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to have. And that which has need of another for perfection and for being itself will be much more in need.

For if substance is better than form, as they say, and if that being, which is what they wish to say, has been able to provide this for itself or simply to have it, how was it not sufficient simply to have or to provide for itself the lesser thing, I mean the form? But if that being, which those who dare to ascribe beginninglessness to things that are after God and from God wish to call either substance or matter (for we are not disputing about this), was not sufficient to provide the lesser thing for itself, or simply to have it, how has it, having been unable to have the lesser, been able to have the greater, being itself (14∆_238> I say, either simply or from itself? But if matter has in no way been able to have the lesser thing from itself or simply, much more 1184 will it not be able to have being itself simply, or in some way from itself. Therefore, having proven weak, as has been shown, in having the lesser, I mean the form, it could never in any way be able to have the greater, being itself, I say. But if this is so, then being and form have certainly been given by God to existing things, since they exist; and if every substance, both matter and all form, is from God, no one, unless entirely deprived of sound reasoning, would venture to say that matter is without beginning or ungenerated, knowing God to be the maker and creator of existing things.

59. PROOF THAT EVERYTHING THAT IS MOVED ... CANNOT BE INFINITE...

Proof that everything that is moved, or is contemplated from eternity together with another thing different in substance, cannot be infinite, and that the dyad is neither a principle nor without beginning, and that the monad alone is properly a principle and without beginning.

And again, if matter existed, as some say, it has clearly not come into being, and if it has not come into being,

it is not moved, and if it is not moved, it did not begin to be, and if it did not begin to be, it is certainly without beginning, and if without beginning, also infinite, and if infinite, certainly also unmoved (for the infinite is certainly unmoved, for that which is not defined has nowhere to be moved), and if this is so, there are certainly two infinites, without beginning and unmoved, God and matter, which is impossible. For a dyad can be neither infinite, nor without beginning, nor unmoved, nor will it be able not to be the principle of anything at all, being circumscribed by both union and division, by union, as having for its existence the synthesis of monads, by which it is contained as by parts and into which it can be divided as parts (14∆_240> (and nothing divisible or divided, or composite or composed, by nature or position or in any other conceivable way, nor even division or synthesis simply so-called, will be able to be infinite, except for that which is simple and alone, and not numerable or numbered or counted with, or simply free from any relation whatsoever; for all these things are considered in relation, but the infinite is without relation, for it has absolutely nothing joined to it by relation), and by division, as moved by number, from which it began and by which it is contained, since it does not have its being by nature and without relation. For every dyad and every monad contributing to a part of it exists by number, by which the monads within it deprive one another of uncircumscribability.

And no one who has any share at all in reasoning would say that something is infinite with which something different in substance is contemplated or co-contemplated from eternity, knowing that, for one who thinks thus, the argument concerning the infinite will certainly fail. For the infinite is infinite in every respect, reason, and manner, in substance, in power, in activity, at both limits, I mean the upper and the lower, that is, according to the beginning and the end. For it is uncontained in substance, and inconceivable in power, and uncircumscribable in 1185 activity, and the infinite is without beginning from above and without end from below, and to speak more truly, simply, and all things

57

ἔχειν. Τό δέ ἑτέρου προσδεόμενον πρός τελείωσιν καί πρός αὐτό τό εἶναι πολλῷ μᾶλλον προσδεηθήσεται.

Εἰ γάρ εἴδους κρείττων, ὥς φασιν, ἡ οὐσία καθέστηκε, ταύτην δέ ἑαυτῷ παρασχεῖν ἤ ἁπλῶς ἔχειν δεδύνηται ἐκεῖνο τό ὄν, ὅπερ αὐτοί φάναι βούλονται, πῶς πρός τό ἔχειν ἁπλῶς ἤ παρασχεῖν ἑαυτῷ τό ἦττον, φημί δέ τό εἶδος, οὐκ ἐπήρκεσε; Εἰ δέ πρός τό παρασχεῖν ἑαυτῷ τό ἦττον, ἤ ἁπλῶς ἔχειν ἐκεῖνο τό ὄν, ὅπερ εἴ τε οὐσίαν, εἴ τε ὕλην καλεῖν βούλονται οἱ τό ἄναρχον τοῖς μετά Θεόν καί ἐκ Θεοῦ προσάπτειν τολμῶντες (οὐ γάρ περί τούτου διαφερόμεθα ) οὐκ ἐπήρκεσε, πῶς τό κρεῖττον, αὐτό τό εἶναί (14∆_238> φημι, ἤ ἁπλῶς ἤ παρ᾿ ἑαυτοῦ ἔχειν δεδύνηται, τό πρός τό ἔχειν τό ἦττον ἀδυνατῆσαν; Εἰ δέ παρ᾿ ἑαυτῆς ἤ ἁπλῶς ἔχειν τό ἦττον οὐδαμῶς ἡ ὕλη δεδύνηται, πολλῷ μᾶλλον 1184 αὐτό τό εἶναι ἁπλῶς, ἤ πῶς παρ᾿ ἑαυτῆς ἔχειν οὐ δυνηθήσεται. Ἅρ᾿ οὖν ἡ πρός τό ἔχειν, ὡς δέδεικται, τό ἦττον, λέγω δέ τό εἶδος, ἀτονήσασα οὐδέ τό κρεῖττον, αὐτό τό εἶναί φημι, κἄν ὁπωσοῦν ἔχειν δυνηθείη ποτέ. Εἰ δέ τοῦτο, πάντως ἐκ Θεοῦ τό εἶναι τοῖς οὖσι καί τό εἶδος δεδώρηται, ἐπείπερ εἰσίν· εἰ δέ ἐκ Θεοῦ πᾶσα οὐσία, καί ὕλη καί εἶδος ἅπαν ἐστίν, οὐδείς ἄν μή πάντη σώφρονος λογισμοῦ ἐστερημένος εἰπεῖν ἀνάσχοιτο ἄναρχον ἤ ἀγένητον τήν ὕλην, Θεόν εἰδώς τῶν ὄντων ποιητήν καί δημιουργόν.

ΝΘ (59). ΑΠΟ∆ΕΙΞΙΣ ΟΤΙ ΠΑΝ ΚΙΝΟΥΜΕΝΟΝ ... ΑΠΕΙΡΟΝ ΕΙΝΑΙ ΟΥ ∆ΥΝΑΤΑΙ...

Ἀπόδειξις ὅτι πᾶν κινούμενον, ἤ ἄλλῳ διαφόρῳ κατά τήν οὐσίαν ἐξ ἀϊδίου συνθεωρούμενον, ἄπειρον εἶναι οὐ δύναται, καί ὅτι ἡ δυάς οὔτε ἀρχή ἐστιν, οὔτε ἄναρχος, καί ὅτι ἡ μονάς μόνη κυρίως ἀρχή καί ἄναρχος.

Καί πάλιν, εἰ ἦν, ὥς τινές φασιν, ἡ ὕλη, οὐ γέγονε δηλονότι, εἰ δέ μή γέγονεν,

οὐδέ κινεῖται, εἰ δέ μή κινεῖται, οὔτε τοῦ εἶναι ἤρξατο, εἰ δέ τοῦ εἶναι μή ἤρξατο, πάντως ἄναρχον, εἰ δέ ἄναρχον, καί ἄπειρον, εἰ δέ ἄπειρον, πάντως καί ἀκίνητον (ἀκίνητον γάρ πάντως τό ἄπειρον, οὐ γάρ ἔχει ποῦ κινηθῆναι τό μή ὁριζόμενον), εἰ δέ τοῦτο, δύο πάντως τά ἄπειρα καί ἄναρχα καί ἀκίνητα, Θεός καί ὕλη, ὅπερ εἶναι ἀμήχανον. ∆υάς γάρ οὔτε ἄπειρος, οὔτε ἄναρχος, οὔτε ἀκίνητος, οὔτε μή ἀρχή καθόλου τινός εἶναι δυνήσεται, καθ᾿ ἕνωσίν τε καί διαίρεσιν περιγραφομένη, καθ᾿ ἕνωσιν μέν ὡς ὕπαρξιν ἔχουσα τῶν μονάδων τήν σύνθεσιν, ὑφ᾿ ὧν ὡς μερῶν περιέχεται καί εἰς ἅς ὡς μέρη τέμνεσθαι (14∆_240> δύναται (οὐδέν δέ διαιρετόν ἤ διαιρούμενον, ἤ σύνθετον ἤ συντιθέμενον, κατά φύσιν ἤ θέσιν ἤ ἄλλον τινά ἐπινοηθῆναι δυνάμενον τρόπον, ἀλλ᾿ οὐδέ αὐτή ἡ ἁπλῶς λεγομένη διαίρεσις ἤ σύνθεσις, ἄπειρον εἶναι δυνήσεται, ὅτι μή καί ἁπλοῦν καί μόνον, καί μή ἀριθμητόν ἤ ἀριθμούμενον ἤ συναριθμούμενον, ἤ πάσης ἁπλῶς ἐλεύθερον τῆς οἱασδήποτε σχέσεως· πάντα γάρ ταῦτα ἐν σχέσει θεωρεῖται, τό δέ ἄπειρον ἄσχετον, οὐ γάρ ἔχει τι κατά σχέσιν συνημμένον παντάπασι), κατά διαίρεσιν δέ ὡς ἀριθμῷ κινουμένη, ἐξ οὗπερ ἤρξατό τε καί ὑφ᾿ οὗ περιέχεται, ἐπείπερ οὐ φύσει τό εἶναι καί ἄσχετον ἔχει. Ἀριθμῷ γάρ πᾶσα δυάς καί πᾶσα μονάς εἰς μέρος αὐτῆς συντελοῦσα εἶναι καθέστηκε, καθ᾿ ὅν ἀλλήλων αἱ κατ᾿ αὐτήν μονάδες, ἀφαιροῦνται τό ἀπερίγραφον.

Οὐδείς δέ μεμοιραμένος καί ὁπωσοῦν τοῦ λογίζεσθαι εἴποι ἄν ἄπειρον εἶναι ᾧ ἐξ ἀϊδίου συνθεωρεῖταί τι ἤ συνεπιθεωρεῖται κατ᾿ οὐσίαν διάφορον, εἰδώς διαπεσεῖσθαι πάντως αὐτῷ τόν περί τοῦ ἀπείρου λόγον οὕτω φρονοῦντι. Τό γάρ ἄπειρον κατά πάντα καί λόγον καί τρόπον ἐστίν ἄπειρον, κατ᾿ οὐσίαν, κατά δύναμιν, κατ᾿ ἐνέργειαν, κατ᾿ ἄμφω τά πέρατα, τό ἄνω τε λέγω καί τό κάτω, τουτέστι κατά τήν ἀρχήν καί τό τέλος. Ἀχώρητον γάρ κατά τήν οὐσίαν, καί ἀπερινόητον κατά τήν δύναμιν, καί κατά τήν 1185 ἐνέργειαν ἀπερίγραφον, καί ἄναρχον ἄνωθεν, καί ἀτελεύτητον κάτωθέν ἐστι τό ἄπειρον, καί ἁπλῶς εἰπεῖν ἀληθέστερον, καί πάντα