PYTHAGORAS TO PLATO must be because they participate in an Idea of F But by (2) this cannot be the Idea Wrst postulated So there must be another Idea of F; but this in turn, by (3), will be F, and so on ad inWnitum If we are to avoid this regress, we must abandon one or other of the principles that generate it To this day scholars are divided as to how seriously Plato took this diYculty, and which, if any, of his principles he modiWed in order to solve it I shall return to the question when we engage in a fuller discussion of Plato’s metaphysics.28 Plato applied his Theory of Ideas to many philosophical problems: he oVered them as the basis of moral values, the bedrock of scientiWc knowledge, and the ultimate origin of all being One problem to which Plato oVered his theory as an answer is often called the problem of universals: the problem of the meaning of universal terms such as ‘man’, ‘bed’, ‘virtue’, ‘good’ Because Plato’s answer turned out to be unsatisfactory, the problem was to remain on the philosophical agenda In succeeding chapters we shall see how Aristotle handled the issue The problem had a continuing history through the Middle Ages and up to our own time A number of notions that occur in modern discussions of the problem bear a resemblance to Plato’s Ideas Predicates In modern logic a sentence such as ‘Socrates is wise’ is considered as having a subject, ‘Socrates’, and a predicate, which consists of the remainder of the sentence, i.e ‘ is wise’ Some philosophers of logic, following Gottlob Frege, have regarded predicates as having an extramental counterpart: an objective predicate (Frege called it a ‘function’) corresponding to ‘ is a man’ in a way similar to that in which the man Socrates corresponds to the name ‘Socrates’ Frege’s functions, such as the function x is a man, are objective entities: they are more like the Wfth items of the Seventh Letter than like the fourth items They share some of the transcendental properties of Ideas: the function x is a man does not grow or die as human beings do, and nowhere in the world can one view or handle the function x is divisible by But functions not conform to the Principles of Self-Predication or Uniqueness How could one ever imagine that the function x is a man, and only that function, was really and truly a human being? Classes Functions serve as principles according to which objects can be collected into classes: objects that satisfy the function x is human, for 28 See p 208V below 54