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Title: Aristotle's Syllogistic as a Deductive System
Authors: Kulicki, Piotr
Keywords: Aristotle's logic; syllogistic; completeness; Jan Łukasiewicz; axiomatic refutation
Issue Date: 19-May-2020
Publisher: MDPI
Citation: "Axioms" 2020, 9(2), 56;
Abstract: Aristotle's syllogistic is the first ever deductive system. After centuries, Aristotle's ideas are still interesting for logicians who develop Aristotle's work and draw inspiration from his results and even more from his methods. In the paper we discuss the essential elements of the Aristotelian system of syllogistic and Łukasiewicz's reconstruction of it based on the tools of modern formal logic. We pay special attention to the notion of completeness of a deductive system as discussed by both authors. We describe in detail how completeness can be defined and proved with the use of an axiomatic refutation system. Finally, we apply this methodology to different axiomatizations of syllogistic presented by Łukasiewicz, Lemmon and Shepherdson.
DOI: 10.3390/axioms9020056
Appears in Collections:Artykuły naukowe (WF)

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