Cephalos Ceph.How, then, being of such a nature, 141acan it be either younger or older or of the same age as anything? In no way. Then the one cannot be younger or older or of the same age as anything. No, evidently not. And can the one exist in time at all, if it is of such a nature? Must it not, if it exists in time, always be growing older than itself? It must. And the older is always older than something younger? Certainly. Then that which grows older than itself grows at the same time younger than itself, if it is to have something than which it grows older. What do you mean? 141b This is what I mean: A thing which is different from another does not have to become different from that which is already different, but it must be different from that which is already different, it must have become different from that which has become so, it will have to be different from that which will be so, but from that which is becoming different it cannot have become, nor can it be going to be, nor can it already be different: it must become different, and that is all. There is no denying that. 141c But surely the notion “older” is a difference with respect to the younger and to nothing else. Yes, so it is. But that which is becoming older than itself must at the same time be becoming younger than itself. So it appears. But surely it cannot become either for a longer or for a shorter time than itself; it must become and be and be about to be for an equal time with itself. That also is inevitable. Apparently, then, it is inevitable that everything which exists in time and partakes of time 141d is of the same age as itself and is also at the same time becoming older and younger than itself. I see no escape from that. But the one had nothing to do with such affections. No, it had not. It has nothing to do with time, and does not exist in time. No, that is the result of the argument.
Well, and do not the words “was,” “has become,” and “was becoming” appear to denote participation in past time? Certainly. 141e And “will be,” “will become,” and “will be made to become,” in future time? Yes. And “is” and “is becoming” in the present? Certainly. Then if the one has no participation in time whatsoever, it neither has become nor became nor was in the past, it has neither become nor is it becoming nor is it in the present, and it will neither become nor be made to become nor will it be in the future. Very true. Can it then partake of being in any other way than in the past, present, or future? It cannot. Then the one has no share in being at all. Apparently not. Then the one is not at all. Evidently not.
Ceph.Then it has no being even so as to be one, for if it were one, it would be and would partake of being; but apparently one neither is nor is one, if this argument is to be trusted. 142aThat seems to be true. But can that which does not exist have anything pertaining or belonging to it? Of course not. Then the one has no name, nor is there any description or knowledge or perception or opinion of it. Evidently not. And it is neither named nor described nor thought of nor known, nor does any existing thing perceive it. Apparently not. Is it possible that all this is true about the one ? I do not think so.
Shall we then return to our hypothesis and see 142b if a review of our argument discloses any new point of view? By all means. We say, then, that if the one exists, we must come to an agreement about the consequences, whatever they may be, do we not? Yes. Now consider the first point. If one is, can it be and not partake of being? No, it cannot. Then the being of one will exist, but will not be identical with one; for if it were identical with one, it would not be the being of one, nor would one partake of it, 142c but the statement that one is would be equivalent to the statement that one is one but our hypothesis is not if one is one, what will follow, but if one is. Do you agree? Certainly. In the belief that one and being differ in meaning? Most assuredly. Then if we say concisely “one is,” it is equivalent to saying that one partakes of being? Certainly. Let us again say what will follow if one is and consider whether this hypothesis must not necessarily show that one is of such a nature as to have parts. How does that come about ? In this way: 142d If being is predicated of the one which exists and unity is predicated of being which is one, and being and the one are not the same, but belong to the existent one of our hypothesis, must not the existent one be a whole of which the one and being are parts? Inevitably. And shall we call each of these parts merely a part, or must it, in so far as it is a part, be called a part of the whole? A part of the whole. Whatever one, then, exists is a whole and has a part. Certainly. Well then, can either of these two parts of existent one—unity and being—abandon the other? 142e Can unity cease to be a part of being or being to be a part of unity? No.
Ceph. And again each of the parts possesses unity and being, and the smallest of parts is composed of these two parts, and thus by the same argument any part whatsoever has always these two parts; for always unity has being and being has unity; 143a and, therefore, since it is always becoming two, it can never be one. Certainly. Then it results that the existent one would be infinite in number? Apparently.
Let us make another fresh start. In what direction? We say that the one partakes of being, because it is? Yes. And for that reason the one, because it is, was found to be many. Yes. Well then, will the one, which we say partakes of being, if we form a mental conception of it alone by itself, without that of which we say it partakes, be found to be only one, or many? One, I should say. 143b Just let us see; must not the being of one be one thing and one itself another, if the one is not being, but, considered as one, partakes of being? Yes, that must be so. Then if being is one thing and one is another, one is not other than being because it is one, nor is being other than one because it is being, but they differ from each other by virtue of being other and different. Certainly. Therefore the other is neither the same as one nor as being. Certainly not. Well, then, if we make a selection among them, 143c whether we select being and the other, or being and one, or one and the other, in each instance we select two things which may properly be called both? What do you mean? I will explain. We can speak of being? Yes. And we can also speak of one? Yes, that too. Then have we not spoken of each of them? Yes. And when I speak of being and one, do I not speak of both? Certainly. And also when I speak of being and other, or other and one, in every case I speak of each pair as both? 143d Yes. If things are correctly called both, can they be both without being two? They cannot. And if things are two, must not each of them be one? Certainly. Then since the units of these pairs are together two, each must be individually one. That is clear. But if each of them is one, by the addition of any sort of one to any pair whatsoever the total becomes three? Yes. And three is an odd number, and two is even? Of course. 143e Well, when there are two units, must there not also be twice, and when there are three, thrice, that is, if two is twice one and three is thrice one? There must. But if there are two and twice, must there not also be twice two? And again, if there are three and thrice, must there not be thrice three? Of course. Well then, if there are three and twice and two and thrice, must there not also be twice three and thrice two? Inevitably.
Ceph. Then there would be even times even, 144a odd times odd, odd times even, and even times odd. Yes. Then if that is true, do you believe any number is left out, which does not necessarily exist? By no means. Then if one exists, number must also exist. It must. But if number exists, there must be many, indeed an infinite multitude, of existences; or is not number infinite in multitude and participant of existence? Certainly it is. Then if all number partakes of existence, every part of number will partake of it? Yes. 144b Existence, then, is distributed over all things, which are many, and is not wanting in any existing thing from the greatest to the smallest? Indeed, is it not absurd even to ask that question? For how can existence be wanting in any existing thing? It cannot by any means. Then it is split up into the smallest and greatest and all kinds of existences nothing else is so much divided, 144c and in short the parts of existence are infinite. That is true. Its parts are the most numerous of all. Yes, they are the most numerous. Well, is there any one of them which is a part of existence, but is no part? How could that be? But if there is, it must, I imagine, so long as it is, be some one thing; it cannot be nothing. That is inevitable. Then unity is an attribute of every part of existence and is not wanting to a smaller or larger or any other part. True. 144d Can the one be in many places at once and still be a whole? Consider that question. I am considering and I see that it is impossible. Then it is divided into parts, if it is not a whole; for it cannot be attached to all the parts of existence at once unless it is divided. I agree. And that which is divided into parts must certainly be as numerous as its parts. It must. Then what we said just now—that existence was divided into the greatest number of parts—was not true for it is not divided, you see, into any more parts than one, 144e but, as it seems, into the same number as one for existence is not wanting to the one, nor the one to existence, but being two they are equal throughout. That is perfectly clear. The one, then, split up by existence, is many and infinite in number. Clearly. Then not only the existent one is many, but the absolute one divided by existence, must be many. Certainly.
Cephalos can it be either younger or older or of the same age as anything? In no way. Then the one cannot be younger or older or of the same age as anything. No, evidently not. And can the one exist in time at all, if it is of such a nature? Must it not, if it exists in time, always be growing older than itself? It must. And the older is always older than something younger? Certainly. Then that which grows older than itself grows at the same time younger than itself, if it is to have something than which it grows older. What do you mean?
Κέφαλος οἷόν τε ἔσται τινὸς ἢ πρεσβύτερον ἢ νεώτερον εἶναι ἢ τὴν αὐτὴν ἡλικίαν ἔχειν τῳ τοιοῦτον ὄν; οὐδαμῶς. οὐκ ἄρα ἂν εἴη νεώτερόν γε οὐδὲ πρεσβύτερον οὐδὲ τὴν αὐτὴν ἡλικίαν ἔχον τὸ ἓν οὔτε αὑτῷ οὔτε ἄλλῳ. οὐ φαίνεται. ἆρʼ οὖν οὐδὲ ἐν χρόνῳ τὸ παράπαν δύναιτο ἂν εἶναι τὸ ἕν, εἰ τοιοῦτον εἴη; ἢ οὐκ ἀνάγκη, ἐάν τι ᾖ ἐν χρόνῳ, ἀεὶ αὐτὸ αὑτοῦ πρεσβύτερον γίγνεσθαι; ἀνάγκη. οὐκοῦν τό γε πρεσβύτερον ἀεὶ νεωτέρου πρεσβύτερον; τί μήν;
Cephalos This is what I mean: A thing which is different from another does not have to become different from that which is already different, but it must be different from that which is already different, it must have become different from that which has become so, it will have to be different from that which will be so, but from that which is becoming different it cannot have become, nor can it be going to be, nor can it already be different: it must become different, and that is all. There is no denying that.
Κέφαλος τὸ πρεσβύτερον ἄρα ἑαυτοῦ γιγνόμενον καὶ νεώτερον ἑαυτοῦ ἅμα γίγνεται, εἴπερ μέλλει ἔχειν ὅτου πρεσβύτερον γίγνηται. πῶς λέγεις; ὧδε· διάφορον ἕτερον ἑτέρου οὐδὲν δεῖ γίγνεσθαι ἤδη ὄντος διαφόρου, ἀλλὰ τοῦ μὲν ἤδη ὄντος ἤδη εἶναι, τοῦ δὲ γεγονότος γεγονέναι, τοῦ δὲ μέλλοντος μέλλειν, τοῦ δὲ γιγνομένου οὔτε γεγονέναι οὔτε μέλλειν οὔτε εἶναί πω διάφορον, ἀλλὰ γίγνεσθαι καὶ ἄλλως
Cephalos But surely the notion “older” is a difference with respect to the younger and to nothing else. Yes, so it is. But that which is becoming older than itself must at the same time be becoming younger than itself. So it appears. But surely it cannot become either for a longer or for a shorter time than itself; it must become and be and be about to be for an equal time with itself. That also is inevitable. Apparently, then, it is inevitable that everything which exists in time and partakes of time
Κέφαλος οὐκ εἶναι. ἀνάγκη γὰρ δή. ἀλλὰ μὴν τό γε πρεσβύτερον διαφορότης νεωτέρου ἐστὶν καὶ οὐδενὸς ἄλλου. ἔστι γάρ. τὸ ἄρα πρεσβύτερον ἑαυτοῦ γιγνόμενον ἀνάγκη καὶ νεώτερον ἅμα ἑαυτοῦ γίγνεσθαι. ἔοικεν. ἀλλὰ μὴν καὶ μήτε πλείω ἑαυτοῦ γίγνεσθαι χρόνον μήτε ἐλάττω, ἀλλὰ τὸν ἴσον χρόνον καὶ γίγνεσθαι ἑαυτῷ καὶ εἶναι καὶ γεγονέναι καὶ μέλλειν ἔσεσθαι. ἀνάγκη γὰρ οὖν καὶ ταῦτα. ἀνάγκη ἄρα ἐστίν, ὡς ἔοικεν, ὅσα γε ἐν χρόνῳ ἐστὶν
Cephalos is of the same age as itself and is also at the same time becoming older and younger than itself. I see no escape from that. But the one had nothing to do with such affections. No, it had not. It has nothing to do with time, and does not exist in time. No, that is the result of the argument.
Well, and do not the words “was,” “has become,” and “was becoming” appear to denote participation in past time? Certainly.
Κέφαλος καὶ μετέχει τοῦ τοιούτου, ἕκαστον αὐτῶν τὴν αὐτήν τε αὐτὸ αὑτῷ ἡλικίαν ἔχειν καὶ πρεσβύτερόν τε αὑτοῦ ἅμα καὶ νεώτερον γίγνεσθαι. κινδυνεύει. ἀλλὰ μὴν τῷ γε ἑνὶ τῶν τοιούτων παθημάτων οὐδὲν μετῆν. οὐ γὰρ μετῆν. οὐδὲ ἄρα χρόνου αὐτῷ μέτεστιν, οὐδʼ ἔστιν ἔν τινι χρόνῳ. οὔκουν δή, ὥς γε ὁ λόγος αἱρεῖ.
τί οὖν; τὸ ἦν καὶ τὸ γέγονε καὶ τὸ ἐγίγνετο οὐ χρόνου μέθεξιν δοκεῖ σημαίνειν τοῦ ποτὲ γεγονότος; καὶ μάλα.
And “will be,” “will become,” and “will be made to become,” in future time? Yes. And “is” and “is becoming” in the present? Certainly. Then if the one has no participation in time whatsoever, it neither has become nor became nor was in the past, it has neither become nor is it becoming nor is it in the present, and it will neither become nor be made to become nor will it be in the future. Very true. Can it then partake of being in any other way than in the past, present, or future? It cannot. Then the one has no share in being at all. Apparently not. Then the one is not at all. Evidently not.
Cephalos Ceph.Then it has no being even so as to be one, for if it were one, it would be and would partake of being; but apparently one neither is nor is one, if this argument is to be trusted.
τί δέ; τὸ ἔσται καὶ τὸ γενήσεται καὶ τὸ γενηθήσεται οὐ τοῦ ἔπειτα ; ναί. τὸ δὲ δὴ ἔστι καὶ τὸ γίγνεται οὐ τοῦ νῦν παρόντος; πάνυ μὲν οὖν. εἰ ἄρα τὸ ἓν μηδαμῇ μηδενὸς μετέχει χρόνου, οὔτε ποτὲ γέγονεν οὔτʼ ἐγίγνετο οὔτʼ ἦν ποτέ, οὔτε νῦν γέγονεν οὔτε γίγνεται οὔτε ἔστιν, οὔτʼ ἔπειτα γενήσεται οὔτε γενηθήσεται οὔτε ἔσται. ἀληθέστατα. ἔστιν οὖν οὐσίας ὅπως ἄν τι μετάσχοι ἄλλως ἢ κατὰ τούτων τι; οὐκ ἔστιν. οὐδαμῶς ἄρα τὸ ἓν οὐσίας μετέχει. οὐκ ἔοικεν. οὐδαμῶς ἄρα ἔστι τὸ ἕν. οὐ φαίνεται.
Κέφαλος οὐδʼ ἄρα οὕτως ἔστιν ὥστε ἓν εἶναι· εἴη γὰρ ἂν ἤδη ὂν καὶ οὐσίας μετέχον· ἀλλʼ ὡς ἔοικεν, τὸ ἓν οὔτε ἕν ἐστιν οὔτε ἔστιν, εἰ δεῖ τῷ
Cephalos That seems to be true. But can that which does not exist have anything pertaining or belonging to it? Of course not. Then the one has no name, nor is there any description or knowledge or perception or opinion of it. Evidently not. And it is neither named nor described nor thought of nor known, nor does any existing thing perceive it. Apparently not. Is it possible that all this is true about the one ? I do not think so.
Shall we then return to our hypothesis and see
Κέφαλος τοιῷδε λόγῳ πιστεύειν. κινδυνεύει. ὃ δὲ μὴ ἔστι, τούτῳ τῷ μὴ ὄντι εἴη ἄν τι αὐτῷ ἢ αὐτοῦ; καὶ πῶς; οὐδʼ ἄρα ὄνομα ἔστιν αὐτῷ οὐδὲ λόγος οὐδέ τις ἐπιστήμη οὐδὲ αἴσθησις οὐδὲ δόξα. οὐ φαίνεται. οὐδʼ ὀνομάζεται ἄρα οὐδὲ λέγεται οὐδὲ δοξάζεται οὐδὲ γιγνώσκεται, οὐδέ τι τῶν ὄντων αὐτοῦ αἰσθάνεται. οὐκ ἔοικεν. ἦ δυνατὸν οὖν περὶ τὸ ἓν ταῦτα οὕτως ἔχειν; οὔκουν ἔμοιγε δοκεῖ.
if a review of our argument discloses any new point of view? By all means. We say, then, that if the one exists, we must come to an agreement about the consequences, whatever they may be, do we not? Yes. Now consider the first point. If one is, can it be and not partake of being? No, it cannot. Then the being of one will exist, but will not be identical with one; for if it were identical with one, it would not be the being of one, nor would one partake of it,
βούλει οὖν ἐπὶ τὴν ὑπόθεσιν πάλιν ἐξ ἀρχῆς ἐπανέλθωμεν, ἐάν τι ἡμῖν ἐπανιοῦσιν ἀλλοῖον φανῇ; πάνυ μὲν οὖν βούλομαι. οὐκοῦν ἓν εἰ ἔστιν, φαμέν, τὰ συμβαίνοντα περὶ αὐτοῦ, ποῖά ποτε τυγχάνει ὄντα, διομολογητέα ταῦτα· οὐχ οὕτω; ναί. ὅρα δὴ ἐξ ἀρχῆς. ἓν εἰ ἔστιν, ἆρα οἷόν τε αὐτὸ εἶναι μέν, οὐσίας δὲ μὴ μετέχειν; οὐχ οἷόν τε. οὐκοῦν καὶ ἡ οὐσία τοῦ ἑνὸς εἴη ἂν οὐ ταὐτὸν οὖσα τῷ ἑνί· οὐ γὰρ ἂν ἐκείνη ἦν ἐκείνου οὐσία, οὐδʼ ἂν
but the statement that one is would be equivalent to the statement that one is one but our hypothesis is not if one is one, what will follow, but if one is. Do you agree? Certainly. In the belief that one and being differ in meaning? Most assuredly. Then if we say concisely “one is,” it is equivalent to saying that one partakes of being? Certainly. Let us again say what will follow if one is and consider whether this hypothesis must not necessarily show that one is of such a nature as to have parts. How does that come about ? In this way:
ἐκεῖνο, τὸ ἕν, ἐκείνης μετεῖχεν, ἀλλʼ ὅμοιον ἂν ἦν λέγειν ἕν τε εἶναι καὶ ἓν ἕν. νῦν δὲ οὐχ αὕτη ἐστὶν ἡ ὑπόθεσις, εἰ ἓν ἕν, τί χρὴ συμβαίνειν, ἀλλʼ εἰ ἓν ἔστιν· οὐχ οὕτω; πάνυ μὲν οὖν. οὐκοῦν ὡς ἄλλο τι σημαῖνον τὸ ἔστι τοῦ ἕν; ἀνάγκη. ἆρα οὖν ἄλλο ἢ ὅτι οὐσίας μετέχει τὸ ἕν, τοῦτʼ ἂν εἴη τὸ λεγόμενον, ἐπειδάν τις συλλήβδην εἴπῃ ὅτι ἓν ἔστιν; πάνυ γε. πάλιν δὴ λέγωμεν, ἓν εἰ ἔστιν, τί συμβήσεται. σκόπει οὖν εἰ οὐκ ἀνάγκη ταύτην τὴν ὑπόθεσιν τοιοῦτον ὂν τὸ ἓν σημαίνειν, οἷον
If being is predicated of the one which exists and unity is predicated of being which is one, and being and the one are not the same, but belong to the existent one of our hypothesis, must not the existent one be a whole of which the one and being are parts? Inevitably. And shall we call each of these parts merely a part, or must it, in so far as it is a part, be called a part of the whole? A part of the whole. Whatever one, then, exists is a whole and has a part. Certainly. Well then, can either of these two parts of existent one—unity and being—abandon the other?
μέρη ἔχειν; πῶς; ὧδε· εἰ τὸ ἔστι τοῦ ἑνὸς ὄντος λέγεται καὶ τὸ ἓν τοῦ ὄντος ἑνός, ἔστι δὲ οὐ τὸ αὐτὸ ἥ τε οὐσία καὶ τὸ ἕν, τοῦ αὐτοῦ δὲ ἐκείνου οὗ ὑπεθέμεθα, τοῦ ἑνὸς ὄντος, ἆρα οὐκ ἀνάγκη τὸ μὲν ὅλον ἓν ὂν εἶναι αὐτό, τούτου δὲ γίγνεσθαι μόρια τό τε ἓν καὶ τὸ εἶναι; ἀνάγκη. πότερον οὖν ἑκάτερον τῶν μορίων τούτων μόριον μόνον προσεροῦμεν, ἢ τοῦ ὅλου μόριον τό γε μόριον προσρητέον; τοῦ ὅλου. καὶ ὅλον ἄρα ἐστί, ὃ ἂν ἓν ᾖ, καὶ μόριον ἔχει. πάνυ γε. τί οὖν; τῶν μορίων ἑκάτερον
Can unity cease to be a part of being or being to be a part of unity? No.
Cephalos Ceph. And again each of the parts possesses unity and being, and the smallest of parts is composed of these two parts, and thus by the same argument any part whatsoever has always these two parts; for always unity has being and being has unity;
τούτων τοῦ ἑνὸς ὄντος, τό τε ἓν καὶ τὸ ὄν, ἆρα ἀπολείπεσθον ἢ τὸ ἓν τοῦ εἶναι μορίου ἢ τὸ ὂν τοῦ ἑνὸς μορίου; οὐκ ἂν εἴη.
Κέφαλος πάλιν ἄρα καὶ τῶν μορίων ἑκάτερον τό τε ἓν ἴσχει καὶ τὸ ὄν, καὶ γίγνεται τὸ ἐλάχιστον ἐκ δυοῖν αὖ μορίοιν τὸ μόριον, καὶ κατὰ τὸν αὐτὸν λόγον οὕτως ἀεί, ὅτιπερ ἂν μόριον γένηται, τούτω τὼ μορίω ἀεὶ ἴσχει· τό τε γὰρ ἓν τὸ ὂν ἀεὶ ἴσχει καὶ τὸ ὂν τὸ ἕν· ὥστε ἀνάγκη
Cephalos and, therefore, since it is always becoming two, it can never be one. Certainly. Then it results that the existent one would be infinite in number? Apparently.
Let us make another fresh start. In what direction? We say that the one partakes of being, because it is? Yes. And for that reason the one, because it is, was found to be many. Yes. Well then, will the one, which we say partakes of being, if we form a mental conception of it alone by itself, without that of which we say it partakes, be found to be only one, or many? One, I should say.
Κέφαλος δύʼ ἀεὶ γιγνόμενον μηδέποτε ἓν εἶναι. παντάπασι μὲν οὖν. οὐκοῦν ἄπειρον ἂν τὸ πλῆθος οὕτω τὸ ἓν ὂν εἴη; ἔοικεν.
ἴθι δὴ καὶ τῇδε ἔτι. πῇ; οὐσίας φαμὲν μετέχειν τὸ ἕν, διὸ ἔστιν; ναί. καὶ διὰ ταῦτα δὴ τὸ ἓν ὂν πολλὰ ἐφάνη. οὕτω. τί δέ; αὐτὸ τὸ ἕν, ὃ δή φαμεν οὐσίας μετέχειν, ἐὰν αὐτὸ τῇ διανοίᾳ μόνον καθʼ αὑτὸ λάβωμεν ἄνευ τούτου οὗ φαμεν μετέχειν, ἆρά γε ἓν μόνον φανήσεται ἢ καὶ πολλὰ τὸ αὐτὸ τοῦτο; ἕν, οἶμαι ἔγωγε.
Just let us see; must not the being of one be one thing and one itself another, if the one is not being, but, considered as one, partakes of being? Yes, that must be so. Then if being is one thing and one is another, one is not other than being because it is one, nor is being other than one because it is being, but they differ from each other by virtue of being other and different. Certainly. Therefore the other is neither the same as one nor as being. Certainly not. Well, then, if we make a selection among them,
ἴδωμεν δή· ἄλλο τι ἕτερον μὲν ἀνάγκη τὴν οὐσίαν αὐτοῦ εἶναι, ἕτερον δὲ αὐτό, εἴπερ μὴ οὐσία τὸ ἕν, ἀλλʼ ὡς ἓν οὐσίας μετέσχεν. ἀνάγκη. οὐκοῦν εἰ ἕτερον μὲν ἡ οὐσία, ἕτερον δὲ τὸ ἕν, οὔτε τῷ ἓν τὸ ἓν τῆς οὐσίας ἕτερον οὔτε τῷ οὐσία εἶναι ἡ οὐσία τοῦ ἑνὸς ἄλλο, ἀλλὰ τῷ ἑτέρῳ τε καὶ ἄλλῳ ἕτερα ἀλλήλων. πάνυ μὲν οὖν. ὥστε οὐ ταὐτόν ἐστιν οὔτε τῷ ἑνὶ οὔτε τῇ οὐσίᾳ τὸ ἕτερον. πῶς γάρ;
whether we select being and the other, or being and one, or one and the other, in each instance we select two things which may properly be called both? What do you mean? I will explain. We can speak of being? Yes. And we can also speak of one? Yes, that too. Then have we not spoken of each of them? Yes. And when I speak of being and one, do I not speak of both? Certainly. And also when I speak of being and other, or other and one, in every case I speak of each pair as both?
τί οὖν; ἐὰν προελώμεθα αὐτῶν εἴτε βούλει τὴν οὐσίαν καὶ τὸ ἕτερον εἴτε τὴν οὐσίαν καὶ τὸ ἓν εἴτε τὸ ἓν καὶ τὸ ἕτερον, ἆρʼ οὐκ ἐν ἑκάστῃ τῇ προαιρέσει προαιρούμεθά τινε ὣ ὀρθῶς ἔχει καλεῖσθαι ἀμφοτέρω; πῶς; ὧδε· ἔστιν οὐσίαν εἰπεῖν; ἔστιν. καὶ αὖθις εἰπεῖν ἕν; καὶ τοῦτο. ἆρʼ οὖν οὐχ ἑκάτερον αὐτοῖν εἴρηται; ναί. τί δʼ ὅταν εἴπω οὐσία τε καὶ ἕν, ἆρα οὐκ ἀμφοτέρω; πάνυ γε. οὐκοῦν καὶ ἐὰν οὐσία τε καὶ ἕτερον ἢ ἕτερόν τε καὶ ἕν, καὶ οὕτω πανταχῶς ἐφʼ ἑκάστου ἄμφω λέγω; ναί.
Yes. If things are correctly called both, can they be both without being two? They cannot. And if things are two, must not each of them be one? Certainly. Then since the units of these pairs are together two, each must be individually one. That is clear. But if each of them is one, by the addition of any sort of one to any pair whatsoever the total becomes three? Yes. And three is an odd number, and two is even? Of course.
ὣ δʼ ἂν ἄμφω ὀρθῶς προσαγορεύησθον, ἆρα οἷόν τε ἄμφω μὲν αὐτὼ εἶναι, δύο δὲ μή; οὐχ οἷόν τε. ὣ δʼ ἂν δύο ἦτον, ἔστι τις μηχανὴ μὴ οὐχ ἑκάτερον αὐτοῖν ἓν εἶναι; οὐδεμία. τούτων ἄρα ἐπείπερ σύνδυο ἕκαστα συμβαίνει εἶναι, καὶ ἓν ἂν εἴη ἕκαστον. φαίνεται. εἰ δὲ ἓν ἕκαστον αὐτῶν ἐστι, συντεθέντος ἑνὸς ὁποιουοῦν ᾑτινιοῦν συζυγίᾳ οὐ τρία γίγνεται τὰ πάντα; ναί. τρία δὲ οὐ περιττὰ καὶ δύο ἄρτια; πῶς δʼ οὔ; τί δέ; δυοῖν ὄντοιν οὐκ
Well, when there are two units, must there not also be twice, and when there are three, thrice, that is, if two is twice one and three is thrice one? There must. But if there are two and twice, must there not also be twice two? And again, if there are three and thrice, must there not be thrice three? Of course. Well then, if there are three and twice and two and thrice, must there not also be twice three and thrice two? Inevitably.
Cephalos Ceph. Then there would be even times even,
ἀνάγκη εἶναι καὶ δίς, καὶ τριῶν ὄντων τρίς, εἴπερ ὑπάρχει τῷ τε δύο τὸ δὶς ἓν καὶ τῷ τρία τὸ τρὶς ἕν; ἀνάγκη. δυοῖν δὲ ὄντοιν καὶ δὶς οὐκ ἀνάγκη δύο δὶς εἶναι; καὶ τριῶν καὶ τρὶς οὐκ ἀνάγκη αὖ τρία τρὶς εἶναι; πῶς δʼ οὔ; τί δέ; τριῶν ὄντων καὶ δὶς ὄντων καὶ δυοῖν ὄντοιν καὶ τρὶς ὄντοιν οὐκ ἀνάγκη τε τρία δὶς εἶναι καὶ δύο τρίς; πολλή γε.
Κέφαλος ἄρτιά τε ἄρα ἀρτιάκις ἂν εἴη καὶ
Cephalos odd times odd, odd times even, and even times odd. Yes. Then if that is true, do you believe any number is left out, which does not necessarily exist? By no means. Then if one exists, number must also exist. It must. But if number exists, there must be many, indeed an infinite multitude, of existences; or is not number infinite in multitude and participant of existence? Certainly it is. Then if all number partakes of existence, every part of number will partake of it? Yes.
Κέφαλος περιττὰ περιττάκις καὶ ἄρτια περιττάκις καὶ περιττὰ ἀρτιάκις. ἔστιν οὕτω. εἰ οὖν ταῦτα οὕτως ἔχει, οἴει τινὰ ἀριθμὸν ὑπολείπεσθαι ὃν οὐκ ἀνάγκη εἶναι; οὐδαμῶς γε. εἰ ἄρα ἔστιν ἕν, ἀνάγκη καὶ ἀριθμὸν εἶναι. ἀνάγκη. ἀλλὰ μὴν ἀριθμοῦ γε ὄντος πολλὰ ἂν εἴη καὶ πλῆθος ἄπειρον τῶν ὄντων· ἢ οὐκ ἄπειρος ἀριθμὸς πλήθει καὶ μετέχων οὐσίας γίγνεται; καὶ πάνυ γε. οὐκοῦν εἰ πᾶς ἀριθμὸς οὐσίας μετέχει, καὶ τὸ μόριον ἕκαστον τοῦ ἀριθμοῦ μετέχοι ἂν αὐτῆς; ναί.
Cephalos Existence, then, is distributed over all things, which are many, and is not wanting in any existing thing from the greatest to the smallest? Indeed, is it not absurd even to ask that question? For how can existence be wanting in any existing thing? It cannot by any means. Then it is split up into the smallest and greatest and all kinds of existences nothing else is so much divided,
ἐπὶ πάντα ἄρα πολλὰ ὄντα ἡ οὐσία νενέμηται καὶ οὐδενὸς ἀποστατεῖ τῶν ὄντων, οὔτε τοῦ σμικροτάτου οὔτε τοῦ μεγίστου; ἢ τοῦτο μὲν καὶ ἄλογον ἐρέσθαι; πῶς γὰρ ἂν δὴ οὐσία γε τῶν ὄντων του ἀποστατοῖ; οὐδαμῶς. κατακεκερμάτισται ἄρα ὡς οἷόν τε σμικρότατα καὶ μέγιστα καὶ πανταχῶς ὄντα, καὶ μεμέρισται πάντων μάλιστα, καὶ ἔστι
Cephalos and in short the parts of existence are infinite. That is true. Its parts are the most numerous of all. Yes, they are the most numerous. Well, is there any one of them which is a part of existence, but is no part? How could that be? But if there is, it must, I imagine, so long as it is, be some one thing; it cannot be nothing. That is inevitable. Then unity is an attribute of every part of existence and is not wanting to a smaller or larger or any other part. True.
μέρη ἀπέραντα τῆς οὐσίας. ἔχει οὕτω. πλεῖστα ἄρα ἐστὶ τὰ μέρη αὐτῆς. πλεῖστα μέντοι. τί οὖν; ἔστι τι αὐτῶν ὃ ἔστι μὲν μέρος τῆς οὐσίας, οὐδὲν μέντοι μέρος; καὶ πῶς ἄν τοῦτο γένοιτο; ἀλλʼ εἴπερ γε οἶμαι ἔστιν, ἀνάγκη αὐτὸ ἀεί, ἕωσπερ ἂν ᾖ, ἕν γέ τι εἶναι, μηδὲν δὲ ἀδύνατον. ἀνάγκη. πρὸς ἅπαντι ἄρα τῷ τῆς οὐσίας μέρει πρόσεστιν τὸ ἕν, οὐκ ἀπολειπόμενον οὔτε σμικροτέρου οὔτε μείζονος μέρους οὔτε ἄλλου οὐδενός. οὕτω. ἆρα οὖν ἓν
Cephalos Can the one be in many places at once and still be a whole? Consider that question. I am considering and I see that it is impossible. Then it is divided into parts, if it is not a whole; for it cannot be attached to all the parts of existence at once unless it is divided. I agree. And that which is divided into parts must certainly be as numerous as its parts. It must. Then what we said just now—that existence was divided into the greatest number of parts—was not true for it is not divided, you see, into any more parts than one,
ὂν πολλαχοῦ ἅμα ὅλον ἐστί; τοῦτο ἄθρει. ἀλλʼ ἀθρῶ καὶ ὁρῶ ὅτι ἀδύνατον. μεμερισμένον ἄρα, εἴπερ μὴ ὅλον· ἄλλως γάρ που οὐδαμῶς ἅμα ἅπασι τοῖς τῆς οὐσίας μέρεσιν παρέσται ἢ μεμερισμένον. ναί. καὶ μὴν τό γε μεριστὸν πολλὴ ἀνάγκη εἶναι τοσαῦτα ὅσαπερ μέρη. ἀνάγκη. οὐκ ἄρα ἀληθῆ ἄρτι ἐλέγομεν λέγοντες ὡς πλεῖστα μέρη ἡ οὐσία νενεμημένη εἴη. οὐδὲ γὰρ πλείω τοῦ ἑνὸς νενέμηται, ἀλλʼ
Cephalos but, as it seems, into the same number as one for existence is not wanting to the one, nor the one to existence, but being two they are equal throughout. That is perfectly clear. The one, then, split up by existence, is many and infinite in number. Clearly. Then not only the existent one is many, but the absolute one divided by existence, must be many. Certainly.
ἴσα, ὡς ἔοικε, τῷ ἑνί· οὔτε γὰρ τὸ ὂν τοῦ ἑνὸς ἀπολείπεται οὔτε τὸ ἓν τοῦ ὄντος, ἀλλʼ ἐξισοῦσθον δύο ὄντε ἀεὶ παρὰ πάντα. παντάπασιν οὕτω φαίνεται. τὸ ἓν ἄρα αὐτὸ κεκερματισμένον ὑπὸ τῆς οὐσίας πολλά τε καὶ ἄπειρα τὸ πλῆθός ἐστιν. φαίνεται. οὐ μόνον ἄρα τὸ ὂν ἓν πολλά ἐστιν, ἀλλὰ καὶ αὐτὸ τὸ ἓν ὑπὸ τοῦ ὄντος διανενεμημένον πολλὰ ἀνάγκη εἶναι. παντάπασι μὲν οὖν.
καὶ μὴν ὅτι γε ὅλου τὰ μόρια μόρια, πεπερασμένον ἂν εἴη κατὰ τὸ ὅλον τὸ ἕν· ἢ οὐ περιέχεται ὑπὸ τοῦ ὅλου τὰ
Page 5 of 12 · Parmenides, Plato , tr. Harold North Fowler · Perseus Digital Library