Plato’s representation of the Protagorean doctrine in intimate conjunction with the Herakleitean.
This doctrine of the Eleate in the Platonic Sophistes coincides with the Protagorean — Homo Mensura — construed in its true meaning: Object is implicated with, limited or measured by, Subject: a doctrine proclaiming the relativeness of all objects perceived, conceived, known, or felt — and the omnipresent involution of the perceiving, conceiving, knowing, or feeling, Subject: the object varying with the Subject. “As things appear to me, so they are to me: as they appear to you, so they are to you.” This theory is just and important, if rightly understood and explained: but whether Protagoras did so explain or understand it, we cannot say; nor does the language of Plato enable us to make out. Plato passes on from this theory to another, which he supposes Protagoras to have held without distinctly stating it: That there is no Ens distinguishable in itself or permanent, or stationary: that all existences are in perpetual flux, motion, change — acting and reacting upon each other, combining with or disjoining from each other.[28]
[28] Plato, Theætêt. p. 152 D.
Though Plato states the grounds of this theory in his ironical way, as if it were an absurd fancy, yet it accidentally coincides with the largest views of modern physical science. Absolute rest is unknown in nature: all matter is in perpetual movement, molecular as well as in masses.
Relativity of sensible facts, as described by him.
Turning to the special theory of Protagoras (Homo Mensura), and producing arguments, serious or ironical in its defence, Sokrates says — What you call colour has no definite place or existence either within you or without you. It is the result of the passing collision between your eyes and the flux of things suited to act upon them. It is neither in the agent nor in the patient, but is something special and momentary generated in passing between the two. It will vary with the subject: it is not the same to you, to another man, to a dog or horse, or even to yourself at different times. The object measured or touched cannot be in itself either great, or white, or hot: for if it were, it would not appear different to another Subject. Nor can the Subject touching or measuring be in itself great, or white, or hot: for if so, it would always be so, and would not be differently modified when applied to a different object. Great, white, hot, denote no positive and permanent attribute either in Object or Subject, but a passing result or impression generated between the two, relative to both and variable with either.[29]
[29] Plato, Theætêt. pp. 153-154. ὃ δὴ ἕκαστον εἶναί φαμεν χρῶμα, οὔτε τὸ προσβάλλον οὔτε τὸ προσβαλλόμενον ἔσται, ἀλλὰ μεταξύ τι ἑκαστῳ ἴδιον γεγονός.
Relations are nothing in the object purely and simply without a comparing subject.
To illustrate this farther (continues Sokrates) — suppose we have here six dice. If I compare them with three other dice placed by the side of them, I shall call the six dice more and double: if I put twelve other dice by the side of them, I shall call the six fewer and half. Or take an old man — and put a growing youth by his side. Two years ago the old man was taller than the youth: now, the youth is grown, so that the old man is the shorter of the two. But the old man, and the six dice, have remained all the time unaltered, and equal to themselves. How then can either of them become either greater or less? or how can either really be so, when they were not so before?[30]
[30] Plato, Theætêt. pp. 154-155. Compare the reasoning in the Phædon, pp. 96-97-101.