Authors/Aristotle/metaphysics/l10/c6

Chapter 6

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ὁμοίως δὲ καὶ περὶ τοῦ ἑνὸς καὶ τῶν πολλῶν ἀπορήσειεν ἄν τις. εἰ γὰρ τὰ πολλὰ τῷ ἑνὶ ἁπλῶς ἀντίκειται, [5] συμβαίνει ἔνια ἀδύνατα.	Similiter autem et de uno et multis dubitabit utique ali↵quis. Nam si multa simpliciter uni opponuntur, accidunt quaedam impossibilia *.	Chapter 6. We might raise similar questions about the one and the many. For if the many are absolutely opposed to the one, certain impossible results follow.
τὸ γὰρ ἓν ὀλίγον ἢ ὀλίγα ἔσται: τὰ γὰρ πολλὰ καὶ τοῖς ὀλίγοις ἀντίκειται. ἔτι τὰ δύο πολλά, εἴπερ τὸ διπλάσιον πολλαπλάσιον λέγεται δὲ κατὰ τὰ δύο: ὥστε τὸ ἓν ὀλίγον: πρὸς τί γὰρ πολλὰ τὰ δύο εἰ μὴ πρὸς ἕν τε καὶ τὸ ὀλίγον; οὐθὲν γάρ ἐστιν ἔλαττον.	Nam unum * paucum aut pauca erit; nam multa et paucis opponuntur. Amplius ipsa duo sunt multa, si duplex * multiplex, dicitur autem secundum duo. Quare unum * paucum; ad quid enim sunt multa ipsa duo nisi ad ƿ unum et paucum? Nihil enim est minus.	One will then be few, whether few be treated here as singular or plural; for the many are opposed also to the few. Further, two will be many, since the double is multiple and double derives its meaning from two ; therefore one will be few; for what is that in comparison with which two are many, except one, which must therefore be few? For there is nothing fewer.
[10] ἔτι εἰ ὡς ἐν μήκει τὸ μακρὸν καὶ βραχύ, οὕτως ἐν πλήθει τὸ πολὺ καὶ ὀλίγον, καὶ ὃ ἂν ᾖ πολὺ καὶ πολλά, καὶ τὰ πολλὰ πολύ (εἰ μή τι ἄρα διαφέρει ἐν συνεχεῖ εὐορίστῳ), τὸ ὀλίγον πλῆθός τι ἔσται. ὥστε τὸ ἓν πλῆθός τι, εἴπερ καὶ ὀλίγον: τοῦτο δ᾽ ἀνάγκη, εἰ τὰ δύο πολλά.	Amplius si ut in ↵ longitudine productum et breue, sic in multitudine multum et paucum, et quodcumque fuerit multum et multa, et multa multum (si non aliquid forte differat in continuo bene terminabili): paucum multitudo quaedam erit. Quare unum multitudo quaedam est, siquidem et paucum. Hoc autem necesse, si duo sunt multa.	Further, if the much and the little are in plurality what the long and the short are in length, and whatever is much is also many, and the many are much (unless, indeed, there is a difference in the case of an easily-bounded continuum), the little (or few) will be a plurality. Therefore one is a plurality if it is few; and this it must be, if two are many.
[15] ἴσως τὰ πολλὰ λέγεται μέν πως καὶ [τὸ] πολύ, ἀλλ᾽ ὡς διαφέρον, οἷον ὕδωρ πολύ, πολλὰ δ᾽ οὔ. ἀλλ᾽ ὅσα διαιρετά, ἐν τούτοις λέγεται,	Sed forsan multa dicuntur quidem ut et multum, sed ut dif↵ferens; velut ydor id est aqua multum, multa autem non. Sed quaecumque divisa, in hiis dicitur.	But perhaps, while the many are in a sense said to be also much , it is with a difference; e.g. water is much but not many. But many is applied to the things that are divisible;
ἕνα μὲν τρόπον ἐὰν ᾖ πλῆθος ἔχον ὑπεροχὴν ἢ ἁπλῶς ἢ πρός τι (καὶ τὸ ὀλίγον ὡσαύτως πλῆθος ἔχον ἔλλειψιν), τὸ δὲ ὡς ἀριθμός, ὃ καὶ ἀντίκειται τῷ ἑνὶ [20] μόνον. οὕτως γὰρ λέγομεν ἓν ἢ πολλά, ὥσπερ εἴ τις εἴποι ἓν καὶ ἕνα ἢ λευκὸν καὶ λευκά, καὶ τὰ μεμετρημένα πρὸς τὸ μέτρον [καὶ τὸ μετρητόν]: οὕτως καὶ τὰ πολλαπλάσια λέγεται: πολλὰ γὰρ ἕκαστος ὁ ἀριθμὸς ὅτι ἕνα καὶ ὅτι μετρητὸς ἑνὶ ἕκαστος, καὶ ὡς τὸ ἀντικείμενον τῷ ἑνί, οὐ τῷ [25] ὀλίγῳ. οὕτω μὲν οὖν ἐστὶ πολλὰ καὶ τὰ δύο, ὡς δὲ πλῆθος ἔχον ὑπεροχὴν ἢ πρός τι ἢ ἁπλῶς οὐκ ἔστιν, ἀλλὰ πρῶτον. ὀλίγα δ᾽ ἁπλῶς τὰ δύο: πλῆθος γάρ ἐστιν ἔλλειψιν ἔχον πρῶτον	Uno quidem modo si fuerit multitudo habens excedentiam aut simpliciter aut ad aliquid; et paucum similiter multitudo defectum habens. Hoc autem ut numerus, quod et opponitur uni solum. Ita enim ↵ dicimus * unum aut multa, ut si quis dicat unum et una aut album et alba, et mensurata ad metrum et mensurabile. Sic et multiplicia dicuntur. Multa enim unusquisque numerus quia unum et quia mensurabilis uno unusquisque, et ut quod oppoƿ↵nitur uni, non pauco. Sic igitur sunt multa et ipsa duo, ut autem multitudo habens excedentiam aut ad aliquid aut simpliciter non sunt. Sed primum pauca simpliciter ipsa duo; multitudo enim est defectum habens prima.	in the one sense it means a plurality which is excessive either absolutely or relatively (while few is similarly a plurality which is deficient), and in another sense it means number, in which sense alone it is opposed to the one. For we say one or many , just as if one were to say one and ones or white thing and white things , or to compare the things that have been measured with the measure. It is in this sense also that multiples are so called. For each number is said to be many because it consists of ones and because each number is measurable by one; and it is many as that which is opposed to one, not to the few. In this sense, then, even two is many-not, however, in the sense of a plurality which is excessive either relatively or absolutely; it is the first plurality. But without qualification two is few; for it is first plurality which is deficient
(διὸ καὶ οὐκ ὀρθῶς ἀπέστη Ἀναξαγόρας εἰπὼν ὅτι ὁμοῦ πάντα χρήματα ἦν ἄπειρα καὶ πλήθει καὶ μικρότητι, [30] ἔδει δ᾽ εἰπεῖν ἀντὶ τοῦ "καὶ μικρότητι""καὶ ὀλιγότητι": οὐ γὰρ ἄπειρα), ἐπεὶ τὸ ὀλίγον οὐ διὰ τὸ ἕν, ὥσπερ τινές φασιν, ἀλλὰ διὰ τὰ δύο.	Quapropter non recte destitit Anaxagoras cum dixisset quia simul omnes res erant, infinite et multitudine et parvui↵tate, oportebat autem dicere pro * ‘et paruitate’ ‘et paucitate’. Non enim infinite, quoniam paucum non propter unum, ut quidam dicunt, sed propter duo.	(for this reason Anaxagoras was not right in leaving the subject with the statement that "all things were together, boundless both in plurality and in smallness" – where for "and in smallness" he should have said "and in fewness"; for they could not have been boundless in fewness), since it is not one, as some say, but two, that make a few.
ἀντίκειται δὴ τὸ ἓν καὶ τὰ πολλὰ τὰ ἐν ἀριθμοῖς ὡς μέτρον μετρητῷ: ταῦτα δὲ ὡς τὰ πρός τι, ὅσα μὴ καθ᾽ αὑτὰ τῶν πρός τι. διῄρηται δ᾽ [35] ἡμῖν ἐν ἄλλοις ὅτι διχῶς λέγεται τὰ πρός τι, τὰ μὲν ὡς ἐναντία, τὰ δ᾽ ὡς ἐπιστήμη πρὸς ἐπιστητόν, τῷ λέγεσθαί τι ἄλλο πρὸς αὐτό.	Opponitur itaque unum multis ut metrum mensurabili; haec autem ut quae ad aliquid, quaecumque non secundum se eorum ↵ quae * ad aliquid. Divisum autem est a nobis in aliis quia dupliciter dicuntur quae ad aliquid, alia namque ut contraria, alia ↵ ut scientia ad scibile, quia dicitur aliquid aliud ad ipsum.	The one is opposed then to the many in numbers as measure to thing measurable; and these are opposed as are the relatives which are not from their very nature relatives. We have distinguished elsewhere the two senses in which relatives are so called: – (1) as contraries; (2) as knowledge to thing known, a term being called relative [57a] because another is relative to it.
[1057α] [1] τὸ δὲ ἓν ἔλαττον εἶναι τινός, οἷον τοῖν δυοῖν, οὐδὲν κωλύει: οὐ γάρ, εἰ ἔλαττον, καὶ ὀλίγον. τὸ δὲ πλῆθος οἷον γένος ἐστὶ τοῦ ἀριθμοῦ: ἔστι γὰρ ἀριθμὸς πλῆθος ἑνὶ μετρητόν, καὶ ἀντίκειταί πως τὸ ἓν καὶ ἀριθμός, οὐχ ὡς [5] ἐναντίον ἀλλ᾽ ὥσπερ εἴρηται τῶν πρός τι ἔνια: ᾗ γὰρ μέτρον τὸ δὲ μετρητόν, ταύτῃ ἀντίκειται, διὸ οὐ πᾶν ὃ ἂν ᾖ ἓν ἀριθμός ἐστιν, οἷον εἴ τι ἀδιαίρετόν ἐστιν.	Unum autem esse minus aliquo, puta duobus, nihil prohibet; non enim si minus, et paucum. Multitudo autem quasi genus est numeri; est enim numerus multitudo uno mensurabilis. Et ↵ opponuntur aliqualiter unum et numerus, non ut contrarium sed sicut dictum est eorum quae ad aliquid quaedam; in quantum enim metrum, hoc * autem mensurabile: sic opponuntur. Quapropter non omne quodcumque fuerit unum numerus est, puta si quid indivisum est.	There is nothing to prevent one from being fewer than something, e.g. than two; for if one is fewer, it is not therefore few. Plurality is as it were the class to which number belongs; for number is plurality measurable by one, and one and number are in a sense opposed, not as contrary, but as we have said some relative terms are opposed; for inasmuch as one is measure and the other measurable, they are opposed. This is why not everything that is one is a number; i.e. if the thing is indivisible it is not a number.
ὁμοίως δὲ λεγομένη ἡ ἐπιστήμη πρὸς τὸ ἐπιστητὸν οὐχ ὁμοίως ἀποδίδωσιν. δόξειε μὲν γὰρ ἂν μέτρον ἡ ἐπιστήμη εἶναι τὸ δὲ ἐπιστητὸν [10] τὸ μετρούμενον, συμβαίνει δὲ ἐπιστήμην μὲν πᾶσαν ἐπιστητὸν εἶναι τὸ δὲ ἐπιστητὸν μὴ πᾶν ἐπιστήμην, ὅτι τρόπον τινὰ ἡ ἐπιστήμη μετρεῖται τῷ ἐπιστητῷ.	Similiter autem dicta scientia ad scibile, non similiter assignatur. Videbitur enim utique scien↵tia metrum esse, scibile vero quod mensuratur; accidit autem scientiam quidem omnem scibile esse, scibile vero non omne scientiam, quia modo quodam scientia mensuratur scibili.	But though knowledge is similarly spoken of as relative to the knowable, the relation does not work out similarly; for while knowledge might be thought to be the measure, and the knowable the thing measured, the fact that all knowledge is knowable, but not all that is knowable is knowledge, because in a sense knowledge is measured by the knowable.
τὸ δὲ πλῆθος οὔτε τῷ ὀλίγῳ ἐναντίον—ἀλλὰ τούτῳ μὲν τὸ πολὺ ὡς ὑπερέχον πλῆθος ὑπερεχομένῳ πλήθει—οὔτε τῷ ἑνὶ πάντως: ἀλλὰ τὸ μὲν [15] ὥσπερ εἴρηται, ὅτι διαιρετὸν τὸ δ᾽ ἀδιαίρετον, τὸ δ᾽ ὡς πρός τι ὥσπερ ἡ ἐπιστήμη ἐπιστητῷ, ἐὰν ᾖ ἀριθμὸς τὸ δ᾽ ἓν μέτρον.	Multitudo autem nec pauco est contraria — Sed huic quidem mulƿtum sicut excedens multitudo excesse multitudini — * neque ipsi uni omni modo; sed hoc quidem ut dictum est, quia divisi↵bile illud vero indivisibile, hoc * ut ad aliquid ut scientia scibili, si fuerit numerus * unum vero metrum.	Plurality is contrary neither to the few (the many being contrary to this as excessive plurality to plurality exceeded), nor to the one in every sense; but in the one sense these are contrary, as has been said, because the former is divisible and the latter indivisible, while in another sense they are relative as knowledge is to knowable, if plurality is number and the one is a measure.