§1.9#3ἀλλὰ μὴν οὐδὲ γένος τὸ πλατὺ τοῦ βαθέος· ἦν γὰρ ἂν ἐπίπεδόν τι τὸ σῶμα.
Indeed, the wide is not the genus of the deep either; for if it were, body would be a kind of plane.
ἔτι αἱ στιγμαὶ ἐκ τίνος ἐνυπάρξουσιν;
Further, from what will the points be present in them?
τούτῳ μὲν οὖν τῷ γένει καὶ διεμάχετο Πλάτων ὡς ὄντι γεωμετρικῷ δόγματι, ἀλλʼ ἐκάλει ἀρχὴν γραμμῆς—τοῦτο δὲ πολλάκις ἐτίθει—τὰς ἀτόμους γραμμάς.
Plato indeed used to fight against this class of things as being a geometrical dogma, and rather called the 'indivisible lines' the principle of a line—and this he often posited.
καίτοι ἀνάγκη τούτων εἶναί τι πέρας· ὥστʼ ἐξ οὗ λόγου γραμμὴ ἔστι, καὶ στιγμὴ ἔστιν. —ὅλως δὲ ζητούσης τῆς σοφίας περὶ τῶν φανερῶν τὸ αἴτιον, τοῦτο μὲν εἰάκαμεν (οὐθὲν γὰρ λέγομεν περὶ τῆς αἰτίας ὅθεν ἡ ἀρχὴ τῆς μεταβολῆς), τὴν δʼ οὐσίαν οἰόμενοι λέγειν αὐτῶν ἑτέρας μὲν οὐσίας εἶναί φαμεν, ὅπως δʼ ἐκεῖναι τούτων οὐσίαι, διὰ κενῆς λέγομεν·
Yet these must have some limit; so that by the same argument that a line exists, a point also exists. —But on the whole, although wisdom searches for the cause of visible things, we have abandoned this (for we say nothing about the cause from which the principle of change begins).
τὸ γὰρ μετέχειν, ὥσπερ καὶ πρότερον εἴπομεν, οὐθέν ἐστιν.
And while we think we are speaking of their substance, we assert that there are other substances, but how those are the substances of these, we speak in vain; for 'participating', as we said before, is nothing.
οὐδὲ δὴ ὅπερ ταῖς ἐπιστήμαις ὁρῶμεν ὂν αἴτιον, διʼ ὃ καὶ πᾶς νοῦς καὶ πᾶσα φύσις ποιεῖ, οὐδὲ ταύτης τῆς αἰτίας, ἥν φαμεν εἶναι μίαν τῶν ἀρχῶν, οὐθὲν ἅπτεται τὰ εἴδη, ἀλλὰ γέγονε τὰ μαθήματα τοῖς νῦν ἡ φιλοσοφία, φασκόντων ἄλλων χάριν αὐτὰ δεῖν πραγματεύεσθαι.
Nor do the Forms touch in any way upon that cause which we see to be the cause in the sciences, through which every intellect and every nature acts—not even upon this cause, which we say is one of the principles. Instead, philosophy has become mathematics for modern thinkers, although they say that mathematics should be studied for the sake of other things.
ἔτι δὲ τὴν ὑποκειμένην οὐσίαν ὡς ὕλην μαθηματικωτέραν ἄν τις ὑπολάβοι, καὶ μᾶλλον κατηγορεῖσθαι καὶ διαφορὰν εἶναι τῆς οὐσίας καὶ τῆς ὕλης ἢ ὕλην, οἷον τὸ μέγα καὶ τὸ μικρόν, ὥσπερ καὶ οἱ φυσιολόγοι φασὶ τὸ μανὸν καὶ τὸ πυκνόν, πρώτας τοῦ ὑποκειμένου φάσκοντες εἶναι διαφορὰς ταύτας· ταῦτα γάρ ἐστιν ὑπεροχή τις καὶ ἔλλειψις.
Further, one might suppose that the underlying substance as matter is rather mathematical, and is predicated of and is a difference of substance and of matter, rather than being matter itself. For example, 'the great and the small', just as the natural philosophers speak of 'the rare and the dense', saying that these are the primary differences of the substrate; for these are a kind of excess and defect.
περί τε κινήσεως, εἰ μὲν ἔσται ταῦτα κίνησις, δῆλον ὅτι κινήσεται τὰ εἴδη· εἰ δὲ μή, πόθεν ἦλθεν;
And as for movement, if these are to be movement, it is clear that the Forms will be moved; but if not, where did movement come from?
ὅλη γὰρ ἡ περὶ φύσεως ἀνῄρηται σκέψις.
For the whole study of nature is done away with.
ὅ τε δοκεῖ ῥᾴδιον εἶναι, τὸ δεῖξαι ὅτι ἓν ἅπαντα, οὐ γίγνεται·
And what seems to be easy, namely to show that all things are one, does not follow.
τῇ γὰρ ἐκθέσει οὐ γίγνεται πάντα ἓν ἀλλʼ αὐτό τι ἕν, ἂν διδῷ τις πάντα· καὶ οὐδὲ τοῦτο, εἰ μὴ γένος δώσει τὸ καθόλου εἶναι· τοῦτο δʼ ἐν ἐνίοις ἀδύνατον.
For by exposition all things do not become one, but rather some 'one-itself' is formed, even if one grants all premises; and not even this follows, unless one grants that the universal is a genus, which in some cases is impossible.
οὐθένα δʼ ἔχει λόγον οὐδὲ τὰ μετὰ τοὺς ἀριθμοὺς μήκη τε καὶ ἐπίπεδα καὶ στερεά, οὔτε ὅπως ἔστιν ἢ ἔσται οὔτε τίνα ἔχει δύναμιν·
Nor is there any explanation for the lengths, planes, and solids which come after numbers, either as to how they exist or will exist, or what power they possess.
ταῦτα γὰρ οὔτε εἴδη οἷόν τε εἶναι (οὐ γάρ εἰσιν ἀριθμοί) οὔτε τὰ μεταξύ (μαθηματικὰ γὰρ ἐκεῖνα) οὔτε τὰ φθαρτά, ἀλλὰ πάλιν τέταρτον ἄλλο φαίνεται τοῦτό τι γένος.
For these can neither be Forms (for they are not numbers), nor the intermediates (for those are the mathematical objects), nor destructible things; rather, this appears to be some other, fourth class.
ὅλως τε τὸ τῶν ὄντων ζητεῖν στοιχεῖα μὴ διελόντας, πολλαχῶς λεγομένων, ἀδύνατον εὑρεῖν, ἄλλως τε καὶ τοῦτον τὸν τρόπον ζητοῦντας ἐξ οἵων ἐστὶ στοιχείων.
On the whole, to search for the elements of existing things without distinguishing them, when they are spoken of in many ways, makes it impossible to find them, especially when one searches in this way for the elements out of which they are composed.
ἐκ τίνων γὰρ τὸ ποιεῖν ἢ πάσχειν ἢ τὸ εὐθύ, οὐκ ἔστι δήπου λαβεῖν, ἀλλʼ εἴπερ, τῶν οὐσιῶν μόνον ἐνδέχεται·
For out of what elements 'acting' or 'being acted upon', or 'the straight', are composed is surely impossible to grasp; but if it is possible, it is possible only for substances.
ὥστε τὸ τῶν ὄντων ἁπάντων τὰ στοιχεῖα ἢ ζητεῖν ἢ οἴεσθαι ἔχειν οὐκ ἀληθές.
Therefore, either to search for the elements of all existing things, or to think that one has them, is incorrect.
πῶς δʼ ἄν τις καὶ μάθοι τὰ τῶν πάντων στοιχεῖα;
And how could one learn the elements of all things?
δῆλον γὰρ ὡς οὐθὲν οἷόν τε προϋπάρχειν γνωρίζοντα πρότερον.
For it is clear that it is not possible to have any prior knowledge.
ὥσπερ γὰρ τῷ γεωμετρεῖν μανθάνοντι ἄλλα μὲν ἐνδέχεται προειδέναι, ὧν δὲ ἡ ἐπιστήμη καὶ περὶ ὧν μέλλει μανθάνειν οὐθὲν προγιγνώσκει, οὕτω δὴ καὶ ἐπὶ τῶν ἄλλων, ὥστʼ εἴ τις τῶν πάντων ἔστιν ἐπιστήμη, οἵαν δή τινές φασιν, οὐθὲν ἂν προϋπάρχοι γνωρίζων οὗτος.
For just as one who is learning geometry may know other things beforehand, but knows nothing beforehand of the things with which the science is concerned and which he is about to learn, so it is also with other things; so that if there is a science of all things, such as some say exists, he who learns it would have no prior knowledge at all.
καίτοι πᾶσα μάθησις διὰ προγιγνωσκομένων ἢ πάντων ἢ τινῶν ἐστί, καὶ ἡ διʼ ἀποδείξεως καὶ ἡ διʼ ὁρισμῶν (δεῖ γὰρ ἐξ ὧν ὁ ὁρισμὸς προειδέναι καὶ εἶναι γνώριμα)· ὁμοίως δὲ καὶ ἡ διʼ ἐπαγωγῆς.
Yet all learning is through things previously known, whether all or some, both that which is by demonstration and that by definition (for the elements from which the definition is made must be known beforehand and be familiar); and similarly also that which is by induction.
ἀλλὰ μὴν εἰ καὶ τυγχάνοι σύμφυτος οὖσα, θαυμαστὸν πῶς λανθάνομεν ἔχοντες τὴν κρατίστην τῶν ἐπιστημῶν.
But indeed, even if it should happen to be innate, it is wonderful how we are unaware of possessing the greatest of sciences.
ἔτι πῶς τις γνωριεῖ ἐκ τίνων ἐστί, καὶ πῶς ἔσται δῆλον;
Further, how will one know what elements it consists of, and how will it be clear?
καὶ γὰρ τοῦτʼ ἔχει ἀπορίαν·
For this also presents a difficulty.
ἀμφισβητήσειε γὰρ ἄν τις ὥσπερ καὶ περὶ ἐνίας συλλαβάς· οἱ μὲν γὰρ τὸ ζα ἐκ τοῦ ς καὶ δ καὶ α φασὶν εἶναι, οἱ δέ τινες ἕτερον φθόγγον φασὶν εἶναι καὶ οὐθένα τῶν γνωρίμων.
For one might dispute about it, just as about certain syllables; for some say that the syllable 'za' is composed of s, d, and a, while others say it is a different sound, and not any of the familiar ones.
ἔτι δὲ ὧν ἐστὶν αἴσθησις, ταῦτα πῶς ἄν τις μὴ ἔχων τὴν αἴσθησιν γνοίη;
Further, how could one know the objects of sense without possessing the sense?
καίτοι ἔδει, εἴγε πάντων ταὐτὰ στοιχεῖά ἐστιν ἐξ ὧν, ὥσπερ αἱ σύνθετοι φωναί εἰσιν ἐκ τῶν οἰκείων στοιχείων.
Yet they ought to, if indeed the elements of which all things consist are the same, just as composite sounds are made of their own proper elements.