Plato's Unhypothetical Principle

Plato's Unhypothetical Principle LYNN E. ROSE T~is PAP2R SUGO~STSa new interpretation of the unhypothetical first principle that Plato briefly mentions in the Republic. The interpretation will be supported by a preliminary examination of Plato's conception of the role of hypotheses in dialectic. As the following passages indicate, one of the reasons for distinguishing mathematicians from dialecticians is that they have different attitudes toward hypotheses and consequently use them in different ways: Those who are concerned with geometry and calculation and such matters hypothesize the odd and the even and the figures and three kinds of angles and other things related to these in each enquiry; taking these as known, they make them their hypotheses,zand do not expect to give any account of them either to themselves or to others, in that they are manifest to all. They start from these, go through the rest, and conclude consistently regarding that which they started out to investigate.2 The objects of dialectic . . . reason itself grasps by the power of dialectic, and it makes the hypotheses not starting points (hpx&~),but literally hypotheses (r~ 5pT~bwoS~), like steps (~t~a~tr) and starting-points (Sp~hr), so that, going up as far as the unhypotheticaJ (ro~hvm-o0~rou)to the starting-point of all (hpx~)v),it may grasp it, and, by again holding on to the things which depend on this, so descend to a conclusion (r~X~-~)~).a Both bpgil and apx/7 have been translated as "starting-point," but they are not starting-points in the same sense. The dialectician here begins by taking questioned hypotheses as starting-points (bpghs) and gives an account of each by deducing it from some further hypothesis or hypotheses. Then, if one of these latter hypotheses is questioned, he can continue in the same manner, always deducing the questioned hypothesis from other hypotheses, until finally he comes to base his argument on the unhypothetical principle. This unhypothetical is a starting-point (hpx~) in another sense: it is to be introduced as an ultimate premise from which we are to deduce some conclusion (reXevriT), usually a hypothesis which had been questioned but is now seen to follow from the unhypothetical principle. The auwbO~rov is presumably not the only hpxiT, since any hypothesis which remains unchallenged and undemonstrated and which is used in an argument is an ~px/1 or starting-point of that argument. It will be convenient to refer to the following diagram, in which I have indicated what it might be like to backtrack along the upward path via the denial of hypotheses . Suppose that the philosopher or dialectician wishes to establish the conclusion , T. He will show the interlocutor or student that T follows from the three 1For a summary of the various views which have been held about the sort of mathematical hypotheses Plato is referring to, see Richard Robinson, Plato's Earlier Dialectic (2nd ed.; Oxford: 1953), pp. 103-105. 2Republic, 510c2-d3. *Republic, 511b4-8. [189] 190 HISTORY OF PHILOSOPHY A ~ H7 H5 H6 H~ H 3 T T -- that which is to be shown (r~,~) H. -~ various hypotheses ( ~ ) A -- the unhypothetical (&v~r~rov) Each arrow represents a single argument; the head points to the conclusion, and a branch of the tail comesfrom each premise. hypotheses, H~, H~, and H~. If the interlocutor accepts these three hypotheses without question, the matter is settled, and T is accepted. In such an argument H1, H~, and H~would be apxaL or ultimate starting-points. But the interlocutor may either question or else deny one or more of the three hypotheses. Suppose he questions or denies H~. Then the dialectician must select one or more "higher" hypotheses -suppose he selects He--from which he must deduce the questioned hypothesis, H~. Again, the student may either accept or question H4. If He is questioned, it must then be deduced from still higher hypotheses (such as H6 and H6). This backtracking continues until the student has either accepted all the hypotheses upon which the now-expanded argument depends or else has been shown that the questioned hypotheses follow from the unhypothetical starting-point A. Thus, he might question H5...