Popunar conceptions on the subject of squaring the circle are so vague and so entirely erroneous that to do justice to Aristotle’s handling of the question will be impossible without some introductory remarks. In the first place, what is squaring the circle? It is reducing the area of a circle to an equal area bounded by straight lines, for any plane rectilinear figure can be quite easily converted into a square of the same size.
The problem then is to find a plane rectilinear figure equal in area to a given circle. That it is inherently possible that there should be such a rectilinear area is obvious (for the size of the area does not depend on the shape) and a very convincing proof of this was already known to Aristotle as we shall see.* No contradiction of this is in any way intended by the statement that the circle cannot be squared. The question is not whether there is or can be a rectilinear area which will equal the area swept out by a given radius rotating round one of its extreme points (for that is the most enlightening definition of a circle), but whether such an area can be diagrammatically constructed. It is perfectly easy to construct it, but not within the limits prescribed for constructions by Euclid, and evidently by the tradition he followed. For Euclid undertook to show how far he could carry elementary Geometry on the condition of having no implements allowed to him but compasses and a ruler, and of never 98 PHYSICS, I. EXCURSUS making use of any diagrammatic figure which he had not been able to construct under these conditions. Even these instruments, the compasses and the ruler, he only allows himself to use under certain restrictions, but with these we need not concern ourselves. He claims no logical superiority for constructions in which these two instru- ments alone have been used, above other constructions which require other instruments; but he is simply trying how far he can carry the science forward on this ver narrow basis. There are many simple operations whic cannot be so performed (for instance, with ruler and com- passes only you cannot, in general, trisect an angle), and among them is the construction of a rectilinear figure equal in area to a given circle.
Archimedes (+212 5.0.) did not restrict his reasoning to figures constructed under the Euclidean tradition, and he tells us that the right-angle triangle of which the sides containing the right angle are respectively equal to the circumference and radius of the circle, is equal in area to the circle. He proves this by demonstrating rigorously that any area greater than that of the triangle will be greater than that of the circle, and any area less than that of the triangle will be less than that of the circles There is no suggestion of construction here, his reasoning does not depend on being able to construct the triangle and it is obvious that such a triangle exists. Therefore, though he makes no attempt here to solve the problem as originally conceived, he completely disposes of the misconception that, because a square equal to a given circle cannot be constructed by means of compasses and ruler only, there can be no such square.
Having thus reduced the problem of measuring the area of a circle to that of measuring its circumference, he goes on to show how successive approximations can he made to the numerical expression of 7 (the ratio of the circum- ference to the radius).
Again there is a vague idea in some minds that the reason why the circle cannot be squared is that 7 is in- @ Archimedes, On the Measurement of the Circle.
99 ARISTOTLE commensurable, i.e. cannot be exactly expressed numeri- cally; and that you cannot construct a figure involving incommensurable ratios. But if that were the difficulty it would he impossible to constrnet a circle itself from a given radius.
There is no inherent difficulty in constructing a line that is incommensurable with a given Ine. The simplest case of all is that of a side and the diagonal of a square, and it is generally supposed to be historically true that it was in this connexion that the problem of incommensurables was first confronted. Drawing the diagonal is a simple act of construction, and it is only by the construction that we can ἊΝ a perfectly definite length to the diagonal relatively to that of the side, the length of the diagonal being in- commensurable with that of the side. So too by drawin a cirele to a radius we obtain the circumference, the jena of the circumference being incommensurable with that of the radius.
Aristotle has been blamed for hig contemptuous treat- ment of Antiphon,* because it is assumed that he ought to have seen in him an rn ee attempt to apply the principle of approximations which was developed by Archimedes and ultimately by Newton and Leibniz in the calculus. But this is hardly reasonable, for, according to the account given by Simplicius, Antiphon does not really supply so much as a hint of this method. He simply assumes at the end what he might as well have assumed at the beginning, that the cir- cumference is already a polygon with very minute sides; in other words he believes in atomic (2.¢. indivisible) lines; which belief lies at the root of endless confusion of thought.”
Aristotle is perfectly clear and explicit on this question, hes his teaching has been migunderstood or neglected even y such men as Galileo 5 and Leibniz.¢ + See Gen. Introd. pp. Ixxx ἢ, and Ixxxvii ff.
® Galileo, Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze (Leyden, 1538); Opere (Edizione Nazionale), vol. viii. pp. 80 sqq. and 91 sqq.
4 Guvres inédits de Leibniz, p. 106 Couturat.
PHYSICS, I. EXCURSUS Galileo has exposed Aristotle’s worst mistakes, but he has fallen into others of his own by neglect of Aristotle’s principles in these matters. And the adoption of Leibniz’s system of notation in preference to that of Newton, while amply justified on practical grounds, still tends to impede the progress of young students to perfect clarity of mind to this day.
ARISTOTLE or stuffy which they called the ‘ nature of things.’ The speculation inspired by Socrates saw the nature of a thing in the ‘ form’ or essential character, given in the definition of ‘ what it is to be’ a thing of that sort. This is the truer view; and consequently this form or essence must be identical with the internal source of movement by which we have defined natural objects. The form is also the final goal towards which the development of the thing moves and in which that development comes to rest.
Such forms as these have their being in the changing world of Nature; they are immersed in matter, and cannot be studied in abstraction froin matter. Thus Physics is distinguished, on the one hand, from mathematics, which isolates in thought the forms it studies from the power of movement, and on the other hand from First Philosophy (metaphysics), which is concerned with pure immaterial forms-—God, the intelligences of the heavenly spheres, the human reason.
The rest of the Book is occupied with the character of the ‘ causes’ of natural things and of their motions and changes. The term ‘ cause’ has a wider sense than in the English use. It covers all the ‘ conditions necessary but not separately sufficient to account for the existence of a thing ’ (see Ross, Aristotle, p. 73). Greek philosophy had always been intent upon the task of discovering, not laws of succession in phenomena, but what things in themselves are. Hence among the ‘ causes’ of a thing—what we need to know in order to give a full account of it—tho two internal constituents, the matter and the form, stand first. As already hinted in the first chapter, the form of the thing is also the moving or ‘ efficient ’ cause of its coming into being and behaving as it does; and the form is also the ‘end,’ wherein its nature igs fully realized. Thus there are four ‘ causes ’—material, formal, efficient, and final—to be known, if the existence and behaviour of any natural object is to be fully accounted for.
Popular thought further recognizes the agency of Luck or Chance; and the inveterate belief that events just “happen ἡ by the blind working of forces pushing from PHYSICS, II.
behind, without any intelligent direction, has been countenanced or tacitly assumed by men of science. To such a view of the world Aristotle, as the successor of Plato and Socrates, is fundamentally opposed. He does not, however, deny validity to the conceptions of Chance and Luck; he sets himself to analyse them and to find for them a meaning and a sphere consistent with the belief that the workings of Nature cannot be completely under- stood as the outcome of chance or of mere necessity, but reveal the presence of some kind of purpose aiming at a goal desired. The Book closes with an attempt to establish this teleology. —C.].
B CHAPTER I ARGUMENT [The scope of Physics is now determined by defi ining ‘nature. ‘ Natural things’ or ‘ things which have a nature,’ as distinct from artificial products as such, contain an internal tendency to move (i.e. be moved or changed) in certain ways. Thus, the elements and inanimate compounds of them tend to rise or fail in space and undergo change; living things move about, change, and grow. The ‘nature’ is this innate tendency to movement and change. Its existence is an obvious fact of experience (192 b 8-198 a 10).
1208 Τῶν γὰρ ὄντων τὰ μὲν ἔστι φύσει, τὰ δὲ Sv ἄλλας αἰτίας--φύσει μὲν τά τε CHa καὶ τὰ μέρη τὸ αὐτῶν καὶ τὰ φυτὰ καὶ τὰ ἁπλᾶ τῶν σωμάτων (οἷον γῆ καὶ πῦρ καὶ ἀὴρ καὶ ὕδωρ)" ταῦτα γὰρ εἶναι καὶ τὰ τοιαῦτα φύσει φαμέν. πάντα δὲ τὰ ῥηθέντα φαίνεται διαφέροντα πρὸς τὰ μὴ φύσει συνεστῶτα. τὰ μὲν γὰρ φύσει ὄντα πᾶντα φαί- νεται ἔχοντα ἐν ἑαυτοῖς ἀρχὴν κινήσεως καὶ 15 στάσεως--τὰ μὲν κατὰ τόπον, τὰ δὲ κατ᾽ αὔξησιν καὶ φθίσιν, τὰ δὲ κατ᾽ ἀλλοίωσιν--κλίνη δὲ καὶ ἱμάτιον καὶ εἴ τι τοιοῦτον ἄλλο γένος ἐστίν, ἧ μὲν τετύχηκε, τῆς κατηγορίας ἑκάστης καὶ καθ᾽ ὅσον ἐστὶν ἀπὸ τέχνης, οὐδεμίαν ὁρμὴν ἔχει μεταβολῆς BOOK Ii CHAPTER I ARGUMENT (continued) By some the‘ nature’ of a concrete thing is identified with the matter it consists of, and the ‘nature of things’ in generat, with an ultimate eternal stuff. Others find the nature af athing inits ‘form.’ Taking this latter view him- self, Aristotle restates his definition of ‘nature’ in terms that imply his identification of the internal principle of move- ment with the form, existing in the concrete thing; and he supports this by several arguments (a 10-b 21).—C.]
Some things exist, or come into existence, by nature; and some otherwise. Animals and their organs, plants, and the elementary substances— earth, fire, air, water—these and their likes we say exist by nature. For all these seem distinguishable from those that are not constituted by nature; and the common feature that characterizes them all seems to be that they have within themselves a principle of movement (or change) and rest—in some cases local only, in others quantitive, as in growth and shrinkage, and in others again qualitive, in the way of modification. But a bedstead or a garment or the like, in the capacity which is signified by its name and in so far as it is craft-work, has within itself no such inherent trend towards change, though ARISTOTLE ARISTOTLE 1920 ἔμφυτον, ἡ δὲ συμβέβηκεν αὐτοῖς εἶναι λιθίνοις ἢ 20 γηΐνοις ἣ μικτοῖς, ἐἰς τούτων ἔχει καὶ κατὰ τοσοῦ- τον, ὡς οὔσης τῆς φύσεως ἀρχῆς Twos καὶ αἰτίας τοῦ κινεῖσθαι καὶ ἠρεμεῖν ἐν ᾧ ὑπάρχει πρώτως καθ᾽ αὑτὸ καὶ μὴ κατὰ συμβεβηκός. λέγω δὲ τὸ μὴ κατὰ συμβεβηκός, ὅτι γένοιτ᾽ ἂν αὐτὸς αὑτῷ 25 TIS αἴτιος ὑγιείας ὧν ἰατρός" ἀλλ᾽ ὅμως οὐ καθὸ ὑγιάζεται τὴν ἰατρικὴν ἔχει, ἀλλὰ συμβέβηκε τὸν αὐτὸν ἰατρὸν εἶναι καὶ ὑγιαξόμενον' διὸ καὶ χω- ρίξεταί mor’ ἀπ᾽ ἀλλήλων. ὁμοίως δὲ καὶ τῶν ἄλλων ὁ ἕκαστον τῶν ποιουμένων" οὐδὲν γὰρ αὐτῶν ἔχει τὴν ἀρχὴν ἐν ἑαυτῷ τῆς ποιήσεως, ἀλλὰ τὰ 80 μὲν ἐν ἄλλοις, καὶ ἔξωθεν (οἷον οἰκία καὶ τῶν ἄλλων τῶν χειροκμήτων ἕκαστον), τὰ δ᾽ ἐν αὑτοῖς μὲν GAN’ od καθ᾽ αὗτά, ὅσα κατὰ συμβεβηκὸς αἴτια γένοιτ᾽ ἂν αὑτοῖς.
Φύσις μὲν οὖν ἐστι τὸ ῥηθέν' φύσιν δὲ ἔχει. ὅσα τοιαύτην ἔχει ἀρχήν. καὶ ἔστι πάντα ταῦτα οὐσία. ὑποκείμενον γάρ τι, καὶ ἐν ὑποκειμένῳ ἐστὶν ἡ φύσις ἀεί.
8. Κατὰ φύσιν δὲ ταῦτά τε καὶ ὅσα τούτοις ὑπάρχει 5 [I have repunctuated the text, taking ἐκ τούτων not with μικτοῖς but with ἔχει: ‘it has one derived from these (natural a) and in so far (as it is composed of them).— Ae ah cannot reproduce the ambiguity of ἡ φύσι», which (like the French la nature) may mean ‘the nature’ (of any natural thing) or ‘ Nature ’ collectively, the sum total of such natures.—C. | ¢ (Strictly, ‘ of being moved (κινεῖσθαι) and being at rest’ (not of initiating motion from within), The heavenly bodies, which have no principle of rest, are here ignored.—C. ] 4 Wave a substantive existence, 1.6. are concrete entities, Cf. Gen. Introd. pp. lili.
PHYSICS, II. 1 owing to the fact of its being composed of earth or stone or some mixture of substances, it in- cidentally has within itself the prineples of change which inhere primarily in these materials.4 For nature > is the principle and cause of motion and rest ° to those things, and those things only, in which she inheres primarily, as distinct from incidentally. What I mean by ‘as distinct from incidentally ’ is like this: If a man were a physician and prescribed successfully for himself, the patient would cure him- self; butit would not be qua patient that he possessed the healing arl, though in this particular case it happened that the physician’s personality coincided with that of the patient, which is not always the ease. And so it is with all manufactured or ‘ made’ things: none of them has within itself the principle of its own making. Generally this principle resides in some cxternal agent, as in the case of the house and its builder, and so with all hand-made things. In other cases, such as that of the physician-patient, though the patient does indeed contain in himself the principle of action, yet he does so only incidentally, for it is not gua subject acted on'that he has in himself the causative principle of the action.
This, then, being what we mean by ‘ nature,’ any- thing that has in itself such a principle as we have described may be said to ‘ possess a nature’ of its own inherently. And all such things have a sub- stantive existence ὦ. for each of them is a substratum or ‘ subject ’ presupposed by any other category, and it is only in such substrata that nature ever has her seat. ᾿ Further, not only nature itself and all things that ‘ have a nature,’ but also the behaviour of these things ARISTOTLE 195} καθ᾽ αὑτά, οἷον τῷ πυρὶ φέρεσθαι ἄνω" τοῦτο yap 198ι φύσις μὲν οὐκ ἔστιν, οὐδ᾽ ἔχει φύσιν, φύσει δὲ καὶ κατὰ φύσιν ἐστίν. Τί μὲν οὖν ἐστιν ἡ φύσις, εἴρηται, καὶ τί τὸ φύσει καὶ κατὰ φύσιν. ὡς δ᾽ ἔστιν ἡ φύσις, πειρᾶσθαι δεικνύναι γελοῖον: φανερὸν γὰρ ὅτι τοιαῦτα τῶν ὄντων ἐστὶ πολλά. τὸ δὲ δεικνύναι 57a φανερὰ διὰ τῶν ἀφανῶν οὐ δυναμένου κρίνειν ἐστὶ τὸ δι’ αὑτὸ καὶ μὴ δι’ αὐτὸ γνώριμον. ὅτι δ᾽ ἐνδέχεται τοῦτο πάσχειν, οὐκ ἄδηλον' συλ- λογίσαιτο γὰρ ἄν τις ἐκ γενετῆς ὧν τυφλὸς περὶ χρωμάτων: ὥστε ἀνάγκη τοῖς τοιούτοις περὶ τῶν ὀνομάτων εἶναι τὸν λόγον, νοεῖν δὲ μηδέν.
3 Δοκεῖ δ᾽ ἡ φύσις καὶ ἡ οὐσία τῶν φύσει ὄντων ἐνίοις εἶναι τὸ πρῶτον ἐνυπάρχον ἑκάστῳ ἀρ- ρύθμιστον καθ᾽ ἑαυτό, οἷον κλίνης φύσις τὸ ξύλον, ἀνδριάντος δ᾽ ὁ χαλκός. (σημεῖον δέ φησιν ᾿Αντιφῶν ὅτι, εἴ τις κατορύξειε κλίνην καὶ λάβοι δύναμιν ἡ σηπεδὼν ὥστε ἀνεῖναι βλαστόν, οὐκ ἂν 1 γενέσθαι κλίνην ἀλλὰ ξύλον, ὡς τὸ μὲν κατὰ συμβεβηικὸς ὑπάρχον--τὴν κατὰ νόμον διάθεσιν καὶ τὴν τέχνην--τὴν δ᾽ οὐσίαν οὖσαν ἐκείνην ἣ καὶ διαμένει ταῦτα πάσχουσα συνεχῶς). εἰ δὲ καὶ τούτων ἕκαστον πρὸς ἕτερόν τι ταὐτὸ τοῦτο « [Or ‘a thing’s proximate constituent, in itself unformed,’ 9.0. the wood of a bedstead, which is ‘ proximate ’ to the form, as contrasted with the remoter elements into which the wood might be analyscd—‘ simple bodies’ or ‘ ultimate matter.’
> [Antiphon, frag. 15 (Diels, Vors.* ii. 295) εἴ τις κατορύξεια κλίνην καὶ ἡ σηπεδὼν τοῦ ξύλον ἔμβιος γένοιτο, οὐκ ἂν γένοιτο κλίνη ἀλλὰ ξύλον. For σηπεδών (putrefaction) as cause of PHYSICS, II. 1.
in virtue of their inherent characteristics is spoken of as ‘natural.’ For instance, for fire actually to rise, as distinct from having the tendency to risc, neither ig nature nor has a nature; but it comes about ‘by nature ’ and is ‘ natural,’ Such, then, are the definitions of ‘ nature,’ of what exists ‘by nature,’ and of what is ‘ natural.’ Any attempt to prove that nature, in this sense, is a reality. would be childish; for it is patent that many things corresponding to our definitions do actually exist; and to set about proving the obvious trom the unobvious betrays confusion of mind as to what is self-evident and what is not. Such confusion, how- ever, is not unknown, though it is like a man born blind arguing about colours, and amounts to reasoning about names without having any corresponding con- cept in the mind.
Now some hold that the nature and substantive existence of natural products resides in their material ἃ on the analogy of the wood of a bedstead or the bronze of a statue. (Antiphon ὃ took it as an indication of this that if a man buried a bedstead and the sap in it took force and threw out a shoot it would be tree and not bedstead that came up, since the artificial arrangement of the material by the craftsman is merely an incident that has occurred to it, whereas its essential and natural quality is to be found in that which persists continuously throughout such experiences.) And in like manner, it is thought,° if the materials themselves bear to yet other sub- stances the same relation which the manufactured generation cf. Plato, Phaedo 96 5 (Burnet ad loc.), Hippoer. Περὶ σαρκῶν 3.—C.] ὁ [εἶναι (2. 20) depends on δοκεῖ (1. 10).---Ο.]
ARISTOTLE 198 πέπονθεν--οἷον ὁ μὲν χαλκὸς καὶ 6 χρυσὸς πρὸς A 20 “δ 3 8 ΞΘ σι ὕδωρ, τὰ δ᾽ ὀστᾶ καὶ ξύλα πρὸς γῆν, ὁμοίως δὲ καὶ τῶν ἄλλων ὁτιοῦν---ἐκεῖνα τὴν φύσιν εἶναι καὶ τὴν οὐσίαν αὐτῶν. διόπερ οἱ μὲν πῦρ, οἱ δὲ γῆν, οἱ δ᾽ ἀέρα φασίν, οἱ δὲ ὕδωρ, οἱ δ᾽ ἔνια τούτων, of δὲ πάντα ταῦτα τὴν φύσιν εἶναι τὴν τῶν ὄντων. ὃ γάρ τις αὐτῶν ὑπέλαβε τοιοῦτον, εἴτε ἕν εἴτε πλείω, τοῦτο καὶ τοσαῦτά φησιν εἶναι τὴν ἅπασαν οὐσίαν, τὰ δὲ ἄλλα πάντα πάθη τούτων καὶ ἕξεις καὶ διαθέσεις" καὶ τούτων μὲν ὁτιοῦν εἶναι ἀΐδιον —od γὰρ εἶναε μεταβολὴν αὐτοῖς ἐξ αὑτῶν ---τὰ δ᾽ ἄλλα γίγνεσθαι καὶ φθείρεσθαι ἀπειράκις. Ἕνα μὲν οὖν τρόπον οὕτως ἡ φύσις λέγεται, ἡ πρώτη ἑκάστῳ ὑποκειμένη ὕλη τῶν ἐχόντων ἐν αὐτοῖς ἀρχὴν κινήσεως καὶ μεταβολῆς: ἄλλον δὲ τρόπον ἡ μορφὴ καὶ τὸ εἶδος τὸ κατὰ τὸν λόγον. ὥσπερ γὰρ τέχνη λέγεται τὸ κατὰ τέχνην καὶ τὸ τεχνικόν, οὕτω καὶ φύσις τὸ κατὰ φύσιν λέγεται καὶ τὸ φυσικόν. οὔτε δὲ ἐκεῖ πω φαῖμεν ἂν ἔχειν κατὰ τὴν τέχνην οὐδέν, εἰ δυνάμει μόνον ἐστὶ κλίνη μήπω δ᾽ ἔχει τὸ εἶδος τῆς κλίνης, οὐδ᾽ εἶναι 4 (Cf. Met. 1Ο1ὅ ἃ 8 οἷον τῶν χαλκῶν ἔργων πρὸς αὐτὰ μὲν πρῶτος (proximate material) ὁ χαλκός, ὅλως δ᾽ tows ὕδωρ, εἰ πάντα τὰ τηκτὰ ὕδωρ---ἴῃε doctrine of Timaeus 58 Ὁ (Ross ad loc.).—C.]
> (Cf. Met. 989 a 5, No philosopher followed popular thought in making earth the primary form of body.—C.]
* [Or, ‘ related as above described to more complex forms of matter.’-—C.]
4 [Or ‘for they thought them incapable of changing out of themselves’ (putting off their own nature).—C.]
4 [πρώτη ὕλη 1s used ambiguously by Aristotle for ‘ proxi- mate’ or‘ ultimate’ matter. Here (with ἑκάστῳ) it probably PHYSICS, II. 1.
articles bear to them—if, for instance, water is the material of bronze or gold,* or earth of bone or timber, and so forth—then it is in the water or earth that we must look for the ‘nature’ and essential being of the gold and so forth. And this is why some have said that it was earth? that constituted the nature of things, some fire, some air, some water, and some several and some all of these elemental substances. For whichever substance or substances each thinker assumed to be primary ° he regarded as constituting the substantive existence of all things in general, all else being mere modifications, states, and dispositions of them. Any such ultimate sub- stance they regarded as eternal (for they did not admit the transformation of elementary substances into each other %), while they held that all else passed into existence and out of it endlessly.
This then is one way of regarding ‘ nature ’—as the ultimately ὁ underlying material of all things that have in themselves the principle of movement and change. But from another point of view we may think of the nature of a thing as residing rather in its form, that is to say in the ‘ kind’ of thing it is by definition. For as we give the name of ‘ art’ to a thing which is the product of art and is itself artistic, so we give the name of ‘nature’ to the products of nature which themselves are ‘ natural,’ ἡ And as, in the case of art, we should not allow that what was only potentially a bedstead and had not yet received the form of bed had in it as yet any art-formed element, or could be called ‘ art,’ so in ued Ἣ proximate material of any given thing, as at 1.
t [κατὰ φύσιν, as above defined, 192 Ὁ 35.—C.].
VOL. I I 118 ARISTOTLE an + 193b τέχνην, οὔτ᾽ ἐν τοῖς φύσει συνισταμένοις" TO yap δυνάμει σὰρξ ἢ ὀστοῦν οὔτ᾽ ἔχει πω τὴν ἑαυτοῦ φύσιν, πρὶν ἂν λάβῃ τὸ εἶδος τὸ κατὰ τὸν λόγον - ὃ ὁριζόμενοι λέγομεν τί ἐστι σὰρξ ἢ ὀστοῦν--οὔτε φύσει ἐστίν. ὥστε ἄλλον τρόπον ἡ φύσις ἂν εἴη τῶν ἐχόντων ἐν αὑτοῖς κινήσεως ἀρχὴν ἡ μορφὴ δ καὶ τὸ εἶδος, οὐ χωριστὸν ὃν ἀλλ᾽ ἢ κατὰ τὸν λόγον. (τὸ 8 ἐκ τούτων φύσις μὲν οὐκ ἔστι, φύσει δέ, οἷον ἄνθρωπος.) καὶ μᾶλλον αὕτη φύσις τῆς ὕλης" ἕκαστον γὰρ τότε λέγεται ὅταν ἐντελεχείᾳ x ἢ μᾶλλον ἢ ὅταν δυνάμει. Ἔτι γίνεται ἄνθρωπος ἐξ ἀνθρώπου, ἀλλ᾽ οὐ κλίνη ἐκ κλίνης" διὸ καί φασιν od τὸ σχῆμα εἶναι 10 τὴν φύσιν ἀλλὰ τὸ ξύλον, ὅτι γένοιτ᾽ ἄν, εἰ βλα- στάνοι, οὐ κλίνη ἀλλὰ ξύλον. εἰ δ᾽ ἄρα τοῦτο τέχνη, καὶ ἡ μορφὴ φύσις" γίνεται γὰρ ἐξ ἀνθρώπου ἄνθρωπος. "Ere δ᾽ ἡ φύσις ἡ λεγομένη ὡς γένεσις ὁδός ἐστιν εἰς φύσιν. οὐ γὰρ ὥσπερ ἡ ἰάτρευσις λέγεται οὐκ εἰς ἰατρικὴν ὁδὸς ἀλλ᾽ εἰς ὑγίειαν' 2 The revised definition lays stress on the form while including the matter.
ὃ jean * But if this (the artificial shape) is “ art,” it follows that the form (of the natural product—the timber, or the man—which does reproduce itself) is ‘‘ nature.” ’—C.].
© So, too, in Latin na-tura derived from the na of na-scor and na-tivitas, [In fact (g)natura is derived from the same a ir gi-gno, γίγνομαι, Cf. Met. 1014 Ὁ 17 and Ross ad PHYSICS, 11. τ.
the case of natural products; what is potentially flesh or bone has not yet the ‘nature’ of flesh until it actually assumes the form indicated by the definition that constitutes it the thing in question, nor is this potential flesh or bone as yet a product of nature. These considerations would lead us to revise our definition of nature as follows: Nature is the distinctive form or quality of such things as have within themselves a principle of motion, such form or characteristic property not being separable from the things themselves, save conceptually. (The compositum—a man, for example—which material and form combine to constitute, is not itself a ‘ nature,’ but a thing that comes to be by natural process.) And this view of where to look for the nature of things is preferable to that which finds it in the material; for when we speak of the thing into the nature of which we are inquiring, we mean by its name an actuality not a potentiality merely.
Again men propagate men, but bedsteads do not propagate bedsteads; and that is why they say that the natural factor in a bedstead is not its shape but the wood—to wit, because wood and not bedstead would come up if it germinated. If, then, it is this incapacity of reproduction that makes a thing art and not nature, then the form of natural things will be their nature, as in the parallel case of art;° for man is generated by man, whereas a bedstead is not generated from a bedstead.
Again, na-ture is etymologically equivalent to gene-sis and (in Greek) is actually used as a synonym for it; ¢ nature, then, qua genesis proclaims itself as the path to nature qua goal. Now, it is true that healing is so called, not because it is the path to the ARISTOTLE w3bib ἀνάγκη μὲν yap ἀπὸ ἰατρικῆς, οὐκ εἰς ἰατρικήν, ἣν ΜΠ ΕἸ τ ΠΣ ¢, Mv i εἶναι τὴν ἰάτρευσιν, οὐχ οὕτω δ᾽ ἡ φύσις ἔχει πρὸς τ? ιν τὴν φύσιν, ἀλλὰ τὸ φυόμενον ἐκ τινὸς εἰς τὶ ἔρχεται, ἡ φύεται. εἰς τί οὖν φύεται; οὐχὶ ἐξ οὗ, ἀλλ᾽ εἰς 6. ἡ dpa μορφὴ φύσις. ἡ δέ ye μορφὴ καὶ ἡ Ἅἢ ψ' a ao 2 φύσις διχῶς λέγεται" καὶ yap ἡ στέρησις εἶδός πώς > ἐστιν. εἰ δ᾽ ἐστὶν ἡ στέρησις Kat ἐναντίον τι περὶ ἃς ἐὰ λῇ! BY \ ὧν “ ’ ͵ THY arTranyv YEVEOLV Ἢ μὴ ἐστιν, ὑστέρον ἐπισκέπτεον.
CHAPTER II ARGUMENT [Physics is distinguished from mathematics and from metaphysics.
Lhe objects of mathematics, though they do not exist apart Srom natural bodies, can be studied in abstraction from that power af movement by which we defined ‘ nature.’ But Physics studies natural bodies as essentially possessing this power. (Cf. Met. E 1 and Ross, Aristotle, p. 68). The Platonisis are wrong in attempting to abstract entities (e.g. ‘ man,’ ‘ flesh’) whose nature involves matter (198 Ὁ 22— 2 Ἐπεὶ δὲ διώρισται ποσαχῶς ἡ φύσις λέγεται, * Which is the return to the perfect form which it started without at birth.
> The question is frequently discussed in other works of Aristotle, notably in Physics v. and in the De gen. et cor. A3. The answer in substance is that there is really no such thing PHYSICS, II. 1-1.
healing art, but because it is the path to health, for of necessity healing proceeds from the healing art, not to the healing art itself; but this is not the rela- tion of nature to nature, for that which is born starts as something and advances or grows towards some- thing else. Towards what, then, does it grow? Not towards its origina] state at birth, but towards its final state or goal.? It is, then, the form that is nature; but, since ‘form’ and ‘nature’ are ambigu- ous terms, inasmuch as shortage 1s a kind of form, we shall leave to future investigation whether shortage is, or is not, a sort of contrasted term (opposed to positive form) in absolute generation.?
CHAPTER II ARGUMENT (continued) Physics must take account of both matter and form. In this respect it is like art: the doctor must know both the nature of health (form) and the material constituents of the body. Also, matter is related to the ‘ nature’ (form) as means to end. Matter, moreover, is only a relative term. But Physics is concerned only with forms immersed in matter. Pure forms fall under Metaphysics or Theology Now that we have determined the different senses in which ‘‘ nature’ may be understood (as signifying as absolute genesis and therefore no contrast to concrete entity. But we say that a concrete entity has perished when the indestructible matter which lies at the core of it has assumed forms which evade our ability to recognize its identity any longer.
ARISTOTLE 198.» μετὰ τοῦτο θεωρητέον τίνι διαφέρει ὁ μαθηματικὸς τοῦ φυσικοῦ' καὶ yap ἐπίπεδα καὶ στερεὰ ἔχει τὰ \ a φυσικὰ σώματα καὶ μήκη Kal στιγμάς, περὶ ὧν σκοπεῖ ὁ μαθηματικός. ἔτι ἡ ἀστρολογία ἑτέρα ἢ μέρος τῆς φυσικῆς" εἰ γὰρ τοῦ φυσικοῦ τὸ τί ἐστιν ἥλιος ἢ σελήνη εἰδέναι, τῶν δὲ συμβεβηκότων καθ᾽ αὑτὰ μηδέν, ἄτοπον, ἄλλως τε καὶ ὅτι φαίνονται λέγοντες οἱ περὶ φύσεως καὶ περὶ σχή- 80 ματος σελήνης καὶ ἡλίου, καὶ πότερον σφαιροειδὴς ἡ γῆ καὶ ὁ κόσμος ἢ οὔ. Περὶ τούτων μὲν οὖν πραγματεύεται καὶ 6 / μαθηματικός, ἀλλ᾽ οὐχ ἣ φυσικοῦ σώματος πέρας ἕκαστον’ οὐδὲ τὰ συμβεβηκότα θεωρεῖ ἣ τοιούτοις οὖσι συμβέβηκεν. διὸ καὶ χωρίζει: χωριστὰ γὰρ a5 Τῇ νοήσει κινήσεώς ἐστι, καὶ οὐδὲν διαφέρει, οὐδὲ ΓΑ ΓΝ / γίνεται ψεῦδος χωριζόντων. Λανθάνουσι δὲ τοῦτο ποιοῦντες καὶ οἱ τὰς ἰδέας 1948 λέγοντες" τὰ γὰρ φυσικὰ χωρίζουσιν, ἧττον ὄντα χωριστὰ τῶν μαθηματικῶν. γίγνοιτο δ᾽ ἂν τοῦτο δηλ, w é é _~ i ‘ e ἤλον, εἴ τις ἑκατέρων πειρῷτο λέγειν τοὺς ὅρους, καὶ αὐτῶν καὶ τῶν συμβεβηκότων. τὸ μὲν γὰρ 5 [.6, ἔτι δ᾽ εἰ ἡ ἀστρ. This reading (Tauchnitz ed. 1881) seems to have πὸ authority.—C.]
PHYSICS, ΤΙ, τι.
either ‘material’ or ‘form’), we have next to consider how the mathematician differs from the physicist or natural philosopher; for natural bodies have surfaces and occupy spaces, have lengths and present points, all which are subjects of mathe- matical study. And then there is the connected question * whether astronomy is a separate science from physics or only a special branch of it; for if the student of Nature is concerned to know what the sun and moon are, it were strange if he could avoid inquiry into their essential properties; especially as we find that writers on Nature have, as a fact, discoursed on the shape of the moon and sun and raised the question whether the earth, or the cosmos, is spherical or otherwise.
Physicists, astronomers, and mathematicians, then, all have to deal with lines, figures and the rest. But the mathematician is not concerned with these con- cepts qua boundaries of natural bodies, nor with their properties as manifested in such bodies, There- fore he abstracts them from physical conditions; for they are capable of being considered in the mind in separation from the motions of the bodies to which they pertain, and such abstraction does not affect the validity of the reasoning or lead to any false conclusions, Now the exponents of the philosophy of ‘ Ideas’ also make abstractions, but in doing so they fall unawares into error; for they abstract physical entities, which are not really susceptible to the process as mathematical entities are. And _ this would become obvious if one should undertake to define, respectively, the mathematical and the ‘ideal’ entities, together with their properties; for ARISTOTLE 1945 περιττὸν ἔσται Kal τὸ ἄρτιον Kal τὸ εὐθὺ Kal τὸ " καμπύλον, ἔτι δὲ ἀριθμὸς καὶ γραμμὴ καὶ σχῆμα, ἄνευ κινήσεως" σὰρξ δὲ καὶ ὀστοῦν καὶ ἄνθρωπος οὐκέτι, ἀλλὰ ταῦτα ὥσπερ ῥὶς σιμὴ ἀλλ᾽ ody ὡς τὸ καμπύλον λέγεται. δηλοῖ δὲ καὶ τὰ φυσικώτερα τῶν μαθημάτων, οἷον ὀπτικὴ καὶ ἁρμονικὴ καὶ ἀστρολογία: ἀνάπαλιν γὰρ τρόπον τιν᾽ ἔχουσι τῇ τὸ γεωμετρίᾳ: ἡ μὲν γὰρ γεωμετρία περὶ γραμμῆς φυσικῆς σκοπεῖ, ἀλλ᾽ ody ἣ φυσική, ἡ δ᾽ ὀπτικὴ θ A A? LAN’? x θ \ μαθηματικὴν μὲν γραμμήν, ἀλλ᾽ οὐχ ἣ μαθηματικὴ ἀλλ᾽ ἢ φυσική. ᾿Επεὶ δ᾽ ἡ φύσις διχῶς---τό τε εἶδος καὶ ἡ ὕλη--- ὡς ἄν εἰ περὶ σιμότητος σκοποῖμεν τί ἐστιν, οὕτω θεωρητέον: wor οὔτ᾽ ἄνευ ὕλης τὰ τοιαῦτα, τὸ οὔτε κατὰ τὴν ὕλην.
Ἰζαὶ γὰρ δὴ καὶ περὶ τούτου διχῶς ἀπορήσειεν ἄν τις---ἐπεὶ δύο αἱ φύσεις, περὶ ποτέρας τοῦ φυσικοῦ, ἢ περὶ τοῦ ἐξ ἀμφοῖν. ἀλλ᾽ εἰ περὶ τοῦ ἐξ ἀμφοῖν, καὶ περὶ ἑκατέρας" πότερον οὖν τῆς αὐτῆς ἢ ἄλλης ἑκατέραν γνωρίζειν; Ris μὲν γὰρ τοὺς ἀρχαίους ἀποβλέψαντι δόξειεν ἂν εἶναι τῆς ὅλης" ἐπὶ μικρὸν γάρ τι μέρος Ἔμ- πεδοκλῆς καὶ Δημόκριτος τοῦ εἴδους καὶ τοῦ τί ἦν εἶναι ἥψαντο. εἰ δὲ ἡ τέχνη μιμεῖται τὴν 2 =) 5 tie. Em pedocles, who analysed organic substances into elements Gaatien and the ratio of their mixture (form), and Democritus, who ‘ in a sort of way defined the hot and the cold’ (Met. 1078 Ὁ 19, De part. anim. 642 a 24), had some- thing to say about ‘ form,” but not much.—C.]
PHYSICS, II. τι.
the concepts ‘ odd,’ ‘ even,’ ‘ straight,’ ‘ curved,’ will be found to be independent of movement; and so too with ‘number,’ ‘line,’ and ‘figure.’ But of ‘flesh ’ and ‘ bone’ and ‘man.’ this is no longer true, for these are in the same case as a‘ turned-up nose,’ ὃ not in the same case as ‘curved.’ The point is further illustrated by those sciences which are rather physical than mathematical, though combining both disciplines, such as optics, harmonics, and astro- nomy; for the relations between them and geometry are, so to speak, reciprocal; since the geometer deals with physical lines, but not qua physical, whereas optics deals with mathematical lines, but qua physical not qua mathematical.