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Ancient Greek
Logic: Aristotle

Aristotle. Born: 384 BC in Stagirus, Macedonia, Greece;Died: 322 BC in Chalcis, Euboea, Greece.Aristotle's work on logic was the basis for any logical research until the mid of the 19th century.Aristotle, more than any other thinker,determined the orientation and the content of Western intellectual history.His concepts are still engraved in Western thinking.

 Bild Aristoteles


  • An Intensional Leibniz Semantics for Aristotelian Logic [PDF] (The Review of Symbolic Logic, Published online by Cambridge University Press 17 Mar 2010 doi:10.1017/S1755020309990396)
    • Since Frege’s predicate logical transcription of Aristotelian categorical logic, the standardsemantics of Aristotelian logic considers terms as standing for sets of individuals. From aphilosophical standpoint, this extensional model poses problems: There exist serious doubts thatAristotle’s terms were meant to refer always to sets, that is, entities composed of individuals. Classicalphilosophy up to Leibniz and Kant had a different view on this question—they looked at termsas standing for concepts (“Begriffe”). In 1972, Corcoran presented a formal system for Aristotelianlogic containing a calculus of natural deduction, while, with respect to semantics, he still madeuse of an extensional interpretation. In this paper we deal with a simple intensional semantics forCorcoran’s syntax—intensional in the sense that no individuals are needed for the construction of acomplete Tarski model of Aristotelian syntax. Instead, we view concepts as containing or excludingother, “higher” concepts—corresponding to the idea which Leibniz used in the construction of hischaracteristic numbers. Thus, this paper is an addendum to Corcoran’s work, furnishing his formalsyntax with an adequate semantics which is free from presuppositions which have entered intomodern interpretations of Aristotle’s theory via predicate logic.

  • Aristotelian Logic from a Computational-Combinatorical Point of View [PDF] (Journal of Logic and Computation 2005 15(6):949-973)
    • This paper translates Aristotle's syllogistic logic of the Analytica Priora into the sphere of computational - combinatorical research methods. The task is accomplished by formalising Aristotle's logical system in terms of rule-based reduction relations on a suitable basic set, which allow us to apply standard concepts of the theory of such structures (Newman lemma) to the ancient logical system.

  • Zur Übersetzung der Aristotelischen Logik in die Prädikatenlogik (in German) [PDF] (2005)
    • Seit denAnfängen der modernen symbolischen Logik hat es immer wiederVersuche gegeben, die Aristotelische assertorische Syllogistik indie Prädikatenlogik (mit monadischen, d.h. einstelligenPrädikaten) zu übersetzen. Aber alle diese Versuche modifizierenklassische Gesetze der Aristotelischen Logik oder beachten sieeinfach nicht. DerFehlschlag solcher Versuche liegt nun daran, dass es überhauptkeine vernünftige derartige Übersetzung gibt!

    Since the beginning of modern symbolic logic, there have been attempts to translate Aristotelianlogic into monadic predicate logic. However, all these attempts do not reproduce classical laws of Aristotelian logic.In this paper we use a computer-based approach for the proof of the fact that there does not exist any satisfactory such translationof Aristotelian logic into predicate logic.

  • Algorithmic Aristotelian Logic:
    Online experiments with SYLLOgism
    • Aristotle's logic of the Analytica Priora has been formalized in many different wayssince Leibniz' and, later but independently, Boole's invention of an Algebra of Logic . We present an online accessible site where Aristotelian logic has been implementedin the framework of a computer software utilizing "rule-based reasoning". Thus, our system SYLLOgismis a young relative of the "traditional" syllogistic theory as well as of the "systems of natural deduction"developed in the 1970s by Corcoran and Smiley.This site is meant not only as a tool for gaining elementary understanding of the basic syntactical and semantical concepts of Aristotelian logic but also as a research instrument for those who are convinced that the formal power of Aristotelian logic in the computer age has not yet come to light in an adequate manner.