Authors/Aristotle/metaphysics/l5/c15

Chapter 15 Relative

Greek	Latin	English
πρός τι λέγεται τὰ μὲν ὡς διπλάσιον πρὸς ἥμισυ καὶ τριπλάσιον πρὸς τριτημόριον, καὶ ὅλως πολλαπλάσιον πρὸς πολλοστημόριον καὶ ὑπερέχον πρὸς ὑπερεχόμενον: τὰ δ᾽ ὡς τὸ θερμαντικὸν πρὸς τὸ θερμαντὸν καὶ τὸ τμητικὸν πρὸς τὸ [30] τμητόν, καὶ ὅλως τὸ ποιητικὸν πρὸς τὸ παθητικόν: τὰ δ᾽ ὡς τὸ μετρητὸν πρὸς τὸ μέτρον καὶ ἐπιστητὸν πρὸς ἐπιστήμην καὶ αἰσθητὸν πρὸς αἴσθησιν.	Ad aliquid dicuntur alia ut duplum ad dimidium et triplum ad tertiam partem, et totaliter multiplicatum ad multiplicati partem et continens ad contentum. Alia ut calefactivum ↵ ad calefactibile et sectivum ad secabile, et omne activum ad passivum. Alia ut mensurabile ad mensuram et scibile ad scientiam et sensibile ad sensum.	Chapter 15. Things are relative (1) as double to half, and treble to a third, and in general that which contains something else many times to that which is contained many times in something else, and that which exceeds to that which is exceeded; (2) as that which can heat to that which can be heated, and that which can cut to that which can be cut, and in general the active to the passive; (3) as the measurable to the measure, and the knowable to knowledge, and the perceptible to perception.
λέγεται δὲ τὰ μὲν πρῶτα κατ᾽ ἀριθμὸν ἢ ἁπλῶς ἢ ὡρισμένως, πρὸς αὐτοὺς ἢ πρὸς ἕν (οἷον τὸ μὲν διπλάσιον πρὸς ἓν ἀριθμὸς ὡρισμένος, τὸ δὲ πολλαπλάσιον [35] κατ᾽ ἀριθμὸν πρὸς ἕν, οὐχ ὡρισμένον δέ, οἷον τόνδε ἢ τόνδε: [1021α] [1] τὸ δὲ ἡμιόλιον πρὸς τὸ ὑφημιόλιον κατ᾽ ἀριθμὸν πρὸς ἀριθμὸν ὡρισμένον: τὸ δ᾽ ἐπιμόριον πρὸς τὸ ὑπεπιμόριον κατὰ ἀόριστον, ὥσπερ τὸ πολλαπλάσιον πρὸς τὸ ἕν: τὸ δ᾽ ὑπερέχον πρὸς τὸ ὑπερεχόμενον ὅλως ἀόριστον κατ᾽ ἀριθμόν: [5] ὁ γὰρ ἀριθμὸς σύμμετρος, κατὰ μὴ συμμέτρου δὲ ἀριθμὸς οὐ λέγεται, τὸ δὲ ὑπερέχον πρὸς τὸ ὑπερεχόμενον τοσοῦτόν τέ ἐστι καὶ ἔτι, τοῦτο δ᾽ ἀόριστον: ὁπότερον γὰρ ἔτυχέν ἐστιν, ἢ ἴσον ἢ οὐκ ἴσον): ταῦτά τε οὖν τὰ πρός τι πάντα κατ᾽ ἀριθμὸν λέγεται καὶ ἀριθμοῦ πάθη,	Dicuntur autem prima quidem secundum numerum aut simpliciter aut determinate, ad ipsos aut ad unum. Ut duplum qui↵dem ad unum numerus determinatus; multiplex vero secundum numerum ad unum, non determinatum autem, ut hunc ↵ aut hunc; emiolium autem ad subemiolium secundum numerum ad numerum determinatum; superparticulare autem ad subsuperparticulare secundum indeterminatos, ut multiplex ad unum . Continens autem ad contentum omnino indetermina↵tum secundum numerum; numerus enim commensurabilis, secundum non commensurabilem autem numerum dicuntur; ƿ continens enim ad contentum tantumque est et amplius, hoc autem indeterminatum; quodcumque enim evenit est, aut equale aut non equale. Haec igitur ad aliquid omnia secundum numerum dicuntur et numeri passiones.	(1) Relative terms of the first kind are numerically related either indefinitely or definitely, to numbers themselves or to 1. E.g. the double is in a definite numerical relation to 1, and that which is many times as great is in a numerical, but not a definite, relation to 1, i.e. not in this [21a] or in that numerical relation to it; the relation of that which is half as big again as something else to that something is a definite numerical relation to a number; that which is n+1/n times something else is in an indefinite relation to that something, as that which is many times as great is in an indefinite relation to 1; the relation of that which exceeds to that which is exceeded is numerically quite indefinite; for number is always commensurate, and number is not predicated of that which is not commensurate, but that which exceeds is, in relation to that which is exceeded, so much and something more; and this something is indefinite; for it can, indifferently, be either equal or not equal to that which is exceeded. – All these relations, then, are numerically expressed and are determinations of number,
καὶ ἔτι τὸ ἴσον καὶ [10] ὅμοιον καὶ ταὐτὸ κατ᾽ ἄλλον τρόπον (κατὰ γὰρ τὸ ἓν λέγεται πάντα, ταὐτὰ μὲν γὰρ ὧν μία ἡ οὐσία, ὅμοια δ᾽ ὧν ἡ ποιότης μία, ἴσα δὲ ὧν τὸ ποσὸν ἕν: τὸ δ᾽ ἓν τοῦ ἀριθμοῦ ἀρχὴ καὶ μέτρον, ὥστε ταῦτα πάντα πρός τι λέγεται κατ᾽ ἀριθμὸν μέν, οὐ τὸν αὐτὸν δὲ τρόπον):	Et amplius equale et simile et idem secundum alium modum; secundum enim ↵ unum dicuntur omnia. Eadem namque quorum una est substantia, similia vero quorum qualitas est una, equalia vero quorum quantitas est una; unum autem numeri principium et metrum, quare haec omnia ad aliquid dicuntur secundum numerum quidem, non eodem autem modo.	and so in another way are the equal and the like and the same. For all refer to unity. Those things are the same whose substance is one; those are like whose quality is one; those are equal whose quantity is one; and 1 is the beginning and measure of number, so that all these relations imply number, though not in the same way.
τὰ δὲ [15] ποιητικὰ καὶ παθητικὰ κατὰ δύναμιν ποιητικὴν καὶ παθητικὴν καὶ ἐνεργείας τὰς τῶν δυνάμεων, οἷον τὸ θερμαντικὸν πρὸς τὸ θερμαντὸν ὅτι δύναται, καὶ πάλιν τὸ θερμαῖνον πρὸς τὸ θερμαινόμενον καὶ τὸ τέμνον πρὸς τὸ τεμνόμενον ὡς ἐνεργοῦντα. τῶν δὲ κατ᾽ ἀριθμὸν οὐκ εἰσὶν ἐνέργειαι ἀλλ᾽ [20] ἢ ὃν τρόπον ἐν ἑτέροις εἴρηται: αἱ δὲ κατὰ κίνησιν ἐνέργειαι οὐχ ὑπάρχουσιν. τῶν δὲ κατὰ δύναμιν καὶ κατὰ χρόνους ἤδη λέγονται πρός τι οἷον τὸ πεποιηκὸς πρὸς τὸ πεποιημένον καὶ τὸ ποιῆσον πρὸς τὸ ποιησόμενον. οὕτω γὰρ καὶ πατὴρ υἱοῦ λέγεται πατήρ: τὸ μὲν γὰρ πεποιηκὸς τὸ δὲ πεπονθός [25] τί ἐστιν. ἔτι ἔνια κατὰ στέρησιν δυνάμεως, ὥσπερ τὸ ἀδύνατον καὶ ὅσα οὕτω λέγεται, οἷον τὸ ἀόρατον.	Activa vero et passiva secundum potentiam activam et pas↵sivam sunt et actiones potentiarum; ut calefactivum ad calefactibile quia potest, et iterum calefaciens ad id quod calefit et secans ad id quod secatur tamquam agentia. Eorum vero quae sunt secundum numerum non sunt actiones sed aut quomodo ↵ in aliis dictum est; quae autem secundum motum actiones non existunt. Eorum autem quae secundum potentiam et secundum tempora iam dicuntur ad aliquid, ut quod fecit ad factum * et facturum ad faciendum. Sic enim pater filii dicitur pater; hoc quidem enim fecit, illud autem passum quid est. Amplius ↵ quaedam secundum privationem potentie, ut impossibile et quaecumque sic dicuntur, ut invisibile.	(2) Things that are active or passive imply an active or a passive potency and the actualizations of the potencies; e.g. that which is capable of heating is related to that which is capable of being heated, because it can heat it, and, again, that which heats is related to that which is heated and that which cuts to that which is cut, in the sense that they actually do these things. But numerical relations are not actualized except in the sense which has been elsewhere stated; actualizations in the sense of movement they have not. Of relations which imply potency some further imply particular periods of time, e.g. that which has made is relative to that which has been made, and that which will make to that which will be made. For it is in this way that a father is called the father of his son; for the one has acted and the other has been acted on in a certain way. Further, some relative terms imply privation of potency, i.e. incapable and terms of this sort, e.g. invisible .
τὰ μὲν οὖν κατ᾽ ἀριθμὸν καὶ δύναμιν λεγόμενα πρός τι πάντα ἐστὶ πρός τι τῷ ὅπερ ἐστὶν ἄλλου λέγεσθαι αὐτὸ ὅ ἐστιν, ἀλλὰ μὴ τῷ ἄλλο πρὸς ἐκεῖνο: τὸ δὲ μετρητὸν καὶ τὸ ἐπιστητὸν καὶ τὸ [30] διανοητὸν τῷ ἄλλο πρὸς αὐτὸ λέγεσθαι πρός τι λέγονται. τό τε γὰρ διανοητὸν σημαίνει ὅτι ἔστιν αὐτοῦ διάνοια, οὐκ ἔστι δ᾽ ἡ διάνοια πρὸς τοῦτο οὗ ἐστὶ διάνοια (δὶς γὰρ ταὐτὸν εἰρημένον ἂν εἴη), ὁμοίως δὲ καὶ τινός ἐστιν ἡ ὄψις ὄψις, οὐχ οὗ ἐστὶν ὄψις (καίτοι γ᾽ ἀληθὲς τοῦτο εἰπεῖν) ἀλλὰ πρὸς χρῶμα ἢ πρὸς ἄλλο τι τοιοῦτον. ἐκείνως δὲ δὶς τὸ αὐτὸ λεχθήσεται, ὅτι ἐστὶν οὗ ἐστὶν ἡ ὄψις.	Secundum numerum quidem igitur et potentiam dicta ad aliquid omnia sunt ad aliquid eo quod quod quidem est alterius dicitur ipsum quod est, sed non eo quod aliud ad illud; mensurabile vero et scibile et intellectuale eo quod aliud ↵ ad ipsum dicitur ad aliquid dicuntur. Nam intellectuale significat quia ipsius est intellectus, non est autem intellectus ad hoc cuius est intellectus; bis enim idem dictum utique erit. Similiter autem et alicuius visus est visus, non cuius est ↵ ƿ visus (* quamvis verum hoc dicere) sed ad colorem aut ad aliud aliquid tale. Illo vero modo bis idem dicetur: quia est visus cuius est visus.	Relative terms which imply number or potency, therefore, are all relative because their very essence includes in its nature a reference to something else, not because something else involves a reference to it; but (3) that which is measurable or knowable or thinkable is called relative because something else involves a reference to it. For that which is thinkable implies that the thought of it is possible, but the thought is not relative to that of which it is the thought ; for we should then have said the same thing twice. Similarly sight is the sight of something, not of that of which it is the sight (though of course it is true [21b] to say this); in fact it is relative to colour or to something else of the sort. But according to the other way of speaking the same thing would be said twice, – the sight is of that of which it is.
[1021β] [1] τὰ μὲν οὖν καθ᾽ ἑαυτὰ λεγόμενα πρός τι τὰ μὲν οὕτω λέγεται,τὰ δὲ ἂν τὰ [5] γένη αὐτῶν ᾖ τοιαῦτα, οἷον ἡ ἰατρικὴ τῶν πρός τι ὅτι τὸ γένος αὐτῆς ἡ ἐπιστήμη δοκεῖ εἶναι πρός τι: ἔτι καθ᾽ ὅσα τὰ ἔχοντα λέγεται πρός τι, οἷον ἰσότης ὅτι τὸ ἴσον καὶ ὁμοιότης ὅτι τὸ ὅμοιον:	Secundum se quidem igitur dicta ad aliquid haec quidem ↵ sic dicuntur, illa vero si ipsorum genera sint talia, ut medicina eorum quae ad aliquid quia ipsius genus scientia videtur esse eorum quae ad aliquid. Amplius secundum quaecumque habentia dicuntur ad aliquid, ut equalitas quia equale et similitudo quia simile.	Things that are by their own nature called relative are called so sometimes in these senses, sometimes if the classes that include them are of this sort; e.g. medicine is a relative term because its genus, science, is thought to be a relative term. Further, there are the properties in virtue of which the things that have them are called relative, e.g. equality is relative because the equal is, and likeness because the like is.
τὰ δὲ κατὰ συμβεβηκός, οἷον ἅνθρωπος πρός τι ὅτι συμβέβηκεν αὐτῷ διπλασίῳ εἶναι, [10] τοῦτο δ᾽ ἐστὶ τῶν πρός τι: ἢ τὸ λευκόν, εἰ τῷ αὐτῷ συμβέβηκε διπλασίῳ καὶ λευκῷ εἶναι.	Alia vero secundum accidens, ut homo ad aliquid quia ↵ ei accidit duplum esse, hoc autem est eorum quae ad aliquid; aut album, si accidit eidem album * et duplum esse.	Other things are relative by accident; e.g. a man is relative because he happens to be double of something and double is a relative term; or the white is relative, if the same thing happens to be double and white.