§3.77 Πάλιν οὖν ἐπισκεπτέον τίς ὁ τρόπος τῆς ἐξ ἀλλήλων γενέσεως, πότερον ὡς Ἐμπεδοκλῆς λέγει καὶ Δημόκριτος) ἢ ὡς οἱ εἰς τὰ ἐπίπεδα διαλύοντες, ἢ ἔστιν ἄλλος τις τρόπος παρὰ τούτους.
7 Therefore, we must investigate again what is the manner of their generation from one another, whether it is as Empedocles and Democritus say, or as those who dissolve into planes, or whether there is some other manner besides these.
οἱ μὲν οὖν περὶ Ἐμπεδοκλέα καὶ Δημόκριτον λανθάνουσιν αὐτοὶ αὑτοὺς οὐ γένεσιν ἐξ ἀλλήλων ποιοῦντες ἀλλὰ φαινομένην γένεσιν· ἐνυπάρχον γὰρ ἕκαστον ἐκκρίνεσθαί φασιν, ὥσπερ ἐξ ἀγγείου τῆς γενέσεως οὕσης ἀλλʼ οὐκ ἔκ τινος ὕλης, οὐδὲ γίγνεσθαι μεταβάλλοντος.
Now, those around Empedocles and Democritus, without realizing it themselves, make not a generation from one another but an apparent generation; for they say that each thing, pre-existing within, is separated out, as if the generation were from a vessel but not from some matter, nor coming to be by changing.
ἔπειτα κἂν οὕτως οὐδὲν ἧττον ἄλογα τὰ συμβαίνοντα.
Secondly, even if this is so, the consequences are no less absurd.
τὸ γὰρ αὐτὸ μέγεθος οὐ δοκεῖ συμπιληθὲν γίνεσθαι βαρύτερον.
For the same volume does not seem to become heavier by being compressed.
ἀνάγκη δὲ τοῦτο λέγειν τοῖς φάσκουσιν ἐκκρίνεσθαι τὸ ὕδωρ ἐκ τοῦ ἀέρος ἐνυπάρχον· ὅταν γὰρ ὕδωρ ἐξ ἀέρος γένηται, βαρύτερόν ἐστιν.
But this must necessarily be said by those who claim that water is separated out from air, pre-existing in it; for whenever water comes to be from air, it is heavier.
ἔτι δὲ τῶν μεμιγμένων σωμάτων οὐκ ἀνάγκη χωρισθὲν θάτερον ἀεὶ πλείω τόπον ἐπέχειν· ὅταν δʼ ἐξ ὕδατος ἀὴρ γένηται, πλείω καταλαμβάνει τόπον· τὸ δὲ λεπτομερέστερον ἐν πλείονι τόπῳ γίγνεται.
Moreover, in the case of mixed bodies, it is not necessary that one of them, when separated, always occupies more space; but whenever air comes to be from water, it occupies more space; and that which consists of finer parts comes to be in more space.
φανερὸν δὲ τοῦτό γε καὶ ἐν τῇ μεταβάσει· διατμιζομένου γὰρ καὶ πνευματουμένου τοῦ ὑγροῦ ῥήγνυται τὰ περιέχοντα τοὺς ὄγκους ἀγγεῖα διὰ τὴν στενοχωρίαν.
And this at least is manifest also in the transition; for as the liquid is vaporized and turned into air, the vessels enclosing the volumes are ruptured because of the narrowness of space.
ὥστʼ εἰ μὲν ὅλως μή ἐστι κενὸν μηδʼ ἐπεκτείνεται τὰ σώματα, καθάπερ φασὶν οἱ ταῦτα λέγοντες, φανερὸν τὸ ἀδύνατον· εἰ δʼ ἔστι κενὸν καὶ ἐπέκτασις, ἄλογον τὸ ἐξ ἀνάγκης ἀεὶ πλείω τόπον ἐπιλαμβάνειν τὸ χωριζόμενον.
So that if on the one hand there is no void at all and bodies do not expand, as those who say these things claim, the impossibility is manifest; but if on the other hand there is void and expansion, it is unreasonable that that which is separated should necessarily always occupy more space.
ἀλλʼ ἀνάγκη καὶ ὑπολείπειν τὴν ἐξ ἀλλήλων γένεσιν, εἴπερ ἐν τῷ πεπερασμένῳ μεγέθει μὴ ἐνυπάρχει ἄπειρα μεγέθη πεπερασμένα.
But indeed, the generation from one another must also fail, if there are not infinite finite magnitudes pre-existing in a finite magnitude.
ὅταν γὰρ ἐκ γῆς ὕδωρ γένηται, ἀφῄρηταί τι τῆς γῆς, εἴπερ ἐκκρίσει ἡ γένεσις· καὶ πάλιν ὅταν ἐκ τῆς ὑπολειπομένης, ὡσαύτως.
For whenever water comes to be from earth, something has been taken away from the earth, if indeed the generation is by separation; and again, whenever it comes to be from that which is left, likewise.
εἰ μὲν οὖν ἀεὶ τοῦτʼ ἔσται, συμβήσεται ἐν τῷ πεπερασμένῳ ἄπειρα ἐνυπάρχειν· ἐπεὶ δὲ τοῦτʼ ἀδύνατον, οὐκ ἂν ἀεὶ γίγνοιτο ἐξ ἀλλήλων.
If indeed, therefore, this is always to happen, it will turn out that infinite magnitudes pre-exist in the finite; but since this is impossible, they could not always come to be from one another.
ὅτι μὲν οὖν οὐκ ἔστι τῇ ἐκκρίσει ἡ εἰς ἄλληλα μετάβασις, εἴρηται.
That the transition into one another is not by separation, then, has been said.
λείπεται δʼ εἰς ἄλληλα μεταβάλλοντα γίγνεσθαι τοῦτο δὲ διχῶς· ἢ γὰρ τῇ μετασχηματίσει, καθάπερ ἐκ τοῦ αὐτοῦ κηροῦ γίγνοιτʼ ἄν σφαῖρα καὶ κύβος, ἢ τῇ διαλύσει τῇ εἰς τὰ ἐπίπεδα, ὥσπερ ἔνιοί φασιν.
It remains, then, for them to come to be by changing into one another; and this in two ways: either indeed by alteration of shape, just as a sphere and a cube might come to be from the same wax, or by the dissolution into planes, as some say.
εἰ μὲν οὖν τῇ μετασχηματίσει γίνεται, συμβαίνει ἐξ ἀνάγκης ἄτομα λέγειν τὰ σώματα· διαιρετῶν γὰρ ὄντων οὐκ ἔσται τὸ τοῦ πυρὸς μέρος πῦρ, οὐδὲ τὸ τῆς γῆς γῇ, διὰ τὸ μὴ εἶναι μήτε τὸ τῆς πυραμίδος μέρος πάντως πυραμίδα μήτε τὸ τοῦ κύβου κύβον.
If indeed, therefore, they come to be by alteration of shape, it turns out of necessity that they say bodies are indivisible; for if they are divisible, the part of fire will not be fire, nor that of earth earth, due to the fact that neither is the part of a pyramid always a pyramid, nor that of a cube a cube.
εἰ δὲ τῇ τῶν ἐπιπέδων διαλύσει, πρῶτον μὲν ἄτοπον τὸ μὴ πάντα γεννᾶν ἐξ ἀλλήλων, ὅπερ ἀνάγκη λέγειν αὐτοῖς, καὶ λέγουσιν.
But if by the dissolution of planes, first of all it is absurd not to generate all things from one another, which they must necessarily say, and indeed do say.
οὕτε γὰρ εὔλογον ἓν μόνον ἄμοιρον γενέσθαι τῆς μεταβάσεως, οὔτε φαίνεται κατὰ τὴν αἴσθησιν, ἀλλʼ ὁμοίως πάντα μεταβάλλειν εἰς ἄλληλα.
For neither is it reasonable that only one thing should be without a share in the transition, nor does it appear so according to perception, but rather that all things change into one another in like manner.
συμβαίνει δὲ περὶ τῶν φαινομένων λέγουσι μὴ ὁμολογούμενα λέγειν τοῖς φαινομένοις.
And it turns out that, while speaking about appearances, they say things that do not agree with the appearances.
τούτου δʼ αἴτιον τὸ μὴ καλῶς λαβεῖν τὰς πρώτας ἀρχάς, ἀλλά. πάντα βούλεσθαι πρός τινας δόξας ὡρισμένας ἀνάγειν· δεῖ γὰρ ἴσως τῶν μὲν αἰσθητῶν αἰσθητάς, τῶν δὲ ἀϊδίων ἀϊδίους, τῶν δὲ φθαρτῶν φθαρτὰς εἶναι τὰς ἀρχάς, ὅλως δʼ ὁμογενεῖς τοῖς ὑποκειμένοις.
And the cause of this is their not having grasped the first principles well, but rather wishing to refer everything to certain defined opinions; for indeed, the principles of perceptible things ought perhaps to be perceptible, those of eternal things eternal, and those of perishable things perishable, and in general homogeneous with the subject matters.
οἱ δὲ διὰ τὴν τούτων φιλίαν ταὐτὸ ποιεῖν ἐοίκασι τοῖς τὰς θέσεις ἐν τοῖς λόγοις διαφυλάττουσιν· ἅπαν γὰρ ὑπομένουσι το συμβαῖνον ὡς ἀληθεῖς ἔχοντες ἀρχάς, ὥσπερ οὐκ ἐνίας δέον κρίνειν ἐκ τῶν ἀποβαινόντων, καὶ μάλιστα ἐκ τοῦ τέλους.
But they, because of their love for these [opinions], seem to do the same thing as those who defend their theses in arguments; for they submit to every consequence, as if they held true principles, as though we ought not to judge some [principles] from their results, and especially from the end.
τέλος δὲ τῆς μὲν ποιητικῆς ἐπιστήμης τὸ ἔργον, τῆς δὲ φυσικῆς τὸ φαινόμενον ἀεὶ κυρίως κατὰ τὴν αἴσθησιν.
And the end of productive science is the work, but of natural science it is the appearance, always authoritative according to perception.
συμβαίνει δʼ αὐτοῖς μάλιστα τὴν γῆν εἶναι στοιχεῖον, καὶ μόνην ἄφθαρτον, εἴπερ τὸ ἀδιάλυτον ἄφθαρτόν τʼ ἐστὶ καὶ στοιχεῖον· ἡ γὰρ γῆ μόνη ἀδιάλυτος εἰς ἄλλο σῶμα.
And it turns out for them that earth is especially an element, and alone indestructible, if indeed that which is insoluble is indestructible and an element; for earth alone is insoluble into another body.
ἀλλα μὴν οὐδʼ ἐν τοῖς διαλυομένοις ἡ τῶν τριγώνων παραιώρησις εὔλογος.
But indeed, neither in the case of those that are dissolved is the leaving aside of triangles reasonable.
συμβαίνει δὲ καὶ τοῦτο ἐν τῇ εἰς ἄλληλα μεταβάσει διὰ τὸ ἐξ ἀνίσων τῷ πλήθει συνεστάναι τριγώνων.
And this also happens in the transition into one another, because they consist of triangles that are unequal in number.
ἔτι δʼ ἀνάγκη τοῖς ταῦτα λέγουσιν οὐκ ἐκ σώματος ποιεῖν γένεσιν· ὅταν γὰρ ἐξ ἐπιπέδων γένηται, οὐκ ἐκ σώματος ἔσται γεγονός.
Furthermore, it is necessary for those who say these things to make generation not from a body; for whenever it comes to be from planes, it will not have come to be from a body.
πρὸς δὲ τούτοις ἀνάγκη μὴ πᾶν σῶμα λέγειν διαιρετόν, ἀλλὰ μάχεσθαι ταῖς ἀκριβεστάταις ἐπιστήμαις· αἱ μὲν γὰρ καὶ τὸ νοητὸν λαμβάνουσι διαιρετόν, αἱ μαθηματικαί, οἱ δὲ οὐδὲ τὸ αἰσθητὸν ἅπαν συγχωροῦσι διὰ τὸ βούλεσθαι σώζειν τὴν ὑπόθεσιν.
In addition to these, they must necessarily deny that every body is divisible, and thus fight against the most exact sciences; for while these, namely the mathematical sciences, assume even the intelligible to be divisible, they do not even concede that every perceptible thing is so, because of wishing to save their hypothesis.
ἀνάγκη γὰρ ὅσοι σχῆμα ποιοῦσιν ἑκάστου τῶν στοιχείων καὶ τούτῳ διορίζουσι τὰς οὐσίας αὐτῶν, ἀδιαίρετα ποιεῖν αὐτά· τῆς γὰρ πυραμίδος ἢ τῆς σφαίρας διαιρεθείσης πως οὐκ ἔσται τὸ λειπόμενον σφαῖρα ἢ πυραμίς.
For it is necessary for as many as make a shape for each of the elements and define their substances by this, to make them indivisible; for if a pyramid or a sphere is divided in some way, the remaining part will not be a sphere or a pyramid.
ὥστε ἢ τὸ τοῦ πυρὸς μέρος οὐ πῦρ, ἀλλʼ ἔσται τι πρότερον τοῦ 306b στοιχείου, διὰ τὸ πᾶν εἶναι ἢ στοιχεῖον ἢ ἐκ στοιχείων, ἢ οὐχ ἅπαν σῶμα διαιρετόν.
So that either the part of fire is not fire, but there will be something prior to the element (since everything is either an element or from elements), or not every body is divisible.