Plato · Theaetetus §204

Examining the Distinction Between the Whole and the Sum

Passage 41 of 45 · Greek

Summary

Socrates questions Theaetetus on the distinction between 'the whole' (τὸ ὅλον) and 'the sum' (τὸ πᾶν), using the counting of numbers as an example to establish that what consists of parts is identical to the sum of its parts.

§204ΣΩ. ἐχέτω δὴ ὡς νῦν φαμεν, μία ἰδέα ἐξ ἑκάστων τῶν συναρμοττόντων στοιχείων γιγνομένη ἡ συλλαβή, ὁμοίως ἔν τε γράμμασι καὶ ἐν τοῖς ἄλλοις ἅπασι.

SOCRATES: Let it be then as we now say: that the syllable is a single form arising from each of the elements that fit together, similarly both in the case of letters and in all other things.

ΘΕΑΙ. πάνυ μὲν οὖν.

THEAETETUS: Absolutely so.

ΣΩ. οὐκοῦν μέρη αὐτῆς οὐ δεῖ εἶναι.

SOCRATES: Therefore, it must not have parts.

ΘΕΑΙ. τί δή;

THEAETETUS: Why so?

ΣΩ. ὅτι οὗ ἂν ᾖ μέρη, τὸ ὅλον ἀνάγκη τὰ πάντα μέρη εἶναι.

SOCRATES: Because, where there are parts, the whole must of necessity be all the parts.

ἢ καὶ τὸ ὅλον ἐκ τῶν μερῶν λέγεις γεγονὸς ἕν τι εἶδος ἕτερον τῶν πάντων μερῶν;

Or do you also say that the whole is some single form arisen from the parts, different from all the parts?

ΘΕΑΙ. ἔγωγε.

THEAETETUS: I do.

ΣΩ. τὸ δὲ δὴ πᾶν καὶ τὸ ὅλον πότερον ταὐτὸν καλεῖς ἢ ἕτερον ἑκάτερον;

SOCRATES: But then do you call 'the sum' and 'the whole' the same thing, or is each of them different?

ΘΕΑΙ. ἔχω μὲν οὐδὲν σαφές, ὅτι δὲ κελεύεις προθύμως ἀποκρίνασθαι, παρακινδυνεύων λέγω ὅτι ἕτερον.

THEAETETUS: I have nothing clear in mind, but because you bid me answer eagerly, risking it, I say that they are different.

ΣΩ. ἡ μὲν προθυμία, ὦ Θεαίτητε, ὀρθή· εἰ δὲ καὶ ἡ ἀπόκρισις, σκεπτέον.

SOCRATES: Your eagerness, Theaetetus, is right; but whether your answer is also, must be examined.

ΘΕΑΙ. δεῖ γε δή.

THEAETETUS: It certainly must.

ΣΩ. οὐκοῦν διαφέροι ἂν τὸ ὅλον τοῦ παντός, ὡς ὁ νῦν λόγος;

SOCRATES: Therefore, the whole would differ from the sum, according to the present argument?

ΘΕΑΙ. ναί.

THEAETETUS: Yes.

ΣΩ. τί δὲ δή;

SOCRATES: What about this?

τὰ πάντα καὶ τὸ πᾶν ἔσθʼ ὅτι διαφέρει;

Is there any difference between 'all things' and 'the sum'?

οἷον ἐπειδὰν λέγωμεν ἕν, δύο, τρία, τέτταρα, πέντε, ἕξ, καὶ ἐὰν δὶς τρία ἢ τρὶς δύο ἢ τέτταρά τε καὶ δύο ἢ τρία καὶ δύο καὶ ἕν, πότερον ἐν πᾶσι τούτοις τὸ αὐτὸ ἢ ἕτερον λέγομεν;

For instance, when we say 'one, two, three, four, five, six', and if we say 'twice three' or 'thrice two' or 'four and two' or 'three and two and one', do we in all these cases speak of the same thing or something different?

ΘΕΑΙ. τὸ αὐτό.

THEAETETUS: The same.

ΣΩ. ἆρʼ ἄλλο τι ἢ ἕξ;

SOCRATES: Is it anything other than six?

ΘΕΑΙ. οὐδέν.

THEAETETUS: Nothing.

ΣΩ. οὐκοῦν ἐφʼ ἑκάστης λέξεως πάντα ἓξ εἰρήκαμεν;

SOCRATES: Therefore, in each way of speaking, have we not spoken of all six?

ΘΕΑΙ. ναί.

THEAETETUS: Yes.

ΣΩ. πᾶν δʼ οὐδὲν λέγομεν τὰ πάντα λέγοντες;

SOCRATES: And do we not speak of a sum when we say 'all things'?

ΘΕΑΙ. ἀνάγκη.

THEAETETUS: Necessarily.

ΣΩ. ἦ ἄλλο τι ἢ τὰ ἕξ;

SOCRATES: Is it anything other than the six?

ΘΕΑΙ. οὐδέν.

THEAETETUS: Nothing.

ΣΩ. ταὐτὸν ἄρα ἔν γε τοῖς ὅσα ἐξ ἀριθμοῦ ἐστι τό τε πᾶν προσαγορεύομεν καὶ τὰ ἅπαντα;

SOCRATES: Therefore, at least in the case of things that consist of number, do we call 'the sum' and 'all things' the same?

ΘΕΑΙ. φαίνεται.

THEAETETUS: So it appears.

ΣΩ. ὧδε δὴ περὶ αὐτῶν λέγωμεν.

SOCRATES: Let us speak of them in this way.

ὁ τοῦ πλέθρου ἀριθμὸς καὶ τὸ πλέθρον ταὐτόν·

Is the number of the plethron and the plethron itself the same?

ἦ γάρ;

Is it not?

ΘΕΑΙ. ναί.

THEAETETUS: Yes.

ΣΩ. καὶ ὁ τοῦ σταδίου δὴ ὡσαύτως.

SOCRATES: And that of the stadion likewise.

ΘΕΑΙ. ναί.

THEAETETUS: Yes.

ΣΩ. καὶ μὴν καὶ ὁ τοῦ στρατοπέδου γε καὶ τὸ στρατόπεδον, καὶ πάντα τὰ τοιαῦτα ὁμοίως;

SOCRATES: And indeed also the number of the army and the army, and all such things likewise?

ὁ γὰρ ἀριθμὸς πᾶς τὸ ὂν πᾶν ἕκαστον αὐτῶν ἐστιν.

For the entire number is the entire being of each of them.

ΘΕΑΙ. ναί.

THEAETETUS: Yes.

ΣΩ. ὁ δὲ ἑκάστων ἀριθμὸς μῶν ἄλλο τι ἢ μέρη ἐστίν;

SOCRATES: And is the number of each of them anything other than parts?

ΘΕΑΙ. οὐδέν.

THEAETETUS: Nothing.

ΣΩ. ὅσα ἄρα ἔχει μέρη, ἐκ μερῶν ἂν εἴη;

SOCRATES: Therefore, whatever has parts would consist of parts?

ΘΕΑΙ. φαίνεται.

THEAETETUS: So it appears.

ΣΩ. τὰ δέ γε πάντα μέρη τὸ πᾶν εἶναι ὡμολόγηται, εἴπερ καὶ ὁ πᾶς ἀριθμὸς τὸ πᾶν ἔσται.

SOCRATES: But indeed all the parts have been agreed to be the sum, if indeed the entire number is to be the sum.

ΘΕΑΙ. οὕτως.

THEAETETUS: That is so.

ΣΩ. τὸ ὅλον ἄρʼ οὐκ ἔστιν ἐκ μερῶν. πᾶν γὰρ ἂν εἴη τὰ πάντα ὂν μέρη.

SOCRATES: Therefore, the whole is not made of parts; for if it were, it would be the sum, being all the parts.

ΘΕΑΙ. οὐκ ἔοικεν.

THEAETETUS: It does not seem so.

ΣΩ. μέρος δʼ ἔσθʼ ὅτου ἄλλου ἐστὶν ὅπερ ἐστὶν ἢ τοῦ ὅλου;

SOCRATES: But is a part a part of anything else than the whole?

ΘΕΑΙ. τοῦ παντός γε.

THEAETETUS: Of the sum, at least.

Notes

204aἐχέτω δὴ ὡς νῦν φαμεν — The third-person singular active imperative ἐχέτω of ἔχω is used here intransitively or impersonally (with 'the matter' implied as subject), meaning 'let it be so' or 'let it hold' as a tentative premise.
204aὅτι οὗ ἂν ᾖ μέρη, τὸ ὅλον ἀνάγκη τὰ πάντα μέρη εἶναι. — The genitive relative pronoun οὗ depends on μέρη ('parts of which'). The main clause is governed by the impersonal ἀνάγκη with an accusative and infinitive construction: τὸ ὅλον as the subject accusative, τὰ πάντα μέρη as the predicate, and εἶναι as the infinitive.
204dὁ γὰρ ἀριθμὸς πᾶς τὸ ὂν πᾶν ἕκαστον αὐτῶν ἐστιν. — While ὁ ἀριθμὸς πᾶς ('the entire number') is the subject, τὸ ὂν πᾶν ('the whole being/existence') functions as the predicate of ἕκαστον αὐτῶν ('each of them'), asserting a strict equivalence between numerical totality and existential reality.
204eμέρος δʼ ἔσθʼ ὅτου ἄλλου ἐστὶν ὅπερ ἐστὶν ἢ τοῦ ὅλου; — The relative clause ὅπερ ἐστίν ('which indeed it is') functions idiomatically to emphasize the essential nature of the part as a part (i.e. 'a part, being precisely what it is'). ὅτου ἄλλου ... ἢ τοῦ ὅλου constitutes a genitive of comparison/relation ('of any other thing than the whole').

Cite this passage

Plato, Theaetetus §204. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0059.tlg006.humanitext-grc2:204

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