Document Type : Research Paper

Author

• Davud Heidari

Abstract

This article deals with Lukasiewicz’s view of Aristotle's syllogistic. His fundamental work on the syllogism is Aristotle's Syllogistic from the Standpoint of Modern Formal Logic. The Lukasiewiczian view takes Aristotle’s logic to be an axiomatized system presupposing the propositional calculus. Lukasiewicz noted that Aristotle generally presents syllogisms in conditional form. For example, Barbara is stated as: “if A is said of every B and B of every C, then it is necessary for A to be predicated of every C.” This suggests that syllogisms aren’t inferences but implications. The strong claim constituting Lukasiewicz’s view is that Aristotle’s theory of syllogism is a system of true propositions. He calls all true propositions (whether axioms or theorems) “theses”. From this point of view, imperfect syllogisms are not axioms and need to be proved, i.e. established as theorems. To do that, Aristotle uses a few methods of proof, namely proofs by conversion, proofs by ecthesis and proofs by reductio ad impossibile.

Keywords

• syllogism
• implication
• Axiom
• Propositional Calculus
• Theorem
• Theses
• Conversion
• Ecthesis
• Reductio ad Impossible
• Rejection