§6.4#1Πότερον μὲν οὖν καλῶς ἢ οὐ καλῶς, διὰ τούτων καὶ τῶν τοιούτων ἐπισκεπτέον· πότερον δ᾿ εἴρηκε καὶ ὥρισται τὸ τί ἦν εἶναι ἢ οὐχί, ἐκ τῶνδε.
Whether, then, a definition has been stated well or not well must be examined through these and such topics; but whether he has stated and defined what it is to be (the essence) or not, must be examined from the following.
Πρῶτον μὲν εἰ μὴ διὰ προτέρων καὶ γνωριμωτέρων πεποίηται τὸν ὁρισμόν.
First, indeed, if he has not made the definition through things that are prior and more knowable.
Ἐπεὶ γὰρ ὁ ὅρος ἀποδίδοται τοῦ γνωρίσαι χάριν τὸ λεχθέν, γνωρίζομεν δ᾿ οὐκ ἐκ τῶν τυχόντων ἀλλ᾿ ἐκ τῶν προτέρων καὶ γνωριμωτέρων, καθάπερ ἐν ταῖς ἀποδείξεσιν (οὕτω γὰρ πᾶσα διδασκαλία καὶ μάθησις ἔχει), φανερὸν ὅτι ὁ μὴ διὰ τοιούτων ὁριζόμενος οὐχ ὥρισται.
For since the definition is rendered for the sake of making known what is said, and we know not from random things but from things that are prior and more knowable, just as in demonstrations (for this is how all teaching and learning is), it is manifest that he who does not define through such things has not defined at all.
Εἰ δὲ μή, πλείους ἔσονται τοῦ αὐτοῦ ὁρισμοί.
Otherwise, there will be several definitions of the same thing.
Δῆλον γὰρ ὅτι καὶ ὁ διὰ προτέρων καὶ γνωριμωτέρων βέλτιον ὥρισται, ὥστε ἀμφότεροι ἂν εἴησαν ὅροι τοῦ αὐτοῦ.
For it is clear that the one made through things that are prior and more knowable is defined better, so that both would be definitions of the same thing.
Τὸ δὲ τοιοῦτον οὐ δοκεῖ· ἑκάστῳ γὰρ τῶν ὄντων ἕν ἐστι τὸ εἶναι ὅπερ ἐστίν·
But such a thing does not seem to be the case; for to each of existing things, what it is to be what it is is one.
ὥστ᾿ εἰ πλείους ἔσονται τοῦ αὐτοῦ ὁρισμοί, ταὐτὸν ἔσται τῷ ὁριζομένῳ τὸ εἶναι ὅπερ καθ᾿ ἑκάτερον τῶν ὁρισμῶν δηλοῦται.
So, if there are to be several definitions of the same thing, what it is to be what it is for the thing defined will be the same as what is declared by each of the definitions.
Ταῦτα δ᾿ οὐ ταὐτά ἐστιν, ἐπειδὴ οἱ ὁρισμοὶ ἕτεροι.
But these are not the same, since the definitions are different.
Δῆλον οὖν ὅτι οὐχ ὥρισται ὁ μὴ διὰ προτέρων καὶ γνωριμωτέρων ὁρισάμενος.
It is clear, then, that he who has not defined through things that are prior and more knowable has not defined.
Τὸ μὲν οὖν μὴ διὰ γνωριμωτέρων εἰρῆσθαι τὸν ὅρον διχῶς ἔστιν ἐκλαβεῖν· ἢ γὰρ εἰ ἁπλῶς ἐξ ἀγνωστοτέρων ἢ εἰ ἡμῖν ἀγνωστοτέρων· ἐνδέχεται γὰρ ἀμφοτέρως.
Now, to say that the definition has not been stated through things that are more knowable can be understood in two ways: either if it is made from things less known absolutely, or from things less known to us; for it is possible in both ways.
Ἁπλῶς μὲν οὖν γνωριμώτερον τὸ πρότερον τοῦ ὑστέρου, οἷον στιγμὴ γραμμῆς καὶ γραμμὴ ἐπιπέδου καὶ ἐπίπεδον στερεοῦ, καθάπερ καὶ μονὰς ἀριθμοῦ· πρότερον γὰρ καὶ ἀρχὴ παντὸς ἀριθμοῦ.
Absolutely, then, what is prior is more knowable than what is posterior, for example, a point than a line, a line than a plane, and a plane than a solid, just as a unit also is more knowable than a number; for it is prior and the principle of all number.
Ὁμοίως δὲ καὶ στοιχεῖον συλλαβῆς.
And likewise also an element than a syllable.
Ἡμῖν δ᾿ ἀνάπαλιν ἐνίοτε συμβαίνει· μάλιστα γὰρ τὸ στερεὸν ὑπὸ τὴν αἴσθησιν πίπτει, τὸ δ᾿ ἐπίπεδον μᾶλλον τῆς γραμμῆς, γραμμὴ δὲ σημείου μᾶλλον.
But to us, the reverse sometimes happens; for the solid falls especially under sense, and the plane more than the line, and the line more than the point.
Οἱ πολλοὶ γὰρ τὰ τοιαῦτα προγνωρίζουσιν· τὰ μὲν γὰρ τῆς τυχούσης τὰ δ᾿ ἀκριβοῦς καὶ περιττῆς διανοίας καταμαθεῖν ἐστίν.
For the many know such things beforehand; for the former are within the grasp of any random mind, but the latter are to be comprehended by an accurate and exceptional intellect.
Ἁπλῶς μὲν οὖν βέλτιον τὸ διὰ τῶν πρότερον τὰ ὕστερα πειρᾶσθαι γνωρίζειν· ἐπιστημονικώτερον γὰρ τὸ τοιοῦτόν ἐστιν.
Absolutely, then, it is better to try to know posterior things through prior things; for such a way is more scientific.
Οὐ μὴν ἀλλὰ πρὸς τοὺς ἀδυνατοῦντας γνωρίζειν διὰ τῶν τοιούτων ἀναγκαῖον ἴσως διὰ τῶν ἐκείνοις γνωρίμων ποιεῖσθαι τὸν λόγον.
Nevertheless, for those who are unable to know through such things, it is perhaps necessary to make the formula through things that are known to them.
Εἰσὶ δὲ τῶν τοιούτων ὁρισμῶν ὅ τε τῆς στιγμῆς καὶ ὁ τῆς γραμμῆς καὶ ὁ τοῦ ἐπιπέδου· πάντες γὰρ διὰ τῶν ὑστέρων τὰ πρότερα δηλοῦσιν· τὸ μὲν γὰρ γραμμῆς, τὸ δ᾿ ἐπιπέδου, τὸ δὲ στερεοῦ φασὶ πέρας εἶναι.
And of such definitions are those of a point, a line, and a plane; for all these declare prior things through posterior things, for they say that a point is the limit of a line, a line of a plane, and a plane of a solid.
Οὐ δεῖ δὲ λανθάνειν ὅτι τοὺς οὕτως ὁριζομένους οὐκ ἐνδέχεται τὸ τί ἦν εἶναι τῷ ὁριζομένῳ δηλοῦν, ἐὰν μὴ τυγχάνῃ ταὐτὸν ἡμῖν τε γνωριμώτερον καὶ ἁπλῶς γνωριμώτερον, εἴπερ δεῖ μὲν διὰ τοῦ γένους καὶ τῶν διαφορῶν ὁρίζεσθαι τὸν καλῶς ὁριζόμενον, ταῦτα δὲ τῶν ἁπλῶς γνωριμωτέρων καὶ προτέρων τοῦ εἴδους ἐστίν.
But it must not escape notice that those who define in this way cannot declare what it is to be for the thing defined, unless it happens that the same thing is both more knowable to us and more knowable absolutely; if indeed he who defines well must define through the genus and differences, and these belong to things that are absolutely more knowable and prior to the species.
Συναναιρεῖ γὰρ τὸ γένος καὶ ἡ διαφορὰ τὸ εἶδος, ὥστε πρότερα ταῦτα τοῦ εἴδους.
For the genus and difference co-annihilate the species, so that these are prior to the species.
Ἔστι δὲ καὶ γνωριμώτερα· τοῦ μὲν γὰρ εἴδους γνωριζομένου ἀνάγκη καὶ τὸ γένος καὶ τὴν διαφορὰν γνωρίζεσθαι (ὁ γὰρ ἄνθρωπον γνωρίζων καὶ ζῷον καὶ πεζὸν γνωρίζει), τοῦ δὲ γένους ἢ τῆς διαφορᾶς γνωριζομένης οὐκ ἀνάγκη καὶ τὸ εἶδος γνωρίζεσθαι, ὥστε ἀγνωστότερον τὸ εἶδος.
And they are also more knowable; for if the species is known, both the genus and difference must also be known (for he who knows man also knows animal and pedestrian), but if the genus or difference is known, it is not necessary that the species also be known, so that the species is less known.
Ἔτι τοῖς κατ᾿ ἀλήθειαν τοὺς τοιούτους ὁρισμοὺς φάσκουσιν εἶναι, τοὺς ἐκ τῶν ἑκάστῳ γνωρίμων, πολλοὺς τοῦ αὐτοῦ συμβήσεται λέγειν ὁρισμοὺς εἶναι· ἕτερα γὰρ ἑτέροις καὶ οὐ ταὐτὰ πᾶσι τυγχάνει γνωριμώτερα ὄντα, ὥστε πρὸς ἕκαστον ἕτερος ἂν εἴη ὁρισμὸς ἀποδοτέος, εἴπερ ἐκ τῶν ἑκάστοις γνωριμωτέρων τὸν ὁρισμὸν ποιεῖσθαι χρή.
Further, for those who assert that such definitions are truly definitions, namely those made from things known to each individual, it will follow that they say there are many definitions of the same thing; for different things happen to be more knowable to different people, and not the same things to all, so that a different definition would have to be rendered to each person, if indeed one must make the definition from what is more knowable to each.
Ἔτι τοῖς αὐτοῖς ἄλλοτ᾿ ἄλλα μᾶλλον γνώριμα, ἐξ ἀρχῆς μὲν τὰ αἰσθητά, ἀκριβεστέροις δὲ γινομένοις ἀνάπαλιν, ὥστ᾿ οὐδὲ πρὸς τὸν αὐτὸν ἀεὶ ὁ αὐτὸς ὁρισμὸς ἀποδοτέος τοῖς διὰ τῶν ἑκάστοις γνωριμωτέρων τὸν ὁρισμὸν φάσκουσιν ἀποδοτέον εἶναι.
Further, to the same people different things are more knowable at different times: at first, sensible things, but as they become more accurate, the reverse; so that not even to the same person must the same definition always be rendered, according to those who say that the definition must be rendered through what is more knowable to each.
Δῆλον οὖν ὅτι οὐχ ὁριστέον διὰ τῶν τοιούτων, ἀλλὰ διὰ τῶν ἁπλῶς γνωριμωτέρων· μόνως γὰρ ἂν οὕτως εἷς καὶ ὁ αὐτὸς ὁρισμὸς ἀεὶ γίνοιτο.
It is clear, then, that one must not define through such things, but through things that are absolutely more knowable; for only in this way would there always be one and the same definition.
Ἴσως δὲ καὶ τὸ ἁπλῶς γνώριμον οὐ τὸ πᾶσι γνώριμόν ἐστιν, ἀλλὰ τὸ τοῖς εὖ διακειμένοις τὴν διάνοιαν, καθάπερ καὶ τὸ ἁπλῶς ὑγιεινὸν τὸ τοῖς εὖ ἔχουσι τὸ σῶμα.
And perhaps what is absolutely knowable is not what is knowable to all, but what is knowable to those who are in a good mental state, just as what is absolutely healthy is what is healthy to those in a good bodily condition.
Δεῖ μὲν οὖν ἕκαστα τῶν τοιούτων ἐξακριβοῦν, χρῆσθαι δὲ διαλεγομένους πρὸς τὸ συμφέρον.
Each of such things, then, must be precisely determined, and those who engage in discussion must use them as is advantageous.
Μάλιστα δ᾿ ὁμολογουμένως ἀναιρεῖν ἐνδέχεται τὸν ὁρισμόν, ἐὰν μήτ᾿ ἐκ τῶν ἁπλῶς γνωριμωτέρων μήτ᾿ ἐκ τῶν ἡμῖν τυγχάνῃ τὸν λόγον πεποιημένος.
But most confessedly, it is possible to demolish a definition if the formula happens to have been made neither from things that are absolutely more knowable nor from those more knowable to us.