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Theaetetus

§154

Relativity of Perception and the Dice Paradox

Socrates explains that sensory properties like colors are relative phenomena generated by the contact of eyes and motion, and introduces a paradox using the example of dice, where an unchanged object appears differently depending on what it is compared to.

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§154

ΣΩ. ἑπώμεθα τῷ ἄρτι λόγῳ, μηδὲν αὐτὸ καθʼ αὑτὸ ἓν ὂν τιθέντες· καὶ ἡμῖν οὕτω μέλαν τε καὶ λευκὸν καὶ ὁτιοῦν ἄλλο χρῶμα ἐκ τῆς προσβολῆς τῶν ὀμμάτων1 πρὸς τὴν προσήκουσαν φορὰν φανεῖται γεγενημένον, καὶ ὃ δὴ ἕκαστον εἶναί φαμεν χρῶμα οὔτε τὸ προσβάλλον οὔτε τὸ προσβαλλόμενον ἔσται, ἀλλὰ μεταξύ τι ἑκάστῳ ἴδιον γεγονός· ἢ σὺ διισχυρίσαιο ἂν ὡς οἷον σοὶ φαίνεται ἕκαστον χρῶμα, τοιοῦτον καὶ κυνὶ καὶ ὁτῳοῦν ζῴῳ; ΘΕΑΙ. μὰ Δίʼ οὐκ ἔγωγε. ΣΩ. τί δέ; ἄλλῳ ἀνθρώπῳ ἆρʼ ὅμοιον καὶ σοὶ φαίνεται ὁτιοῦν; ἔχεις τοῦτο ἰσχυρῶς, ἢ πολὺ μᾶλλον ὅτι οὐδὲ σοὶ αὐτῷ ταὐτὸν διὰ τὸ μηδέποτε ὁμοίως αὐτὸν σεαυτῷ ἔχειν; ΘΕΑΙ. τοῦτο μᾶλλόν μοι δοκεῖ ἢ ἐκεῖνο. ΣΩ. οὐκοῦν εἰ μὲν ᾧ παραμετρούμεθα2 ἢ οὗ ἐφαπτόμεθα μέγα ἢ λευκὸν ἢ θερμὸν ἦν, οὐκ ἄν ποτε ἄλλῳ προσπεσὸν ἄλλο ἂν ἐγεγόνει, αὐτό γε μηδὲν μεταβάλλον· εἰ δὲ αὖ τὸ παραμετρούμενον ἢ ἐφαπτόμενον ἕκαστον ἦν τούτων, οὐκ ἂν αὖ ἄλλου προσελθόντος ἤ τι παθόντος αὐτὸ μηδὲν παθὸν ἄλλο ἂν ἐγένετο. ἐπεὶ νῦν γε, ὦ φίλε, θαυμαστά τε καὶ γελοῖα εὐχερῶς πως ἀναγκαζόμεθα λέγειν, ὡς φαίη ἂν Πρωταγόρας τε καὶ πᾶς ὁ τὰ αὐτὰ ἐκείνῳ ἐπιχειρῶν λέγειν. ΘΕΑΙ. πῶς δὴ καὶ ποῖα λέγεις; ΣΩ. σμικρὸν λαβὲ παράδειγμα, καὶ πάντα εἴσῃ ἃ βούλομαι. ἀστραγάλους γάρ που ἕξ, ἂν μὲν τέτταρας αὐτοῖς προσενέγκῃς, πλείους φαμὲν εἶναι τῶν τεττάρων καὶ ἡμιολίους, ἐὰν δὲ δώδεκα, ἐλάττους καὶ ἡμίσεις, καὶ οὐδὲ ἀνεκτὸν ἄλλως λέγειν· ἢ σὺ ἀνέξῃ; ΘΕΑΙ. οὐκ ἔγωγε. ΣΩ. τί οὖν; ἄν σε Πρωταγόρας ἔρηται ἤ τις ἄλλος· ὦ Θεαίτητε, ἔσθʼ ὅπως τι μεῖζον ἢ πλέον γίγνεται ἄλλως ἢ αὐξηθέν; τί ἀποκρινῇ; ΘΕΑΙ. ἐὰν μέν, ὦ Σώκρατες, τὸ δοκοῦν πρὸς τὴν νῦν ἐρώτησιν ἀποκρίνωμαι, ὅτι οὐκ ἔστιν· ἐὰν δὲ πρὸς τὴν προτέραν, φυλάττων μὴ ἐναντία εἴπω, ὅτι ἔστιν. ΣΩ. εὖ γε νὴ τὴν Ἥραν, ὦ φίλε, καὶ θείως. ἀτάρ, ὡς ἔοικεν, ἐὰν ἀποκρίνῃ ὅτι ἔστιν, Εὐριπίδειόν τι συμβήσεται· ἡ μὲν γὰρ γλῶττα ἀνέλεγκτος ἡμῖν ἔσται, ἡ δὲ φρὴν οὐκ ἀνέλεγκτος. ΘΕΑΙ. ἀληθῆ. ΣΩ. οὐκοῦν εἰ μὲν δεινοὶ καὶ σοφοὶ ἐγώ τε καὶ σὺ ἦμεν, πάντα τὰ τῶν φρενῶν ἐξητακότες, ἤδη ἂν τὸ λοιπὸν ἐκ περιουσίας ἀλλήλων ἀποπειρώμενοι, συνελθόντες σοφιστικῶς εἰς μάχην τοιαύτην, ἀλλήλων τοὺς λόγους τοῖς λόγοις ἐκρούομεν·3 νῦν δὲ ἅτε ἰδιῶται πρῶτον βουλησόμεθα θεάσασθαι αὐτὰ πρὸς αὑτὰ τί ποτʼ ἐστὶν ἃ διανοούμεθα, πότερον ἡμῖν ἀλλήλοις συμφωνεῖ ἢ οὐδʼ ὁπωστιοῦν. ΘΕΑΙ. πάνυ μὲν οὖν ἔγωγε τοῦτʼ ἂν βουλοίμην.

​SOCRATES: Let us follow the recent argument, positing that nothing is one itself by itself. And thus black and white and any other color will appear to us to have been generated from the impact of the eyes upon the appropriate motion, and that which we say each color is will be neither the impacting thing nor the impacted thing, but something generated in between, which is peculiar to each individual. Or would you strongly maintain that as each color appears to you, so it also appears to a dog or any other animal? THEAETETUS: By Zeus, not I. SOCRATES: And what of this? Does anything appear similar to another human being as it does to you? Do you hold this firmly, or rather that it does not even appear the same to yourself, because you are never in the same state as yourself? THEAETETUS: The latter seems to me more likely than the former. SOCRATES: Therefore, if that against which we measure ourselves or which we touch were large or white or hot, it would never, by coming into contact with something else, have become different, while it itself underwent no change. And if, on the other hand, the thing measuring or touching were each of these, then when something else approached it or was affected in some way, it would not, while itself undergoing no affection, have become different. For as it is, my friend, we are somehow easily forced to say things that are wonderful and ridiculous, as Protagoras and anyone who attempts to say the same things as he would assert. THEAETETUS: How so, and what kind of things do you mean? SOCRATES: Take a small example, and you will know everything I mean. For instance, if you bring four dice near six dice, we say that the six are more than the four and are one and a half times as many; but if you bring twelve, they are fewer and half, and it is not even tolerable to say otherwise. Or would you tolerate it? THEAETETUS: Not I, indeed. SOCRATES: What then? If Protagoras or someone else should ask you: “Theaetetus, is there any way that anything becomes larger or more otherwise than by being increased?” What will you answer? THEAETETUS: If, Socrates, I answer what seems true in response to this present question, I should say “No, there is not”; but if I answer with regard to the former case, guarding against saying contradictory things, I should say “Yes, there is.” SOCRATES: Well said, by Hera, my friend, and divinely! But, as it seems, if you answer that there is, something Euripidean will happen: for our tongue will be unrefuted, but our mind will not be unrefuted. THEAETETUS: True. SOCRATES: Therefore, if you and I were clever and wise, having thoroughly examined all the things of the mind, then for the rest, out of sheer abundance, we would try to test each other, and coming together in a sophistical manner into such a battle, we would clash each other’s arguments with arguments. But as it is, since we are ordinary people, we shall first want to inspect our thoughts themselves in relation to themselves, to see what they actually are, and whether they agree with one another or not at all. THEAETETUS: I would indeed wish this very much.

Syntax notes3 items
  1. 154τῶν ὀμμάτων

    The genitive τῶν ὀμμάτων associated with the noun προσβολή (impact, clash) is best understood as a subject genitive (the eyes clashing with something), rather than an objective genitive. This is supported by the subsequent active expression 'the clashing thing' (τὸ προσβάλλον).

  2. 154bᾧ παραμετρούμεθα

    The contrast between the middle-voice relation ᾧ παραμετρούμεθα ('that by which we measure [ourselves]') and the passive-voice participle τὸ παραμετρούμενον ('that which is measured'). The grammar carefully distinguishes between the objective standard used for measurement and the individual subject or object being measured.

  3. 154dἂν ... ἐκρούομεν

    The apodosis of a second-class (contrary-to-fact) conditional sentence. Following the protasis εἰ μὲν δεινοὶ καὶ σοφοὶ ... ἦμεν ('if we were clever and wise'), the imperfect indicative with ἂν (ἐκρούομεν) expresses a conclusion contrary to present reality (in fact, we are not clashing our arguments).

Translated by Gemini 3.5 Flash (published 2026-05-22)urn:cts:greekLit:tlg0059.tlg006.humanitext-grc2:154