There is a science which studies Being qua Being, and the properties inherent in it in virtue of its own nature. This science is not the same as any of the so-called particular sciences, for none of the others contemplates Being generally qua Being; they divide off some portion of it and study the attribute of this portion, as do for example the mathematical sciences. But since it is for the first principles and the most ultimate causes that we are searching, clearly they must belong to something in virtue of its own nature. Hence if these principles were investigated by those also who investigated the elements of existing things, the elements must be elements of Being not incidentally, but qua Being. Therefore it is of Being qua Being that we too must grasp the first causes. The term “being” is used in various senses, but with reference to one central idea and one definite characteristic, and not as merely a common epithet. Thus as the term “healthy” always relates to health (either as preserving it or as producing it or as indicating it or as receptive of it), and as “medical” relates to the art of medicine (either as possessing it or as naturally adapted for it or as being a function of medicine)—and we shall find other terms used similarly to these— so “being” is used in various senses, but always with reference to one principle.
ἔστιν ἐπιστήμη τις ἣ θεωρεῖ τὸ ὂν ᾗ ὂν καὶ τὰ τούτῳ ὑπάρχοντα καθʼ αὑτό. αὕτη δʼ ἐστὶν οὐδεμιᾷ τῶν ἐν μέρει λεγομένων ἡ αὐτή· οὐδεμία γὰρ τῶν ἄλλων ἐπισκοπεῖ καθόλου περὶ τοῦ ὄντος ᾗ ὄν, ἀλλὰ μέρος αὐτοῦ τι ἀποτεμόμεναι περὶ τούτου θεωροῦσι τὸ συμβεβηκός, οἷον αἱ μαθηματικαὶ τῶν ἐπιστημῶν. ἐπεὶ δὲ τὰς ἀρχὰς καὶ τὰς ἀκροτάτας αἰτίας ζητοῦμεν, δῆλον ὡς φύσεώς τινος αὐτὰς ἀναγκαῖον εἶναι καθʼ αὑτήν. εἰ οὖν καὶ οἱ τὰ στοιχεῖα τῶν ὄντων ζητοῦντες ταύτας τὰς ἀρχὰς ἐζήτουν, ἀνάγκη καὶ τὰ στοιχεῖα τοῦ ὄντος εἶναι μὴ κατὰ συμβεβηκὸς ἀλλʼ ᾗ ὄν· διὸ καὶ ἡμῖν τοῦ ὄντος ᾗ ὂν τὰς πρώτας αἰτίας ληπτέον. τὸ δὲ ὂν λέγεται μὲν πολλαχῶς, ἀλλὰ πρὸς ἓν καὶ μίαν τινὰ φύσιν καὶ οὐχ ὁμωνύμως ἀλλʼ ὥσπερ καὶ τὸ ὑγιεινὸν ἅπαν πρὸς ὑγίειαν, τὸ μὲν τῷ φυλάττειν τὸ δὲ τῷ ποιεῖν τὸ δὲ τῷ σημεῖον εἶναι τῆς ὑγιείας τὸ δʼ ὅτι δεκτικὸν αὐτῆς, καὶ τὸ ἰατρικὸν πρὸς ἰατρικήν (τὸ μὲν γὰρ τῷ ἔχειν ἰατρικὴν λέγεται ἰατρικὸν τὸ δὲ τῷ εὐφυὲς εἶναι πρὸς αὐτὴν τὸ δὲ τῷ ἔργον εἶναι τῆς ἰατρικῆς), ὁμοιοτρόπως δὲ καὶ ἄλλα ληψόμεθα λεγόμενα τούτοις,— οὕτω δὲ καὶ τὸ ὂν λέγεται πολλαχῶς μὲν ἀλλʼ ἅπαν πρὸς μίαν ἀρχήν·
For some things are said to “be” because they are substances; others because they are modifications of substance; others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of terms relating to substance, or negations of certain of these terms or of substance. (Hence we even say that not-being is not-being.) And so, just as there is one science of all healthy things, so it is true of everything else. For it is not only in the case of terms which express one common notion that the investigation belongs to one science, but also in the case of terms which relate to one particular characteristic; for the latter too, in a sense, express one common notion. Clearly then the study of things which are, qua being, also belongs to one science. Now in every case knowledge is principally concerned with that which is primary, i.e. that upon which all other things depend, and from which they get their names. If, then, substance is this primary thing, it is of substances that the philosopher must grasp the first principles and causes. Now of every single class of things, as there is one perception, so there is one science: e.g., grammar, which is one science, studies all articulate sounds.
τὰ μὲν γὰρ ὅτι οὐσίαι, ὄντα λέγεται, τὰ δʼ ὅτι πάθη οὐσίας, τὰ δʼ ὅτι ὁδὸς εἰς οὐσίαν ἢ φθοραὶ ἢ στερήσεις ἢ ποιότητες ἢ ποιητικὰ ἢ γεννητικὰ οὐσίας ἢ τῶν πρὸς τὴν οὐσίαν λεγομένων, ἢ τούτων τινὸς ἀποφάσεις ἢ οὐσίας· διὸ καὶ τὸ μὴ ὂν εἶναι μὴ ὄν φαμεν. καθάπερ οὖν καὶ τῶν ὑγιεινῶν ἁπάντων μία ἐπιστήμη ἔστιν, ὁμοίως τοῦτο καὶ ἐπὶ τῶν ἄλλων. οὐ γὰρ μόνον τῶν καθʼ ἓν λεγομένων ἐπιστήμης ἐστὶ θεωρῆσαι μιᾶς ἀλλὰ καὶ τῶν πρὸς μίαν λεγομένων φύσιν· καὶ γὰρ ταῦτα τρόπον τινὰ λέγονται καθʼ ἕν. δῆλον οὖν ὅτι καὶ τὰ ὄντα μιᾶς θεωρῆσαι ᾗ ὄντα. πανταχοῦ δὲ κυρίως τοῦ πρώτου ἡ ἐπιστήμη, καὶ ἐξ οὗ τὰ ἄλλα ἤρτηται, καὶ διʼ ὃ λέγονται. εἰ οὖν τοῦτʼ ἐστὶν ἡ οὐσία, τῶν οὐσιῶν ἂν δέοι τὰς ἀρχὰς καὶ τὰς αἰτίας ἔχειν τὸν φιλόσοφον.—ἅπαντος δὲ γένους καὶ αἴσθησις μία ἑνὸς καὶ ἐπιστήμη, οἷον γραμματικὴ μία οὖσα πάσας θεωρεῖ τὰς φωνάς·
Hence the study of all the species of Being qua Being belongs to a science which is generically one, and the study of the several species of Being belongs to the specific parts of that science. Now if Being and Unity are the same, i.e. a single nature, in the sense that they are associated as principle and cause are, and not as being denoted by the same definition (although it makes no difference but rather helps our argument if we understand them in the same sense), since “one man” and “man” and “existent man” and “man” are the same thing, i.e. the duplication in the statement “he is a man and an existent man” gives no fresh meaning (clearly the concepts of humanity and existence are not dissociated in respect of either coming to be or ceasing to be), and similarly in the case of the term “one,” so that obviously the additional term in these phrases has the same significance, and Unity is nothing distinct from Being; and further if the substance of each thing is one in no accidental sense, and similarly is of its very nature something which is—then there are just as many species of Being as of Unity. And to study the essence of these species (I mean, e.g., the study of Same and Other and all the other similar concepts— roughly speaking all the “contraries” are reducible to this first principle;
διὸ καὶ τοῦ ὄντος ᾗ ὂν ὅσα εἴδη θεωρῆσαι μιᾶς ἐστὶν ἐπιστήμης τῷ γένει, τά τε εἴδη τῶν εἰδῶν. εἰ δὴ τὸ ὂν καὶ τὸ ἓν ταὐτὸν καὶ μία φύσις τῷ ἀκολουθεῖν ἀλλήλοις ὥσπερ ἀρχὴ καὶ αἴτιον, ἀλλʼ οὐχ ὡς ἑνὶ λόγῳ δηλούμενα (διαφέρει δὲ οὐθὲν οὐδʼ ἂν ὁμοίως ὑπολάβωμεν, ἀλλὰ καὶ πρὸ ἔργου μᾶλλον)· ταὐτὸ γὰρ εἷς ἄνθρωπος καὶ ἄνθρωπος, καὶ ὢν ἄνθρωπος καὶ ἄνθρωπος, καὶ οὐχ ἕτερόν τι δηλοῖ κατὰ τὴν λέξιν ἐπαναδιπλούμενον τὸ εἷς ἄνθρωπος καὶ εἷς ὢν ἄνθρωπος (δῆλον δʼ ὅτι οὐ χωρίζεται οὔτʼ ἐπὶ γενέσεως οὔτʼ ἐπὶ φθορᾶς), ὁμοίως δὲ καὶ ἐπὶ τοῦ ἑνός, ὥστε φανερὸν ὅτι ἡ πρόσθεσις ἐν τούτοις ταὐτὸ δηλοῖ, καὶ οὐδὲν ἕτερον τὸ ἓν παρὰ τὸ ὄν, ἔτι δʼ ἡ ἑκάστου οὐσία ἕν ἐστιν οὐ κατὰ συμβεβηκός, ὁμοίως δὲ καὶ ὅπερ ὄν τι·—ὥσθʼ ὅσα περ τοῦ ἑνὸς εἴδη, τοσαῦτα καὶ τοῦ ὄντος· περὶ ὧν τὸ τί ἐστι τῆς αὐτῆς ἐπιστήμης τῷ γένει θεωρῆσαι, λέγω δʼ οἷον περὶ ταὐτοῦ καὶ ὁμοίου καὶ τῶν ἄλλων τῶν τοιούτων. σχεδὸν δὲ πάντα ἀνάγεται τἀναντία εἰς τὴν ἀρχὴν ταύτην·
but we may consider that they have been sufficiently studied in the “Selection of Contraries” ) is the province of a science which is generically one. And there are just as many divisions of philosophy as there are kinds of substance; so that there must be among them a First Philosophy and one which follows upon it. For Being and Unity at once entail genera, and so the sciences will correspond to these genera. The term “philosopher” is like the term “mathematician” in its uses; for mathematics too has divisions—there is a primary and a secondary science, and others successively, in the realm of mathematics. Now since it is the province of one science to study opposites, and the opposite of unity is plurality, and it is the province of one science to study the negation and privation of Unity, because in both cases we are studying Unity, to which the negation (or privation) refers, stated either in the simple form that Unity is not present, or in the form that it is not present in a particular class; in the latter case Unity is modified by the differentia, apart from the content of the negation (for the negation of Unity is its absence); but in privation there is a substrate of which the privation is predicated.— The opposite of Unity, then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness, Dissimilarity, Inequality and everything else which is derived from these or from Plurality or Unity— fall under the cognizance of the aforesaid science.
τεθεωρήσθω δʼ ἡμῖν ταῦτα ἐν τῇ ἐκλογῇ τῶν ἐναντίων. καὶ τοσαῦτα μέρη φιλοσοφίας ἔστιν ὅσαι περ αἱ οὐσίαι· ὥστε ἀναγκαῖον εἶναί τινα πρώτην καὶ ἐχομένην αὐτῶν. ὑπάρχει γὰρ εὐθὺς γένη ἔχον τὸ ὂν [καὶ τὸ ἕν]· διὸ καὶ αἱ ἐπιστῆμαι ἀκολουθήσουσι τούτοις. ἔστι γὰρ ὁ φιλόσοφος ὥσπερ ὁ μαθηματικὸς λεγόμενος· καὶ γὰρ αὕτη ἔχει μέρη, καὶ πρώτη τις καὶ δευτέρα ἔστιν ἐπιστήμη καὶ ἄλλαι ἐφεξῆς ἐν τοῖς μαθήμασιν.—ἐπεὶ δὲ μιᾶς τἀντικείμενα θεωρῆσαι, τῷ δὲ ἑνὶ ἀντίκειται πλῆθος—ἀπόφασιν δὲ καὶ στέρησιν μιᾶς ἐστὶ θεωρῆσαι διὰ τὸ ἀμφοτέρως θεωρεῖσθαι τὸ ἓν οὗ ἡ ἀπόφασις ἢ ἡ στέρησις (ἢ ⟨γὰρ⟩ ἁπλῶς λέγομεν ὅτι οὐχ ὑπάρχει ἐκεῖνο, ἤ τινι γένει· ἔνθα μὲν οὖν †τῷ ἑνὶ ἡ διαφορὰ πρόσεστι παρὰ τὸ ἐν τῇ ἀποφάσει†, ἀπουσία γὰρ ἡ ἀπόφασις ἐκείνου ἐστίν, ἐν δὲ τῇ στερήσει καὶ ὑποκειμένη τις φύσις γίγνεται καθʼ ἧς λέγεται ἡ στέρησις) [τῷ δʼ ἑνὶ πλῆθος ἀντίκειται]—ὥστε καὶ τἀντικείμενα τοῖς εἰρημένοις, τό τε ἕτερον καὶ ἀνόμοιον καὶ ἄνισον καὶ ὅσα ἄλλα λέγεται ἢ κατὰ ταῦτα ἢ κατὰ πλῆθος καὶ τὸ ἕν, τῆς εἰρημένης γνωρίζειν ἐπιστήμης·
And one of them is Oppositeness; for this is a form of Difference, and Difference is a form of Otherness. Hence since the term “one” is used in various senses, so too will these terms be used; yet it pertains to one science to take cognizance of them all. For terms fall under different sciences, not if they are used in various senses, but if their definitions are neither identical nor referable to a common notion. And since everything is referred to that which is primary, e.g. all things which are called “one” are referred to the primary “One,” we must admit that this is also true of Identity and Otherness and the Contraries. Thus we must first distinguish all the senses in which each term is used, and then attribute them to the primary in the case of each predicate, and see how they are related to it; for some will derive their name from possessing and others from producing it, and others for similar reasons. Thus clearly it pertains to one science to give an account both of these concepts and of substance (this was one of the questions raised in the “Difficulties” ), and it is the function of the philosopher to be able to study all subjects.
ὧν ἐστὶ καὶ ἡ ἐναντιότης· διαφορὰ γάρ τις ἡ ἐναντιότης, ἡ δὲ διαφορὰ ἑτερότης. ὥστʼ ἐπειδὴ πολλαχῶς τὸ ἓν λέγεται, καὶ ταῦτα πολλαχῶς μὲν λεχθήσεται, ὅμως δὲ μιᾶς ἅπαντά ἐστι γνωρίζειν· οὐ γὰρ εἰ πολλαχῶς, ἑτέρας, ἀλλʼ εἰ μήτε καθʼ ἓν μήτε πρὸς ἓν οἱ λόγοι ἀναφέρονται. ἐπεὶ δὲ πάντα πρὸς τὸ πρῶτον ἀναφέρεται, οἷον ὅσα ἓν λέγεται πρὸς τὸ πρῶτον ἕν, ὡσαύτως φατέον καὶ περὶ ταὐτοῦ καὶ ἑτέρου καὶ τῶν ἐναντίων ἔχειν· ὥστε διελόμενον ποσαχῶς λέγεται ἕκαστον, οὕτως ἀποδοτέον πρὸς τὸ πρῶτον ἐν ἑκάστῃ κατηγορίᾳ πῶς πρὸς ἐκεῖνο λέγεται· τὰ μὲν γὰρ τῷ ἔχειν ἐκεῖνο τὰ δὲ τῷ ποιεῖν τὰ δὲ κατʼ ἄλλους λεχθήσεται τοιούτους τρόπους.—φανερὸν οὖν [ὅπερ ἐν ταῖς ἀπορίαις ἐλέχθη] ὅτι μιᾶς περὶ τούτων καὶ τῆς οὐσίας ἐστὶ λόγον ἔχειν (τοῦτο δʼ ἦν ἓν τῶν ἐν τοῖς ἀπορήμασιν), καὶ ἔστι τοῦ φιλοσόφου περὶ πάντων δύνασθαι θεωρεῖν.
If this is not so, who is it who in will investigate whether “Socrates” and “Socrates seated” are the same thing; or whether one thing has one contrary, or what the contrary is, or how many meanings it has? and similarly with all other such questions. Thus since these are the essential modifications of Unity qua Unity and of Being qua Being, and not qua numbers or lines or fire, clearly it a pertains to that science to discover both the essence and the attributes of these concepts. And those who investigate them err, not in being unphilosophical, but because the substance, of which they have no real knowledge, is prior. For just as number qua number has its peculiar modifications, e.g. oddness and evenness, commensurability and equality, excess and defect, and these things are inherent in numbers both considered independently and in relation to other numbers; and as similarly other peculiar modifications are inherent in the solid and the immovable and the moving and the weightless and that which has weight; so Being qua Being has certain peculiar modifications, and it is about these that it is the philosopher’s function to discover the truth. And here is evidence of this fact. Dialecticians and sophists wear the same appearance as the philosopher, for sophistry is Wisdom in appearance only, and dialecticians discuss all subjects, and Being is a subject common to them all; but clearly they discuss these concepts because they appertain to philosophy.
εἰ γὰρ μὴ τοῦ φιλοσόφου, τίς ἔσται ὁ ἐπισκεψόμενος εἰ ταὐτὸ Σωκράτης καὶ Σωκράτης καθήμενος, ἢ εἰ ἓν ἑνὶ ἐναντίον, ἢ τί ἐστι τὸ ἐναντίον ἢ ποσαχῶς λέγεται; ὁμοίως δὲ καὶ περὶ τῶν ἄλλων τῶν τοιούτων. ἐπεὶ οὖν τοῦ ἑνὸς ᾗ ἓν καὶ τοῦ ὄντος ᾗ ὂν ταῦτα καθʼ αὑτά ἐστι πάθη, ἀλλʼ οὐχ ᾗ ἀριθμοὶ ἢ γραμμαὶ ἢ πῦρ, δῆλον ὡς ἐκείνης τῆς ἐπιστήμης καὶ τί ἐστι γνωρίσαι καὶ τὰ συμβεβηκότʼ αὐτοῖς. καὶ οὐ ταύτῃ ἁμαρτάνουσιν οἱ περὶ αὐτῶν σκοπούμενοι ὡς οὐ φιλοσοφοῦντες, ἀλλʼ ὅτι πρότερον ἡ οὐσία, περὶ ἧς οὐθὲν ἐπαΐουσιν, ἐπεὶ ὥσπερ ἔστι καὶ ἀριθμοῦ ᾗ ἀριθμὸς ἴδια πάθη, οἷον περιττότης ἀρτιότης, συμμετρία ἰσότης, ὑπεροχὴ ἔλλειψις, καὶ ταῦτα καὶ καθʼ αὑτοὺς καὶ πρὸς ἀλλήλους ὑπάρχει τοῖς ἀριθμοῖς (ὁμοίως δὲ καὶ στερεῷ καὶ ἀκινήτῳ καὶ κινουμένῳ ἀβαρεῖ τε καὶ βάρος ἔχοντι ἔστιν ἕτερα ἴδια), οὕτω καὶ τῷ ὄντι ᾗ ὂν ἔστι τινὰ ἴδια, καὶ ταῦτʼ ἐστὶ περὶ ὧν τοῦ φιλοσόφου ἐπισκέψασθαι τὸ ἀληθές. σημεῖον δέ· οἱ γὰρ διαλεκτικοὶ καὶ σοφισταὶ τὸ αὐτὸ μὲν ὑποδύονται σχῆμα τῷ φιλοσόφῳ· ἡ γὰρ σοφιστικὴ φαινομένη μόνον σοφία ἐστί, καὶ οἱ διαλεκτικοὶ διαλέγονται περὶ ἁπάντων, κοινὸν δὲ πᾶσι τὸ ὄν ἐστιν, διαλέγονται δὲ περὶ τούτων δῆλον ὅτι διὰ τὸ τῆς φιλοσοφίας ταῦτα εἶναι οἰκεῖα.
For sophistry and dialectic are concerned with the same class of subjects as philosophy, but philosophy differs from the former in the nature of its capability and from the latter in its outlook on life. Dialectic treats as an exercise what philosophy tries to understand, and sophistry seems to be philosophy; but is not. Further, the second column of contraries is privative, and everything is reducible to Being and Not being, and Unity and Plurality; e.g. Rest falls under Unity and Motion under Plurality. And nearly everyone agrees that substance and existing things are composed of contraries; at any rate all speak of the first principles as contraries— some as Odd and Even, some as Hot and Cold, some as Limit and Unlimited, some as Love and Strife. And it is apparent that all other things also are reducible to Unity and Plurality (we may assume this reduction);
περὶ μὲν γὰρ τὸ αὐτὸ γένος στρέφεται ἡ σοφιστικὴ καὶ ἡ διαλεκτικὴ τῇ φιλοσοφίᾳ, ἀλλὰ διαφέρει τῆς μὲν τῷ τρόπῳ τῆς δυνάμεως, τῆς δὲ τοῦ βίου τῇ προαιρέσει· ἔστι δὲ ἡ διαλεκτικὴ πειραστικὴ περὶ ὧν ἡ φιλοσοφία γνωριστική, ἡ δὲ σοφιστικὴ φαινομένη, οὖσα δʼ οὔ. ἔτι τῶν ἐναντίων ἡ ἑτέρα συστοιχία στέρησις, καὶ πάντα ἀνάγεται εἰς τὸ ὂν καὶ τὸ μὴ ὄν, καὶ εἰς ἓν καὶ πλῆθος, οἷον στάσις τοῦ ἑνὸς κίνησις δὲ τοῦ πλήθους· τὰ δʼ ὄντα καὶ τὴν οὐσίαν ὁμολογοῦσιν ἐξ ἐναντίων σχεδὸν ἅπαντες συγκεῖσθαι· πάντες γοῦν τὰς ἀρχὰς ἐναντίας λέγουσιν· οἱ μὲν γὰρ περιττὸν καὶ ἄρτιον, οἱ δὲ θερμὸν καὶ ψυχρόν, οἱ δὲ πέρας καὶ ἄπειρον, οἱ δὲ φιλίαν καὶ νεῖκος. πάντα δὲ καὶ τἆλλα ἀναγόμενα φαίνεται εἰς τὸ ἓν καὶ πλῆθος (εἰλήφθω γὰρ ἡ ἀναγωγὴ ἡμῖν), αἱ δʼ ἀρχαὶ καὶ παντελῶς αἱ παρὰ τῶν ἄλλων ὡς εἰς γένη ταῦτα πίπτουσιν.
and the principles adduced by other thinkers fall entirely under these as genera. It is clear, then, from these considerations also, that it pertains to a single science to study Being qua Being; for all things are either contraries or derived from contraries, and the first principles of the contraries are Unity and Plurality. And these belong to one science, whether they have reference to one common notion or not. Probably the truth is that they have not; but nevertheless even if the term “one” is used in various senses, the others will be related to the primary sense (and similarly with the contraries)— even if Being or Unity is not a universal and the same in all cases, or is not separable from particulars (as it presumably is not; the unity is in some cases one of reference and in others one of succession). For this very reason it is not the function of the geometrician to inquire what is Contrariety or Completeness or Being or Unity or Identity or Otherness, but to proceed from the assumption of them. Clearly, then, it pertains to one science to study Being qua Being, and the attributes inherent in it qua Being; and the same science investigates, besides the concepts mentioned above, Priority and Posteriority, Genus and Species, Whole and Part, and all other such concepts. We must pronounce whether it pertains to the same science to study both the so-called axioms in mathematics and substance, or to different sciences.
φανερὸν οὖν καὶ ἐκ τούτων ὅτι μιᾶς ἐπιστήμης τὸ ὂν ᾗ ὂν θεωρῆσαι. πάντα γὰρ ἢ ἐναντία ἢ ἐξ ἐναντίων, ἀρχαὶ δὲ τῶν ἐναντίων τὸ ἓν καὶ πλῆθος. ταῦτα δὲ μιᾶς ἐπιστήμης, εἴτε καθʼ ἓν λέγεται εἴτε μή, ὥσπερ ἴσως ἔχει καὶ τἀληθές. ἀλλʼ ὅμως εἰ καὶ πολλαχῶς λέγεται τὸ ἕν, πρὸς τὸ πρῶτον τἆλλα λεχθήσεται καὶ τὰ ἐναντία ὁμοίως, [καὶ διὰ τοῦτο] καὶ εἰ μὴ ἔστι τὸ ὂν ἢ τὸ ἓν καθόλου καὶ ταὐτὸ ἐπὶ πάντων ἢ χωριστόν, ὥσπερ ἴσως οὐκ ἔστιν ἀλλὰ τὰ μὲν πρὸς ἓν τὰ δὲ τῷ ἐφεξῆς. καὶ διὰ τοῦτο οὐ τοῦ γεωμέτρου θεωρῆσαι τί τὸ ἐναντίον ἢ τέλειον ἢ ἓν ἢ ὂν ἢ ταὐτὸν ἢ ἕτερον, ἀλλʼ ἢ ἐξ ὑποθέσεως. ὅτι μὲν οὖν μιᾶς ἐπιστήμης τὸ ὂν ᾗ ὂν θεωρῆσαι καὶ τὰ ὑπάρχοντα αὐτῷ ᾗ ὄν, δῆλον, καὶ ὅτι οὐ μόνον τῶν οὐσιῶν ἀλλὰ καὶ τῶν ὑπαρχόντων ἡ αὐτὴ θεωρητική, τῶν τε εἰρημένων καὶ περὶ προτέρου καὶ ὑστέρου, καὶ γένους καὶ εἴδους, καὶ ὅλου καὶ μέρους καὶ τῶν ἄλλων τῶν τοιούτων. λεκτέον δὲ πότερον μιᾶς ἢ ἑτέρας ἐπιστήμης περί τε τῶν ἐν τοῖς μαθήμασι καλουμένων ἀξιωμάτων καὶ περὶ τῆς οὐσίας.
It is obvious that the investigation of these axioms too pertains to one science, namely the science of the philosopher; for they apply to all existing things, and not to a particular class separate and distinct from the rest. Moreover all thinkers employ them—because they are axioms of Being qua Being, and every genus possesses Being— but employ them only in so far as their purposes require; i.e., so far as the genus extends about which they are carrying out their proofs. Hence since these axioms apply to all things qua Being (for this is what is common to them), it is the function of him who studies Being qua Being to investigate them as well. For this reason no one who is pursuing a particular inquiry—neither a geometrician nor an arithmetician—attempts to state whether they are true or false; but some of the physicists did so, quite naturally; for they alone professed to investigate nature as a whole, and Being. But inasmuch as there is a more ultimate type of thinker than the natural philosopher (for nature is only a genus of Being), the investigation of these axioms too will belong to the universal thinker who studies the primary reality.
φανερὸν δὴ ὅτι μιᾶς τε καὶ τῆς τοῦ φιλοσόφου καὶ ἡ περὶ τούτων ἐστὶ σκέψις· ἅπασι γὰρ ὑπάρχει τοῖς οὖσιν ἀλλʼ οὐ γένει τινὶ χωρὶς ἰδίᾳ τῶν ἄλλων. καὶ χρῶνται μὲν πάντες, ὅτι τοῦ ὄντος ἐστὶν ᾗ ὄν, ἕκαστον δὲ τὸ γένος ὄν· ἐπὶ τοσοῦτον δὲ χρῶνται ἐφʼ ὅσον αὐτοῖς ἱκανόν, τοῦτο δʼ ἔστιν ὅσον ἐπέχει τὸ γένος περὶ οὗ φέρουσι τὰς ἀποδείξεις· ὥστʼ ἐπεὶ δῆλον ὅτι ᾗ ὄντα ὑπάρχει πᾶσι (τοῦτο γὰρ αὐτοῖς τὸ κοινόν), τοῦ περὶ τὸ ὂν ᾗ ὂν γνωρίζοντος καὶ περὶ τούτων ἐστὶν ἡ θεωρία. διόπερ οὐθεὶς τῶν κατὰ μέρος ἐπισκοπούντων ἐγχειρεῖ λέγειν τι περὶ αὐτῶν, εἰ ἀληθῆ ἢ μή, οὔτε γεωμέτρης οὔτʼ ἀριθμητικός, ἀλλὰ τῶν φυσικῶν ἔνιοι, εἰκότως τοῦτο δρῶντες· μόνοι γὰρ ᾤοντο περί τε τῆς ὅλης φύσεως σκοπεῖν καὶ περὶ τοῦ ὄντος. ἐπεὶ δʼ ἔστιν ἔτι τοῦ φυσικοῦ τις ἀνωτέρω (ἓν γάρ τι γένος τοῦ ὄντος ἡ φύσις), τοῦ καθόλου καὶ τοῦ περὶ τὴν πρώτην οὐσίαν θεωρητικοῦ καὶ ἡ περὶ τούτων ἂν εἴη σκέψις·
Natural philosophy is a kind of Wisdom, but not the primary kind. As for the attempts of some of those who discuss how the truth should be received, they are due to lack of training in logic; for they should understand these things before they approach their task, and not investigate while they are still learning. Clearly then it is the function of the philosopher, i.e. the student of the whole of reality in its essential nature, to investigate also the principles of syllogistic reasoning. And it is proper for him who best understands each class of subject to be able to state the most certain principles of that subject; so that he who understands the modes of Being qua Being should be able to state the most certain principles of all things. Now this person is the philosopher, and the most certain principle of all is that about which one cannot be mistaken; for such a principle must be both the most familiar (for it is about the unfamiliar that errors are always made), and not based on hypothesis. For the principle which the student of any form of Being must grasp is no hypothesis; and that which a man must know if he knows anything he must bring with him to his task. Clearly, then, it is a principle of this kind that is the most certain of all principles. Let us next state what this principle is. “It is impossible for the same attribute at once to belong and not to belong to the same thing and in the same relation”; and we must add any further qualifications that may be necessary to meet logical objections.
ἔστι δὲ σοφία τις καὶ ἡ φυσική, ἀλλʼ οὐ πρώτη. ὅσα δʼ ἐγχειροῦσι τῶν λεγόντων τινὲς περὶ τῆς ἀληθείας ὃν τρόπον δεῖ ἀποδέχεσθαι, διʼ ἀπαιδευσίαν τῶν ἀναλυτικῶν τοῦτο δρῶσιν· δεῖ γὰρ περὶ τούτων ἥκειν προεπισταμένους ἀλλὰ μὴ ἀκούοντας ζητεῖν.—ὅτι μὲν οὖν τοῦ φιλοσόφου, καὶ τοῦ περὶ πάσης τῆς οὐσίας θεωροῦντος ᾗ πέφυκεν, καὶ περὶ τῶν συλλογιστικῶν ἀρχῶν ἐστὶν ἐπισκέψασθαι, δῆλον· προσήκει δὲ τὸν μάλιστα γνωρίζοντα περὶ ἕκαστον γένος ἔχειν λέγειν τὰς βεβαιοτάτας ἀρχὰς τοῦ πράγματος, ὥστε καὶ τὸν περὶ τῶν ὄντων ᾗ ὄντα τὰς πάντων βεβαιοτάτας. ἔστι δʼ οὗτος ὁ φιλόσοφος. βεβαιοτάτη δʼ ἀρχὴ πασῶν περὶ ἣν διαψευσθῆναι ἀδύνατον· γνωριμωτάτην τε γὰρ ἀναγκαῖον εἶναι τὴν τοιαύτην (περὶ γὰρ ἃ μὴ γνωρίζουσιν ἀπατῶνται πάντες) καὶ ἀνυπόθετον. ἣν γὰρ ἀναγκαῖον ἔχειν τὸν ὁτιοῦν ξυνιέντα τῶν ὄντων, τοῦτο οὐχ ὑπόθεσις· ὃ δὲ γνωρίζειν ἀναγκαῖον τῷ ὁτιοῦν γνωρίζοντι, καὶ ἥκειν ἔχοντα ἀναγκαῖον. ὅτι μὲν οὖν βεβαιοτάτη ἡ τοιαύτη πασῶν ἀρχή, δῆλον· τίς δʼ ἔστιν αὕτη, μετὰ ταῦτα λέγωμεν. τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτό (καὶ ὅσα ἄλλα προσδιορισαίμεθʼ ἄν, ἔστω προσδιωρισμένα πρὸς τὰς λογικὰς δυσχερείας)·
This is the most certain of all principles, since it possesses the required definition; for it is impossible for anyone to suppose that the same thing is and is not, as some imagine that Heraclitus says —for what a man says does not necessarily represent what he believes. And if it is impossible for contrary attributes to belong at the same time to the same subject (the usual qualifications must be added to this premiss also), and an opinion which contradicts another is contrary to it, then clearly it is impossible for the same man to suppose at the same time that the same thing is and is not; for the man who made this error would entertain two contrary opinions at the same time. Hence all men who are demonstrating anything refer back to this as an ultimate belief; for it is by nature the starting-point of all the other axioms as well. There are some, however, as we have said, who both state themselves that the same thing can be and not be, and say that it is possible to hold this view.
αὕτη δὴ πασῶν ἐστὶ βεβαιοτάτη τῶν ἀρχῶν· ἔχει γὰρ τὸν εἰρημένον διορισμόν. ἀδύνατον γὰρ ὁντινοῦν ταὐτὸν ὑπολαμβάνειν εἶναι καὶ μὴ εἶναι, καθάπερ τινὲς οἴονται λέγειν Ἡράκλειτον. οὐκ ἔστι γὰρ ἀναγκαῖον, ἅ τις λέγει, ταῦτα καὶ ὑπολαμβάνειν· εἰ δὲ μὴ ἐνδέχεται ἅμα ὑπάρχειν τῷ αὐτῷ τἀναντία (προσδιωρίσθω δʼ ἡμῖν καὶ ταύτῃ τῇ προτάσει τὰ εἰωθότα), ἐναντία δʼ ἐστὶ δόξα δόξῃ ἡ τῆς ἀντιφάσεως, φανερὸν ὅτι ἀδύνατον ἅμα ὑπολαμβάνειν τὸν αὐτὸν εἶναι καὶ μὴ εἶναι τὸ αὐτό· ἅμα γὰρ ἂν ἔχοι τὰς ἐναντίας δόξας ὁ διεψευσμένος περὶ τούτου. διὸ πάντες οἱ ἀποδεικνύντες εἰς ταύτην ἀνάγουσιν ἐσχάτην δόξαν· φύσει γὰρ ἀρχὴ καὶ τῶν ἄλλων ἀξιωμάτων αὕτη πάντων. εἰσὶ δέ τινες οἵ, καθάπερ εἴπομεν, αὐτοί τε ἐνδέχεσθαί φασι τὸ αὐτὸ εἶναι καὶ μὴ εἶναι, καὶ ὑπολαμβάνειν οὕτως.
Many even of the physicists adopt this theory. But we have just assumed that it is impossible at once to be and not to be, and by this means we have proved that this is the most certain of all principles. Some, indeed, demand to have the law proved, but this is because they lack education; for it shows lack of education not to know of what we should require proof, and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity, so that even so there would be no proof. If on the other hand there are some things of which no proof need be sought, they cannot say what principle they think to be more self-evident. Even in the case of this law, however, we can demonstrate the impossibility by refutation, if only our opponent makes some statement. If he makes none, it is absurd to seek for an argument against one who has no arguments of his own about anything, in so far as he has none; for such a person, in so far as he is such, is really no better than a vegetable. And I say that proof by refutation differs from simple proof in that he who attempts to prove might seem to beg the fundamental question, whereas if the discussion is provoked thus by someone else, refutation and not proof will result. The starting-point for all such discussions is not the claim that he should state that something is or is not so (because this might be supposed to be a begging of the question), but that he should say something significant both to himself and to another (this is essential if any argument is to follow; for otherwise such a person cannot reason either with himself or with another); and if this is granted, demonstration will be possible, for there will be something already defined.
χρῶνται δὲ τῷ λόγῳ τούτῳ πολλοὶ καὶ τῶν περὶ φύσεως. ἡμεῖς δὲ νῦν εἰλήφαμεν ὡς ἀδυνάτου ὄντος ἅμα εἶναι καὶ μὴ εἶναι, καὶ διὰ τούτου ἐδείξαμεν ὅτι βεβαιοτάτη αὕτη τῶν ἀρχῶν πασῶν. ἀξιοῦσι δὴ καὶ τοῦτο ἀποδεικνύναι τινὲς διʼ ἀπαιδευσίαν· ἔστι γὰρ ἀπαιδευσία τὸ μὴ γιγνώσκειν τίνων δεῖ ζητεῖν ἀπόδειξιν καὶ τίνων οὐ δεῖ· ὅλως μὲν γὰρ ἁπάντων ἀδύνατον ἀπόδειξιν εἶναι (εἰς ἄπειρον γὰρ ἂν βαδίζοι, ὥστε μηδʼ οὕτως εἶναι ἀπόδειξιν), εἰ δέ τινων μὴ δεῖ ζητεῖν ἀπόδειξιν, τίνα ἀξιοῦσιν εἶναι μᾶλλον τοιαύτην ἀρχὴν οὐκ ἂν ἔχοιεν εἰπεῖν. ἔστι δʼ ἀποδεῖξαι ἐλεγκτικῶς καὶ περὶ τούτου ὅτι ἀδύνατον, ἂν μόνον τι λέγῃ ὁ ἀμφισβητῶν· ἂν δὲ μηθέν, γελοῖον τὸ ζητεῖν λόγον πρὸς τὸν μηθενὸς ἔχοντα λόγον, ᾗ μὴ ἔχει· ὅμοιος γὰρ φυτῷ ὁ τοιοῦτος ᾗ τοιοῦτος ἤδη. τὸ δʼ ἐλεγκτικῶς ἀποδεῖξαι λέγω διαφέρειν καὶ τὸ ἀποδεῖξαι, ὅτι ἀποδεικνύων μὲν ἂν δόξειεν αἰτεῖσθαι τὸ ἐν ἀρχῇ, ἄλλου δὲ τοῦ τοιούτου αἰτίου ὄντος ἔλεγχος ἂν εἴη καὶ οὐκ ἀπόδειξις. ἀρχὴ δὲ πρὸς ἅπαντα τὰ τοιαῦτα οὐ τὸ ἀξιοῦν ἢ εἶναί τι λέγειν ἢ μὴ εἶναι (τοῦτο μὲν γὰρ τάχʼ ἄν τις ὑπολάβοι τὸ ἐξ ἀρχῆς αἰτεῖν), ἀλλὰ σημαίνειν γέ τι καὶ αὑτῷ καὶ ἄλλῳ·
But the person responsible is not he who demonstrates but he who acquiesces; for though he disowns reason he acquiesces to reason. Moreover, he who makes such an admission as this has admitted the truth of something apart from demonstration [so that not everything will be “so and not so”]. Thus in the first place it is obvious that this at any rate is true: that the term “to be” or “not to be” has a definite meaning; so that not everything can be “so and not so.” Again, if “man” has one meaning, let this be “two-footed animal.” By “has one meaning” I mean this: if X means “man,” then if anything is a man, its humanity will consist in being X. And it makes no difference even if it be said that “man” has several meanings, provided that they are limited in number;
τοῦτο γὰρ ἀνάγκη, εἴπερ λέγοι τι. εἰ γὰρ μή, οὐκ ἂν εἴη τῷ τοιούτῳ λόγος, οὔτʼ αὐτῷ πρὸς αὑτὸν οὔτε πρὸς ἄλλον. ἂν δέ τις τοῦτο διδῷ, ἔσται ἀπόδειξις· ἤδη γάρ τι ἔσται ὡρισμένον. ἀλλʼ αἴτιος οὐχ ὁ ἀποδεικνὺς ἀλλʼ ὁ ὑπομένων· ἀναιρῶν γὰρ λόγον ὑπομένει λόγον. ἔτι δὲ ὁ τοῦτο συγχωρήσας συγκεχώρηκέ τι ἀληθὲς εἶναι χωρὶς ἀποδείξεως [ὥστε οὐκ ἂν πᾶν οὕτως καὶ οὐχ οὕτως ἔχοι].—πρῶτον μὲν οὖν δῆλον ὡς τοῦτό γʼ αὐτὸ ἀληθές, ὅτι σημαίνει τὸ ὄνομα τὸ εἶναι ἢ μὴ εἶναι τοδί, ὥστʼ οὐκ ἂν πᾶν οὕτως καὶ οὐχ οὕτως ἔχοι· ἔτι εἰ τὸ ἄνθρωπος σημαίνει ἕν, ἔστω τοῦτο τὸ ζῷον δίπουν. λέγω δὲ τὸ ἓν σημαίνειν τοῦτο· εἰ τοῦτʼ ἔστιν ἄνθρωπος, ἂν ᾖ τι ἄνθρωπος, τοῦτʼ ἔσται τὸ ἀνθρώπῳ εἶναι (διαφέρει δʼ οὐθὲν οὐδʼ εἰ πλείω τις φαίη σημαίνειν μόνον δὲ ὡρισμένα, τεθείη γὰρ ἂν ἐφʼ ἑκάστῳ λόγῳ ἕτερον ὄνομα·
for one could assign a different name to each formula. For instance, it might be said that “man” has not one meaning but several, one of which has the formula “two-footed animal,” and there might be many other formulae as well, if they were limited in number; for a particular name could be assigned to each for formula. If on the other hand it be said that “man” has an infinite number of meanings, obviously there can be no discourse; for not to have one meaning is to have no meaning, and if words have no meaning there is an end of discourse with others, and even, strictly speaking, with oneself; because it is impossible to think of anything if we do not think of one thing; and even if this were possible, one name might be assigned to that of which we think. Now let this name, as we said at the beginning, have a meaning; and let it have one meaning. Now it is impossible that “being man” should have the same meaning as “not being man,” that is, if “man” is not merely predicable of one subject but has one meaning (for we do not identify “having one meaning” with “being predicable of one subject,” since in this case “cultured” and “white” and “man” would have one meaning, and so all things would be one; for they would all have the same meaning). And it will be impossible for the same thing to be and not to be, except by equivocation, as e.g. one whom we call “man” others might call “not-man”; but the problem is whether the same thing can at once be and not be “man,” not in name, but in fact.
λέγω δʼ οἷον, εἰ μὴ φαίη τὸ ἄνθρωπος ἓν σημαίνειν, πολλὰ δέ, ὧν ἑνὸς μὲν εἷς λόγος τὸ ζῷον δίπουν, εἶεν δὲ καὶ ἕτεροι πλείους, ὡρισμένοι δὲ τὸν ἀριθμόν· τεθείη γὰρ ἂν ἴδιον ὄνομα καθʼ ἕκαστον τὸν λόγον· εἰ δὲ μή [τεθείη], ἀλλʼ ἄπειρα σημαίνειν φαίη, φανερὸν ὅτι οὐκ ἂν εἴη λόγος· τὸ γὰρ μὴ ἓν σημαίνειν οὐθὲν σημαίνειν ἐστίν, μὴ σημαινόντων δὲ τῶν ὀνομάτων ἀνῄρηται τὸ διαλέγεσθαι πρὸς ἀλλήλους, κατὰ δὲ τὴν ἀλήθειαν καὶ πρὸς αὑτόν· οὐθὲν γὰρ ἐνδέχεται νοεῖν μὴ νοοῦντα ἕν, εἰ δʼ ἐνδέχεται, τεθείη ἂν ὄνομα τούτῳ τῷ πράγματι ἕν).—ἔστω δή, ὥσπερ ἐλέχθη κατʼ ἀρχάς, σημαῖνόν τι τὸ ὄνομα καὶ σημαῖνον ἕν· οὐ δὴ ἐνδέχεται τὸ ἀνθρώπῳ εἶναι σημαίνειν ὅπερ ἀνθρώπῳ μὴ εἶναι, εἰ τὸ ἄνθρωπος σημαίνει μὴ μόνον καθʼ ἑνὸς ἀλλὰ καὶ ἕν (οὐ γὰρ τοῦτο ἀξιοῦμεν τὸ ἓν σημαίνειν, τὸ καθʼ ἑνός, ἐπεὶ οὕτω γε κἂν τὸ μουσικὸν καὶ τὸ λευκὸν καὶ τὸ ἄνθρωπος ἓν ἐσήμαινεν, ὥστε ἓν ἅπαντα ἔσται· συνώνυμα γάρ). καὶ οὐκ ἔσται εἶναι καὶ μὴ εἶναι τὸ αὐτὸ ἀλλʼ ἢ καθʼ ὁμωνυμίαν, ὥσπερ ἂν εἰ ὃν ἡμεῖς ἄνθρωπον καλοῦμεν, ἄλλοι μὴ ἄνθρωπον καλοῖεν·
If “man” and “not-man” have not different meanings, clearly “not being a man” will mean nothing different from “being a man”; and so “being a man” will be “not being a man”; they will be one. For “to be one” means, as in the case of “garment” and “coat,” that the formula is one. And if “being man” and “being not-man” are to be one, they will have the same meaning; but it has been proved above that they have different meanings. If then anything can be truly said to be “man,” it must be “two-footed animal”; for this is what “man” was intended to mean. And if this is necessarily so, it is impossible that at the same time the same thing should not be “two-footed animal.” For “to be necessarily so” means this: that it is impossible not to be so. Thus it cannot be true to say at the same time that the same thing is and is not man. And the same argument holds also in the case of not being man;
τὸ δʼ ἀπορούμενον οὐ τοῦτό ἐστιν, εἰ ἐνδέχεται τὸ αὐτὸ ἅμα εἶναι καὶ μὴ εἶναι ἄνθρωπον τὸ ὄνομα, ἀλλὰ τὸ πρᾶγμα. εἰ δὲ μὴ σημαίνει ἕτερον τὸ ἄνθρωπος καὶ τὸ μὴ ἄνθρωπος, δῆλον ὅτι καὶ τὸ μὴ εἶναι ἀνθρώπῳ τοῦ εἶναι ἀνθρώπῳ· ὥστʼ ἔσται τὸ ἀνθρώπῳ εἶναι μὴ ἀνθρώπῳ εἶναι· ἓν γὰρ ἔσται. τοῦτο γὰρ σημαίνει τὸ εἶναι ἕν, τὸ ὡς λώπιον καὶ ἱμάτιον, εἰ ὁ λόγος εἷς· εἰ δὲ ἔσται ἕν, ἓν σημανεῖ τὸ ἀνθρώπῳ εἶναι καὶ μὴ ἀνθρώπῳ. ἀλλʼ ἐδέδεικτο ὅτι ἕτερον σημαίνει. ἀνάγκη τοίνυν, εἴ τί ἐστιν ἀληθὲς εἰπεῖν ὅτι ἄνθρωπος, ζῷον εἶναι δίπουν (τοῦτο γὰρ ἦν ὃ ἐσήμαινε τὸ ἄνθρωπος)· εἰ δʼ ἀνάγκη τοῦτο, οὐκ ἐνδέχεται μὴ εἶναι ⟨τότε⟩ τὸ αὐτὸ ζῷον δίπουν (τοῦτο γὰρ σημαίνει τὸ ἀνάγκη εἶναι, τὸ ἀδύνατον εἶναι μὴ εἶναι [ἄνθρωπον])· οὐκ ἄρα ἐνδέχεται ἅμα ἀληθὲς εἶναι εἰπεῖν τὸ αὐτὸ ἄνθρωπον εἶναι καὶ μὴ εἶναι ἄνθρωπον. ὁ δʼ αὐτὸς λόγος καὶ ἐπὶ τοῦ μὴ εἶναι ἄνθρωπον·
because “being man” and “being not-man” have different meanings if “being white” and “being man” have different meanings (for the opposition is much stronger in the former case so as to produce different meanings). And if we are told that “white” too means one and the same thing, we shall say again just what we said before, that in that case all things, and not merely the opposites, will be one. But if this is impossible, what we have stated follows; that is, if our opponent answers our question; but if when asked the simple question he includes in his answer the negations, he is not answering our question. There is nothing to prevent the same thing from being “man” and “white” and a multitude of other things; but nevertheless when asked whether it is true to say that X is man, or not, one should return an answer that means one thing, and not add that X is white and large. It is indeed impossible to enumerate all the infinity of accidents; and so let him enumerate either all or none. Similarly therefore, even if the same thing is ten thousand times “man” and “not-man,” one should not include in one’s answer to the question whether it is “man” that it is at the same time also “not-man,” unless one is also bound to include in one’s answer all the other accidental things that the subject is or is not.
τὸ γὰρ ἀνθρώπῳ εἶναι καὶ τὸ μὴ ἀνθρώπῳ εἶναι ἕτερον σημαίνει, εἴπερ καὶ τὸ λευκὸν εἶναι καὶ τὸ ἄνθρωπον εἶναι ἕτερον· πολὺ γὰρ ἀντίκειται ἐκεῖνο μᾶλλον, ὥστε σημαίνειν ἕτερον. εἰ δὲ καὶ τὸ λευκὸν φήσει τὸ αὐτὸ καὶ ἓν σημαίνειν, πάλιν τὸ αὐτὸ ἐροῦμεν ὅπερ καὶ πρότερον ἐλέχθη, ὅτι ἓν πάντα ἔσται καὶ οὐ μόνον τὰ ἀντικείμενα. εἰ δὲ μὴ ἐνδέχεται τοῦτο, συμβαίνει τὸ λεχθέν, ἂν ἀποκρίνηται τὸ ἐρωτώμενον. ἐὰν δὲ προστιθῇ ἐρωτῶντος ἁπλῶς καὶ τὰς ἀποφάσεις, οὐκ ἀποκρίνεται τὸ ἐρωτώμενον. οὐθὲν γὰρ κωλύει εἶναι τὸ αὐτὸ καὶ ἄνθρωπον καὶ λευκὸν καὶ ἄλλα μυρία τὸ πλῆθος· ἀλλʼ ὅμως ἐρομένου εἰ ἀληθὲς εἰπεῖν ἄνθρωπον τοῦτο εἶναι ἢ οὔ, ἀποκριτέον τὸ ἓν σημαῖνον καὶ οὐ προσθετέον ὅτι καὶ λευκὸν καὶ μέγα. καὶ γὰρ ἀδύνατον ἄπειρά γʼ ὄντα τὰ συμβεβηκότα διελθεῖν· ἢ οὖν ἅπαντα διελθέτω ἢ μηθέν. ὁμοίως τοίνυν εἰ καὶ μυριάκις ἐστὶ τὸ αὐτὸ ἄνθρωπος καὶ οὐκ ἄνθρωπος, οὐ προσαποκριτέον τῷ ἐρομένῳ εἰ ἔστιν ἄνθρωπος, ὅτι ἐστὶν ἅμα καὶ οὐκ ἄνθρωπος, εἰ μὴ καὶ τἆλλα ὅσα συμβέβηκε προσαποκριτέον, ὅσα ἐστὶν ἢ μὴ ἔστιν· ἐὰν δὲ τοῦτο ποιῇ, οὐ διαλέγεται.—ὅλως δʼ ἀναιροῦσιν οἱ τοῦτο λέγοντες οὐσίαν καὶ τὸ τί ἦν εἶναι.
And if one does this, he is not arguing properly. In general those who talk like this do away with substance and essence, for they are compelled to assert that all things are accidents, and that there is no such thing as “being essentially man” or “animal.” For if there is to be such a thing as “being essentially man,” this will not be “being not-man” nor “not-being man” (and yet these are negations of it); for it was intended to have one meaning, i.e. the substance of something. But to denote a substance means that the essence is that and nothing else; and if for it “being essentially man” is the same as either “being essentially not-man” or “essentially not-being man,” the essence will be something else. Thus they are compelled to say that nothing can have such a definition as this, but that all things are accidental; for this is the distinction between substance and accident: “white” is an accident of “man,” because although he is white, he is not white in essence. And since the accidental always implies a predication about some subject, if all statements are accidental, there will be nothing primary about which they are made;
πάντα γὰρ ἀνάγκη συμβεβηκέναι φάσκειν αὐτοῖς, καὶ τὸ ὅπερ ἀνθρώπῳ εἶναι ἢ ζῴῳ εἶναι μὴ εἶναι. εἰ γὰρ ἔσται τι ὅπερ ἀνθρώπῳ εἶναι, τοῦτο οὐκ ἔσται μὴ ἀνθρώπῳ εἶναι ἢ μὴ εἶναι ἀνθρώπῳ (καίτοι αὗται ἀποφάσεις τούτου)· ἓν γὰρ ἦν ὃ ἐσήμαινε, καὶ ἦν τοῦτό τινος οὐσία. τὸ δʼ οὐσίαν σημαίνειν ἐστὶν ὅτι οὐκ ἄλλο τι τὸ εἶναι αὐτῷ. εἰ δʼ ἔσται αὐτῷ τὸ ὅπερ ἀνθρώπῳ εἶναι ἢ ὅπερ μὴ ἀνθρώπῳ εἶναι ἢ ὅπερ μὴ εἶναι ἀνθρώπῳ, ἄλλο ἔσται, ὥστʼ ἀναγκαῖον αὐτοῖς λέγειν ὅτι οὐθενὸς ἔσται τοιοῦτος λόγος, ἀλλὰ πάντα κατὰ συμβεβηκός· τούτῳ γὰρ διώρισται οὐσία καὶ τὸ συμβεβηκός· τὸ γὰρ λευκὸν τῷ ἀνθρώπῳ συμβέβηκεν ὅτι ἔστι μὲν λευκὸς ἀλλʼ οὐχ ὅπερ λευκόν. εἰ δὲ πάντα κατὰ συμβεβηκὸς λέγεται, οὐθὲν ἔσται πρῶτον τὸ καθʼ οὗ, εἰ ἀεὶ τὸ συμβεβηκὸς καθʼ ὑποκειμένου τινὸς σημαίνει τὴν κατηγορίαν.
so the predication must proceed to infinity. But this is impossible, for not even more than two accidents can be combined in predication. An accident cannot be an accident of an accident unless both are accidents of the same thing. I mean, e.g., that “white” is “cultured” and “cultured” “white” merely because both are accidents of a man. But it is not in this sense—that both terms are accidents of something else—that Socrates is cultured. Therefore since some accidents are predicated in the latter and some in the former sense, such as are predicated in the way that “white” is of Socrates cannot be an infinite series in the upper direction; e.g. there cannot be another accident of “white Socrates,” for the sum of these predications does not make a single statement. Nor can “white” have a further accident, such as “cultured”; for the former is no more an accident of the latter than vice versa; and besides we have distinguished that although some predicates are accidental in this sense, others are accidental in the sense that “cultured” is to Socrates; and whereas in the former case the accident is an accident of an accident, it is not so in the latter; and thus not all predications will be of accidents. Therefore even so there will be something which denotes substance. And if this is so, we have proved that contradictory statements cannot be predicated at the same time. Again, if all contradictory predications of the same subject at the same time are true, clearly all things will be one.
ἀνάγκη ἄρα εἰς ἄπειρον ἰέναι. ἀλλʼ ἀδύνατον· οὐδὲ γὰρ πλείω συμπλέκεται δυοῖν· τὸ γὰρ συμβεβηκὸς οὐ συμβεβηκότι συμβεβηκός, εἰ μὴ ὅτι ἄμφω συμβέβηκε ταὐτῷ, λέγω δʼ οἷον τὸ λευκὸν μουσικὸν καὶ τοῦτο λευκὸν ὅτι ἄμφω τῷ ἀνθρώπῳ συμβέβηκεν. ἀλλʼ οὐχ ὁ Σωκράτης μουσικὸς οὕτως, ὅτι ἄμφω συμβέβηκεν ἑτέρῳ τινί. ἐπεὶ τοίνυν τὰ μὲν οὕτως τὰ δʼ ἐκείνως λέγεται συμβεβηκότα, ὅσα οὕτως λέγεται ὡς τὸ λευκὸν τῷ Σωκράτει, οὐκ ἐνδέχεται ἄπειρα εἶναι ἐπὶ τὸ ἄνω, οἷον τῷ Σωκράτει τῷ λευκῷ ἕτερόν τι συμβεβηκός· οὐ γὰρ γίγνεταί τι ἓν ἐξ ἁπάντων. οὐδὲ δὴ τῷ λευκῷ ἕτερόν τι ἔσται συμβεβηκός, οἷον τὸ μουσικόν· οὐθέν τε γὰρ μᾶλλον τοῦτο ἐκείνῳ ἢ ἐκεῖνο τούτῳ συμβέβηκεν, καὶ ἅμα διώρισται ὅτι τὰ μὲν οὕτω συμβέβηκε τὰ δʼ ὡς τὸ μουσικὸν Σωκράτει· ὅσα δʼ οὕτως, οὐ συμβεβηκότι συμβέβηκε συμβεβηκός, ἀλλʼ ὅσα ἐκείνως, ὥστʼ οὐ πάντα κατὰ συμβεβηκὸς λεχθήσεται. ἔσται ἄρα τι καὶ ὣς οὐσίαν σημαῖνον. εἰ δὲ τοῦτο, δέδεικται ὅτι ἀδύνατον ἅμα κατηγορεῖσθαι τὰς ἀντιφάσεις.—ἔτι εἰ ἀληθεῖς αἱ ἀντιφάσεις ἅμα κατὰ τοῦ αὐτοῦ πᾶσαι, δῆλον ὡς ἅπαντα ἔσται ἕν.
For if it is equally possible either to affirm or deny anything of anything, the same thing will be a trireme and a wall and a man; which is what necessarily follows for those who hold the theory of Protagoras. For if anyone thinks that a man is not a trireme, he is clearly not a trireme; and so he also is a trireme if the contradictory statement is true. And the result is the dictum of Anaxagoras, “all things mixed together”; so that nothing truly exists. It seems, then, that they are speaking of the Indeterminate; and while they think that they are speaking of what exists, they are really speaking of what does not; for the Indeterminate is that which exists potentially but not actually. But indeed they must admit the affirmation or negation of any predicate of any subject, for it is absurd that in the case of each term its own negation should be true, and the negation of some other term which is not true of it should not be true. I mean, e.g., that if it is true to say that a man is not a man, it is obviously also true to say that he is or is not a trireme. Then if the affirmation is true, so must the negation be true; but if the affirmation is not true the negation will be even truer than the negation of the original term itself.
ἔσται γὰρ τὸ αὐτὸ καὶ τριήρης καὶ τοῖχος καὶ ἄνθρωπος, εἰ κατὰ παντός τι ἢ καταφῆσαι ἢ ἀποφῆσαι ἐνδέχεται, καθάπερ ἀνάγκη τοῖς τὸν Πρωταγόρου λέγουσι λόγον. εἰ γάρ τῳ δοκεῖ μὴ εἶναι τριήρης ὁ ἄνθρωπος, δῆλον ὡς οὐκ ἔστι τριήρης· ὥστε καὶ ἔστιν, εἴπερ ἡ ἀντίφασις ἀληθής. καὶ γίγνεται δὴ τὸ τοῦ Ἀναξαγόρου, ὁμοῦ πάντα χρήματα· ὥστε μηθὲν ἀληθῶς ὑπάρχειν. τὸ ἀόριστον οὖν ἐοίκασι λέγειν, καὶ οἰόμενοι τὸ ὂν λέγειν περὶ τοῦ μὴ ὄντος λέγουσιν· τὸ γὰρ δυνάμει ὂν καὶ μὴ ἐντελεχείᾳ τὸ ἀόριστόν ἐστιν. ἀλλὰ μὴν λεκτέον γʼ αὐτοῖς κατὰ παντὸς ⟨παντὸς⟩ τὴν κατάφασιν ἢ τὴν ἀπόφασιν· ἄτοπον γὰρ εἰ ἑκάστῳ ἡ μὲν αὐτοῦ ἀπόφασις ὑπάρξει, ἡ δʼ ἑτέρου ὃ μὴ ὑπάρχει αὐτῷ οὐχ ὑπάρξει· λέγω δʼ οἷον εἰ ὀληθὲς εἰπεῖν τὸν ἄνθρωπον ὅτι οὐκ ἄνθρωπος, δῆλον ὅτι καὶ ἢ τριήρης ἢ οὐ τριήρης. εἰ μὲν οὖν ἡ κατάφασις, ἀνάγκη καὶ τὴν ἀπόφασιν· εἰ δὲ μὴ ὑπάρχει ἡ κατάφασις, ἥ γε ἀπόφασις ὑπάρξει μᾶλλον ἢ ἡ αὐτοῦ.
Therefore if the latter negation is true, the negation of “trireme” will also be true; and if this is true, the affirmation will be true too. And not only does this follow for those who hold this theory, but also that it is not necessary either to affirm or to deny a statement. For if it is true that X is both man and not-man, clearly he will be neither man nor not-man; for to the two statements there correspond two negations, and if the former is taken as a single statement compounded out of two, the latter is also a single statement and opposite to it. Again, either this applies to all terms, and the same thing is both white and not-white, and existent and non-existent, and similarly with all other assertions and negations; or it does not apply to all, but only to some and not to others. And if it does not apply to all, the exceptions will be admitted; but if it does apply to all, again either (a) the negation will be true wherever the affirmation is true, and the affirmation will be true wherever the negation is true, or (d) the negation will be true wherever the assertion is true, but the assertion will not always be true where the negation is true. And in the latter case there will be something which definitely is not, and this will be a certain belief; and if that it is not is certain and knowable, the opposite assertion will be still more knowable. But if what is denied can be equally truly asserted, it must be either true or false to state the predicates separately and say, e.g., that a thing is white, and again that it is not-white.
εἰ οὖν κἀκείνη ὑπάρχει, ὑπάρξει καὶ ἡ τῆς τριήρους· εἰ δʼ αὕτη, καὶ ἡ κατάφασις.—ταῦτά τε οὖν συμβαίνει τοῖς λέγουσι τὸν λόγον τοῦτον, καὶ ὅτι οὐκ ἀνάγκη ἢ φάναι ἢ ἀποφάναι. εἰ γὰρ ἀληθὲς ὅτι ἄνθρωπος καὶ οὐκ ἄνθρωπος, δῆλον ὅτι καὶ οὔτʼ ἄνθρωπος οὔτʼ οὐκ ἄνθρωπος ἔσται· τοῖν γὰρ δυοῖν δύο ἀποφάσεις, εἰ δὲ μία ἐξ ἀμφοῖν ἐκείνη, καὶ αὕτη μία ἂν εἴη ἀντικειμένη.—ἔτι ἤτοι περὶ ἅπαντα οὕτως ἔχει, καὶ ἔστι καὶ λευκὸν καὶ οὐ λευκὸν καὶ ὂν καὶ οὐκ ὄν, καὶ περὶ τὰς ἄλλας φάσεις καὶ ἀποφάσεις ὁμοιοτρόπως, ἢ οὒ ἀλλὰ περὶ μέν τινας, περί τινας δʼ οὔ. καὶ εἰ μὲν μὴ περὶ πάσας, αὗται ἂν εἶεν ὁμολογούμεναι· εἰ δὲ περὶ πάσας, πάλιν ἤτοι καθʼ ὅσων τὸ φῆσαι καὶ ἀποφῆσαι καὶ καθʼ ὅσων ἀποφῆσαι καὶ φῆσαι, ἢ κατὰ μὲν ὧν φῆσαι καὶ ἀποφῆσαι, καθʼ ὅσων δὲ ἀποφῆσαι οὐ πάντων φῆσαι. καὶ εἰ μὲν οὕτως, εἴη ἄν τι παγίως οὐκ ὄν, καὶ αὕτη βεβαία δόξα, καὶ εἰ τὸ μὴ εἶναι βέβαιόν τι καὶ γνώριμον, γνωριμωτέρα ἂν εἴη ἡ φάσις ἡ ἀντικειμένη· εἰ δὲ ὁμοίως καὶ ὅσα ἀποφῆσαι φάναι, ἀνάγκη ἤτοι ἀληθὲς διαιροῦντα λέγειν, οἷον ὅτι λευκὸν καὶ πάλιν ὅτι οὐ λευκόν, ἢ οὔ.