§2.1.1## ΑΝΑΛΥΤΙΚΩΝ ΥΣΤΕΡΩΝ Α.
Πᾶσα διδασκαλία καὶ πᾶσα μάθησις διανοητικὴ ἐκ προϋπαρχούσης γίνεται γνώσεως.
POSTERIOR ANALYTICS BOOK I All teaching and all intellectual learning arise from pre-existing knowledge.
φανερόν δὲ τοῦτο θεωροῦσιν ἐπὶ πασῶν· αἵ τε γὰρ μαθηματικαὶ τῶν ἐπιστημῶν διὰ τούτου τοῦ τρόπου παραγίνονται καὶ τῶν ἄλλων ἑκάστη τεχνῶν.
This is evident to those who examine all cases; for both the mathematical of the sciences are acquired through this manner, and each of the other arts.
ὁμοίως δὲ καὶ περὶ τοὺς λόγους οἵ τε διὰ συλλογισμῶν καὶ οἱ διʼ ἐπαγωγῆς· ἀμφότεροι γὰρ διὰ προγινωσκομένων ποιοῦνται τὴν διδασκαλίαν, οἱ μὲν λαμβάνοντες ὡς παρὰ ξυνιέντων, οἱ δὲ δεικνύντες τὸ καθόλου διὰ τοῦ δῆλον εἶναι τὸ καθʼ ἕκαστον.
Likewise also concerning arguments, both those through deductions and those through induction; for both perform their teaching through things previously known, the former assuming from those who understand, the latter proving the universal through the fact that the particular is clear.
ὡς δʼ αὔτως καὶ οἱ ῥητορικοὶ συμπείθουσιν· ἢ γὰρ διὰ παραδειγμάτων, ὅ ἐστιν ἐπαγωγή, ἢ διʼ ἐνθυμημάτων, ὅπερ ἐστὶ συλλογισμός.
And in the same way rhetorical persuasion also convinces; for it is either through examples, which is induction, or through enthymemes, which is deduction.
διχῶς δʼ ἀναγκαῖον προγινώσκειν· τὰ μὲν γάρ, ὅτι ἔστι, προϋπολαμβάνειν ἀναγκαῖον, τὰ δέ, τί τὸ λεγόμενόν ἐστι, ξυνιέναι δεῖ, τὰ δʼ ἄμφω, οἷον ὅτι μὲν ἅπαν ἢ φῆσαι ἢ ἀποφῆσαι ἀληθές, ὅτι ἔστι, τὸ δὲ τρίγωνον, ὅτι τοδὶ σημαίνει, τὴν δὲ μονάδα ἄμφω, καὶ τί σημαίνει καὶ ὅτι ἔστιν·
It is necessary to have prior knowledge in two ways: for of some things, one must pre-suppose that they exist; of others, one must understand what the thing said is; and of others, both. For instance, that "everything is true either to affirm or to deny," one must pre-suppose that it is; of the triangle, that it signifies this; and of the unit, both—what it signifies and that it exists.
οὐ γὰρ ὁμοίως τούτων ἕκαστον δῆλον ἡμῖν.
For each of these is not equally clear to us.
Ἔστι δὲ γνωρίζειν τὰ μὲν πρότερον γνωρίσαντα, τῶν δὲ καὶ ἅμα λαμβάνοντα τὴν γνῶσιν, οἷον ὅσα τυγχάνει ὄντα ὑπὸ τὸ καθόλου οὗ ἔχει τὴν γνῶσιν.
And it is possible to recognize some things having recognized them beforehand, but to acquire knowledge of others at the very same time, such as all those things which happen to fall under the universal of which one has knowledge.
ὅτι μὲν γὰρ πᾶν τρίγωνον ἔχει δυσὶν ὀρθαῖς ἴσας, προῄδει· ὅτι δὲ τόδε τὸ ἐν τῷ ἡμικυκλίῳ τρίγωνόν ἐστιν, ἅμα ἐπαγόμενος ἐγνώρισεν. (ἐνίων γὰρ τοῦτον τόν τρόπον ἡ μάθησίς ἐστι, καὶ οὐ διὰ τοῦ μέσου τὸ ἔσχατον γνωρίζεται, ὅσα ἤδη τῶν καθʼ ἕκαστα τυγχάνει ὄντα καὶ μὴ καθʼ ὑποκειμένου τινός. ) πρίν δʼ ἐπαχθῆναι ἢ λαβεῖν συλλογισμόν τρόπον μέν τινα ἴσως φατέον ἐπίστασθαι, τρόπον δʼ ἄλλον οὔ.
For that every triangle has angles equal to two right angles, one knew beforehand; but that this figure in the semicircle is a triangle, one recognized at the same time as one was being led on. (For of some things learning is of this manner, and the extreme is not recognized through the middle term, namely, all those things which happen to be particulars and are not predicated of any subject.) But before being led on or receiving a deduction, in one way perhaps one must say that one knows, but in another way not.
ὅ γὰρ μὴ ἤδει εἰ ἔστιν ἀπλῶς, τοῦτο πῶς ἤδει ὅτι δύο ὀρθὰς ἔχει ἀπλῶς;
For that which one did not know if it exists unqualifiedly, how did one know that it has two right angles unqualifiedly?
ἀλλὰ δῆλον ὡς ὡδὶ μὲν ἐπίσταται, ὅτι καθόλου ἐπίσταται, ἁπλῶς δʼ οὐκ ἐπίσταται.
But it is clear that in this way one knows, namely, because one knows it universally, but unqualifiedly one does not know it.
εἰ δὲ μή, τὸ ἐν τῷ Μένωνι ἀπόρημα συμβήσεται· ἢ γὰρ οὐδὲν μαθήσεται ἢ ἃ οἶδεν.
Otherwise, the puzzle in the Meno will result: for one will either learn nothing or what one knows.
οὐ γὰρ δή, ὥς γέ τινες ἐγχειροῦσι λύειν, λεκτέον. ἆρʼ οἶδας ἅπασαν δυάδα ὅτι ἀρτία ἢ οὔ; φήσαντος δὲ προήνεγκάν τινα δυάδα ἢν οὐκ ᾤετ’ εἶναι, ὥστ’ οὐδʼ ἀρτίαν.
For indeed one must not say what some attempt to use as a solution: "Do you know that every pair is even, or not?" and when he says yes, they bring forward some pair which he did not think existed, and therefore did not think was even.
λύουσι γὰρ οὐ φάσκοντες εἰδέναι πᾶσαν δυάδα ἀρτίαν οὖσαν, ἀλλʼ ἥν ἴσασιν ὅτι δυάς.
For they solve it by denying that they knew that every pair is even, but only that which they know is a pair.
καίτοι ἴσασι μὲν οὔπερ τὴν ἀπόδειξιν ἔχουσι καὶ οὗ ἔλαβον, ἔλαβον δʼ οὐχὶ παντὸς οὗ ἄν εἰδῶσιν ὅτι τρίγωνον ἢ ὅτι ἀριθμός, ἀλλʼ ἀπλῶς κατὰ παντὸς ἀριθμοῦ καὶ τριγώνου· οὐδεμία γὰρ πρότασις λαμβάνεται τοιαύτη, ὅτι ὅν σὺ οἶδας ἀριθμὸν ἢ ὅ σὺ οἶδας εὐθύγραμμον, ἀλλὰ κατὰ παντός.
Yet they know that of which they have the demonstration and of which they took [premises], and they took them not of everything which they may know to be a triangle or to be a number, but unqualifiedly of every number and triangle; for no premise is taken of such a kind as "the number which you know" or "the rectilinear figure which you know," but of every one.
ἀλλʼ οὐδέν (οἶμαι) κωλύει, ὅ μανθάνει, ἔστιν ὡς ἐπίστασθαι, ἔστι δʼ ὡς ἀγνοεῖν· ἄτοπον γὰρ οὐκ εἰ οἶδέ πως ὅ μανθάνει, ἀλλʼ εἰ ὡδί, οἷον ᾗ μανθάνει καὶ ὥς.
But nothing (I think) prevents that what one learns, in one way one knows, and in another way is ignorant of; for it is not absurd if one knows in some way what one learns, but if in this way—namely, in the very way and as he learns it.