It is a primæval inspiration (he says) granted by the Gods to man along with the fire of Prometheus, and handed down to us as a tradition from that heroic race who were in nearer kindred with the Gods — That all things said to exist are composed of Unity and Multitude, and include in them a natural coalescence of Finiteness and Infinity.[13] This is the fundamental order of Nature, which we must assume and proceed upon in our investigations. We shall find everywhere the Form of Unity conjoined with the Form of Infinity. But we must not be satisfied simply to find these two forms. We must look farther for those intermediate Forms which lie between the two. Having found the Form of One, we must next search for the Form of Two, Three, Four, or some definite number: and we must not permit ourselves to acquiesce in the Form of Infinite, until no farther definite number can be detected. In other words, we must not be satisfied with knowing only one comprehensive Genus, and individuals comprised under it. We must distribute the Genus into two, three, or more Species: and each of those Species again into two or more sub-species, each characterised by some specific mark: until no more characteristic marks can be discovered upon which to found the establishment of a distinct species. When we reach this limit, and when we have determined the number of subordinate species which the case presents, nothing remains except the indefinite mass and variety of individuals.[14] The whole scheme will thus comprise — The One, the Summum Genus, or Highest Form: The Many, a definite number of Species or sub-Species or subordinate Forms: The Infinite, a countless heap of Individuals.
[13] Plato, Philêbus, p. 16 C. ὡς ἐξ ἑνὸς μὲν καὶ ἐκ πολλῶν ὄντων τῶν ἀεὶ λεγομένων εἶναι, πέρας δὲ καὶ ἀπειρίαν ἑν αὑτοῖς ξύμφυτον ἐχόντων.
[14] Plato, Philêbus, p. 16 D. δεῖν οὖν ἡμᾶς τούτων οὕτω διακεροσμημένων, ἀεὶ μίαν ἰδέαν περὶ παντὸς ἑκάστοτε θεμένους ζητεῖν· εὑρήσειν γὰρ ἐνοῦσαν· ἐὰν οὖν μεταλάβωμεν, μετὰ μίαν δύο, εἴ πως εἰσί, σκοπεῖν, εἰ δὲ μή, τρεῖς ἤ τινα ἄλλον ἀριθμόν, καὶ τὸ ἓν ἐκείνων ἕκαστον πάλιν ὡσαύτως, μέχρι περ ἂν τὸ κατ’ ἀρχὰς ἓν μὴ ὅτι ἓν καὶ πολλὰ καὶ ἄπειρά ἐστι μόνον ἴδῃ τις ἀλλὰ καὶ ὅποσα· τὴν δὲ τοῦ ἀπείρου ἰδέαν πρὸς τὸ πλῆθος μὴ προσφέρειν, πρὶν ἄν τις τὸν ἀριθμὸν αὐτοῦ πάντα κατίδῃ τὸν μεταξὺ τοῦ ἀπείρου τε καὶ τοῦ ἑνός· τότε δ’ ἤδη τὸ ἓν ἕκαστον τῶν πάντων εἰς τὸ ἄπειρον μεθέντα χαίρειν ἐᾷν.
Plato here recognises a Form of the Infinite, ἀπείρου ἰδέαν; again, p. 18 A, ἀπείρου φύσιν.
Mistake commonly made — To look only for the One, and the Infinite Many, without looking for the intermediate subdivisions.
The mistake commonly made (continues Sokrates) by clever men of the present day, is, that they look for nothing beyond the One and the Infinite Many: one comprehensive class, and countless individuals included in it. They take up carelessly any class which strikes them,[15] and are satisfied to have got an indefinite number of individuals under one name. But they never seek for intermediate sub-divisions between the two, so as to be able to discriminate one portion of the class from other by some definite mark, and thus to constitute a sub-class. They do not feel the want of such intermediate sub-divisions, nor the necessity of distinguishing one portion of this immense group of individuals from another. Yet it is exactly upon these discriminating marks that the difference turns, between genuine dialectical argument and controversy without result.[16]
[15] Plato, Philêbus, p. 17 A. οἱ δὲ νῦν τῶν ἀνθρώπων σοφοὶ ἓν μέν, ὅπως ἂν τύχωσι, καὶ πολλὰ θᾶττον καὶ βραδύτερον ποιοῦσι τοῦ δέοντος, μετὰ δὲ τὸ ἓν ἄπειρα εὐθύς, τὰ δὲ μέσα αὐτοὺς ἐκφεύγει, &c.
Stallbaum conjectures that the words καὶ πολλὰ after τύχωσι ought not to be in the text. He proposes to expunge them. The meaning of the passage certainly seems clearer without them.
[16] Plato, Philêbus, p. 17 A. οἷς διακεχώρισται τό τε διαλεκτικῶς πάλιν καὶ τὸ ἐριστικῶς ἡμᾶς ποιεῖσθαι πρὸς ἀλλήλους τοὺς λόγους.