Politeia'daki Bölünmüş Çizgi Analojisi'nde Matematik Ara Nesneler Sorunu

Bu çalışmada, Platon'un Politeia'sının altıncı kitabında üzerinde durduğu ve felsefesinin epistemolojik, ontolojik, etik, politik yönleriyle bağlantıları olan Bölünmüş Çizgi Analojisi ele alınmıştır.Çalışmanın merkezinde ise Bölünmüş Çizgi'nin dianoia olarak isimlendirilen ve matematik ara nesnelertartışmasına zemin oluşturan bölümü bulunmaktadır. Dianoianın nesnesinin matematik ara nesneler mi;yoksa idealar mı olduğu, dahası idealardan ayrı matematik ara nesnelerden bahsedilip bahsedilemeyeceğigibi sorular uzun soluklu tartışmalara sebep olmuştur. Çünkü bu konu Platon felsefesinin en ciddi epistemolojik sorunlarını açık etmektedir. Bu tartışmalarda ortaya çıkan temel görüşleri sergileyerek sorunlunoktalara işaret edebilmek için önce Platon'un ifadelerine dayanarak Bölünmüş Çizgi'nin bir serimi yapılmış, ardından matematik ara nesneler konusundaki çeşitli görüşler aktarılmış ve bu görüşlerin dayandıkları temeller üzerinde durularak eleştiriye açık olan yönleri irdelenmiştir. Son olarak da konuyla ilgili bazıyorumlar yapılmaya çalışılmıştır.

A Discussion of Mathematical Intermediaries in the Analogy of the Divided Line in the Politeia

This article investigates the analogy of the Divided Line which is introduced in the sixth book ofPlato's Republic and which has epistemological, ontological, ethical and political aspects in Plato'sphilosopy. The third section of the Divided Line, which is termed the dianoia, is at the centre of thisstudy, because this section forms a basis for the discussion of mathematical intermediates. Questions suchas, "are the obj ects of dianoia mathematical intermediates or ideas", "can we sp eak on mathematicalintermediates excep t ideas" resulted in endless discussion as these issues reveal the most serious episte- mological problems of Plato's philosophy. In order to display the main approachs in these debates, weattempt to describe the Divided Line by relying on Plato's own statements, then we introduce the differentapproachs concerning the mathematical intermediates both by showing their philosophical basis andthrough emphasizing their weak points which are open to criticism. Finally, some comments are madeconcerning these issues.

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