مرکز منطقه ای اطلاع رساني علوم و فناوري - A Discussion of Mathematical Intermediaries in the Analogy of the Divided Line in the Politeia

Abstract :

This article investigates the analogy of the Divided Line which is introduced in the sixth book of Plato s Republic and which has epistemological, ontological, ethical and political aspects in Plato s philosopy. The third section of the Divided Line, which is termed the dianoia, is at the centre of this study, because this section forms a basis for the discussion of mathematical intermediates. Questions such as, are the objects of dianoia mathematical intermediates or ideas, can we speak on mathematical intermediates except ideas resulted in endless discussion as these issues reveal the most serious epistemological problems of Plato s philosophy. In order to display the main approachs in these debates, we attempt to describe the Divided Line by relying on Plato s own statements, then we introduce the different approachs concerning the mathematical intermediates both by showing their philosophical basis and through emphasizing their weak points which are open to criticism. Finally, some comments are made concerning these issues.