§B.65## τὸ πρότερον — τὸ ὕστερον.
## The prior — the posterior.
τὸ πρότερον λέγεται πενταχῶς.
The prior is said in five ways.
ἢ γὰρ φύσει ἢ χρόνῳ ἢ δυνάμει ἢ θέσει ἢ τάξει λεχθήσεται.
For it will be said either by nature, by time, by power, by position, or by order.
θέσει μὲν οὖν, οἷον ὃ ἐπὶ τῶν κειμένων ψήφων εἰώθαμεν λέγειν, οἷον ὅτι προτέρα αὕτη ταύτης.
Now by position, for example, is that which we are accustomed to say in the case of placed counters, for instance that this one is prior to that one.
τάξει δέ, οἷον ὁ ταξίαρχος τοῦ λοχαγοῦ καὶ ὁ λοχαγὸς τοῦ ἰδιώτου καὶ τὸ ᾱ τοῦ β.
And by order, for example, the commander is prior to the captain, and the captain to the private, and alpha to beta.
δυνάμει δέ φαμεν εἶναι πρότερον τὸν στρατηγὸν τοῦ στρατιώτου καὶ ἁπλῶς τὸν δυνάστην τοῦ ἰδιώτου.
And by power we say that the general is prior to the soldier, and simply the ruler to the private citizen.
χρόνῳ δέ, οἷον πατὴρ υἱοῦ καὶ πᾶν τὸ πρεσβύτερον τοῦ νεωτέρου.
And by time, for example, a father to a son, and everything older to the younger.
φύσει δέ ἐστι πρότερον, οἷον ἥ τε μονὰς τῆς δυάδος καὶ τὸ μέρος τοῦ ὅλου καὶ τὸ γένος τοῦ εἴδους, καὶ ἀπλῶς ὅσα αὐτὰ ἀλλήλοις μὴ συναναιρεῖται, τούτων τὸ μὲν συναναιροῦν πρότερόν ἐστι, τὸ φύσει δὲ συναναιρούμενον ὕστερον· οἷον τῆς μονάδος ἀναιρεθείσης ἡ δυὰς ἀναιρεῖται καὶ πᾶς ἀριθμός, δυάδος δὲ ἀναιρεθείσης οὐδὲν κωλύει μονάδα εἶναι· πρότερον τοίνυν τῇ φύσει μονὰς δυάδος.
And by nature is prior, for example, the monad to the dyad, the part to the whole, and the genus to the species; and simply, of as many things as do not mutually destroy one another, that which destroys the other is prior, and that which is naturally destroyed along with it is posterior; for example, when the monad is destroyed, the dyad is destroyed and every number, but when the dyad is destroyed, nothing prevents the monad from existing; the monad, therefore, is prior by nature to the dyad.
ὁμοίως δὲ καὶ τοῦ μέρους ἀναιρεθέντος τὸ ὅλον ἀναιρεῖται, τοῦ δὲ ὅλου μὴ ὄντος οὐδὲν κωλύει τὸ μέρος εἶναι.
And likewise also, when the part is destroyed, the whole is destroyed, but when the whole does not exist, nothing prevents the part from existing.
φανερὸν δὲ ὅτι ὁσαχῶς τὸ πρότερον λέγεται, τοσαυταχῶς καὶ τὸ ὕστερον λεχθήσεται· τὸ γὰρ ὕστερον ἐροῦμεν ἢ φύσει ἢ χρόνῳ ἢ θέσει ἢ τάξει ἢ δυνάμει.
And it is clear that in as many ways as the prior is said, in so many ways also the posterior will be said; for we shall say the posterior either by nature, by time, by position, by order, or by power.
§B.66## τὸ ἅμα.
## Simultaneously.
ὁσαχῶς τὸ πρότερον καὶ τὸ ὕστερον λέγεται, τοσαυταχῶς καὶ περὶ τοῦ ἅμα λεχθήσεται, οἷον ἢ φύσει ἢ θέσει ἢ δυνάμει ἢ χρόνῳ ἢ τάξει.
In as many ways as the prior and the posterior are said, in so many ways also it will be said concerning the simultaneous, for example either by nature, by position, by power, by time, or by order.
θέσει μὲν οὖν εἰσι τὰ τοιαῦτα ἅμα, ὅσα τῷ τόπῳ ἐξ ἴσου ἐστίν, οἷον τὰ τρέχοντα ἅμα φαμὲν εἶναι καὶ τὰ ἑστηκότα.
Now by position such things are simultaneous as are equal in place, for example we say that those running are simultaneous and those standing are simultaneous.
τάξει δέ ἐστιν τὰ τοιαῦτα ἅμα, οἷον οἱ τοῖς ζυγοῖς στοιχοῦντες, δυνάμει δὲ ἅμα λέγομεν τὰ μηδὲν ἀλλήλων πλέον δυνάμενα, χρόνῳ δὲ τὰ τοιαῦτα φαμὲν εἶναι ἅμα τὰ κατὰ τὸν αὐτὸν χρόνον ὄντα, φύσει δὲ λεκτέον ἅμα εἶναι τά τε συναναιροῦντα ἄλληλα καὶ τὰ μὴ δυνάμενα χωρὶς ἀλλήλων εἶναι, οἷον τό τε διπλάσιον καὶ τὸ ἥμισυ· ταῦτα γὰρ συναναιροῦνται ἀλλήλοις καὶ τὸ ἕτερον χωρὶς τοῦ ἑτέρου ἀδύνατον εἶναι· διπλασίου γὰρ ἀναιρεθέντος οὐκ ἔσται ἥμισυ καὶ ἡμίσους ἀναιρεθέντος οὐκ ἔσται διπλάσιον καὶ ἀδύνατόν ἐστι διπλασίου ὄντος μὴ εἶναι ἥμισυ.
And by order such things are simultaneous as, for example, those standing in the same rank. And by power we say those things are simultaneous which are able to do nothing more than one another. And by time we say such things are simultaneous as exist at the same time. And by nature we must say such things are simultaneous as mutually destroy one another and are not able to exist apart from one another, such as the double and the half; for these are mutually destroyed with one another, and it is impossible for the one to exist apart from the other; for when the double is destroyed, there will not be a half, and when the half is destroyed, there will not be a double, and it is impossible for there to be a double and not be a half.
τούτων οὕτως ἀποδειχθέντων ἀκόλουθον εἰπεῖν περὶ τῶν ὄντων.
These things having been thus demonstrated, it is consequential to speak about existing things.
§B.68## τὰ ἐναντία.
## Opposites.
διαιροῦνται τὰ ἐναντία οὕτως.
Opposites are divided as follows.
τῶν ὄντων τῶν μὲν ἔστι τι ἐναντίον, τῶν δὲ οὔ.
Of existing things, of some there is something opposite, and of others not.
χρυσῷ μὲν γὰρ καὶ ἀνθρώπῳ καὶ ἱματίῳ καὶ τοῖς τοιούτοις οὐδέν ἐστιν ἐναντίον, ἀρετῇ δὲ καὶ ἀγαθῷ καὶ θερμῷ ἔστι 〈τι〉 ἐναντίον· ἀγαθῷ μὲν γὰρ ἐναντίον τὸ κακόν, ἀρετῇ δὲ κακία, θερμῷ δὲ ψυχρόν.
For to gold and human and clothing and such things there is nothing opposite, but to virtue and good and hot there is something opposite; for to the good the opposite is the bad, to virtue vice, and to hot cold.
τῶν ἐναντίων τοίνυν αὐτῶν τὰ μὲν ἔχουσί τι ἀνὰ μέσον, τὰ δὲ οὔ.
Now of these opposites themselves, some have something in between, and others not.
ἀγαθοῦ μὲν γὰρ καὶ κακοῦ ἔστι τι ἀνὰ μέσον, κινήσεως δὲ καὶ ἠρεμίας οὐδέν ἐστιν ἀνὰ μέσον· ἐξ ἀνάγκης γὰρ πάντα ἢ κινεῖται ἢ ἠρεμεῖ.
For of the good and the bad there is something in between, but of motion and rest there is nothing in between; for of necessity all things either move or rest.
καὶ ζωῆς καὶ θανάτου οὐδέν ἐστιν ἀνὰ μέσον· ἐξ ἀνάγκης γὰρ ὅπερ τῆς ζωῆς δεκτικόν ἐστιν, ἢ ζῇ ἢ τέθνηκεν. | αὐτὰ δὲ τὰ ἐναντία λέγεται τριττῶς· ἢ γὰρ ὡς ἀγαθῷ κακὸν ἐναντίον ἐστίν, οἷον τῇ δικαιοσύνῃ ἡ ἀδικία καὶ τῇ σωφροσύνῃ ἡ ἀκολασία καὶ τὰ τοιαῦτα, ἢ ὡς οὐδέτερον οὐδετέρῳ ἐναντίον ἐστίν 〈οἷον. . . . τ ο ύτων γὰρ οὐδέν ἐστιν οὔτε κακὸν οὔτε ἀγαθόν.
And of life and death there is nothing in between; for of necessity whatever is receptive of life either lives or has died. | And the opposites themselves are said in three ways; for either as the bad is opposite to the good, for example injustice to justice and licentiousness to temperance and suchlike, or as neither is opposite to neither ⟨such as... for of these⟩ nothing is either bad or good.
ὡς κακὸν κακῷ δὲ ἐναντίον ἐστὶν [κακὸν] ἡ ὑπερβολὴ τῇ ἐνδείᾳ καὶ τὰ καθ’ ὑπερβολὴν καὶ ἔλλειψιν λεγόμενα, οἷον τὸ ὑπερβαλλόντως ψύχεσθαι 〈τῷ ὑπερβαλλόντως θερμοῦσθαι〉 ταῦτα γὰρ καθ’ ὑπερβολὴν λέγεται.
And as bad is opposite to bad is excess to deficiency, and the things said in terms of excess and deficiency, such as to be excessively cooled ⟨to being excessively warmed⟩; for these are said in terms of excess.
καὶ τὸ ἐλλεῖπον τοῦ θερμοῦ τῷ ἐλλείποντι τοῦ ψυχροῦ· καὶ γὰρ ταῦτα κατ’ ἔλλειψιν ἐναντία.
And that which is deficient in the hot to that which is deficient in the cold; for indeed these are opposite in terms of deficiency.
§B.69## περὶ καταφάσεως καὶ ἀποφάσεως.
## On affirmation and negation.
μετὰ ταῦτα τοίνυν περὶ καταφάσεως σκεπτέον πῶς λέγομεν.
After these things, therefore, we must consider concerning affirmation, how we speak.
φαμὲν οὖν πᾶσαν κατηγορίαν ᾖ δηλοῦμεν ὑπάρχειν τι κατάφασιν εἶναι, οἷον τὸ καθῆσθαι τὸν ἄνθρωπον ἢ λευκὸν εἶναι τὸ ἱμάτιον καὶ πάντα τὰ τοῦτον τὸν τρόπον λεγόμενα.
We say then that every predication by which we indicate that something belongs to something is an affirmation, for example that the human is sitting or that the clothing is white, and all things said in this manner.
ἀπόφασις δέ ἐστι τοιοῦτον οἷον τὸ μὴ καθῆσθαι τὸν ἄνθρωπον καὶ τὸ μὴ λευκὸν εἶναι τὸ ἱμάτιον καὶ ἀπλῶς οὗ τὸ μὴ ἢ τὸ οὐ προστεθὲν σημαίνει μὴ ὑπάρχειν τι.
And negation is such a thing as that the human is not sitting and that the clothing is not white, and simply that of which the 'not' or 'no' added signifies that something does not belong.