Dedüktif Bir Sistem Olarak Aristoteles’in Kıyası

Year 2023, Volume: 42 Issue: 2, 208 - 225, 07.02.2024

Translator: İbrahim Oğulcan Erayman

Abstract

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.

Keywords

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

Supporting Institution

Bursa Uludağ Üniversitesi Bilimsel Araştırma Projeleri Birimi (BAP)

Project Number

SOA-2022-1120

Thanks

Bu çalışma, SOA-2022-1120 kodlu, “Modern Formel Mantık Bakımından Aristoteles'in Kıyas Teorisi ve Din Bilimlerinde Kullanılmasının İmkanı” adlı Öncelikli Alan Araştırma Projesi (ÖNAP) kapsamında hazırlanmıştır ve Bursa Uludağ Üniversitesi Bilimsel Araştırma Projeleri Birimi tarafından desteklenmiştir.

Aristotle’s Syllogistic as a Deductive System

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.

Keywords

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

Project Number

SOA-2022-1120

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