Relativity twofold — to the comparing Subject — to another object, besides the one directly described.
The illustration here furnished by Sokrates brings out forcibly the negation of the absolute, and the affirmation of universal relativity in all conceptions, judgments, and predications, which he ascribes to Protagoras and Herakleitus. The predication respecting the six dice denotes nothing real, independent, absolute, inhering in them: for they have undergone no change. It is relative, and expresses a mental comparison made by me or some one else. It is therefore relative in two different senses:— 1. To some other object with which the comparison of the dice is made:— 2. To me as comparing Subject, who determine the objects with which the comparison shall be made.[31] — Though relativity in both senses is comprehended by the Protagorean affirmation — Homo Mensura — yet relativity in the latter sense is all which that affirmation essentially requires. And this is true of all propositions, comparative or not — whether there be or be not reference to any other object beyond that which is directly denoted. But Plato was here illustrating the larger doctrine which he ascribes to Protagoras in common with Herakleitus: and therefore the more complicated case of relativity might suit his purpose better.
[31] The Aristotelian Category of Relation (τὰ πρὸς τί, Categor. p. 6, a. 36) designates one object apprehended and named relatively to some other object — as distinguished from object apprehended and named not thus relatively, which Aristotle considers as per se καθ’ αὑτό (Ethica Nikomach. i. p. 1096, a. 21). Aristotle omits or excludes relativity of the object apprehended to the percipient or concipient subject, which is the sort of relativity directly noted by the Protagorean doctrine.
Occasionally Aristotle passes from relativity in the former sense to relativity in the latter; as when he discusses ἐπιστητὸν and ἐπιστήμη, alluded to in one of my former [notes] on this dialogue. But he seems unconscious of any transition. In the Categories, Object, as implicated with Subject does not seem to have been distinctly present to his reflection. In the third book of the Metaphysica, indeed, he discusses professedly the opinion of Protagoras; and among his objections against it, one is, that it makes everything relative or πρὸς τί (Metaph. Γ. p. 1011, a. 20, b. 5). This is hardly true in the sense which πρὸς τί bears as one of his Categories: but it is true in the other sense to which I have adverted.
A clear and full exposition of what is meant by the Relativity of Human Knowledge, will be found in Mr. John Stuart Mill’s most recent work, ‘Examination of Sir William Hamilton’s Philosophy,’ ch. ii. pp. 6-15.
Sokrates now re-states that larger doctrine, in general terms, as follows.
Statement of the doctrine of Herakleitus — yet so as to implicate it with that of Protagoras.
The universe is all flux or motion, divided into two immense concurrent streams of force, one active, the other passive; adapted one to the other, but each including many varieties. One of these is Object: the other is, sentient, cognizant, concipient, Subject. Object as well as Subject is, in itself and separately, indeterminate and unintelligible — a mere chaotic Agent or Patient. It is only by copulation and friction with each other that they generate any definite or intelligible result. Every such copulation, between parts adapted to each other, generates a twin offspring: two correlative and inseparable results infinitely diversified, but always born in appropriate pairs:[32] a definite perception or feeling, on the subjective side — a definite thing perceived or felt, on the objective. There cannot be one of these without the other: there can be no objective manifestation without its subjective correlate, nor any subjective without its objective. This is true not merely about the external senses — touch, taste, smell, sight, hearing — but also about the internal, — hot and cold, pleasure and pain, desire, fear, and all the countless variety of our feelings which have no separate names.[33] Each of these varieties of feeling has its own object co-existent and correlating with it. Sight, hearing, and smell, move and generate rapidly and from afar; touch and taste, slowly and only from immediate vicinity: but the principle is the same in all. Thus, e.g., when the visual power of the eye comes into reciprocal action with its appropriate objective agent, the result between them is, that the visual power passes out of its abstract and indeterminate state into a concrete and particular act of vision — the seeing a white stone or wood: while the objective force also passes out of its abstract and indeterminate state into concrete — so that it is no longer whiteness, but a piece of white stone or wood actually seen.[34]
[32] Plato, Theætêt. p. 156 A. ὡς τὸ πᾶν κίνησις ἦν, καὶ ἄλλο παρὰ τοῦτο οὐδέν, τῆς δὲ κινήσεως δύο εἴδη, πλήθει μὲν ἄπειρον ἑκάτερον, δύναμιν δὲ τὸ μὲν ποιεῖν ἔχον, τὸ δὲ πάσχειν. Ἐκ δὲ τῆς τούτων ὁμιλίας τε καὶ τρίψεως πρὸς ἄλληλα γίγνεται ἔκγονα πλήθει μὲν ἄπειρα, δίδυμα δέ — τὸ μὲν αἰσθητόν, τὸ δὲ αἴσθησις, ἀεὶ συνεκπίπτουσα καὶ γεννωμένη μετὰ τοῦ αἰσθητοῦ.
[33] Plato, Theætêt. p. 156 B.