§4.3λεκτέον δὲ πότερον μιᾶς ἢ ἑτέρας ἐπιστήμης περί τε τῶν ἐν τοῖς μαθήμασι καλουμένων ἀξιωμάτων καὶ περὶ τῆς οὐσίας.
We must say whether it belongs to one or to another science to inquire both about the so-called axioms in mathematics and about substance.
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.
It is clear, then, that the inquiry about these also belongs to one science, and that of the philosopher; for they belong to all beings, and not to some genus separate and private from the others.
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·
And all make use of them, because they belong to being qua being, and each genus is being; but they use them to such an extent as is sufficient for them, and this is as far as the genus extends about which they bring their proofs.
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.
So that, since it is clear that they belong to all things qua being (for this is what is common to them), the contemplation about these also belongs to the one who cognizes being qua being.
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.
Therefore, none of those who inquire into particulars attempts to say anything about them, whether they are true or not, neither geometer nor arithmetician, but some of the natural philosophers do so, and naturally enough; for they alone thought they were inquiring about the whole of nature and about being.
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·
But since there is someone still higher than the natural philosopher (for nature is one particular genus of being), the inquiry about these would belong to the one who contemplates the universal and the first substance.
ἔστι δὲ σοφία τις καὶ ἡ φυσική, ἀλλʼ οὐ πρώτη.
Natural philosophy is also a kind of wisdom, but not the first.
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.
And as for the attempts of some of those who speak about the truth to state in what way one should accept it, they do this through lack of education in analytics; for they should come prepared with knowledge about these, and not inquire while they are listening to lectures.
—ὅτι μὲν οὖν τοῦ φιλοσόφου, καὶ τοῦ περὶ πάσης τῆς οὐσίας θεωροῦντος ᾗ πέφυκεν, καὶ περὶ τῶν συλλογιστικῶν ἀρχῶν ἐστὶν ἐπισκέψασθαι, δῆλον·
That, therefore, it belongs to the philosopher, and to the one who contemplates all substance qua its natural being, to inquire also about the principles of syllogism, is clear.
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.
And it is fitting for the one who most cognizes about each genus to be able to state the most certain principles of the matter, and so also for the one who cognizes about beings qua beings to state the most certain principles of all.
ἔστι δʼ οὗτος ὁ φιλόσοφος.
And this is the philosopher.
βεβαιοτάτη δʼ ἀρχὴ πασῶν περὶ ἣν διαψευσθῆναι ἀδύνατον· γνωριμωτάτην τε γὰρ ἀναγκαῖον εἶναι τὴν τοιαύτην (περὶ γὰρ ἃ μὴ γνωρίζουσιν ἀπατῶνται πάντες) καὶ ἀνυπόθετον.
And the most certain principle of all is that about which it is impossible to be mistaken; for such a principle must be both the most cognizable (for all are deceived about what they do not cognize) and non-hypothetical.
ἣν γὰρ ἀναγκαῖον ἔχειν τὸν ὁτιοῦν ξυνιέντα τῶν ὄντων, τοῦτο οὐχ ὑπόθεσις· ὃ δὲ γνωρίζειν ἀναγκαῖον τῷ ὁτιοῦν γνωρίζοντι, καὶ ἥκειν ἔχοντα ἀναγκαῖον.
For that which one who understands anything at all of beings must possess is not a hypothesis; and what one must cognize who cognizes anything at all, he must come possessing.
ὅτι μὲν οὖν βεβαιοτάτη ἡ τοιαύτη πασῶν ἀρχή, δῆλον· τίς δʼ ἔστιν αὕτη, μετὰ ταῦτα λέγωμεν.
That, therefore, such a principle is the most certain of all is clear; let us state next what this is.
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)·
For it is impossible for the same thing to belong and not to belong at the same time to the same thing and in the same respect (and whatever other specifications we might add, let them be specified against logical difficulties).
αὕτη δὴ πασῶν ἐστὶ βεβαιοτάτη τῶν ἀρχῶν· ἔχει γὰρ τὸν εἰρημένον διορισμόν.
This, then, is the most certain of all principles; for it has the stated specification.
ἀδύνατον γὰρ ὁντινοῦν ταὐτὸν ὑπολαμβάνειν εἶναι καὶ μὴ εἶναι, καθάπερ τινὲς οἴονται λέγειν Ἡράκλειτον.
For it is impossible for anyone to believe that the same thing is and is not, as some think Heraclitus says.
οὐκ ἔστι γὰρ ἀναγκαῖον, ἅ τις λέγει, ταῦτα καὶ ὑπολαμβάνειν·
For it is not necessary that what one says, one must also believe.
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.
And if it is not possible for contraries to belong to the same thing at the same time (and let the usual specifications be added by us to this premise too), and a contrary opinion to an opinion is that of contradiction, it is manifest that it is impossible for the same person to believe at the same time that the same thing is and is not; for the one who is mistaken about this would have contrary opinions at the same time.
διὸ πάντες οἱ ἀποδεικνύντες εἰς ταύτην ἀνάγουσιν ἐσχάτην δόξαν· φύσει γὰρ ἀρχὴ καὶ τῶν ἄλλων ἀξιωμάτων αὕτη πάντων.
Therefore, all who demonstrate refer to this ultimate belief; for this is by nature the principle also of all the other axioms.