Dedüktif Bir Sistem Olarak Aristoteles’in Kıyası

Yıl 2023, Cilt: 42 Sayı: 2, 208 - 225, 07.02.2024

Çevirmen: İbrahim Oğulcan Erayman

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.

Destekleyen Kurum

Bursa Uludağ Üniversitesi Bilimsel Araştırma Projeleri Birimi (BAP)

Proje Numarası

SOA-2022-1120

Teşekkür

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

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

Proje Numarası

SOA-2022-1120

Kaynakça

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