Aristotle’s Syllogistic as a Deductive System

Öz

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.

Anahtar Kelimeler

• Aristotle’s logic
• syllogistic
• Jan Łukasiewicz
• axiomatic system
• axiomatic refutation
• completeness

Dedüktif Bir Sistem Olarak Aristoteles’in Kıyası

Öz

Aristoteles'in kıyası tarihteki ilk dedüktif sistemdir. Yüzyıllar sonra, Aristoteles'in fikirleri, çalışmalarını geliştirmeye devam eden, onun ulaştığı sonuçlardan ve hatta yöntemlerinden ilham alan mantıkçıların ilgisini hala çekmeye devam etmektedir. Makalede, Aristotelesçi kıyas sisteminin temel unsurlarını ve Łukasiewicz'in bunu modern formel mantığın araçlarına dayalı olarak yeniden inşasını tartışıyoruz. Her iki yazar tarafından da tartışıldığı gibi, dedüktif sisteminin eksiksizliği (completeness) kavramına özel önem atfediyoruz. Bir aksiyomatik çürütme sistemi kullanarak, eksiksizliğin nasıl tanımlanabileceğini ve ispatlanabileceğini ayrıntılı olarak tanımlıyoruz. Son olarak, bu metodolojiyi Łukasiewicz, Lemmon ve Shepherdson tarafından sunulan kıyasın farklı aksiyomlaştırmalarına uyguluyoruz.

Anahtar Kelimeler

• Aristoteles mantığı
• kıyas
• Jan Łukasiewicz
• aksiyomatik sistem
• aksiyomatik çürütme
• eksiksizlik.

Kaynakça

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