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.
- 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 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.
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]
Anfängen der modernen symbolischen Logik hat es immer wieder
Versuche gegeben, die Aristotelische assertorische Syllogistik in
die Prädikatenlogik (mit monadischen, d.h. einstelligen
Prädikaten) zu übersetzen. Aber alle diese Versuche modifizieren
klassische Gesetze der Aristotelischen Logik oder beachten sie
einfach nicht. Der
Fehlschlag solcher Versuche liegt nun daran, dass es überhaupt
keine vernünftige derartige Übersetzung gibt!
Since the beginning of modern symbolic logic, there have been attempts to translate Aristotelian
logic 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 translation
of Aristotelian logic into predicate logic.
- Algorithmic Aristotelian Logic:
Aristotle's logic of the Analytica Priora has been formalized in many different ways
since Leibniz' and, later but independently, Boole's invention of an Algebra of Logic.
We present an online accessible site where Aristotelian logic has been implemented
in the framework of a computer software utilizing "rule-based reasoning". Thus, our system SYLLOgism
is 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.
Online experiments with SYLLOgism