§147ΣΩ. σκέψαι δὴ καὶ τόδε.
SOCRATES: Consider this too.
εἴ τις ἡμᾶς τῶν φαύλων τι καὶ προχείρων ἔροιτο, οἷον περὶ πηλοῦ ὅτι ποτʼ ἐστίν, εἰ ἀποκριναίμεθα αὐτῷ πηλὸς ὁ τῶν χυτρέων καὶ πηλὸς ὁ τῶν ἰπνοπλαθῶν καὶ πηλὸς ὁ τῶν πλινθουργῶν, οὐκ ἂν γελοῖοι εἶμεν;
If someone should ask us about one of the common and obvious things, for example, what clay actually is, and we should answer him that clay is that of the potters, and clay that of the oven-makers, and clay that of the brick-makers, would we not be ridiculous?
ΘΕΑΙ. ἴσως.
THEAETETUS: Perhaps.
ΣΩ. πρῶτον μέν γέ που οἰόμενοι συνιέναι ἐκ τῆς ἡμετέρας ἀποκρίσεως τὸν ἐρωτῶντα, ὅταν εἴπωμεν πηλός, εἴτε ὁ τῶν κοροπλαθῶν προσθέντες εἴτε ἄλλων ὡντινωνοῦν δημιουργῶν.
SOCRATES: First, I suppose, because we think the questioner understands something from our answer when we say "clay," whether we add that of the doll-makers or of any other artisans whatsoever.
ἢ οἴει τίς τι συνίησίν τινος ὄνομα, ὃ μὴ οἶδεν τί ἐστιν;
Or do you think anyone understands the name of anything when he does not know what that thing is?
ΘΕΑΙ. οὐδαμῶς.
THEAETETUS: By no means.
ΣΩ. οὐδʼ ἄρα ἐπιστήμην ὑποδημάτων συνίησιν ὁ ἐπιστήμην μὴ εἰδώς.
SOCRATES: Then he does not understand the knowledge of shoes either, if he does not know what knowledge is.
ΘΕΑΙ. οὐ γάρ.
THEAETETUS: No, indeed.
ΣΩ. σκυτικὴν ἄρα οὐ συνίησιν ὃς ἂν ἐπιστήμην ἀγνοῇ, οὐδέ τινα ἄλλην τέχνην.
SOCRATES: Therefore, he who is ignorant of knowledge does not understand shoemaking, nor any other craft.
ΘΕΑΙ. ἔστιν οὕτως.
THEAETETUS: That is so.
ΣΩ. γελοία ἄρα ἡ ἀπόκρισις τῷ ἐρωτηθέντι ἐπιστήμη τί ἐστιν, ὅταν ἀποκρίνηται τέχνης τινὸς ὄνομα. τινὸς γὰρ ἐπιστήμην ἀποκρίνεται οὐ τοῦτʼ ἐρωτηθείς.
SOCRATES: Therefore, the answer is ridiculous when one is asked what knowledge is, if he replies with the name of some craft; for he answers with a knowledge of something, when he was not asked that.
ΘΕΑΙ. ἔοικεν.
THEAETETUS: So it seems.
ΣΩ. ἔπειτά γέ που ἐξὸν φαύλως καὶ βραχέως ἀποκρίνασθαι περιέρχεται ἀπέραντον ὁδόν.
SOCRATES: Secondly, I suppose, when it is possible to answer easily and briefly, he goes in an endless circle.
οἷον καὶ ἐν τῇ τοῦ πηλοῦ ἐρωτήσει φαῦλόν που καὶ ἁπλοῦν εἰπεῖν ὅτι γῆ ὑγρῷ φυραθεῖσα πηλὸς ἂν εἴη, τὸ δʼ ὅτου ἐᾶν χαίρειν.
For instance, in the question about clay, it is simple and easy to say that earth mixed with moisture would be clay, and to let the question of whose clay it is go.
ΘΕΑΙ. ῥᾴδιον, ὦ Σώκρατες, νῦν γε οὕτω φαίνεται·
THEAETETUS: That seems easy now, Socrates, in this way.
ἀτὰρ κινδυνεύεις ἐρωτᾶν οἷον καὶ αὐτοῖς ἡμῖν ἔναγχος εἰσῆλθε διαλεγομένοις, ἐμοί τε καὶ τῷ σῷ ὁμωνύμῳ τούτῳ Σωκράτει.
But you seem to be asking the sort of thing that occurred to us just recently when we were conversing, myself and your namesake here, Socrates.
ΣΩ. τὸ ποῖον δή, ὦ Θεαίτητε;
SOCRATES: What sort of thing was that, Theaetetus?
ΘΕΑΙ. περὶ δυνάμεών τι ἡμῖν Θεόδωρος ὅδε ἔγραφε, τῆς τε τρίποδος πέρι καὶ πεντέποδος ὅτι μήκει οὐ σύμμετροι τῇ ποδιαίᾳ, καὶ οὕτω κατὰ μίαν ἑκάστην προαιρούμενος μέχρι τῆς ἑπτακαιδεκάποδος· ἐν δὲ ταύτῃ πως ἐνέσχετο.
THEAETETUS: Theodorus here was drawing some figures for us about roots, showing that those of three feet and of five feet are not commensurate in length with the unit foot, and so selecting each one individually up to seventeen feet, at which point he somehow stopped.
ἡμῖν οὖν εἰσῆλθέ τι τοιοῦτον, ἐπειδὴ ἄπειροι τὸ πλῆθος αἱ δυνάμεις ἐφαίνοντο, πειραθῆναι συλλαβεῖν εἰς ἕν, ὅτῳ πάσας ταύτας προσαγορεύσομεν τὰς δυνάμεις.
So a thought of this kind occurred to us, since the roots appeared to be infinite in number, to try to collect them into one, by which we could address all these roots.
ΣΩ. ἦ καὶ ηὕρετέ τι τοιοῦτον;
SOCRATES: And did you find any such thing?
ΘΕΑΙ. ἔμοιγε δοκοῦμεν· σκόπει δὲ καὶ σύ.
THEAETETUS: I think we did; but you must consider it too.
ΣΩ. λέγε.
SOCRATES: Speak.
ΘΕΑΙ. τὸν ἀριθμὸν πάντα δίχα διελάβομεν·
THEAETETUS: We divided all numbers into two classes.
τὸν μὲν δυνάμενον ἴσον ἰσάκις γίγνεσθαι τῷ τετραγώνῳ τὸ σχῆμα ἀπεικάσαντες τετράγωνόν τε καὶ ἰσόπλευρον προσείπομεν.
The number which can be formed by multiplying equal by equal, we likened to the square in shape and called it square and equilateral.
ΣΩ. καὶ εὖ γε.
SOCRATES: And very well too.
§148ΘΕΑΙ. τὸν τοίνυν μεταξὺ τούτου, ὧν καὶ τὰ τρία καὶ τὰ πέντε καὶ πᾶς ὃς ἀδύνατος ἴσος ἰσάκις γενέσθαι, ἀλλʼ ἢ πλείων ἐλαττονάκις ἢ ἐλάττων πλεονάκις γίγνεται, μείζων δὲ καὶ ἐλάττων ἀεὶ πλευρὰ αὐτὸν περιλαμβάνει, τῷ προμήκει αὖ σχήματι ἀπεικάσαντες προμήκη ἀριθμὸν ἐκαλέσαμεν.
THEAETETUS: The number, then, between this, of which three and five and every number that is unable to be formed by equal multiplied by equal, but is formed either of more times fewer or fewer times more, and is always enclosed by a larger and smaller side—this we likened to the oblong shape and called it an oblong number.
ΣΩ. κάλλιστα.
SOCRATES: Excellent!
ἀλλὰ τί τὸ μετὰ τοῦτο;
But what after this?
ΘΕΑΙ. ὅσαι μὲν γραμμαὶ τὸν ἰσόπλευρον καὶ ἐπίπεδον ἀριθμὸν τετραγωνίζουσι, μῆκος ὡρισάμεθα, ὅσαι δὲ τὸν ἑτερομήκη, δυνάμεις, ὡς μήκει μὲν οὐ συμμέτρους ἐκείναις, τοῖς δʼ ἐπιπέδοις ἃ δύνανται. καὶ περὶ τὰ στερεὰ ἄλλο τοιοῦτον.
THEAETETUS: All the lines which square the equilateral and plane number, we defined as "length"; and those which square the oblong, we defined as "powers," because, though not commensurate in length with the former, they are commensurate in the planes which they have the power to form.
ΣΩ. ἄριστά γʼ ἀνθρώπων, ὦ παῖδες·
And a similar thing was done concerning solids.
ὥστε μοι δοκεῖ ὁ Θεόδωρος οὐκ ἔνοχος τοῖς ψευδομαρτυρίοις ἔσεσθαι.
SOCRATES: Best of men, my boys!
ΘΕΑΙ. καὶ μήν, ὦ Σώκρατες, ὅ γε ἐρωτᾷς περὶ ἐπιστήμης οὐκ ἂν δυναίμην ἀποκρίνασθαι ὥσπερ περὶ τοῦ μήκους τε καὶ τῆς δυνάμεως.
So it seems to me Theodorus will not be liable to the charge of bearing false witness.
καίτοι σύ γέ μοι δοκεῖς τοιοῦτόν τι ζητεῖν·
THEAETETUS: And yet, Socrates, I could not answer your question about knowledge as I did about length and power.
ὥστε πάλιν αὖ φαίνεται ψευδὴς ὁ Θεόδωρος.
Although you seem to me to be looking for something of that sort; so that Theodorus appears to be false after all.
ΣΩ. τί δέ;
SOCRATES: What?
εἴ σε πρὸς δρόμον ἐπαινῶν μηδενὶ οὕτω δρομικῷ ἔφη τῶν νέων ἐντετυχηκέναι, εἶτα διαθέων τοῦ ἀκμάζοντος καὶ ταχίστου ἡττήθης, ἧττόν τι ἂν οἴει ἀληθῆ τόνδʼ ἐπαινέσαι;
If he had praised you for running, saying he had never met any of the youths who was such a runner, and then you were defeated in a race by the swiftest runner in his prime, do you think he would have praised you with any less truth?
ΘΕΑΙ. οὐκ ἔγωγε.
THEAETETUS: Not I.
ΣΩ. ἀλλὰ τὴν ἐπιστήμην, ὥσπερ νυνδὴ ἐγὼ ἔλεγον, σμικρόν τι οἴει εἶναι ἐξευρεῖν καὶ οὐ τῶν πάντῃ ἄκρων;
SOCRATES: But do you think that finding out what knowledge is, as I was saying just now, is a small thing and not one of the tasks of the very highest class?
ΘΕΑΙ. νὴ τὸν Δίʼ ἔγωγε καὶ μάλα γε τῶν ἀκροτάτων.
THEAETETUS: By Zeus, I think it is indeed of the very highest.
ΣΩ. θάρρει τοίνυν περὶ σαυτῷ καὶ τὶ οἴου Θεόδωρον λέγειν, προθυμήθητι δὲ παντὶ τρόπῳ τῶν τε ἄλλων πέρι καὶ ἐπιστήμης λαβεῖν λόγον τί ποτε τυγχάνει ὄν.
SOCRATES: Be of good courage then about yourself, and believe that there is something in what Theodorus says, and be eager in every way to get a definition of other things and of knowledge, what it actually is.
ΘΕΑΙ. προθυμίας μὲν ἕνεκα, ὦ Σώκρατες, φανεῖται.
THEAETETUS: As far as eagerness is concerned, Socrates, it will be shown.
ΣΩ. ἴθι δή—καλῶς γὰρ ἄρτι ὑφηγήσω—πειρῶ μιμούμενος τὴν περὶ τῶν δυνάμεων ἀπόκρισιν, ὥσπερ ταύτας πολλὰς οὔσας ἑνὶ εἴδει περιέλαβες, οὕτω καὶ τὰς πολλὰς ἐπιστήμας ἑνὶ λόγῳ προσειπεῖν.
SOCRATES: Come then—for you just now guided us beautifully—try, in imitation of your answer about the powers, just as you embraced them, many as they are, in one class, to address also the many knowledges in one definition.
ΘΕΑΙ. ἀλλʼ εὖ ἴσθι, ὦ Σώκρατες, πολλάκις δὴ αὐτὸ ἐπεχείρησα σκέψασθαι, ἀκούων τὰς παρὰ σοῦ ἀποφερομένας ἐρωτήσεις.
THEAETETUS: But you may be sure, Socrates, I have often tried to examine this, when I heard the questions that are reported from you.
ἀλλὰ γὰρ οὔτʼ αὐτὸς δύναμαι πεῖσαι ἐμαυτὸν ὡς ἱκανῶς τι λέγω οὔτʼ ἄλλου ἀκοῦσαι λέγοντος οὕτως ὡς σὺ διακελεύῃ, οὐ μὲν δὴ αὖ οὐδʼ ἀπαλλαγῆναι τοῦ μέλειν.
But indeed I can neither persuade myself that I say anything sufficient, nor hear anyone else speaking in the way you command, yet on the other hand, I cannot rid myself of the concern.
ΣΩ. ὠδίνεις γάρ, ὦ φίλε Θεαίτητε, διὰ τὸ μὴ κενὸς ἀλλʼ ἐγκύμων εἶναι.
SOCRATES: That is because you are in labor, my dear Theaetetus, because you are not empty, but pregnant.
ΘΕΑΙ. οὐκ οἶδα, ὦ Σώκρατες· ὃ μέντοι πέπονθα λέγω.
THEAETETUS: I do not know, Socrates; but I am telling you what I experience.