loading metrics...

Abstract views

Total abstract views: 155 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th November 2017. This data will be updated every 24 hours.