Difficulty of understanding how the same predicate could belong to more than one subject.
Stilpon (like Antisthenes, as I have remarked above) seems to have had in his mind a type of predication, similar to the type of reasoning which Aristotle laid down the syllogism: such that the form of the proposition should be itself a guarantee for the truth of what was affirmed. Throughout the ancient philosophy, especially in the more methodised debates between the Academics and Sceptics on one side, and the Stoics on the other — what the one party affirmed and the other party denied, was, the existence of a Criterion of Truth: some distinguishable mark, such as falsehood could not possibly carry. To find this infallible mark in propositions, Stilpon admitted none except identical. While agreeing with Antisthenes, that no predicate could belong to a subject different from itself, he added a new argument, by pointing out that predicates applied to one subject were also applied to many other subjects. Now if the predicates belonged to one, they could not (in his view) belong to the others: and therefore they did not really belong to any. He considered that predication involved either identity or special and exclusive implication of the predicate with the subject.
Analogous difficulties in the Platonic Parmenidês.
Stilpon was not the first who had difficulty in explaining to himself how one and the same predicate could be applied to many different subjects. The difficulty had already been set forth in the Platonic Parmenidês.[133] How can the Form (Man, White, Good, &c.) be present at one and the same time in many distinct individuals? It cannot be present as a whole in each: nor can it be divided, and thus present partly in one, partly in another. How therefore can it be present at all in any of them? In other words, how can the One be Many, and how can the Many be One? Of this difficulty (as of many others) Plato presents no solution, either in the Parmenidês or anywhere else.[134] Aristotle alludes to several contemporaries or predecessors who felt it. Stilpon reproduces it in his own way. It is a very real difficulty, requiring to be dealt with by those who lay down a theory of predication; and calling upon them to explain the functions of general propositions, and the meaning of general terms.
[133] Plato, Parmenidês, p. 131. Compare also Philêbus, p. 15, and Stallbaum’s Proleg. to the Parmenidês, pp. 46-47. The long commentary of Proklus (v. 100-110. pp. 670-682 of the edition of Stallbaum) amply attests the δυσκολίαν of the problem.
The argument of Parmenidês (in the dialogue called Parmenidês) is applied to the Platonic εἴδη and to τὰ μετέχοντα. But the argument is just as much applicable to attributes, genera, species: to all general predicates.
[134] Aristot. Physic. i. 2, 185, b. 26-36.
Lykophron and some others anterior to Aristotle proposed to elude the difficulty, by ceasing to use the substantive verb as copula in predication: instead of saying Σωκράτης ἐστὶ λευκός, they said either Σωκράτης λευκός, simply, or Σωκράτης λελεύκωται.
This is a remarkable evidence of the difficulty arising, even in these early days of logic, about the logical function of the copula.