The Divided Line of Plato Rep. VI.

Abstract

At the end of the Sixth Book of the Republic Plato explains the Idea of Good by means of the Figure of the Sun. As the sun is the cause both of the becoming of that which is subject to becoming and of our apprehension of it and of its changes through the eye, so the idea of good is the cause of the being of that which is and also of our knowledge of it. As the sun is beyond γ⋯νεσις, so the Idea of Good is beyond Being. Glaucon says he does not understand. The simile is further elucidated by means of a line, divided into two parts, of which one stands for the νιητ⋯ν γ⋯νος τε κα⋯ τ⋯πος, where the Idea of Good bears rule, the other for the ⋯ρατ⋯ν γ⋯νος τε κα⋯ τ⋯πος, over which the sun is lord. The line is to be divided unequally (the inequality representing the unequal clearness of the objects each division stands for), and subdivided in the same proportions. Thus we get a line consisting of four parts in the ratio (say) 4 : 6 : : 6 : 9. Let us call the four parts A B C D respectively, A being the smallest, D the greatest, B and C necessarily equal. A (as Plato explains) stands for εἱκ⋯νες, shadows, images in water and on polished surfaces, and the like: B stands for animals, plants, and the creations of human industry: C for the objects of that enquiry in which the objects denoted by B are treated as images, i.e. mathematical enquiries: D for the objects apprehended by dialectic, the Ideas themselves. The first equation asserted (510a 8) is—The objects of opinion : objects of knowledge : : representation : original (AB : CD : : A : B). There follows an explanation of the inferiority of mathematical to philosophical reasoning, and an explanation of the statement that the objects denoted by B are used as images or symbols by the enquiry concerned with C; as a result of which Glaucon perceives that the general distinction between C and D is that between the τ⋯χναι (as they were called), i.e. those sciences in which the Guardians (as explained in the following book) were to be educated, and Philosophy or Dialectic. Finally a special π⋯θημα or affection of the soul is allotted to each of the four divisions of the line, to A εἱκασ⋯α, to B π⋯στις, to C δι⋯νοια, to D ν⋯ησις, each π⋯θημα being clear in the same degree in which the objects it is concerned with are true.