ARISTOTLE'S PRIOR AND POSTERIOR ANALYTICS

RELATION OF PRIOR TO POSTERIOR ANALYTICS 19triangular in shape, etc. There is no question of assumingdefinitions.Observe now how much more developed and explicit is Aristotle'stheory of apxa{. He distinguishes first between commonprinciples which lie at the basis of all science, and special principleswhich lie at the basis of this or that science. Among thelatter he distinguishes between hypotheses (assumptions of theexistence of certain entities) and definitions. I And finally he laysit down explicitly that while science assumes the definitions of allits tenus, it assumes the existence only of the primary entities,such as the unit, and proves the existence of the rest. 2Next, while Plato insists that the hypotheses of the sciences arereally only working hypotheses, useful starting-points, requiringfor their justification deduction, such as only philosophy can give,from an unhypotlietical principle, Aristotle insists that all thefirst principles, common and special alike, are known on their ownmerits and need no further justification. And while he retains thename 'hypotheses' for one class of these principles, he is careful tosay of them no less than of the others that they are incapable ofbeing proved-not only incapable of being proved within thescience, as Plato would have agreed, but incapable of being provedat all. The attempt to prove the special principles (which includethe hypotheses) is in one passageJ mentioned but expressly saidto be incapable of success, just as the attempt to prove the commonprinciples is in another passage 4 referred to merely as apossible attempt, v:ithout any suggestion that it could succeed.Further, while the entities which Plato describes mathematiciansas assuming are either Forms, or according to anotherinterpretation the 'intermediates' between Fonus and sensiblethings, the entities of which Aristotle describes mathematiciansas knowing the definition, and either assuming or proving (as thecase may be) the existence, are not transcendent entities at allbut the numbers and shapes which are actually present in sensiblethings, though treated in abstraction from them.In view of all this, valuable as Solmsen's discussion of Greekmathematical method is, I think it does not aid his main contention,that the Posterior A nalytics belongs to an early stage ofAristotle's development in which he was still predominantlyunder Plato's influence.Solmsen claims 5 that the following chapters of the first book5 p. 146 n. 2.