Περὶ τῆς δι’ ὅλων λεγομένης τῶν σωμάτων κράσεως ἐπισκεπτέον. ἆρα ἐνδέχεται ὅλον δι’ ὅλου ὑγρὸν ὑγρῷ συμμιχθὲν ἑκάτερον δι’ ἑκατέρου ἢ θάτερον διὰ θατέρου χωρεῖν; διαφέρει γὰρ οὐδὲν ὁποτερωσοῦν, εἰ γίγνοιτο. οἱ μὲν γὰρ τῇ παραθέσει διδόντες ὡς μιγνύντες μᾶλλον ἢ κιρνάντες ἐατέοι, εἴπερ δεῖ τὴν κρᾶσιν ὁμοιομερὲς τὸ πᾶν ποιεῖν, καὶ ἕκαστον μέρος τὸ σμικρότατον ἐκ τῶν κεκρᾶσθαι λεγομένων εἶναι.
We must look into what is called the total blending of bodies. Is it possible for a liquid blended with a liquid, whole through whole, either for each to pass through the other, or for one to pass through the other? It makes no difference which, if it happens. Those who allow only juxtaposition should be set aside, since they are mixing rather than blending—if blending must make the whole uniform, so that every smallest part is composed of the things said to have been blended.
οἱ μὲν οὖν τὰς ποιότητας μόνας κιρνάντες τὴν δὲ ὕλην παρατιθέντες ἑκατέρου τοῦ σώματος καὶ ἐπ’ αὐτῶν ἐπάγοντες τὰς παρ’ ἑκατέρου ποιότητας πιθανοὶ ἂν εἶεν τῷ διαβάλλειν τὴν δι’ ὅλων κρᾶσιν τῷ τε εἰς τομὰς τὰ μεγέθη συμβαίνειν τῶν ὄγκων ἰέναι, εἰ μηδὲν διάλειμμα μηδετέρῳ τῶν σωμάτων γίγνοιτο, εἰ συνεχὴς ἔσται ἡ διαίρεσις τῷ κατὰ πᾶν τὴν διάδυσιν γίνεσθαι θατέρῳ εἰς θάτερον, καὶ δή, ὅταν τὰ κραθέντα μείζω τόπον κατέχῃ ἢ θάτερον καὶ τοσοῦτον, ὅσον συνελθόντα τὸν ἑκατέρου τόπον. καίτοι, εἰ δι’ ὅλου ὅλον ἦν διεληλυθός, τὸν τοῦ ἑτέρου ἔδει, φασί, μένειν τὸν αὐτόν, εἰς ὃ θάτερον ἐνεβλήθη. οὗ δὲ μὴ μείζων ὁ τόπος γίνεται, ἀέρος τινὰς ἐξόδους αἰτιῶνται, ἀνθ’ ὧν ἐσέδυ θάτερον.
Those who blend only the qualities, and set the matter of each body side by side, bringing onto it the qualities from each, might be persuasive when they attack total blending. They argue that the magnitudes of the bulks end up reduced to cuts, if no gap at all is left in either body, if the division is to be continuous, with the penetration of one into the other happening throughout. And they point out that the blended bodies occupy a greater place than either one—as great as the places of the two put together. Yet, they say, if whole had passed through whole, the place of the body into which the other was put should have remained the same. And where the place does not become greater, they blame certain escapes of air, in place of which the other entered.
καὶ τὸ σμικρὸν δὲ ἐν τῷ μείζονι πῶς ἂν ἐκταθὲν δι’ ὅλου χωρήσειε; καὶ πολλὰ ἄλλα λέγουσιν. οἱ δ’ αὖ τὴν δι’ ὅλων κρᾶσιν εἰσάγοντες τέμνεσθαι μὲν καὶ μὴ εἰς τομὰς ἀναλίσκεσθαι λέγειν ἂν δύναιντο καὶ δι’ ὅλων τῆς κράσεως γιγνομένης· ἐπεὶ καὶ τοὺς ἱδρῶτας οὐ τοῦ σώματος τομὰς ποιεῖν οὐδ’ αὖ κατατετρῆσθαι φήσουσι. καὶ γὰρ εἴ τις λέγοι μηδὲν κωλύειν τὴν φύσιν οὕτω πεποιηκέναι τοῦ διιέναι τοὺς ἱδρῶτας χάριν, ἀλλὰ ἐπὶ τῶν τεχνητῶν, ὅταν λεπτὰ ᾖ καὶ συνεχῆ, ὁρᾶσθαι τὸ ὑγρὸν δι’ ὅλου δεῦον αὐτὰ καὶ διάρρεον ἐπὶ θάτερα· ἀλλὰ σωμάτων ὄντων πῶς οἷόν τε τοῦτο γίγνεσθαι;
And how could the small, spread out in the larger, pass through the whole of it? They say many other things too. Those, on the other hand, who introduce total blending could say that bodies are divided and yet not used up into cuts, even when the blending is through and through. For they will say that even sweat does not make cuts in the body, nor is the body bored full of holes. And if someone says that nothing prevents nature from having made the body so, so that sweat can pass through, still, with artifacts too, when they are thin and continuous, liquid is seen soaking them through and through and flowing out on the other side. But since these are bodies, how can this happen?
ὡς διιέναι μὴ τέμνοντα ἐπινοῆσαι οὐ ῥᾴδιον· τέμνοντα δὲ κατὰ πᾶν ἀναιρήσει ἄλληλα δηλονότι. τὰς δὲ αὔξας ὅταν λέγωσι μὴ γίγνεσθαι πολλαχοῦ, διδόασι τοῖς ἑτέροις ἀέρων ἐξόδους αἰτιᾶσθαι. πρός τε τὴν τῶν τόπων αὔξησιν χαλεπῶς μέν, ὅμως δὲ τί κωλύει λέγειν συνεισφερομένου ἑκατέρου σώματος καὶ τὸ μέγεθος μετὰ τῶν ἄλλων ποιοτήτων ἐξ ἀνάγκης τὴν αὔξην γίνεσθαι; μὴ γὰρ μηδὲ τοῦτο ἀπόλλυσθαι, ὥσπερ οὐδὲ τὰς ἄλλας ποιότητας, καὶ ὥσπερ ἐκεῖ ποιότητος ἄλλο εἶδος μικτὸν ἐξ ἀμφοῖν, οὕτω καὶ μέγεθος ἄλλο· οὗ δὴ τὸ μῖγμα ποιεῖ τὸ ἐξ ἀμφοῖν μέγεθος. ἀλλ’ ἐνταῦθ’ ἂν πρὸς αὐτοὺς οἱ ἕτεροι λέγοιεν, ὡς, εἰ μὲν ἡ ὕλη τῇ ὕλῃ παράκειται καὶ ὁ ὄγκος τῷ ὄγκῳ, ᾧ.
It is not easy to conceive of one body passing through another without cutting it; and if it cuts it throughout, they will obviously destroy each other. And when they say that in many cases no increase occurs, they give the other side grounds to blame escapes of air. As for the increase in place, it is difficult, but still, what prevents one from saying that, since each body brings along its magnitude together with its other qualities, the increase necessarily occurs? For magnitude is not destroyed either, any more than the other qualities are; and just as there another kind of quality comes about, mixed from both, so too another magnitude—for it is the mixture that makes the magnitude out of both. But here the other side might say to them: if matter lies beside matter and bulk beside the bulk with which
σύνεστι τὸ μέγεθος, τὸ ἡμέτερον ἂν λέγοιτε· εἰ δὲ δι’ ὅλου καὶ ἡ ὕλη μετὰ τοῦ ἐπ’ αὐτῇ πρώτως μεγέθους, οὐχ οὕτως ἂν γένοιτο ὡς γραμμὴ γραμμῇ ἐφεξῆς ἂν κέοιτο κατὰ τὰ πέρατα τοῖς σημείοις ἑαυτῶν συνάψασαι, οὗ δὴ αὔξη ἂν γίνοιτο, ἀλλ’ ἐκείνως ὡς ἂν γραμμὴ γραμμῇ ἐφαρμοσθείη, ὥστε αὔξην μὴ γίνεσθαι. τὸ δὲ ἔλαττον διὰ παντὸς τοῦ μείζονος καὶ [τοῦ] μεγίστου τὸ μικρότατον χωρεῖ, ἐφ’ ὧν φανερὸν ὅτι κίρναται. ἐπὶ γὰρ τῶν ἀδήλων ἔξεστι λέγειν μὴ εἰς πᾶν φθάνειν, ἀλλ’ ἐφ’ ὧν γε φανερῶς συμβαίνει, [οὐ] λέγοιτ’ ἄν. καὶ λέγοντες ἐκτάσεις τῶν ὄγκων, οὐ σφόδρα πιθανὰ λέγοιεν ἂν εἰς τοσοῦτον τὸν σμικρότατον ὄγκον ἐκτείνοντες· οὐδὲ γὰρ μεταβάλλοντες τὸ σῶμα μέγεθος αὐτῷ πλέον διδόασιν, ὥσπερ εἰ ἐξ ὕδατος ἀὴρ γίγνοιτο.
the magnitude goes, you would be stating our view. But if matter, together with the magnitude that primarily belongs to it, passes through the whole, it would not happen the way a line lies next to a line, touching at the ends by their points, in which case there would be an increase. It would happen the way a line is fitted onto a line, so that no increase occurs. But the smaller passes through the whole of the larger, and the smallest through the whole of [the] greatest, in cases where it is evident that it is blended. In unclear cases one can say it does not reach everywhere; but in cases where this evidently happens, one could [not] say so. And when they speak of the bulks being stretched, they would not be saying anything very persuasive, stretching the smallest bulk so far. For even when they change the body, they do not give it more magnitude—as would happen if air came to be from water.
τοῦτο δὲ αὐτὸ ἐφ’ ἑαυτοῦ ζητητέον, τί συμβαίνει, ὅταν ὅσπερ ἦν ὄγκος ὕδατος ἀὴρ γίγνηται, πῶς τὸ μεῖζον ἐν τῷ γενομένῳ· νῦν δὲ τὰ μὲν εἰρήσθω πολλῶν καὶ ἄλλων παρ’ ἑκατέρων λεγομένων. ἡμεῖς δὲ ἐφ’ ἑαυτῶν σκοπῶμεν, τί χρὴ λέγειν περὶ τούτου, τίς δόξα σύμφωνος τοῖς λεγομένοις ἢ καὶ τίς ἄλλη παρὰ τὰς νῦν λεγομένας φανεῖται; ὅταν τοίνυν διὰ τοῦ ἐρίου ῥέῃ τὸ ὕδωρ [ἢ] ἡ βίβλος ἐκστάζῃ τὸ ἐν αὐτῇ ὕδωρ, πῶς οὐ τὸ πᾶν ὑδάτινον σῶμα δίεισι δι’ αὐτῆς; ἢ καὶ ὅταν μὴ ῥέῃ, πῶς συνάψομεν τὴν ὕλην τῇ ὕλῃ καὶ τὸν ὄγκον τῷ ὄγκῳ, τὰς δὲ ποιότητας μόνας ἐν συγκράσει ποιησόμεθα;
This question must be investigated on its own: what happens when a bulk that was water becomes air—how the greater size is present in what has come to be. For now, let what has been said suffice, though many other things are said by each side. Let us examine for ourselves what we should say about this: what view agrees with what has been said, or what other view will appear besides those now stated. When water flows through wool, then, [or] a papyrus lets the water in it drip out, how does the whole watery body not pass through it? And even when it does not flow, how shall we join matter to matter and bulk to bulk, and make only the qualities blended?
οὐ γὰρ δὴ ἔξω τῆς βίβλου ἡ τοῦ ὕδατος ὕλη παρακείσεται οὐδ’ αὖ ἔν τισι διαστήμασιν αὐτῆς· πᾶσα γὰρ ὑγρά ἐστι καὶ οὐδαμοῦ ὕλη κενὴ [ὑδατίνης] ποιότητος. εἰ δὲ πανταχοῦ ἡ ὕλη μετὰ τῆς ποιότητος, πανταχοῦ τῆς βίβλου τὸ ὕδωρ. ἢ οὐ τὸ ὕδωρ, ἀλλ’ ἡ τοῦ ὕδατος ποιότης. ἀλλὰ ποῦ ὄντος τοῦ ὕδατος; πῶς οὖν οὐχ ὁ αὐτὸς ὄγκος; ἢ ἐξέτεινε τὴν βίβλον τὸ προστεθέν· ἔλαβε γὰρ μέγεθος παρὰ τοῦ εἰσελθόντος. ἀλλ’ εἰ ἔλαβε, προσετέθη τις ὄγκος· εἰ δὲ προσετέθη, οὐ κατεπόθη ἐν τῷ ἑτέρῳ, δεῖ οὖν ἐν ἄλλῳ καὶ ἄλλῳ τὴν ὕλην εἶναι.
For the matter of the water will not lie outside the papyrus, nor again in certain gaps in it; the whole papyrus is wet, and nowhere is there matter empty of [watery] quality. And if the matter is everywhere along with the quality, the water is everywhere in the papyrus. Or rather, not the water, but the quality of the water. But then where is the water? And how is the bulk not the same? Or rather, what was added stretched the papyrus, which took on magnitude from what came in. But if it took on magnitude, some bulk was added; and if it was added, it was not swallowed up in the other. So the matter must be in different places.
ἢ τί κωλύει, ὥσπερ δίδωσι τῆς ποιότητος καὶ λαμβάνει σῶμα θάτερον παρὰ θατέρου, οὕτω καὶ ἐπὶ τοῦ μεγέθους; ποιότης μὲν γὰρ ποιότητι συνελθοῦσα οὐκ ἐκείνη οὖσα, ἀλλὰ μετ’ ἄλλης, ἐν τῷ μετ’ ἄλλης εἶναι οὐ καθαρὰ οὖσα οὐκ ἔστι παντελῶς ἐκείνη, ἀλλ’ ἠμαύρωται· μέγεθος δὲ συνελθὸν ἄλλῳ μεγέθει οὐκ ἀφανίζεται. τὸ δὲ σῶμα χωροῦν διὰ σώματος πάντως τομὰς ποιεῖν πῶς λέγεται, ἐπιστήσειεν ἄν τις· ἐπεὶ καὶ αὐτοὶ τὰς ποιότητας διὰ τῶν σωμάτων χωρεῖν λέγομεν καὶ οὐ τομὰς ποιεῖν. ἢ ὅτι ἀσώματοι. ἀλλ’ εἰ ἡ ὕλη καὶ αὐτὴ ἀσώματος, διὰ τί τῆς ὕλης ἀσωμάτου οὔσης καὶ τῶν ποιοτήτων, εἰ τοιαῦται εἶεν ὡς ὀλίγαι εἶναι, οὐ μετὰ τῆς ὕλης τὸν αὐτὸν τρόπον διίασι;
Or what prevents one body from giving some of its magnitude to another and receiving some in return, just as they give and receive some of their quality? For a quality that meets another quality is no longer that quality on its own but is with another; and in being with another, no longer pure, it is not entirely what it was but has been dimmed. A magnitude that meets another magnitude, by contrast, does not disappear. As for the claim that a body passing through a body must make cuts, one might stop to ask what it means: after all, we ourselves say that qualities pass through bodies without making cuts. Or is that because qualities are incorporeal? But if matter too is itself incorporeal, why, when matter is incorporeal and so are the qualities (if they are such as to be few), do they not pass through together with the matter in the same way?
μὴ διιέναι δὲ τὰ στερεά, ὅτι τοιαύτας ἔχει τὰς ποιότητας ὡς κωλυθῆναι διιέναι, ἢ πολλὰς ὁμοῦ ἀδυνατεῖν μετὰ τῆς ὕλης ποιεῖν τοῦτο; εἰ μὲν οὖν τὸ πλῆθος τῶν ποιοτήτων τὸ πυκνὸν λεγόμενον σῶμα ποιεῖ, τὸ πλῆθος ἂν εἴη αἴτιον· εἰ δὲ πυκνότης ἰδία ποιότης ἐστίν, ὥσπερ καὶ ἣν λέγουσι σωματότητα, [ἡ] ἰδία ποιότης· ὥστε οὐχ ᾗ ποιότητες τὴν μῖξιν ποιήσονται, ἀλλ’ ᾗ τοιαίδε, οὐδ’ αὖ ἡ ὕλη ᾗ ὕλη οὐ μιχθήσεται, ἀλλ’ ᾗ μετὰ τοιᾶσδε ποιότητος, καὶ μάλιστα, εἰ μέγεθος οἰκεῖον οὐκ ἔχει ἀλλ’ ἢ μὴ ἀποβαλοῦσα τὸ μέγεθος. ταῦτα μὲν οὖν ἔστω καὶ οὕτω διηπορημένα.
And do solids fail to pass through because their qualities are of a kind that prevents them, or because many qualities together are unable to do this along with matter? Now if it is the multitude of qualities that makes what is called a dense body, the multitude would be the cause; but if density is a quality of its own, as is what they call corporeality, then it is that specific quality. So it is not as qualities that they will produce the mixture, but as qualities of a certain kind; nor, again, will matter fail to mix as matter, but as accompanied by a certain kind of quality—especially if it has no magnitude of its own, except insofar as it has not cast off its magnitude. Let this much, then, serve as our discussion of the difficulties.
ἐπεὶ δὲ ἐμνήσθημεν σωματότητος, ἐπισκεπτέον, πότερα ἡ σωματότης ἐστὶ τὸ ἐκ πάντων [σὺν ὕλῃ] συγκείμενον ἢ εἶδός τι καὶ λόγος τις, ὃς ἐγγενόμενος τῇ ὕλῃ σῶμα ποιεῖ. εἰ μὲν οὖν τοῦτό ἐστι τὸ σῶμα τὸ ἐκ πασῶν τῶν ποιοτήτων σὺν ὕλῃ [συγκείμενον], ταὐτὸ ἂν εἴη ἡ σωματότης. καὶ εἰ λόγος δὲ εἴη, ὃς προσελθὼν ποιεῖ τὸ σῶμα, δηλονότι ὁ λόγος ἐμπεριλαβὼν ἔχει τὰς ποιότητας ἁπάσας. δεῖ δὲ τὸν λόγον τοῦτον, εἰ μή ἐστιν ἄλλως ὥσπερ ὁρισμὸς δηλωτικὸς τοῦ τί ἔστι τὸ πρᾶγμα, ἀλλὰ λόγος ποιῶν πρᾶγμα, μὴ τὴν ὕλην συμπεριειληφέναι, ἀλλὰ περὶ ὕλην εἶναι καὶ ἐγγενόμενον ἀποτελεῖν τὸ σῶμα, καὶ εἶναι μὲν τὸ σῶμα ὕλην καὶ λόγον ἐνόντα, αὐτὸν δὲ εἶδος ὄντα ἄνευ ὕλης ψιλὸν θεωρεῖσθαι, κἂν ὅτι μάλιστα ἀχώριστος αὐτὸς ᾖ.
Since we have mentioned corporeality, we should consider whether corporeality is what is composed of all the qualities [together with matter], or a form and a rational principle which, coming to be in matter, makes a body. Now if body is this—what is [composed] of all the qualities together with matter—corporeality would be the same thing. And if it were a rational principle that makes the body by coming to matter, clearly the rational principle embraces and contains all the qualities. But this rational principle, if it is not simply like a definition that shows what the thing is, but a rational principle that makes a thing, must not include matter along with it. It must rather be about matter and, by coming to be in it, complete the body; the body must be matter plus a rational principle present in it, while the rational principle itself, being form, is contemplated bare, without matter, however inseparable it may in fact be.
ὁ γὰρ χωριστὸς ἄλλος, ὁ ἐν νῷ· ἐν νῷ δέ, ὅτι καὶ αὐτὸς νοῦς. ἀλλὰ ταῦτα ἄλλοθι.
For the separate one is different: the one in Intellect. And it is in Intellect because it is itself Intellect too. But that belongs elsewhere.