16 PHYSICS, I. 1.
or things other than its naked self. ΤῸ consider, therefore, whether the natural principle is one in this sense, is like discussing any other paradox that is set up just for the sake of arguing, like the paradox of Heracleitus,t or the contention (should anyone advance 10) that the totality of existence is one single man. If their fundamental paradox is ad- mitted, there is nothing strange im all the other paradoxes followimg from it. Let us then start from the datum that things of Nature, οὐ (to put it at the lowest) some of them, do move and change, as is patent Lo observation; and let us make a note that we are nol bound to answer every kind of objection we may meet, but only such as are erroneously deduced from the accepted principles of the science in question. Thus, it is the geometer’s business to refute the squaring of the circle that proceeds by way of equating the segments, but he nced not * [That ‘ opposites’ are ‘ one,’ eg. ‘good and evil are one,’ Heracleitus, frag. 58 (57 Byw.). Cf b 20. Heracleitus was underslood by some to be denying the masim of contra- diction, Afet. 1005 b 23.—C.]
disappears; for in Chapter II. Aristotle says that, if you accept the paradoxical contlusion that Nature is a rigid unit, all the other paradoxes of the school (as to time and space for instance) inevitably follow. In Chapter III., on e other hand, he starts with the false (because ambiguous) premise that “nothing can come out of nothing” and shows that his opponents do not argue soundly even from that. The words ἢ λύειν λόγον ἐριστικόν (a kind of echo of the ἀμφότεροι γὰρ ἐριστικῶς συλλογίζονται) appear to be an unintelligent editorial attempt to make room for both terms of the contradiction.’
The repetition of the illustration from the geometer (185 a 1-3 and 14-17) suggests that this whole paragraph is a conilation of two recensions.—C.]
VOL, I c 17 ARISTOTLE 185 5 τρικοῦ). od μὴν ἀλλ᾽ ἐπειδὴ περὶ φύσεως μὲν ov, tS φυσικὰς δὲ ἀπορίας συμβαίνει λέγειν αὐτοῖς, ἴσως ἔχει καλῶς ἐπὶ μικρὸν διαλεχθῆναι περὶ αὐτῶν' ¢ ὧν ἔχει γὰρ φιλοσοφίαν ἡ σκέψις.
᾿Αρχὴ δὲ οἰκειοτάτη πασῶν, ἐπειδὴ πολλαχῶς λέγεται τὸ ὄν, πῶς λέγουσιν οἱ λέγοντες εἶναι ἕν τὰ πάντα, πότερον οὐσίαν τὰ πάντα ἢ ποσὰ ἢ ποιά' 1 [After τὸ ὄν E has léetv.—C.]
* The problem of squaring the circle as it was originally penne 1s to construct, by means of ruler and compasses alone, a rectilinear figure whose area is equal to that of a given circle. And il is to this problem that the three solutions mentioned by Aristotle address themselves.
1. The solution by segments: Simplicius tells us that this refers to some very ingenious constructions of menisci, or lunes, by Hippocrates of Chios. Simplicius gives us the constructions and explains them at length. The fallacy in this demonstration, it appears, consists in confusing lunes of different forms, and assuming that, because certain kinds of lunes (as Hippocrates showed) can be squared, others, required for the quadrature of the circle, can alsu be squared, whereas in fact {μὲν cannot. It seems unlikely that Hippocrates himself should be guilty of this confusion, but whoever the author of this demonstration was, he purports to have based it on the accepted principles of geometry, and it is therefore, Aristotle says, the business of the geometer to refute it, by pointing out where the error lies.
2, Antiphon’s solution: Antiphon is only known to us by this passage, but Simplicius informs us that the construction he proposed was to inscribe a square 1n the circle, and on each of the four sides regarded as chords of the circle to build two chords meeting in the midway point of the circumference above it. We shall then have an octagon inscribed in the circle, but the chords which constitute its sides will still be 18 PHYSICS, I. 1.
consider Antipho’s solution.*. And yet, after all, though their (the Blcatics’) contention does not concein the study of Nature, it docs incidentally raise points that are of interest to the physicist; so perhaps it will be as well to examine it briefly, — especially as it has a certain philosophical interest of its own.
Now since the term ‘ existent’ is itself ambiguous,” it lies at the very heat of the matter to inquire whether (1) they who assert all existing things to be ‘one ’ are thinking of all existing things substantively or quantitively or qualitively. Or (2) are all existing short in their total periphery of the length of the cireum- ference of the cirele. But, says Antiphon, you must con- tinue the process until Lhe sides are so small as to fall coinei- dently upon their respective sections of the circumference, and then you will have a polygon equal in arca to the circle.
To this Aristotle simply:emarks that a geometer, as such, has nothing tu say, because it assumes that the circum- ference 15 already made up of minute straight lines, so that a very small chord may be coincident with a corresponding section of it; this is contrary to the axioms and principles of geometry, and the geometer is only cpanctnk with what professes to be paced ca those principles.
3. There was also one Bryson, referred to in the Posterior alnalytics, ix.. 75 Ὁ 40, He argued that any polygon in- seribed in the circle must have a less area, and any polygon circumscribed to it must have a greater area, than the circle. It follows that there must be somewhere a polygon which equals it (observe that the sides of such a polygon would obviously cut the circumference). To this demonstration in itself Aristotle raises no objection, but he says that it is a general or logical, rather than a geometrical demonstration. For the geometer must show you not only that such a polygon is possible, but how you are to construct it. Bryson does not do this.
The question of squaring the circle is further disenssed in an excursus, p. 98.
® See Gen. Introd. p. lin.
19 ARISTOTLE 1850 καὶ πάλιν πότερον οὐσίαν μίαν τὰ πάντα (οἷον 5 ἄνθρωπον ἕνα ἢ ἵππον ἕνα ἢ ψυχὴν μίαν) ἣ ποιόν, ὃν δὲ τοῦτο (οἷον λευκὸν ἢ θερμὸν ἢ τῶν ἄλλων τι τῶν τοιούτων)" ταῦτα γὰρ πάντα διαφέρει τε πολὺ καὶ ἀδύνατα λέγειν. El μὲν γὰρ ἔσται καὶ οὐσία καὶ ποσὸν καὶ ποιόν —xal ταῦτα εἴτ᾽ ἀπολελυμένα ἀπ᾽ ἀλλήλων εἴτε μή--πολλὰ τὰ ὄντα: εἰ δὲ πάντα πριὸν ἢ ποσόν, 80 εἴτ᾽ οὔσης οὐσίας εἴτε μὴ οὔσης, ἄτοπον, εἰ δεῖ ἄτοπον λέγειν τὸ ἀδύνατον. οὐθὲν γὰρ τῶν ἄλλων χωριοτόν ἐστι παρὰ τὴν οὐσίαν' πάντα γὰρ καθ᾽ ὑποκειμένου τῆς οὐσίας λέγεται. Μέλισσος δὲ τὸ ὃν ἄπειρον εἶναί φησιν. ποσὸν ἄρα τι τὸ ὄν" τὸ γὰρ ἄπειρον ἐν τῷ ποσῷ, οὐσίαν δὲ ἄπειρον εἶναι 186} ἢ ποιότητα ἢ πάθος οὐκ ἐνδέχεται εἰ μὴ κατὰ συμβεβηκός (εἰ ἅμα καὶ ποσὰ ἄττα elev): ὁ γὰρ τοῦ ἀπείρου λόγος τῷ ποσῷ προσχρῆται, ἀλλ᾽ οὐκ οὐσίᾳ οὐδὲ τῷ ποιῷ. εἰ μὲν τοίνυν καὶ οὐσία ἐστὶ καὶ ποσόν, δύο καὶ οὐχ ἕν τὸ dv: εἰ δ᾽ οὐσία μόνον, α On the supposition that the ‘life’ or ‘soul’ 1s an in- dependent entity, to which, however, Aristotle must not be supposed to commit himself here.
δ᾽ [1 understand Aristotle's main alternative here to be: Do they mean (1) that all things belong to only one category + ‘all things are Substance,’ or ‘ all things are Quality,’ etc., and, if so, to which category? or (2) that all things are a single thing belonging to one category: ‘all things are a at substance’ (a man), or ‘a single quality’ (white) ἢ © [This refers to the first alternative. (a) If all things belong to one category only, they must choose which category; ‘for if all things are to belong to several categories, there must be ἃ plurality.’ He then points out (δ) that the only 20 PHYSICS, I. τι.
things ‘one substance,’ like ‘one man’ or ‘one horse’ or ‘one soul’? Or as it that they are all one in quality, (say) all the same ‘ white,’ or ‘ hot,’ or so forth, so that the same qualitive predication ean be made of them all? For though all such assertions are impossible, yet they are far from being all identical.
(1) Thus (a) if all things are to be one both sub- stantively, quantitively, and qualitively, then (whether we consider these forms of ‘ being’ as objectively separable from each other or not) in any case existences are many and not only one.“ Whereas (6) if it be meant that all things are one magnitude, or one quality, then, whether there be any sub- stantive exislence at all or no, the assertion is absurd—if we may so call the impossible. For none of the categories except ‘substance’ can exist independently, since all the rest must necessarily be predicated of some substance as their subjectum. But Melissus? says that the Universe is unlimited, which would make it a magnitude or quantum, since ‘limited’ and ‘ unlimited’ pertain to quanta only, so that no substantive being and no quality or affection can, as such, be called unlimited (though it may incidentally be a quantum also); for the con- ception of a quantum enters into the definition of ‘unlimited,’ whereas the conception of substantive existence, or quality, does not. If then (a) the “existent ’ is both a substance and a magnitude, it is two and not one; whereas (6) if it is a substance possible category is Substance; but then Melissus ought not to say that Being is unlimited; for this implies that it is also a magnitude (quantity).—C.] 21 ARISTOTLE 185b5 οὐκ ἄπειρον, οὐδὲ μέγεθος ἕξει οὐδέν: ποσὸν γάρ τι ἔσται. "Ere ἐπεὶ καὶ αὐτὸ τὸ ἕν πολλαχῶς λέγεται ὥσπερ καὶ τὸ ὄν, σκεπτέον τίνα τρόπον λέγουσιν εἶναι ἕν τὸ πᾶν. λέγεται δ᾽ ἕν ἢ τὸ συνεχὲς ἢ τὸ ἀδιαίρετον ἢ ὧν ὁ λόγος ὁ αὐτὸς καὶ εἷς ὁ τοῦ τί τ ἦν εἶναι, ὥσπερ μέθυ καὶ οἶνος. 19 Εἰ μὲν τοίνυν συνεχές, πολλὰ τὸ Ev: εἰς ἄπειρον γὰρ διαιρετὸν τὸ συνεχές. (ἔχει δ᾽ ἀπορίαν περὶ τοῦ μέρους καὶ τοῦ ὅλου---ἴσως δὲ οὐ πρὸς τὸν λόγον ἀλλ᾽ αὐτὴν καθ᾽’ αὑτήν--πότερον ἕν ἢ πλείω τὸ μέρος Kal τὸ ὅλον, Kal πῶς ἕν ἢ πλείω' καὶ εἰ πλείω, πῶς πλείω καὶ περὶ τῶν μερῶν τῶν μὴ 1s συνεχῶν" καὶ εἰ τῷ ὅλῳ ἕν ἑκάτερον ὡς ἀδιαίρετον, ὅτι καὶ αὐτὰ αὑτοῖς.) ᾿Αλλὰ μὴν εἰ ὡς ἀδιαίρετον, οὐθὲν ἔσται ποσὸν , οὐδὲ ποιόν: οὐδὲ δὴ ἄπειρον τὸ ὄν, ὥσπερ Μέλισσός ® Συνεχές (continuous) and ἀδιαίρετον (indivisible) each have several meanings. Both words may be used in the strict mathematical sense, or in the popular sense when συνεχές would apply to any simple or complex body, so held together—whether by nature or by art—that by moving a part you move the whole (1016b 5 sq.), and ἀδιαίρετον to anything which (though not actually undividable) is taken as awhole. Here Aristotle (atter his wont) is thinking of both words primarily in their mathematical sense, which he regards as typical; the ‘continuous’ applying to magni- tudes of one, two, or three dimensions, and the ‘ indivisible’ to their limiting points, lines, and surfaces; points being indivisible as to all three dimensions, lines as to depth ail breadth, surfaces as to depth only. C7. Gen. Introd, p. Ιχχχιν, 22 PHYSICS, 1. π΄.
only, it eannot be unlimited, nor indeed can it have any dimension at all, for otherwise it would be quantitive as well as substantive.
(2) Again, since ‘ one’ is itself quite as ambiguons a term as ‘ existent,’ we must ask in whal sense the ‘ All’ is said to be one. (a) Continuity establishes one kind of unity; (6) indivisibility another 52 (ὦ identity of definition and of constituent characteristics yet a third; as for instance (the Greek) methy and oinos (both of which mean ‘ wine ’) are ‘ one and the same ἡ thing.
So then, (a) if a single continuum is what is meant by ‘ one,’ it follows that ‘ the One ’ is many, for every continuum is divisible without limit. (And this sug- gests” the question—not to our present purpose, perhaps, but interesting on its own account: whether the part and the whole of a continuum are to be regarded as a unity or as existing severally, and in either case in what sense they are a unity or plurality, and if they are regarded as a plurality in what sense a plurality. And the question arises again with respect to a discontinuous whole, consisting of unlike parts: In what sense do such parts cxist, as several from the whole? Or if each is indivisibly one with the whole, are they so with each other?)
Whereas () if ‘ one ’ signifies an ‘ indivisible,’ then it excludes quantity (as well as quality); and there- fore, the One Being, not being a quantum, cannot be ‘ unlimited ’ as Melissus declares it to be; nor indeed ** And this suggests, etc.” This admittedly irrelevant digression I take to refer to the subject elaborately discussed in iv. fii, apropos of the question whether a body can ἡ con- tain itself’ or ‘ be its own place.’ A reference to the whole passage will, I think, justify the expansion, in the translation, of this highly elliptical reference.
23 ARISTOTLE 23 ARISTOTLE ῳ i A 185b φησιν' οὐδὲ πεπερασμένον, ὥσπερ Ilappevidns, τὸ 7 yap πέρας ἀδιαίρετον, οὐ τὸ πεπερασμένον. 4 9. ᾿Αλλὰ μὴν εἰ τῷ λόγῳ ἕν τὰ ὄντα πάντα (ὡς , λώπιον καὶ ἱμάτιον), τὸν Ἡρακλείτου λόγον συμβαίνει λέγειν αὐτοῖς" ταὐτὸν γὰρ ἔσται ἀγαθῷ Μ΄ a ts a καὶ κακῷ εἶναι καὶ μὴ ἀγαθῷ καὶ ἀγαθῷ---ὥστε τὸ αὐτὸ ἔσται ἀγαθὸν καὶ οὐκ ἀγαθὸν καὶ ἄνθρω- πος καὶ ἵππος, καὶ οὐ περὶ τοῦ ἕν εἶναι τὰ ὄντα ὁ oi λόγος ἔσται αὐτοῖς ἀλλὰ περὶ τοῦ μηδέν---καὶ τὸ τοιῳδὲ εἶναι καὶ τοσῳδὶ ταὐτόν. al t ᾿Εθορυβοῦντο δὲ καὶ of ὕστεροι τῶν ἀρχαίων ὅπως μὴ ἅμα γένηται αὐτοῖς τὸ αὐτὸ ἕν καὶ πολλά. ¢ διὸ of μὲν τὸ ἔστιν ἀφεῖλον (ὥσπερ Λυκόφρων), of δὲ τὴν λέξιν μετερρύθμιζον, ὅτι 6 ἄνθρωπος οὐ 80 λευκός ἐστιν ἀλλὰ λελεύκωται, οὐδὲ βαδίζων ἐστὶν ἀλλὰ βαδίζει, ἵνα μή ποτε τὸ ἔστι προσάπτοντες πολλὰ εἶναι ποιῶσι τὸ ἕν, ὡς μοναχῶς λεγομένου am ££ YY Ai a A \ ‘ av a, τοῦ ἑνὸς ἢ τοῦ ὄντος. πολλὰ δὲ τὰ ὄντα ἢ λόγῳ (οἷον ἄλλο τὸ λευκῷ εἶναι καὶ μουσικῷ, τὸ δ᾽ αὐτὸ - ἄμφω: πολλὰ ἄρα τὸ ἕν) ἣ διαιρέσει, ὥσπερ τὸ ὅλον Ὁ (Cf. 185 4 7. If two contradictory predicates can be simultaneously asserted of the same thing, we may just as well say ‘all things are not-one’ (quasi μηδ᾽ ἔν) as say that they are ‘ one.’—C.]
> (Cf. Plato, Soph. 251 a, Philebus 14 Ὁ. Lycophron was a sophist, a pupil of Gorgias (Zeller, 1.5, 1323°).—C.]} 24 PHYSICS, I. τι.
‘ limited ’ as Parmenides has it, for it is the limit only (which is not a quantum), not the continuum which it limits, that complies with the condition of indivisi- bility.
Lastly (0) if the contention is that all things are identically ‘one and the same’ by definition (as ‘ clothes ἡ and ‘ garments ’ are) we are back again at the Heracleitean paradox; for, in that case, being good and being bad will be the same and being not- good the same as being good—with the consequence that the same thing will be both good and not good, or both a man and a horse, and we shall no longer be maintaining that all existences are onc, so much as that none of them is anything @—and being of a certain quality will be the same thing as being of a certain magmtude.
Indeed some of the later ancients were themselves disturbed by the danger of finding themselves admit- ting that the same thing is both onc and many;® and therefore some of them, like Lycophron, banned the word ‘is’ altogether; while others did such violence to language as to substitute for ‘ the man is pale-complexioned’ the phrase ‘the man has complexion-paled,’ or to admit ‘ the man walks’ but not ‘ the man is walking,’ for fear of making the one existent appear many by affixing the word ‘is’; which nervousness resulted from their equating ‘ is ’ with ‘exists’ and ignoring the different senses of ‘one’ or of ‘being. But the fact is that one thing obviously caz be many, either in the sense of being several conceptually distinct things at once (for though it is one thing to be pale-complexioned and another to be cultivated, yet one and the same man can be both, so that ‘ one’ is ‘ many’); or in the 25 ARISTOTLE 186 a καὶ TA μερήη. ἐνταῦθα δὲ ἤδη ἡπόρουν καὶ ὧμο- λόγουν τὸ ἕν πολλὰ elvar—womep οὐκ ἐνδεχόμε- oN a 4 AY f \ > é νον ταὐτὸν ἕν τε Kat πολλὰ εἶναι, μὴ τἀντικείμενα δέ: ἔστι γὰρ τὸ ἕν καὶ δυνάμει καὶ ἐντελεχείᾳ.
CHAPTER III ARGUMENT Elaboration of the reasoning of the last chapter, showing that the school of Parmenides, in addition to its faulty deductions, rests on a false basis, for it ignores the con- ceptual distinctions between the different ways of existing and the different senses in which we can say of A that it ‘is’ Melissus is hopelessly inconsequent. His syllogisms are faulty. He confuses the time at which a gwen state of things ‘ begins’ with the place from which one thing, or territory, ‘ begins’ and at which another ends. Nor does he see the difference between saying that a thing cannot ‘begin to be’ wniless it does so at some definite pont of time, and saying that it cannot ‘ begin to change’ unless ἐξ docs so at some definite point within téiself; or between saying that it 18 ‘all one’ and that it 1s incapable of movement or even of change (a 10-22).
[Aristotle neat examines the possible meanings of Par- menides’ doctrine ‘ Only the One Being is.’ Par menides ignored the various different senses of ‘is’ (a 22-25); and, even if ‘ is’ has only one sense, the inference that there cun be only one thing which is was false (a 25-32). If ‘is’ Tov τε δὴ τρόπον τοῦτον ἐπιοῦσιν ἀδύνατον 6 φαίνεται τὰ ὄντα ἕν εἶναι" καὶ ἐξ ὧν ἐπιδεικνύουσι, 46 PHYSICS, I. w.-11, sense in which a whole can be regarded as being the sum of the parts into which it can be divided. This latter case brought our philosophers to a stand; and they had to admit multiplicity in unity, unwillingly, as though it were a paradox. And so, of course, it would be, if ‘one’ and ‘many’ were used in the sense in which they contradict each other, but not if, for instance, we are regarding the ‘ one’ both in its actual unity and its potential multiplicity. wh μὰν CHAPTER III ARGUMENT (continued) means that the subject of his proposition ig identical with Being, and this subject has attributes, it can he shown that (on his principles) the One Being is a nonentity (a 32-b 12).
The One Being cannot have any magnitude (Ὁ 12-14).
A term which ‘18’ in the substantive sense (e.g. Man) contains an its definition other terme (e.g. Biped, Animal). The Eleatics cannot explain the status of these defining terms either as accidents or as indivisible constituents without admitting the existence of plurality (Ὁ 14-35) Plato is criticized for ‘ giving in’ to Parmenides’ argu- menis, without attacking his fundamental premisses (187 “ Being,’ then, cannot be ‘ one’ in the sense in which the Eleaties assert this (a 10).
(H. Maier, Syllogistik des Aristoteles (Tubzngen, 1896), il. pp. 277 Κ.. classifies the fallacies committed by Aristotle's predecessors through confusing the varivus senses of ‘18’ in propositions. Mater’s results are summarized by Mr. Ross, Metaphysics (1924), 7. p. dawaviii.)—C.]
Fottowine up this line, we shall see that it is im- possible for ‘ all things to be one,’ and we shall have ay 10 1ῦ ARISTOTLE λύειν οὐ χαλεπόν. ἀμφότεροι γὰρ ἐριστικῶς συλ- λογίζονται καὶ Μέλισσος καὶ Παρμενίδης---καὶ γὰρ ψευδῆ λαμβάνουσι καὶ ἀσυλλόγιστοί εἰσιν αὐτῶν οἱ λόγοι---μᾶλλον δ᾽ ὁ Μελίσσου φορτικὸς καὶ οὐκ Ww 2, "λλ᾽ Ἐς. > / ὃ θέ ἀλλ ἔχων ἀπορίαν [ἃ ἑνὸς ἀτόπου δοθέντος τἄλλα συμβαίνει' τοῦτο δ᾽ οὐθὲν χαλεπόν]...Ὅτι μὲν οὖν παραλογίζεται Μέλισσος, δῆλον" οἴεται γὰρ εἰληφέναι, εἰ τὸ γενόμενον ἔχει ἀρχὴν ἅπαν, ὅτι καὶ τὸ μὴ γενόμενον οὐκ ἔχει. εἶτα καὶ τοῦτο ἄτοπον, τὸ παντὸς οἴεσθαι εἶναι ἀρχὴν τοῦ πράγματος καὶ μὴ τοῦ χρόνου, καὶ γενέσεως μὴ τῆς ἁπλῆς ἀλλὰ καὶ ἀλλοιώσεως, ὥσπερ οὐκ ἀθρόας γινομένης μεταβολῆς.
Ἔπειτα διὰ τί ἀκίνητον, εἰ ἕν; ὥσπερ γὰρ καὶ τὸ μέρος ἕν ὃν--τοδὲὶ τὸ ὕδωρ---κινεῖται ἐν ἑαυτῷ, διὰ τί οὐ καὶ πᾶν; ἔπειτα ἀλλοίωσις διὰ τί οὐκ 9 He argues in the form ‘ if all A’s are not-#’s, then all not-A's are B's,’ which is a false syllogism; for the negation of the antecedent does not carry the negation of the con- sequent, though the negation of the consequent does carry that of the antecedent. Thus the correct inference from “all_A’s are not-B’s* would be ‘ all B’s are not-A’s.’
> [Melissus, "rag. 1, ‘ That which was, was always and always will be. For if 1t had come into being, before jt came into being it must have been nothing; if, then, it was nothing, nothing could ever come out of nothing.’ J’rag. 2, ‘ Since then, it did not come into being, and since it is and always was and always will be, it has no beginning or end, but is unlimited.” Aristotle unfairly accuses Melissus of arguing from ‘no beginning in time’ to ‘no beginning (limit) in space ’ (cf. Soph. #1, 167 Ὁ 13), and from ‘ no absolute coming into being out of nothing’ to ‘no beginning of change of quality.’ At 253 Ὁ 25, freezing is given as an instance of ἀθρόα θλλθίωσας ΟῚ ¢ [Or possibly, ‘ for just as a part (of the world), e.g. this mass of water, though it is one, can move on its own axis 28 PHYSICS, I. πὶ.
no difficulty in refuting the arguments by which the assertion that they are is supported. For both Parmenides and Melissus argue sophistically, inas- much as they make unsound assumptions and argue unsoundly from them. But Melissus offends the more grossly of the two, so as really to raise no valuable point for discussion.
The false reasoning of Melissus is palpable;* for, assuming that ‘all that comes inlo existence has a beginning,’ he deduces from it ‘all that does not come into existence has no beginning.’ And, more- over, the assumption itself ‘whatever comes into existence has a beginning ’ is untenable, in so far as ‘ began some-when ’ 1s taken (as Melissus takes it) to be equivalent to ‘ begins some-where ’ (so that if the Universe ‘ had no beginning ’ it ‘ can have no limit,’ and is ‘ unbounded’): and again in so far as no dis- tinction is made between the thing itsclf having to begin-to-be at ‘ some particular point of time,’ and a modification of the thing having to start from ‘ some particular point within the thing itself,’—as if there could not be a simultaneous modification over the whole field affected.’
And again why should unity involve rigidity? Tor if a definite body of water, regarded as a unit without internal distinctions of quality, may have currents of motion within itself, why not the Universe?* And, in any ease, why not modifications other than those (without change of place), why should not the universe do the same?’ go Simplicius, 112.16. Cf. 240 a 30, ἐπὶ τῆς σφαίρας καὶ ἥλως τῶν ἐν αὑτοῖς κινουμένων. The argument is, at any rate, valid as applied to Parmenides’ limited spherical Being, which could rotate without losing its unity in any sense. The arguments in this paragraph seem not to be directed only against Melissus.-—C.]
29 ARISTOTLE 1884 ἂν εἴη; ἀλλὰ μὴν οὐδὲ τῷ εἴδει οἷόν τε ἕν εἶναι 20 (πλὴν τῷ ἐξ οὗ: οὕτως δὲ ἕν Kal τῶν φυσικῶν τινες λέγουσιν, ἐκείνως δ᾽ ov): ἄνθρωπος γὰρ ἵππου ἕτερον τῷ εἴδει, καὶ τἀναντία ἀλλήλων. Καὶ πρὸς Παρμενίδην δὲ ὁ αὐτὸς τρόπος τῶν é ᾿ Ν La 24 γ᾽ σιν ΄ λόγων, καὶ εἴ τινες ἄλλοι εἰσὶν ἴδιοι: καὶ ἡ λύσις τῇ μὲν ὅτι ψευδής, τῇ δὲ ὅτι οὐ συμπεραίνεται-- 2 ψευδὴς μὲν ἦ ἁπλῶς λαμβάνει τὸ ὃν λέγεσθαι, λεγομένου πολλαχῶς, ἀσυμπέραντος δὲ ὅτι, εἰ Z f fol μόνα τὰ λευκὰ ληφθείη, σημαΐνοντος ἕν τοῦ λευκοῦ, οὐθὲν ἧττον πολλὰ τὰ λευκὰ καὶ οὐχ ἕν. οὔτε γὰρ τῇ συνεχείᾳ ἕν ἔσται τὸ λευκὸν οὔτε τῷ , y yoy 4 ΝΜ ama ὡ λόγῳ ἄλλο γὰρ ἔσται τὸ εἶναι λευκῷ καὶ τὸ δεδεγ- 30 μένῳ, καὶ οὐκ ἔσται παρὰ τὸ λευκὸν οὐθὲν χωρι- / A ὧν A 2 A an ica AS στόν" od yap ἣ χωριστὸν ἀλλὰ τῷ εἶναι ἕτερον τὸ λευκὸν καὶ ᾧ ὑπάρχει. ἀλλὰ τοῦτο Παρμενίδης οὕπω ἑώρα.
᾿Ανάγκη δὴ λαβεῖν μὴ μόνον ἕν σημαίνειν τὸ ὄν, καθ᾽ οὗ ἂν κατηγορηθῇ, ἀλλὰ καὶ ὅπερ ὃν καὶ * {Both Parmenides and Melissus denied the reality of any change.—C. ] » lie. imagine a barrages who asserts, ‘ Only what is white exists,’ instead of Parmenides’ proposition: ὁ Only what is (τὸ ὄν) exists.’ Even so, there might still be any number of white things in existence. Similarly Parmenides’ assertion is consistent with the existence of any number of things that are. Also, ‘ what is white’ need not be a single continuous thing (ἕν, συνεχές, Parm. 8. 6).—C.
° [Even if all that exists were one white thing, there would still be a conceptual difference between whiteness and being a subject which has ‘ white’ as attribute, without involving the separate existence of any second thing (for the attribute does not exist separately). Cf. Maier, Syllogistik, ii, 282, 30 PHYSICS, I. 11.
of local movement?* But of course the Universe cannot really be homogencous, like a mass of water (except in Lhe sense of its ultimate constituent bemg uniform; in which sense, though not mn the other, some of the Physicists also have mamtained its unity); for a man is patently different in kind from a horse, and opposites are different in kind from cach other.
The same kind of argument will apply to Par- mendes, as well as such other arguments as par- ticularly apply to his treatment; for here too the refutation Lurns on the falsity of his assumption and the unsoundness of his deductions. His assumption is false inasmuch as he treats ‘bemg’ as having only one meaning, whereas in reality it has several, And his inferences are false, because, even if we accepted such a proposition as ‘ nothing that is not white exists,’ and if ‘ white’ had only one meaning, stall the white things would be many and not one.? Obviously not one in the sense of a homogeneous continuum. Nor in the sense of a conceptual identity, for there remains a conceptual distinction between the subject in which the whiteness is seated, and the qualification of ‘ being white,’ and that distinc- tion does not involve the separate existence of any- thing alongside of ‘that which is white’;* because the pluralty is established not by there being some- thing separate, but by there being a conceptual distinction between white and the subject in which it inheres. But Parmenides had not yet arrived at this principle.
Parmenides, then, must assume not only that the word ‘is,’ whatever it may be predicated of, has only one meaning, but also that it means ‘ 1s identical- 31 ARISTOTLE 1888 ὅπερ ἕ!. τὸ yap συμβεβηκὸς Kal? ὑποκειμένου A 4 Ὁ Pe, x a ἃ; uw so τινὸς Adyerau ὥστε ᾧ συμβέβηκε τὸ ὃν ode ἔσται 186 (ἕτερον γὰρ τοῦ ὄντος)" ἔσται τι ἄρα οὐκ ὄν. οὐ δὴ ἔσται ἄλλῳ ὑπάρχον τὸ ὅπερ dv. οὐ yap ἔσται ὄντι αὐτῷ εἶναι, εἰ μὴ πολλὰ τὸ ὃν σημαίνει οὕτως ὥστε εἶναί τι ἕκαστον: ἀλλ᾽ ὑπόκειται τὸ ὃν σημαΐνειν ἕν. εἰ οὖν τὸ ὅπερ ὃν μηδενὶ συμ- 5 βέβηκεν, ἀλλ᾽ ἐκείνῳ, τί μᾶλλον τὸ ὅπερ ὃν σημαίνει τὸ ὃν ἢ μὴ ὄν; εἰ γὰρ ἔσται τὸ ὅπερ ὃν ταὐτὸ καὶ λευκόν, τὸ λευκῷ δ᾽ εἶναι μὴ ἔστιν ὅπερ dv (οὐδὲ γὰρ συμβεβηκέναι αὐτῷ οἷόν τε τὸ ov: οὐθὲν yap ὃν 6 οὐχ ὅπερ ὄν), οὐκ dpa Gy τὸ λευκόν---οὐχ οὕτω δὲ ὥσπερ τι μὴ ὄν, ἀλλ᾽ ὅλως 10 μὴ ὄν. τὸ ἄρα ὅπερ ὃν οὐκ ὄν' ἀληθὲς γὰρ εἰπεῖν > ὅτι λευκόν, τοῦτο δὲ οὐκ ὃν ἐσήμαινεν: ὥστ᾽ εἰ 82 PHYSICS, I. m.
with-Being,’ and that ‘is one’ means ‘is identical- with-Unity.’ ( Bemg’ will then no longer be re- garded as an attribute); for an attribute is ascribed to some subject (other than itsclf); consequently, the subject to which ‘ being’ (supposing 1t to be an aliribute) is ascribed will have no being at all; for it will be other than ‘ being’ (the attribute aserihed to it) and so will be something which (simply) 18 not. Accordingly ‘ identical-with- Being’ (the sole meaning we have given to the word ‘ is "ἢ cannot. be an attribute of some subject other than itself. Tor in that ease its subject cannot be a thing which is, unless ‘ being’? denotes a plurality of things in the sense that each is some thing that is. But it has been assumed that ‘ being’ denotes only one thing, If, then, what is identical-with- Being is uot an attribute of anything else, but (a subject, so that other things are attributes) of it, is there any reason to say that ‘identical-with-Being’ denotes that which zs (a real entity) any more than that which is not (a nonentity)? (I can show that there is no reason.) Jor suppose the thing which is identical- with-Being also has the attribute ‘ white,’ and that ‘ being white ’ is not identical-with-Being—(the only sense in which it can ‘ be ’at all), for it cannot even have ‘ being’ as an attribute, because (ex hypothesi) nothing except what is identical-with-Being has any being at all—then it follows thal white zs not, and that not merely in the sense that it zs not this or that, but in the sense of an absolute nonentity. Accord- ingly, that which is identical-with-Being (our subject) will be a nonentity; for (we assumed that) it is true to say of it that it is white, and this means that it is a nonentity. So that even if (to escape this diffi- VOL. I D 33 ARISTOTLE 186b καὶ τὸ λευκὸν σημαίνει ὅπερ ὄν, πλείω dpa σημαίνει τὸ ὅν. [Οὐ τοίνυν οὐδὲ μέγεθος ἕξει τὸ ὄν, εἴπερ ὅπερ ὃν τὸ ὄν’ ἑκατέρῳ γὰρ ἕτερον τὸ εἶναι τῶν μορίων." “Ὅτι δὲ διαιρεῦται τὸ ὅπερ ὃν εἰς ὅπερ ov τι 16 ἄλλο, καὶ τῷ λόγῳ φανερόν' οἷον ὁ ἄνθρωπος εἰ ἔστιν ὅπερ ὃν τι, ἀνάγκη καὶ τὸ ζῷον ὅπερ ὄν τι εἶναι καὶ τὸ δίπουν. εἰ γὰρ μὴ ὅπερ ὄν τι, συμ- βεβηκότα ἔσται: ἢ οὖν τῷ ἀνθρώπῳ ἢ ἄλλῳ τινὶ ὑποκειμένῳ. ἀλλ᾽ ἀδύνατον" συμβεβηκός τε γὰρ λέγεται τοῦτο, ἢ ὃ ἐνδέχεται ὑπάρχειν καὶ μὴ 90 ὑπάρχειν, ἢ οὗ ἐν τῷ λόγῳ ὑπάρχει τὸ ᾧ συμ- βέβηκεν" ( (οἷον τὸ μὲν καθῆσθαι ὡς χωριζόμενον, ἐν δὲ τῷ σιμῷ ὑπάρχει ὁ λόγος ὃ τῆς ῥινὸς φαμὲν συμβεβηκέναι τὸ σιμόν). ἔτι ὅσα ἐν τῷ ὁριστικῷ λόγῳ ἔ ἔνεστιν ἢ ἐξ ὧν ἐστιν, ἐν τῷ λόγῳ 95 τῷ τούτων οὐκ ἐνυπάρχει ὁ λόγος ὁ τοῦ Show (οἷον ἐ ἐν τῷ δίποδι ὁ τοῦ ἀνθρώπου, ἢ ἐν τῷ λευκῷ ὄ τοῦ λευκοῦ ἀνθρώπου). εἰ τοίνυν ταῦτα τοῦτον ἔχει τὸν τρόπον καὶ τῷ ἀνθρώπῳ συμβέβηκε τὸ δίπουν, ἀνάγκη χωριστὸν εἶναι αὐτό (ὥστε ἐν- δέχοιτο ἂν μὴ δίπουν εἶναι τὸν ἄνθρωπον), ἢ ἐν τῷ go λόγῳ τῷ τοῦ δίποδος ἐνέσται ὁ τοῦ ἀνθρώπου 1 The words bracketed add nothing to what has been said in the previous chapter and they interrupt the context here. I have treated them as an interpolation, * I reject, as an unmeaning interpolation, the words ἢ ἐν ᾧ ὁ λόγος ὑπάρχει ᾧ συμβέβηκεν (after 20 συμβέβηκεν). [The words are omitted in FI and ignored by Simplicius.—C.
5. {1 have substituted for W.’s rendering of this argument (a 82, ἀνάγκη δὴ--- 12, σημαίνει τὸ ὄν), my own version, im- proved i in one or two details by Prof. Ross.—C.
> [i.e,, if bene is to be confined to the One Being, which is identical-with-Being and identical-with-Unity.—C.]
34 PHYSICS, I. in.
culty) we say that the term ‘ white ’ denotes what is identical-with-Beimg, then ‘being’ has more than one meaning.“ [Nor can ‘the existent’ have any magnitude, if it is to exclude plurality;® for onc part of it will have an existence distinguishable from that οὗ another.°] But the analysing of a substantive entity into other substantive entities (so far from being anything startling) is clearly illustrated by definitions, For instance, if ‘man’ signifies a substantive existence, so must‘ animal’ and‘ biped’ also. Otherwise they would be accidental attributes, whether of ‘man’ or of some other subject. But that is impossible, for an accidental attribute must ether be separable, so as sometimes to apply and sometinies not (e.g. that the man is ‘ sitting down ’), or else must include its subject in its own definition (as ‘ snub’ includes in its definition the definition of ‘ nose,’ of which we say that snubness is an attribute). Now, the terms of the definition (which are the constituent principles of the thing defined) do not themselves severally contain, in their definitions, any mention of the whole thing which they combine to define. For instance, ‘man’ does not enter into the definition of ‘ biped,’ nor does that of ‘ white man’ enter into the definition of ‘ white.’ Therefore, if‘ biped ’ were an attribute of man at all, it would have to be a separable one, so that the man might, on occasion, not be a biped; the only alternative (as we have said) being that ‘man’ should be included in the * [Cf Plato’s criticism (Soph. 244) of Parmenides’ One Being as a sphere extended in space. (The circumference of a sphere must be distinguishable from its centre, ete.)—C.]
Qk 86 ARISTOTLE a A > a λόγος. ἀλλ᾽ ἀδύνατον: ἐκεῖνο yap ἐν TH ἐκείνου λόγῳ ἔνεστιν. εἰ ἄλλῳ συμβέβηκε τὸ δίπουν καὶ τὸ ζῷον καὶ μὴ ἔστιν ἑκάτερον ὅπερ ὄν τι, καὶ ὁ ἄνθρωπος ἂν εἴη τῶν συμβεβηκότων ἑτέρῳ. ἀλλὰ τὸ ὅπερ ὄν τι ἔστω μηδενὶ συμβεβηκός, καὶ καθ᾽ οὗ ἄμφω, καὶ ἑκάτερον καὶ TO ἐκ τούτων λεγέσθω: ἐξ ἀδιαιρέτων dpa τὸ πᾶν. Ἔνιοι δ᾽ ἐνέδοσαν τοῖς λόγοις ἀμφοτέροις, τῷ μὲν ὅτι πάντα ἕν εἰ τὸ ὃν ἕν σημαίνει, ὅτι ἔστι τὸ al - f M ͵ὕ μὴ ὄν, τῷ δὲ ἐκ τῆς διχοτομίας, ἄτομα ποιήσαντες μεγέθη. φανερὸν δὲ καὶ ὅτι οὐκ ἀληθὲς ὡς, εἰ