PLATO’ S DIVIDED LINE

REPUBLIC 509d ff.

 

 

 

                  B

 

                                                                                                

 

 

                                                 UNDERSTANDING (noęsis: The Soul’s arrival at first principle)

                                         

                                                            

                                                                                                    1st Division: Intelligible World

 

 

               E

 

 

                                                 THOUGHT (dianoia: The Soul’s conclusion after  investigating a hypothesis)

                                                                                             

               C

 

                                                

                                                 BELIEF (in things that can produce shadows & reflections, pistis)

                                                                                                    1st Division Visible World

             D                                                                     

 

                                                      IMAGINATION (produces images like shadows & reflections, eikasia)

                A

 

                                                                                                 

 

G. M. A. Grube, Plato’s Thought, pp. 24-27

 

            In the physical world then we have the sun from which we derive light, sight and the eye that sees; in the intelligible [world] we have the good from which we derive truth, knowledge and the mind that knows.  It is to the good that the sun itself owes its existence.  Furthermore, the sun  is not only the cause of sight, its light makes existence possible on the physical plane; so the good is not only the cause of knowledge, but causes the very existence of the knowable and, a fortiori of the physical which derives from the knowable.

            Socrates proceeds at once to make his meaning clear by another image.  Starting from the now familiar division of existence into two classes or forms (ei[dh), the visible and the intelligible, he bids Glaucon draw a line and divide it into two unequal parts, each part being then subdivided into two further sections, as follows, so that “AD” is to “DC” as “CE” is to “EB” as “AC” is to “CB” (509d).

            The main division at C is between the world of sense and the world of Ideas.  We must imagine the highest point in the ladder of truth and reality to be at “B.”  “A” is the lowest point at which a thing can be said to exist at all.  “DC” will then contain all the phenomena of the physical world, the things we apprehend with our bodily perceptions ‘animals, plants and all the manufactured objects,’  whereas in the lowest section “AD” we place their images and shadows in water or mirrors, etc., (and possibly, though Plato does not say so, the products of the fine arts).  The relation between the objects in “DC” and those in “AD” is one we easily understand: it is that between a model and a copy or imitation.

            This relation Plato now uses to express also the relation between the objects of sense and the objects in the higher section “CE.”  He makes his meaning clear by the example of mathematics: the objects studied in geometry are in truth perfect mathematical figures, but in his demonstrations the geometer draws material representations of the perfect square, etc., and uses these in his study of the perfect geometrical figures which can only be seen by the mind’s eye.  That is, he uses the sensible objects of “DC” as copies or images of those mathematical realities which have their being in the higher section “CE.”  This section therefore contains the objects of such sciences as use concrete realities to represent them.  Further, such sciences start from axioms and hypotheses which they take for granted and which it is not their business to call into question.

            There is, however (we are told), a higher kind of science which is purely abstract and uses no concrete illustrations or images.  The objects of these belong to the highest section “EB.”  It is the business of this science to test the truth of the hypotheses and axioms of the lower sciences in terms of hypotheses of still wider application and it will finally base the whole body of knowledge upon one universal proposition which is then one supreme truth.  For as this final basis explains all the rest and is consistent with the whole body of knowledge it can no longer be called hypothetical.  It is the first principle of nature and existence.  This is the Idea of good in the Republic, which we must suppose to exist at “B.”  “EB” will presumably contain the various truths which the philosopher discovers in the course of his ascent from the hypotheses of mathematics to the supreme truth.  Once this is discovered he will descend again through the whole realm of thought.  The lower sciences will now also become knowledge in the highest sense to him because to him they are no longer based on the hypothetical. . . . (511b)

. . . . . . . . . .

            It is interesting to dwell for a moment on the mental processes by which the different grades of reality are perceived.  The main division at “C” is here, as elsewhere, between uncritical belief (dovxa) which is concerned with the phenomenal world and the critical function of the mind which leads to knowledge (novhsi").  When we come to the subdivisions the lowest section contains the objects of eijkasiva which is usually translated as imagination, but it is rather the power of seeing images, for Plato is here thinking of it not so much as a creative faculty but rather as a completely uncritical perception which does not even attempt to relate one perception to another or to differentiate between an object and its reflection in a mirror.  The phenomena themselves in “DC” are the objects of faith or belief (pivsti") which, though it does in a sense correlate its perceptions, does not submit them to critical analysis.  Then knowledge is subdivided into diavnoia, the power of critical and logical analysis, of reasoning from given premises, and nou", understanding, which enables one to go beyond the premises of particular sciences to the grasping of the absolute values behind all reality.