Aristotle

by George Grote

Book Λ.

We have to speculate respecting Essence; for that which we are in search of is the principles and causes of Essences (p. 1069, a. 18). If we look upon the universe as one whole, Essence is the first part thereof: if we look upon it as a series of distinct units (εἰ τῷ ἐφεξῆς, a. 20), even in that view οὐσία stands first, ποιόν next, ποσόν third; indeed these last are not Entia at all, strictly speaking (a. 21) — I mean, for example, qualities and movements, and negative attributes such as not-white and not-straight; though we do talk of these last too as Entia, when we say Est non-album. Moreover Essence alone, and none of the other Categories, is separable. The old philosophers (οἱ ἀρχαῖοι) are in the main concurrent with us on this point, that Essence is prius to all others; for they investigated the principles, the elements, and the causes of Essence. The philosophers of the present day (Plato, &c.) declare Universals, rather than Particulars, to be Essences; for the genera are universal, which these philosophers, from devoting themselves to dialectical discussions, affirm to be more properly considered as Principles and Essences (a. 28); but the old philosophers considered particular things to be Essences, as fire and earth, for example, not the common body or Body in general (οὐ τὸ κοινὸν σῶμα — a. 30).

Now there are three Essences. The Perceivable includes two varieties: one, the Perishable, acknowledged by all, e.g., animals and plants; the other Eternal, of which we must determine the elements, be they many or one. There is also the Immoveable, which some consider to be separable (ἄλλη δὲ ἀκίνητος καὶ ταύτην τινὲς εἶναι φασι χωριστήν — p. 1069, a. 33; οὐσία νοητὴ καὶ ἀκίνητος — Schwegler’s note): either recognizing two varieties thereof, distinct from each other — the Forms and Mathematical Entia; or not recognizing Forms as separable Entia, but only the Mathematical Entia (a. 36). Now the first, or Perceivable Essences, belong to physical science, since they are moveable or endued with motion; the Immoveable Essences, whether there be two varieties of them or only one, belong to a science distinct from physical. The Perceivable and the Immoveable Essences have no common principles (b. 2).

The Perceivable Essence is subject to change (μεταβλητή). Since change takes place either out of Opposites or out of Intermediates, and not out of every variety of Opposites, but only out of Contraries (ἐκ τῆς οἰκείας ἀποφάσεως, ἐκ τῆς οἰκείας στερήσεως — Alexander, pp. 644, 645, Bon.; the voice, e.g., is not white, yet change does not take place from voice to white, these being disparates, or of different genera: τὰ γένει διαφέροντα οὐκ ἔχει ὁδὸν εἰς ἄλληλα — I. iv. p. 1055, a. 6), there must of necessity be a certain Substratum which changes into the contrary condition; for contraries do not change into each other. The substratum remains, but the contraries do not remain: there is therefore a third something besides the contraries; and that is Matter (p. 1069, b. 9). Since then the varieties of change are four: (1) γένεσις and φθορά (κατὰ τὸ τί), (2) αὔξησις καὶ φθίσις (κατὰ τὸ ποσόν), (3) ἀλλοίωσις (κατὰ τὸ πάθος or κατὰ τὸ ποιόν), (4) φορά (κατὰ τόπον or κατὰ τὸ ποῦ), each of these changes will take place into its respective contrary: the Matter will necessarily change, having the potentiality of both contraries (b. 14). Ens being two-fold, all change takes place out of Ens Potentiâ into Ens Actu, e.g., out of potential white into actual white; and the like holds for Increase and Decrease. Thus not only may there be generation from Non-Ens accidentally but all generation takes place also out of Ens; that is, out of Ens Potentiâ, not Ens Actu (b. 20). This Ens Potentiâ is what Anaxagoras really means by his Unum, which is a better phrase than ὁμοῦ πάντα; what Empedokles and Anaxagoras mean by their μῖγμα; what Demokritus means when he says ὁμοῦ πάντα. They mean that all things existed at once potentially, though not actually; and we see that these philosophers got partial hold of the idea of Matter (ὥστε τῆς ὕλης ἂν εἶεν ἡμμένοι — b. 24). All things subject to change possess Matter, but each of them a different Matter; even the eternal things which are not generated but moved in place, possess Matter — not generated, but from whence whither (i.e., the Matter of local movement pure and simple — direction: καὶ τῶν ἀϊδίων ὅσα μὴ γεννητὰ κινητὰ δὲ φορᾷ, ἀλλ’ οὐ γεννητήν (ὕλην), ἀλλὰ πόθεν ποῖ — b. 26).

Since there are three varieties of Non-Ens (p. 1069, b. 27; Alexander and Bonitz explain this τριχῶς differently), it may seem difficult to determine, out of which among the three Generation takes place. But the answer is, that the Potential Ens is not potential of every thing alike and at haphazard, but potential in each case from something towards something (εἰ δὴ τί ἐστι δυνάμει, ἀλλ’ ὅμως οὐ τοῦ τυχόντος, ἀλλ’ ἕτερον ἐξ ἑτέρου — b. 29). Nor is it enough to tell us that all things are huddled together (ὁμοῦ πάντα χρήματα — b. 30); for they differ in respect to Matter or Potentiality. If this were not so, how is it that they are of infinite diversity, and not all One? The Noûs (i.e., according to the theory of Anaxagoras) is One; so that, if the Matter were One also, it would become in actuality that which it was at first in potentiality, and the result would be all One and the Same (b. 32).

The Causes are thus three and the Principles are three: the pair of Contraries, one of them Form (λόγος καὶ εἶδος), the other Privation, and the third Matter (p. 1069, b. 35). But we must keep in mind that neither Materia Prima nor Forma Prima is generated. For in all Change, there is something (the Matter) which undergoes change; something by which the change is effected (the Prime Movent, ὑφ’ οὗ μέν, τοῦ πρώτου κινοῦντος — p. 1070, a. 1); and something into which the change takes place (the Form). The brass becomes round; but, if both the brass becomes and the round becomes, you will be condemned to an infinite regression: you must stop somewhere (ἀνάγκη δὴ στῆναι — a. 4). Moreover, every Essentia is generated out of another Essentia of the same name and form (ἐκ συνωνύμου — a. 5). All generated things proceed either from Nature, Art, Fortune, or Spontaneity. It is Nature, where the principle or beginning is in the subject itself; it is Art, where the principle or beginning is in something apart from the subject; Fortune is the privation of Art; Spontaneity is the privation of Nature (αἱ δὲ λοιπαὶ αἴτιαι στερήσεις τούτων — a. 9). Essentiæ are threefold: (1) Matter, which appears to be Hoc Aliquid but is not so, for detached members or fragments, simply touching each other without coalescing, are matter and substratum (i.e., prepared for something ulterior); (2) Nature, which is really Hoc Aliquid — a certain definite condition, into which generation takes place (ἡ δὲ φύσις καὶ τόδε τι, εἰς ἥν, καὶ ἕξις τις — a. 12); (3) The Concrete of the two preceding — the individual object called Sokrates or Kallias. In some cases there is no Hoc Aliquid except in this Concrete or Compound; thus in artificial objects or productions, such as a house or health, there is no Form except the Art itself: the ideal house, pre-existing in the mind of the builder, is generated and destroyed in a different sense from the real house. It is in the case of natural objects, if in any case, that there exists a Hoc Aliquid independent of the concrete individual (a. 17).

Hence Plato was not wrong in saying that Forms were coextensive with natural objects (ὁπόσα φύσει — p. 1070, a. 18), if there are Forms distinct from these objects: such as fire, flesh, head, which are all properly Matter. The Last Matter (or that which has come most under the influence of Form) belongs to that which is in the fullest sense Essentia (or the individual concrete named Sokrates or Kallias — a. 20). The Moving Causes pre-exist, as real individual beings or objects: the Formal Causes come into existence simultaneously with the individual real compound. When the patient becomes well, then health comes at the same time into existence: when the brazen sphere comes, the sphericity of it comes at the same time (a. 24). Whether any thing of the Form continues after the dissolution of the individual compound, is a problem to be investigated (a. 25). In some cases nothing hinders but what it may continue; for example, the soul may be of such a nature: I do not mean every soul — for every soul perhaps cannot continue — but the Νοῦς or rational soul (a. 27). Still it is plain that this affords no support to the theory of self-existent separate Ideas; for every individual man is begotten by another individual man. In like manner also with respect to the arts; for the medical art affords the Form or rational explanation of health (a. 30; i.e., health is generated, not by the Idea of Health, but by the medical art, or by the artist in whom that art is embodied).

Causes and principles, in one point of view, are different: different subjects; but in another point of view, they are the same for all; that is, if we speak generally and according to analogy (if we confine ourselves to the most general terms, Form, Privation, Matter, &c.). In respect to Essentia, Relatio, and the remainder of the Categories, a difficulty arises to say whether the causes, elements, and principles of all the Categories are the same. It would be strange if they were all the same; because then Essentiæ, as well as Relata, would proceed out of the same causes and elements. For, what can these latter be? They cannot be extra-categorical; since there exists no general class apart from or besides Essentia and the other Categories (p. 1070, b. 1). Nor can any one Category be the element of the others: for the element is prius to that of which it is the element. Nor again can Essentia be the element of Relata; nor is any one of the nine Categories the element of Essentia. Again, how is it possible that the elements of all the Categories can be the same? No element can be the same as that compound of which it is an element: neither B nor A can be the same as B A. If, therefore, there were such elements, they must be extra-categorical; which is impossible. Nor can the element in question (the supposed one and the same) be any cogitable, such as Ens or Unum; for every individual Concrete is both Ens and Unum and the element cannot be identical with the compound put together out of it. Neither Essentia nor Relatio could be said to exist, if Ens were the element out of which they are composed; but these Categories exist necessarily: therefore there is no one and the same element common to all the Categories (b. 9).

Yet we ought perhaps rather to repeat, what was observed before, that in one sense, the elements of all are the same; in another sense, different. Take for example the perceivable bodies. We find here hot as the Form, cold as the Privation; as Matter, there is that which is, primarily and per se, both hot and cold potentially: the hot and the cold are both Essentiæ; likewise other things of which these are the principles, e.g., flesh and bone, which of necessity are different from the principles out of which they proceed (b. 15). Flesh and bone have these elements and principles; other things have other elements and principles. The same specific principles cannot be assigned to all, but only principles analogous to these in each case, as saying, in general terms, that there are three principles — Form, Privation, Matter. Each of these is different in every different genus; thus in colour, the principles are white, black, surface, light, darkness, air, and out of these are generated day and night (b. 21).

The three preceding causes are all intrinsic or immanent (ἐνυπάρχοντα). But there are other causes also extrinsic, such as the Movent. So that Principle and Element are not exactly identical; for Principle as well as Cause includes all the four: τὸ κινοῦν ἢ ἱστάν is a Principle, and is itself an Essentia (p. 1070, b. 25). Thus the analogous Elements are three, while the Principles or Causes are four; but the four are specifically different in each different case. Thus, health is Form; sickness is Privation; body is Matter; the medical art is Movent. House is Form; disorder of a certain sort is Privation; bricks are Matter; the building art is Movent. We thus make out four Causes; yet, in a certain sense, there will be only three (b. 32). For, in natural products, a man is the Movent Cause of a man; in artificial products (ἐν τοῖς ἀπὸ διανοίας) the Movent is Form or Privation. In a certain sense, the medical art is health, and the building art is the Form of a house, and a man begets a man. And farther, over and above these special movent causes, there is the Primum Movens of all (b. 35).

We distinguish what is separable from what is not separable. Now Essentiæ, and they only, are separable; accordingly they are the causes of every thing else, since without Essentiæ there cannot be either affections or movements (p. 1071, a. 2). Such causes would be soul and body, or reason, appetite, and body. Again, in another sense, the principles of all things are generically the same, though specifically different; such are Potentia and Actus. In some cases, the same thing exists now potentially, at another time actually; thus wine, though actually wine, is potentially vinegar; flesh is actually flesh, potentially a man, Potentia and Actus will merge in the above-mentioned causes — Form, Privation, Matter, Movent (a. 7). For the Form (if it be separable), the Concrete (of Form and Matter), and Privation (like darkness or sickness) — all these exist actually; while Matter exists potentially, capable either of Form or Privation. Things differ potentially and actually sometimes through difference in the Matter, sometime through difference in the Form. Thus, the cause of a man is, in the way of Matter, the elements fire and earth; in the way of Form his own Form, and the same Form in another individual — his father and besides these, the Sun with its oblique motion; which last neither Matter, nor Form, nor Privation, nor the like Form in another individual, but a Movent Cause (ἀλλὰ κινοῦντα — a. 17).

We must remember, besides, that some things may be described in general terms, others cannot be so described. The first principles of all things are, speaking in general terms, Hoc Primum Actu and Aliud Primum Potentiâ. These universals do not really exist (p. 1071, a. 19), for the principium of all individuals is some other individual. Man indeed is the principium of the Universal Man but no Universal Man exists (a. 21). Peleus is the principium of Achilles; your father, of you; this B, of that B A; B, the universal, of B A the universal. Next (after the Movent) come the Forms of Essences; but the different genera thereof (as has been already stated), colours, sounds, essences, quantities, &c., have different causes and elements, though the same when described in general terms and by analogy; also different individuals in the same species have different causes and elements, not indeed different in species, but different individually; that is, your Matter, your Movent, your Form, are different from mine, though in general terms and definition they are the same (τῷ καθόλου δὲ λόγῳ ταὐτά â€” a. 29).

When therefore, we enquire, What are the principles or elements of Essences, of Relata, of Qualities &c., and whether they are the same or different? it is plain that, generically speaking (allowing for difference of meaning — πολλαχῶς, p. 1071, a. 31), they are the same in each; but, speaking distributively and with reference to particulars, they are different, and not the same. In the following sense (ὡδί â€” a. 34), they are the same, namely, in the way of Analogy (τῷ ἀνάλογον). They are always Matter, Form, Privation, the Movent; hence the causes of Essences are causes of all other things, since, when Essences disappear, all the rest disappears along with them: besides all these, there is the Primum Movens Actuale, common to all (ἔτι τὸ πρῶτον ἐντελεχείᾳ — a. 36). In the following sense, again, they are different — when we cease to speak of genera, and pass from equivocal terms to particulars: wherever there are different opposites (as white and black, health and sickness) and wherever there are different Matters (καὶ ἔτι αἱ ὗλαι — p. 1071, b. 1; ὗλαι in the plural, rare).

We have thus declared, respecting the principles of Perceivable Essences, what and how many they are; in what respect the same, and in what respect they are different. Essences are threefold; two Physical and one Immoveable. We shall proceed to speak of this last. There exists, of necessity, some Eternal, Immoveable Essence. For Essences are the first of all existent things; and, if they all be perishable, every thing is perishable. But it is impossible that Motion can ever have been generated or can ever be destroyed; for it always existed: it is eternal. There is the like impossibility about Time: for, if Time did not exist, there could be nothing prius and nothing posterius (p. 1071, b. 8). Both Motion and Time are thus eternal; both are also continuous; for either the two are identical, or Time is an affection (πάθος) of Motion. Now no mode of Motion is continuous except local motion; and that in a circle (for rectilinear motion cannot be continuous and eternal). There must be a Movent or Producent Principle (κινητικὸν ἢ ποιητικόν — b. 12); but, if the Movent existed potentially and not actually, there could not be motion continuous and eternal; for that which has mere power may never come into act. There will be no use therefore in such eternal Essences as Plato assumes in his Ideas, unless there be along with them some principle of potential change (εἰ μή τις δυναμένη ἐνέσται ἀρχὴ μεταβάλλειν — b. 15). Nor indeed will even that be sufficient (i.e., any principle of merely potential change), nor any other Essence (such as Numbers — Schwegler) besides or along with the Platonic Ideas; for, if this principium shall not come into Actuality (εἰ μὴ ἐνεργήσει — b. 17), the motion which we postulate, continuous and eternal, will not result from it. Nor will it even be sufficient that the Movent Principle should be supposed to be in actuality or operation (οὐδ’ εἰ ἐνεργήσει, p. 1071, b. 18), if its Essence be Potentiality: the motion resulting therefrom cannot be eternal; for that which exists potentially may perhaps not exist at all. The Movent Principles therefore must be something of which the Essence is Actuality (b. 19), and which shall be without Matter, for they must be eternal, otherwise nothing else can be eternal. They must therefore be essential Actualities (b. 22).

Here however, a difficulty suggests itself. It seems that every thing which is in actuality must also be in potentiality, but that every thing which is in potentiality does not in every case come into actuality: so that Potentiality seems the prius of the two (δοκεῖ γὰρ τὸ μὲν ἐνεργοῦν πᾶν δύνασθαι, τὸ δὲ δυνάμενον οὐ πᾶν ἐνεργεῖν — p. 1071, b. 24; Bonitz compares p. 1060, a. 1: ἀρχὴ γὰρ τὸ συναναιροῦν). But, if this were true, no Entia could exist; for it may be that they exist potentially, but not yet exist actually (b. 26). There is the like impossibility, if we adopt the theory of those theologians (Orpheus, Hesiod, &c.) who take their departure from Night, or of those physical philosophers who begin with a chaotic huddle of all things. In both cases such original condition is one of mere potentiality; and how can it ever be put in motion, if there is to be no cause in actuality (εἰ μηθὲν ἔσται ἐνεργείᾳ αἴτιον — b. 29)? Matter will never cause motion in itself, but must wait for the carpenter’s art; nor will the earth, but must wait for seed.

It is for this reason that some philosophers, like Plato and Leukippus, represent Actuality as eternal; for they say that motion has always existed. But they do not say what variety of motion, nor why that variety, to the exclusion of others. For nothing is moved at haphazard; there must always be some reason why it is moved in one way rather than another: for example, by nature in one way; by other causes, such as violence or Noûs, in some other way (p. 1071, b. 36). But it is not competent to Plato to assume what he sometimes does assume as principium (p. 1072, a. 2 — allusion to Plato Phædrus 245, E), viz., a Self-Movent; for Plato affirms (in Timæus 34, B) that the soul is posterius, and coæval with the Kosmos. The doctrine just mentioned — That the Potential is prior to the Actual — is true in one sense, but not true in another; we have already explained how (εἴρηται δὲ πῶς — a. 4. Schwegler thinks, note p. 254, that this εἴρηται refers to what has been said in Book Θ, p. 1049, b. 3, seq.; and this seems probable, though Bonitz in his note contests it, and refers to his own theory, set forth in his ProÅ“mium pp. 24, 25, that Book Λ is a separate treatise of Aristotle, completely distinct from all the rest of the Metaphysica. This theory of Bonitz may be in the main true; but it is still possible that Book Θ may have been written previously, and that Aristotle may here refer to it, as Schwegler supposes.).

That Actuality is prior to Potentiality, is conformable to the doctrine of Anaxagoras, Noûs in his doctrine existing in Actuality; also to that of Empedokles, who introduces Friendship and Enmity; and again, to that of Leukippus, who affirms Motion to be eternal. So that Chaos or Night (i.e., mere Potentiality) did not prevail for an infinite anterior time, but the same things came round in perpetual vicissitude or rotation; which consists with the doctrine that Actuality is prior to Potentiality. If the same condition comes round periodically, we must necessarily assume something Actual, which perpetually actualizes in the same manner (δεῖ τι ἀεὶ μένειν ὡσαύτως ἐνεργοῦν — p. 1072, a. 10). Again, if generation and destruction are to take place, we must assume something else Actual, which actualizes in a manner perpetually changing (ἄλλο δεῖ εἶναι ἀεὶ ἐνεργοῦν ἄλλως καὶ ἄλλως — a. 12). This last must actualize sometimes per se, sometimes in a different way; that is, according to some other influence, or according to the First (or Uniform) Actual. But it will necessarily actualize according to the First Actual; which will thus be a cause both to itself, and to the variable Actual. Now the First Actual is the best; for it is the cause of perpetual sameness, while the other is cause of variety; both together are the cause of unceasing variety. But this is how the motions really stand. Why then, should we look out for other principles (a. 18)?

Now, since the preceding views are consistent with the facts and may be true (ἐπεὶ δ’ οὕτω τ’ ἐνδέχεται — p. 1072, a. 18) — and, if they be not true, we shall be compelled to admit that every thing proceeds either from Night, or from confused Chaos or Non-Ens — we may consider the problem as solved. There exists something always in unceasing circular motion: this is evident not merely from reason, but from fact. The First Heaven (Aplanês or Fixed Star sphere) will therefore be eternal. There must therefore exist something which causes this unceasing motion, or some Prime Movent. But, since Movens Immobile, Movens Motum, Motum non Movens, form a series of three terms, and since the two last of these certainly exist, we may infer that the first exists also; and that the Prime Movent, which causes the motion of the Aplanês, is immoveable (a. 20-25. — This passage perplexes all the commentators — Schwegler, Bonitz, Alexander, &c. It can hardly be construed without more or less change of the text. I do not see to what real things Aristotle can allude under the description of Mota which are not Moventia. There is much to be said for Pierron and Zévort’s translation, p. 220: “Comme il n'y a que trois sortes d’êtres — ce qui est mu, ce qui meut, et le moyen terme entre ce qui est mu et ce qui meut: c’est un être (i.e., this middle term is an être) qui meut sans être mu.â€� — Bonitz disapproves this interpretation of the word μέσον, and it is certainly singular to say that between Movens and Motum, the term Movens sed non Motum forms a medium: Motum sed non Movens would form just as good a medium.). This Prime Movent, which causes motion without being itself moved, must be eternal, must be Essentia, and must be an Actuality.

Now both the Appetibile (τὸ ὀρεκτόν) and the Cogitabile (τὸ νοητόν) cause motion in this way, i.e., without being moved themselves; moreover the Primum Appetibile and the Primum Cogitabile are coincident or identical (p. 1072, a. 27). For that which appears beautiful, is the object of desire; but that which is beautiful, is the first object of will (a. 28). Cogitation is the principium of the two (the primary fact or fundamental element): we will so and so, because we think it good; it is not true that we think it good because we will it (ὀρεγόμεθα δὲ διότι δοκεῖ, μᾶλλον ἢ δοκεῖ διότι ὀρεγόμεθα — a. 29). Now the Cogitant Mind (νοῦς) is moved by the Cogitabile, and, in the series of fundamental Contraries, the members of one side of the series are Cogitabilia per se (while those of the other side are only Cogitabilia per aliud — νοητὴ δ’ ἡ ἑτέρα συστοιχία καθ’ αὑτήν — a. 31; see Alex., p. 668, 16, Bon.). These Cogitabilia per se are first as to Essentia (i.e., compared with the Cogitabilia per aliud, they are logically priora): and again, among Essentiæ, that variety which is simple and actual comes first (i.e., it is logically prius, as compared with the compound and the potential). Now Unum is not identical with Simplex: Unum signifies that which is a measure of something else, while Simplex denotes a peculiar attribute of the subject in itself (a. 34). But the Pulchrum and the Eligibile per se belongs to the same side of the series of Contraries, as the Cogitabilia per se: and the Primum Pulchrum or Eligibile is the Best or akin thereunto, in its own particular ascending scale (b. 1).

That τὸ οὗ ἕνεκα is among the Immoveables, may be seen by our Treatise De Bono, where we give a string of generic and specific distributions (ἡ διαίρεσις δηλοῖ — p. 1072, b. 2; see the interpretation of Alexander, adopted both by Schwegler and by Bonitz). For τὸ οὗ ἕνεκα is used in a double sense: in one of the two senses it ranks among the Immoveables: in another it does not (ἔστι γὰρ διττὸν τὸ οὗ ἕνεκα, b. 3 — διττόν is Schwegler’s correction, adopted by Bonitz). It causes motion, in the manner of a beloved object; and that which it causes to move, causes motion in the other things (κινεῖ δὲ ὡς ἐρώμενον· τὸ δὲ κινούμενον τἄλλα κινεῖ — b. 3; τὸ δὲ κινούμενον is the conjecture of Schwegler and Bonitz).

Now, if any thing be moved, there is a possibility that it may be in a condition different from that in which it actually is. If the first actuality of the Moveable be translation or motion in space, there is a possibility that it may be otherwise than it is as to place, even though it cannot be otherwise than it is as to Essentia (p. 1072, b. 7).

But, as to the Prime Movent, which is itself immoveable, and which exists in actuality, it is impossible that that can be other than what it is, in any respect whatever (p. 1072, b. 8). For the first of all changes is local motion, or rotation in a circle, and this is exactly what the Prime Movent imparts (but does not itself possess). It exists by necessity, and by that species of necessity which implies the perfect and beautiful: and in this character it is the originating principle. For there are three varieties of necessity: (1) That of violence, in contradiction to the natural impulse; (2) That without which good or perfection cannot be had; (3) That which is what it is absolutely, without possibility of being otherwise. From a principle of this nature (i.e., necessary in the two last senses) depend the Heaven and all Nature (b. 14).

The mode of existence (διαγωγή) of this Prime Movent is for ever that which we enjoy in our best moments, but which we cannot obtain permanently; for its actuality itself is also pleasure (p. 1072, b. 16). As actuality is pleasure, so the various actualities of waking, perceiving, cogitating, are to us the pleasantest part of our life; while hopes and remembrances are pleasing by derivation from them (but these states we men cannot enjoy permanently and without intermittence). Cogitation per se (i.e., cogitation in its most perfect condition) embraces that which is best per se; and most of all when it is most perfect. The Noûs thus cogitates itself through participation of the Cogitabile: for it becomes itself cogitable by touching the Cogitabile and cogitating: so that Cogitans and Cogitabile become identical. For Noûs in general (the human Noûs also) is in potentiality the recipient of the Cogitabile, and of Essentia or Forms; and it comes into actuality by possessing these Forms. So that what the Prime Movent possesses is more divine than the divine element which Noûs in general involves; and the actuality of theorizing is the pleasantest and best of all conditions (νοητὸς γὰρ γίγνεται θιγγάνων καὶ νοῶν, ὥστε ταὐτὸν νοῦς καὶ νοητόν. τὸ γὰρ δεκτικὸν τοῦ νοητοῦ καὶ τῆς οὐσίας νοῦς. ἐνεργεῖ δὲ ἔχων· ὥστ’ ἐκεῖνο μᾶλλον τούτου ὃ δοκεῖ ὁ νοῦς θεῖον ἔχειν, καὶ ἡ θεωρία τὸ ἥδιστον καὶ ἄριστον — b. 24. This is a very difficult passage, in which one cannot be sure of interpreting rightly. None of the commentators are perfectly satisfactory. The pronoun ἐκεῖνο seems to refer to ἡ νόησις ἡ καθ’ αὑτήν — three lines back. The contrast seems to be between the Prime Movent, and Noûs in general, including the human Noûs. Τὸ δεκτικόν cannot refer to the Prime Movent, which has no potentiality, but must refer to the human Noûs, which is not at first, nor always, in a state of actuality. Μᾶλλον seems equivalent to θειότερον. The human Noûs has θεῖόν τι, by reason of its potentiality to theorize.).

Thus it is wonderful, if God has perpetually an existence like that of our best moments; and still more wonderful, if he has a better. Yet such is the fact. Life belongs to him: for the actuality of Noûs is life, and God is actuality. His life, eternal and best, is actuality per se (or par excellence). We declare God to be an Animal Optimum Æternum, so that duration eternal and continuous (αἰὼν συνεχής) belongs to him: for that is God (τοῦτο γὰρ ὁ θεός — p. 1072, b. 30).

The Pythagoreans and Speusippus are mistaken in affirming that Optimum and Pulcherrimum is not to be found in the originating principle (ἐν ἀρχῇ); on the ground that the principles of plants and animals are indeed causes, but that the beautiful and perfect appears first in the results of those principles. For the seed first proceeds out of antecedent perfect animals: the first is not seed, but the perfect animal. Thus we must say that the man is prior to the seed: I do not mean the man who sprang from the seed, but the other man from whom the seed proceeded (p. 1073, a. 2).

From the preceding reasonings, it is evident that there exists an Essence eternal, immoveable, and separated from all the perceivable Essences. We have shown (in Physica; see Schwegler’s note) that this Essence can have no magnitude; that it is without parts and indivisible (p, 1073, a. 6). For it causes in other subjects motion for an infinite time; and nothing finite can have infinite power. For this reason the Prime Movent cannot have finite magnitude; but every magnitude is either finite or infinite, and there is no such thing as infinite magnitude; therefore the Prime Movent can have no magnitude at all. We have also shown that it is unchangeable in quality, and without any affections (ἀπαθὲς καὶ ἀναλλοίωτον). For all other varieties of change are posterior as compared with locomotive change or motion in space, which is the first of all. As the Prime Movent is exempt from this first, much more is it exempt from the others (a. 13).

We must now consider whether we ought to recognize one such Movent or Essence only, or several of the same Essences? and, if several, how many? Respecting the number thereof we must remember that our predecessors have laid down no clear or decisive doctrines (ἀποφάσεις, p. 1073, a. 16). The Platonic theory of Ideas includes no peculiar research on this subject (a. 18). The Platonists call these Ideas Numbers: about which they talk sometimes as if there were an infinite multitude of them, sometimes as if they were fixed as reaching to the dekad and not higher — but they furnish no demonstrative reason why they should stop at the dekad. We shall proceed to discuss the point consistently with our preceding definitions and with the nature of the subjects (a. 23). The Principium, the First of all Entia, is immoveable both per se and per accidens: it causes motion in another subject, to which it imparts the first or locomotive change, one and eternal (a. 25). The Motum must necessarily be moved by something; the Prime Movent must be immoveable per se; eternal motion must be caused by an eternal Movent; and one motion by one Movent (a. 30). But we see that, over and above the simple rotation of the All (or First Heaven), which rotation we affirm to be caused by the Primum Movens Immobile, there are also other eternal rotations of the Planets; for the circular Celestial Body, as we have shown in the Physica, is eternal and never at rest (a. 32). We must therefore necessarily assume that each of these rotations of the Planets is caused by a Movent Immoveable per se — by an eternal Essence (a. 35). For the Stars and Planets are in their nature eternal Essences: that which moves them must be itself eternal, and prior to that which it causes to be moved; likewise that which, is prior to Essence must itself be Essence, and cannot be any thing else (a. 37). It is plain, therefore, that there must necessarily exist a number of Essences, each eternal by nature, immoveable per se, and without magnitude, as Movents to the Heavenly Bodies and equal in number thereto (a. 38). These Essences are arranged in an order of first, second, &c., corresponding to the order of the planetary rotations (b. 2), But what the number of these rotations is, we must learn from Astronomy — that one among the mathematical sciences which is most akin (οἰκειοτάτης) to the First Philosophy; for Astronomy theorizes about Essence perceivable but eternal, while Arithmetic and Geometry do not treat of any Essence at all (περὶ οὐδεμιᾶς οὐσίας — b. 7). That the rotations are more in number than the rotating bodies, is known to all who have any tincture of Astronomy; for each of the Planets is carried round in more than one rotation (b. 10). But what the exact number of these rotations is, we shall proceed to state upon the authority of some mathematicians, for the sake of instruction, that the reader may have some definite number present to his mind: for the rest, he must both investigate for himself and put questions to other investigators; and, if he learns from the scientific men any thing dissenting from what we here lay down, he must love both dissentients but follow that one who reasons most accurately (φιλεῖν μὲν ἀμφοτέρους, πείθεσθαι δὲ τοῖς ἀκριβεστέροις — b. 16).

Aristotle then proceeds to unfold the number and arrangement of the planetary spheres and the corrective or counter-rolling (ἀνελιττούσας) spheres implicated with them (p. 1073, b. 17 — p. 1074, a. 14). He afterwards proceeds: Let the number of spheres thus be forty-seven; so that it will be reasonable to assume the Immoveable Movent Essences and Principles to be forty-seven also, as well as the perceivable spheres (αἰσθητάς — p. 1074, a. 16): we say reasonable (εὔλογον), for we shall leave to stronger heads to declare it necessary. But, since there cannot be any rotation except such as contributes to the rotation of one of the Planets, and since we must assume that each Nature and each Essence is exempt from extraneous affection and possessed per se of the Best as an end, so there will be no other Nature besides the forty-seven above enumerated, and this number will be the necessary total of the Essences (a. 21). For, if there were any others, they would cause motion by serving as an end for some rotation to aspire to (κινοῖεν ἂν ὡς τέλος οὖσαι φορᾶς — a. 23); but it is impossible that there can be any other rotation besides those that have been enumerated.

We may fairly infer this from the bodies which are carried in rotation (ἐκ τῶν φερομένων — p. 1074, a. 24). For, if every carrier exists naturally for the sake of the thing carried, and if every current or rotation is a current of something carried, there can exist no current either for the sake of itself or for the sake of some other current. Every current must exist for the sake of the Planets, and with a view to their rotation. For, if one current existed for the sake of another, this last must exist for the sake of a third, and so on; but you cannot go on in this way ad infinitum; and therefore the end of every current must be, one or other of the Divine Bodies which are carried round in the heavens (a. 31).

That there is only one Heaven, we may plainly see. For, if there were many heavens, as there are many men, the principium of each would be one in specie, though the principia would be many in numero (p. 1074, a. 33). But all things that are many in number, have Matter, and are many, by reason of their Matter; for to all these many, there is one and the same Form (λόγος) — definition or rational explanation: e.g., one for all men, among whom Sokrates is one (a. 35). But the First Essence has no Matter; for it is an Actual (τὸ δὲ τί ἦν εἶναι οὐκ ἔχει ὕλην τὸ πρῶτον· ἐντελέχεια γάρ — a. 36). The Primum Movens Immobile is therefore One, both in definition and in number; accordingly, the Motum — that which is moved both eternally and continuously — is One also. There exists therefore only one Heaven (p. 1074, a. 38).

Now it has been handed down in a mythical way, from the old and most ancient teachers (p. 1074, b. 1) to their successors, that these (Eternal Essences) are gods, and that the divine element comprehends all nature (ὅτι θεοί τέ εἰσιν οὗτοι καὶ περιέχει τὸ θεῖον τὴν ὅλην φύσιν — b. 3). The other accompaniments of the received creed have been superadded with a view to persuading the multitude and to useful purposes for the laws and the common interest (b. 4); wherefore the gods have been depicted as like to men and to some other animals, combined with other similar accompaniments. If a man, abstracting from these stories, accepts only the first and fundamental truth — That they conceived the First Essences as gods, he will consider it as a divine doctrine (θείως ἂν εἰρῆσθαι νομίσειεν — b. 9), preserved and handed down as fragments of truth from the most ancient times. For probably all art and philosophy and truth have been many times discovered, lost, and rediscovered. To this point alone, and thus far, the opinion of our fathers and of the first men is evident to us (b. 14).

There are however various difficulties connected with the Noûs; for it would seem to be more divine than the visible celestial objects, and yet we do not understand what its condition can be to be such (p. 1074, b. 17). For, if it cogitates nothing but is in the condition of slumber and inaction, what ground can there be for respecting it (τί ἂν εἴη τὸ σεμνόν — b. 18)? And, if it cogitates something actually, yet if this process depends upon something foreign and independent (i.e., upon the Cogitatum), the Noûs cannot be the best Essence; since it is then essentially not Cogitation in act, but only the potentiality of Cogitation; while its title to respect arises from actual Cogitation. Again, whether we assume its Essence to be Cogitation actual or Cogitation potential, what does it cogitate? It must cogitate either itself, or something different from itself; and, if the latter, either always the same Cogitatum, or sometimes one, sometimes another. But is there no difference whether its Cogitatum is honourable or vulgar? Are there not some things which it is absurd to cogitate? Evidently the Noûs must cogitate what is most divine and most honourable, without any change; for, if it did change, it must change for the worse, and that very change would at once (ἤδη) be a certain motion; whereas the Noûs is essentially immoveable (b. 27). First of all, if the Essence of the Noûs be, not Cogitation actual but Cogitation potential, we may reasonably conceive that the perpetuity of Cogitation would be fatiguing to it (b. 29); next, we see plainly that there must exist something else more honourable than the Noûs; namely, the Cogitatum; for to cogitate, and the act of cogitation, will belong even to one who cogitates the vilest object. If cogitation of vile objects be detestable (φευκτόν, b. 32) — for not to see some things is better than to see them — Cogitation cannot be the best of all things (i.e., Cogitation absolutely, whatever be the Cogitatum).

Since the Noûs is itself the best of all things, it must employ its cogitation upon itself and nothing else. Its cogitation will thus be Cogitation of Cogitation (αὑτὸν ἄρα νοεῖ, εἴπερ ἐστὶ τὸ κράτιστον, καὶ ἔστιν ἡ νόησις νοήσεως νόησις — p. 1074, b. 35). Yet, if we look to the human mind, Cognition, Perception, Opinion, Mental Discourse, &c., appear always as having direct reference to something else, and as referring each to itself only in an indirect and secondary way (ἀεὶ ἄλλου — αὑτῆς δ’ ἐν παρέργῳ — b. 36); and farther, if to cogitate is one thing and to be cogitated another thing, in which of the two points of view will the bene of the Noûs consist? To be Cogitation, and to be a Cogitatum, are not logically the same (οὐδὲ γὰρ ταὐτὸ τὸ εἶναι νοήσει καὶ νοουμένῳ — b. 38).

But may we not meet these difficulties by replying that there are some things in which Cognition is identical with the Cognitum? that is, in those Cognita which are altogether exempt from Matter? In Constructive cognitions without Matter, the Form and the τ.η.ε. is both Cognitum and Cognitio; in Theoretical cognitions without Matter, the Notion and the Cogitation is itself the Cognitum (ὁ λόγος τὸ πρᾶγμα καὶ ἡ νόησις). Since it appears, therefore, that, wherever there is no Matter, Cogitatum and Noûs are not different, the same will be true of the divine Noûs: its Cogitatio and its Cogitatum will be identical (p. 1075, a. 5).

One farther difficulty remains, if we suppose the Cogitatum to be a Compound (σύνθετον); for, on that supposition, the Cogitans would change in running through the different parts of the whole. But the reply seems to be, that every thing which has not Matter is indivisible and not compound (p. 1075, a. 7). As the human Noûs, being that which deals with compounds, comports itself for a certain time — for it does not attain its bene in cogitating this or that part of the compound, but in apprehending a certain total or completion which is something different from any of the parts — so does the divine Noûs, engaged in cogitation of itself, comport itself in perpetuity (a. 10).

Another point to be considered is — in what manner the nature of the Universe (ἡ τοῦ ὅλου φύσις — p. 1075, a. 11) includes Bonum and Optimum. Is Bonum included as something separate and as an adjunct by itself transcendent? Or is it immanent, pervading the whole arrangement of the constituent parts? Or does it exist in both ways at once, as in the case of a disciplined army; for, in this latter, Bonum belongs both to the array and to the general, and indeed more to the latter, since the array is directed by the general, not the general by the array. All things in the universe are marshalled in a certain orderly way — the aquatic creatures, the aërial, and the plants; but all things are not marshalled alike. The universe is not such that there is no relation between one thing and another: there is such a relation; for every thing is marshalled with a view to one end, though in different degrees. As, in a family, the freemen have least discretion left to them to act at haphazard, but all or most of their proceedings are regulated, while slaves and oxen are not required to do much towards the common good, but are left for the most part to act at hazard, — in this way the principium of each is arranged by nature (a. 23). For example, every thing must necessarily come to the termination of one individual existence to make room for another: there are also some other facts and conditions common to all things in the universe (λέγω δ’ οἷον εἴς γε τὸ διακριθῆναι ἀνάγκη ἁπᾶσιν ἐλθεῖν — a. 23; see the explanation of διακριθῆναι, given by Bonitz, Comm. p. 519 — not very certain).

In concluding this exposition, we must not lose sight of the absurdities and impossibilities which attach to all other, nor what is advanced by the most ingenious philosophers before us, nor which of their theories carries with it the fewest difficulties (p. 1075, a. 27).

That all things proceed from Contraries, all these philosophers agree in affirming. But it is not true that all things are generated, nor that they are generated from contraries; for the celestial substance is not generated at all, nor has it any contrary. Moreover, in those cases where there really are contraries, these philosophers do not teach us how generation can take place out of them; for contraries themselves have no effect upon each other. Now our doctrine solves this difficulty reasonably, by introducing a tertium quid (p. 1075, a. 31) — Matter. Some of these philosophers erroneously consider Matter to be itself one of the contraries: they consider the Unequal as matter or substratum to the Equal; or the Many as matter or substratum to the One; (Evil, as opposed to Good). We resolve this in the same way: our Matter is one, is contrary itself to nothing, but may be potentially either of two contraries. Farthermore, if we admit the doctrine that Evil itself is Matter or one of the elements, the inference will follow that every thing whatever, except the Unum itself, partakes of Evil (a. 6).

Some philosophers do not admit either Good or Evil to be principles at all; but they are manifestly wrong; for in all things Good is most of all the principle (p. 1075, a. 37). Others again are so far right that they recognize Good as a principle: but they do not tell us how it is a principle — whether as End, or as Movent, or as Form.

Empedokles lays down a strange doctrine: he makes Friendship to be the Good (p. 1075, b. 2). But, in his theory, Friendship is principle partly as Movent, for its function is to bring together (συνάγει γὰρ — b. 3); partly as Matter, for it is itself a portion of the mixture (μόριον τοῦ μίγματος — b. 4). Now, even granting the possibility that the same thing may be per accidens (κατὰ συμβεβηκός — b. 5, i.e., by special coincidence in any one particular case) principle as Movent, and also principle as Matter, nevertheless the two are not the same logically and by definition. Under which of the two, therefore, are we to reckon Friendship? It is moreover another strange feature in the theory of Empedokles, that he makes Enmity to be indestructible; for this very Enmity is with him the nature and principle of Evil (b. 8).

Anaxagoras declares Good to be the principle as Movent; for, in his theory, Noûs causes motion; but it causes motion with a view to some end, which is of course different from itself; so that the real principle is different from Noûs: unless indeed he adopted one of our tenets; for we too say that, in a certain sense, the medical art is health (p. 1075, b. 10; Z. vii. p. 1032, b. 10). It is moreover absurd, that Anaxagoras does not recognize any contrary to Good and to the Noûs (b. 11). (Bonitz remarks, Comm. p. 522:— Aristotle means that Anaxagoras was wrong, because he failed “ad eam devenire rationem, ut intellectum sui ipsius intelligentiam ideoque sui ipsius τέλος esse statueretâ€�; farther, he remarks, on the line b. 10 — ἄτοπον δὲ καὶ τὸ ἐναντίον μὴ ποιῆσαι τῷ ἀγαθῷ καὶ τῷ νῷ: “Quid enim? nonne pariter et eodem jure νοῦς ἀμιγής, quem posuit Anaxagoras, ab omni contrarietate et oppositione immunis sit, ac primus motor apud Aristotelem?â€� — Aristotle would have replied to this: “I recognize principles of Evil under the names of ὕλη and στέρησις; the last of the two being directly opposed to Form (Regularity or Good), the first of the two being indifferent and equally ready as a recipient both for evil and for good. My Prime Movent acts like an ἐρώμενον in causing motion in the Celestial Substance: the motion of this last is pure Good, without any mixture of Evil. But, when this motion is transmitted to the sublunary elements, it becomes corrupted by ὕλη and στέρησις, so that Evil becomes mingled with the Good. Anaxagoras recognizes no counteracting principles, analogous to ὕλη and στέρησις, so that Evil, on his theory, remains unexplained.â€�)

Those philosophers who lay down Contraries as their principles, do not make proper use of these Contraries, unless their language be improved or modified (p. 1075, b. 12). Nor do they tell us why some things are destructible, other things indestructible; for they trace all things to the same principles. Some make all things to proceed from Non-Ens; others, to escape that necessity, make all things One (and thus recognize no real change or generation at all — the Eleates, b. 16). Again, not one of them tells us why generation must always be, or what is the cause of generation. Once more, those who recognize two contrary principles must necessarily recognize a third superior to both (b. 18); and the Platonists with their Ideas are under the like necessity. For they must assign some reason why particular things partake of these Ideas.

Other philosophers, moreover, must consistently with their theories recognize something contrary to Wisdom and to the most venerable Cognition. But we are under no such necessity; for there is nothing contrary to the First (τῷ πρώτῳ). All contraries involve Matter, and are in potentiality the same: one of the two contraries is ignorance in regard to the other; but the First has no contrary (p. 1075, b. 24).

Again, if there be no Entia beyond the Perceptibilia, there can be no beginning, no arrangement in order, no generation, no celestial bodies or proceedings (i.e., all these will remain unexplained). There will always be a beginning behind the beginning, ad infinitum; as there is in the theories of all the theologians and physical philosophers (p. 1075, b. 27). And, even if we recognize, beyond the Perceptibilia, Ideas or Numbers, these are causes of nothing; or, if causes of any thing, they are certainly not causes of motion. How, moreover, can Magnitude, and a Continuum arise out of that which has no Magnitude? Number cannot, either as Movent or as Form, produce a Continuum (b. 30).

Again, (Contraries cannot be principles, because) no Contrary can be essentially Constructive and essentially Movent (p. 1075, b. 31); for Contraries involve Matter and Potentiality, and may possibly, therefore, not exist. And, if there be Potentiality, it will come prior to Actuality: upon that supposition therefore (i.e., of Contraries as the fundamental principles) Entia could not be eternal. But Entia are eternal; therefore these theories must be in part amended: we have shown how (b. 34).

Farther, none of these theories explains how it is that numbers coalesce into One; or soul and body into One; or Form and Matter into one Concrete. Nor can they explain this, unless they adopt our doctrine, that the Movent brings about this coalition (p. 1075, b. 37).

Those philosophers (like Speusippus) who recognize many different grades and species of Entia (first the Mathematical Number, &c.), with separate principles for each, make the Essence of the Universe to be incoherent (ἐπεισοδιώδη — p. 1076, a. 1) and set up many distinct principles; for none of these Essences contributes to or bears upon the remainder, whether it exists or does not exist. Now Entia are not willing to be badly governed (τὰ δὲ ὄντα οὐ βούλεται πολιτεύεσθαι κακῶς. “οὐκ ἀγαθὸν πολυκοιρανίη· εἷς κοίρανος.â€� — p. 1076, a. 4).

[IV.]

DE CÅ’LO.

Book I.

CH. 1. — The science of Nature has for its principal object — Bodies, Magnitudes, and the various affections and movements of Bodies and Magnitudes; also the beginnings or principles of this sort of Essence. The Continuous is that which is divisible into parts perpetually divisible: and Body is that which is divisible in every direction. Of magnitudes, some (lines) are divisible only in one direction; others (planes) only in two directions; others again (bodies) in three directions. This is the maximum: there is no other magnitude beyond; for three are all, and to say “in three directionsâ€� is the same as to say “in all directions.â€� As the Pythagoreans say, The Universe and All Things are determined by Three: in End, Middle, and Beginning, lies the number of the Universe, or the Triad. We have received these as laws from nature, and we accordingly employ this number (Three) for solemnities in honour of the Gods. Moreover, we apply our predicates on the same principle; for we call Two, and The Two — Both, but we do not call them all. Three is the first number to which we apply the predicate All. Herein (as was observed before) we follow the lead of Nature herself. Since therefore these three phrases — All Things, The Universe, The Perfect or Complete — do not specifically differ from each other, but are distinguished only in respect of the matter or occasions on which they are applied. Body is the only kind of magnitude which can be declared Perfect or Complete, that is, All; for it is the only magnitude determined or defined by the Three. Being divisible in three directions, it is divisible every way; other magnitudes are divisible either only in one way or only in two. Magnitudes are both divisible and continuous according to the number by which they are designated — continuous in one direction, in two, in three, or all. All divisible magnitudes are also continuous: whether all continuous magnitudes are divisible, is not yet clear. But what is clear is — that there is no upward transition to a higher genus beyond Body, as there is from line to surface, and from surface to Body. If there were, Body would not be perfect or complete as a magnitude; for the transition would be made at the point of deficiency; but the perfect or complete can have no deficiency: it stretches every way. Such is each body included as a part in the universe: it has dimensions in every direction. Yet each is distinguished from its neighbour by contact, and each therefore in a certain sense is many. But the Universe (τὸ πᾶν) including all these parts is of necessity perfect and complete; extending not merely in one way, and in another way not, but πάντῃ, as the word literally means (ss. 1-4).

CH. 2. — Respecting the nature of the Universe, we shall enquire presently whether in the aggregate it be infinite or of finite magnitude. But first let us speak about its different constituent species, proceeding on the following basis. I affirm that all natural bodies and magnitudes are per se locally moveable; and that Nature is to them a beginning or principle of motion. Now all Local Motion (known by the name of φορά) is either Rectilinear or Circular, or compounded of the two; for these two are the only simple motions, by reason that the only two simple magnitudes are the rectilinear and the circular. The circular is motion round the Centre; the rectilinear is motion either downwards towards the centre or upwards from the centre. These three are the only simple modes of motion or currents: as I said in the last chapter that body was made complete in the number three, so also the motion of body is made complete in the number three. Now, as there are some bodies (such as fire, earth, and their cognates) which are simple (i.e. which have in themselves a natural beginning or principle of motion), and others which are compounds of these, so also there must be simple motions belonging to the former and compound motions belonging to the latter; such compound motions being determined by the preponderant element therein. Since, therefore, circular motion is a simple mode of motion, and since simple modes of motion belong only to simple bodies, there must of necessity be a particular variety of simple body, whose especial nature it is to be carried round in circular motion. By violence, indeed, one body might be moved in a mode belonging to another; but not by nature. Moreover, since motion against nature is opposite to motion conformable to nature, and since each mode has one single opposite, simple circular motion, if it be not conformable to the nature of this body, must be against its nature. If then the body rotating in a circle be fire or any of the other elements, its natural mode of motion must be opposite to circular motion. But each thing has only one opposite; and up and down are each other’s opposites. If then the body which rotates in a circle rotates thus against nature, it must have some other mode of motion conformable to nature. But this is impossible: for, if the motion conformable to its nature be motion upwards, the body must be fire or air; if motion downwards, the body must be earth or water (and there is no other simple mode of motion that it can have). Moreover, its rotatory motion must be a first motion; for the perfect is prior in nature to the imperfect. Now the circle is perfect; but no straight line is perfect: neither an infinite straight line, for in order to be perfect, it must have an end and a boundary; nor any finite straight line, for each has something without it and may be prolonged at pleasure. So that, if motion first by nature belong to a body first by nature, if circular motion (as being perfect) be prior to rectilinear motion, and if rectilinear motion belong to a first or a simple body, as we see both in fire and in earth, — we may be sure à fortiori that circular motion belongs to a simple body, and that there is, besides the four elements here, prior to them and more divine than them, a different body cf special nature and essence. Indeed, since circular motion is against the nature of these four elements, there must be some other different body to whose nature it is conformable. There must thus be some simple and primary body, whose nature it is to be carried round in a circle, as earth is carried downwards and fire upwards. On the assumption that the revolving bodies revolved against their own nature, it would be wonderful and even unreasonable that this one single mode of motion, being thus contrary to nature, should be continuous and eternal; for in all other things we see that what is contrary to nature dies away most speedily. Now, if the revolving body were fire, as some affirm, the revolving motion would be just as much contrary to its nature as motion downwards; for the natural motion of fire is upwards or away from the centre. Reasoning from all these premisses, we may safely conclude that, distinct from all these bodies which are here around us, there exists a body whose nature is more honourable in proportion to its greater distance from us here (ss. 1-13).

CH. 3. — We plainly cannot affirm that every body is either heavy or light: meaning by heavy, that which is carried by its nature downwards or towards the centre; by light, that which is carried by its nature upwards or away from the centre. Heaviest (or earth) is that which underlies all other downward moving bodies, lightest (fire) is that which floats above all upward moving bodies. Air and water are both light and heavy, relatively, but relatively to different terms of comparison; thus, water is heavy as compared to air and fire, light as compared to earth. But that body whose nature it is to revolve in a circle, cannot possibly have either heaviness or levity; for it cannot move in a right line, either upwards or downwards, nor either by nature or against nature. Not by nature, for, in that case, it must be identical with some one of the four elements; not against nature, because, if it moved upwards against nature, this would prove that motion downwards was conformable to its nature, and it would thus be identical with earth: we have already seen that, if a body moves upwards against nature, it must move downwards according to nature, and vice versâ. Now the same natural motion which belongs to any body as a whole, belongs also to its minute fragments (to the whole earth and to any of its constituent clods). Accordingly the revolving body in its local movement of revolution cannot possibly be dragged in any other direction, either upward or downward, — neither the whole nor any portion thereof. It is alike reasonable to conceive it as ungenerable, indestructible, incapable both of increase and of qualitative change (ἀναυξὲς καὶ ἀναλλοίωτον). It cannot be generated, because every thing generated comes out of a substratum and an opposite, into which it relapses on being destroyed. Now the revolving body has no opposite; for we have already seen that opposite bodies have their currents of motion opposite, and there is no current of motion opposite to that of circular rotation. Nature has rightly excepted this ungenerable and indestructible substance from the action of contraries, in which generation and destruction occur. It is also incapable of increase or diminution, because these processes take place through the accession of new cognate materials; and in this case there are none such. It is farther incapable of qualitative change, because this always implies the being affected favourably or unfavourably (πάθος); and this last never takes place, in plants or in animals, without some increase or diminution in quantity (ss. 1-5).

This Celestial Substance is thus eternal, ungenerable, indestructible, noway increased nor diminished, neither growing old nor capable of disturbing affections nor changeable in quality. Herein the evidence of reason and that of phenomena concur. For all men, Hellenes and Barbarians, have some belief respecting the Gods, and all who believe Gods to exist assign to the divine nature the uppermost place in the Kosmos; an immortal place going naturally along with immortal persons. Our perceptions confirm this sufficiently, at least when we speak with reference to human belief. For not the smallest change has ever been observed in the celestial substance, throughout all past time. Under these impressions, the ancients gave to it the name which it now bears; for the same opinions suggest themselves to us not once, nor twice, but an infinite number of times. Hence the ancients, regarding the First Body as something distinct from Fire, Earth, Air, or Water, called the uppermost place Æther, from its being always running (ἀπὸ τοῦ θεῖν ἀεί), the adverbial designation being derived from eternal duration. Anaxagoras employs this name improperly: he calls Fire by the name of Æther (s. 6).

It is plain, from all we have said, that the simple bodies cannot be more in number than those just indicated; for a simple body must of necessity have a simple mode of motion, and there are only three simple modes of motion — one circular and two rectilinear, one of these being from the centre, the other towards the centre (s. 7).

CH. 4. — That Circular Rotation has no motion opposed to it, may be shown by several different arguments. If there were any, it would certainly be rectilinear motion; for convex and concave, though each respectively opposed to the other, are, when both put together, opposed as a couple to rectilinear motion. But each variety of rectilinear motion has another variety of rectilinear motion opposed to it; and each thing has but one opposite. Moreover the oppositions between one motion (or one current — φορά) and another are founded upon oppositions of place, which are three in number: (1) Above and Below; (2) Before and Behind; (3) Right and Left. Now the motion in circular rotation from A to B is not opposite to that from B to A: the opposition of motion is along the straight line which joins the two; for an infinite number of different circles may be drawn, not interfering with each other but all passing through the same two points A and B. In the same circle, the opposition between the current from A to B and that from B to A, is along the line of diameter — not along the line of circumference. If one circular current were really opposed to any other circular current, one or other of the two would have existed to no purpose; for both have the same object. That is to say: what is carried round in a circle, let it begin from any point whatever, must necessarily come round equally to all the opposite places, above, below, before, behind, right, left. If the two (presumed) opposite circular currents were equal, they would neutralize each other, and there would be no motion at all of either of them. If one of the two were the more powerful, it would extinguish the other; so that to suppose the existence of both is to suppose that one or both exists in vain (i.e., can never be realized). We say that a sandal exists in vain (μάτην), when it cannot be fastened on. But God and nature do nothing in vain (ss. 1-8).

CH. 5. — Most of the ancient philosophers admitted an infinite body; but this may be shown to be impossible. The question is very important; for the consequences which follow from admitting the Infinite as principium, affect our speculations concerning the whole of Nature (s. 1).

Every body is of necessity either simple or compound. The infinite body therefore, if it exists, must of necessity be either one or the other. But there can be no infinite compound composed of simple bodies finite in magnitude and in number: so that, if an infinite body exist, it must be simple. We shall first enquire whether the First Body, whose nature it is to move in a circle, can be infinite in magnitude. Now, if it were infinite, the radii thrown out from the centre would be infinite, and the distance between them would also be infinite; that is, no finite peripheral line can be found touching all the extremities of the radii without: if any such line be assumed, you may always assume a greater. We call Number infinite, because the greatest number cannot be given; and the like may be said about this distance. Now, as an infinite distance cannot be passed over, no circular motion passing over it is possible, so as to come round to the point of departure. But we see plainly that the First Body or the Heaven does come round in a circle; and it has been shown by reasoning à priori that there is a variety of body whose nature it is to move in a circle. Such a body therefore as the First (revolving) Body cannot be infinite (ss. 2, 3).

Four other arguments are added, proving the same conclusion (s. 4, seq.). One of them is: That an infinite square, circle, or sphere, is an impossibility; each of these figures being defined or determined. As there can be no infinite circle, so neither can an infinite body be moved round in a circle (s. 7).

CH. 6. — As the First Body cannot be infinite, so neither can those bodies be infinite whose nature it is to move to the centre and from the centre — neither the centripetal nor the centrifugal body. For these two currents are opposite in nature; opposite currents being characterized by the opposite places to which they tend. But of two opposites, if the one be fixed and determinate, the other must be fixed and determinate also. Now the centre is determined; for the centripetal body, let it fall from what height it will, can never fall lower than the centre; and, since the centre is determined, the upper region or extremity must also be determined. The places at each extreme being thus determined, the intermediate space must be determined also; otherwise there would exist motion undetermined or infinite, which has been shown in a former treatise to be impossible (Physica, VIII. viii.); and therefore that body which either is therein, or may possibly be therein, must be determined. But it is a fact that the centripetal body and the centrifugal body can be therein; for centripetality and centrifugality are of the nature of each respectively (ss. 1, 2).

Hence we see that there can be no infinite body. There are other reasons also. As the centripetal body is heavy, if it be infinite, its gravity must also be infinite; and, if gravity cannot be infinite, neither can any heavy body be infinite. The like about any light body, such as the centrifugal (s. 3).

He then shows (by a long process of reasoning, not easy to follow) first, that there cannot be an infinite body with finite gravity; next, that there can be no infinite gravity. Accordingly there can be no infinite body at all, having gravity. At the end, he considers that this is established, (1) by the partial arguments (διὰ τῶν κατὰ μέρος) immediately preceding; (2) by the general reasonings in his other treatises respecting first principles, in which he explained the Infinite — in what sense it existed and did not exist; (3) by an argument about the Infinite, upon which he touches in the next chapter (ss. 4-13).

CH. 7. — Every body is of necessity either infinite or finite. If infinite, it is as a whole either of like constituents or of unlike. If the latter, either of a finite number of species, or of an infinite number. The last is impossible, if our fundamental assumptions are allowed to stand. For since the simple modes of motion are limited in number, the simple bodies must be alike limited; each simple mode of notion belonging to its own special simple body, and each natural body having always its own natural motion. But, if the Infinite be composed of a finite number of species, each of these constituent parts must be infinite; that is, water and fire must be infinite. Yet this too, is impossible; for we have seen that there cannot be either infinite levity or infinite gravity (the attributes of fire and water). Moreover, if these bodies be infinite, the places which they occupy, and the motions which they make, must also be infinite; but this also we have shown to be inadmissible, if our fundamental assumptions are admitted. The centripetal body cannot be carried to an infinite distance downward, nor the centrifugal body to an infinite distance upward. That which cannot come to pass, cannot be in course of coming to pass; thus, if a thing cannot come to be white, or a cubit long, or domiciled in Egypt, it cannot be in course of becoming white, or a cubit long, &c. It cannot be in course of being carried to a terminus which cannot be reached. It might be argued that fire, though discontinuous and dispersed, might still be infinite, in the sum total of its different masses. But body is that which is extended in every direction: how can there be many bodies unlike to each other, yet each of them infinite? Each of them, if infinite at all, ought to be infinite in every direction (ss. 1-5).

We thus see that the Infinite cannot consist of unlike constituents. But neither can it consist of constituents all similar. For, first, there are only three simple motions, and one of the three it must have; but we have shown that it cannot have either centripetal or centrifugal motion (i.e., that it cannot have either infinite gravity or infinite levity); nor can it again have circular motion, for the Infinite cannot be carried in a circle: this would amount to saying that the Heaven is infinite, which we have shown to be impossible. The Infinite indeed cannot be moved in any way at all; for, if moved, it must be moved either according to nature, or contrary to nature (violently), and, if its present motion be violent, it must have some other mode of motion which is natural to it. But, if it have any such, this assumes that there exists some other place belonging to it, into which it may be conveyed — an obvious impossibility (ss. 6, 7).

Farthermore, the Infinite cannot act in any way upon the Finite, nor be acted upon thereby (ss. 8-10). Nor can the Infinite be acted upon in any way by the Infinite (ss. 11-12).

If then every perceptible body possesses powers, as agent or patient or both, there can be no perceptible body which is infinite. But all bodies which are in any place are perceptible; therefore no body which is in any place can be infinite. There is no infinite body, indeed there can be no body at all, outside of the Heaven; for that which is outside of the Heaven is in a place. Even if perceivable only up to a certain point (μέχρι τινός), even if merely intelligible, it would still be in a place, and would therefore come under the foregoing argument — that there is no body outside of the Heaven (ss. 13, 14).

The foregoing reasoning may be summed up, in more general language (λογικώτερον), as follows:— The Infinite assumed as homogeneous cannot be moved in a circle, since the Infinite has no centre; nor in a straight line, since this would imply a second infinite place into which it must be moved according to nature, and a third infinite place into which it must be moved against nature, and since in either case the force which causes it to be moved must be infinite. But we have already argued, in treating of Motion (Phys. VIII. x.) that nothing finite can have infinite power, nothing infinite can have finite power; and, if that which is moved according to nature can also be moved contrary to nature, there must of necessity be two Infinites — Movens and Motum. Yet what can that be which causes the Infinite to move? If it cause itself to move, it must be animated (ἔμψυχον): but how can an infinite animated being (ζῷον) exist? And, if there be anything else which causes it to move, there must exist two Infinites, each distinguished from the other in form and power (ss. 15-17).

Again, even if we admit the doctrine of Leukippus and Demokritus — That the whole is not continuous, but discontinuous, atoms divided by intervening spaces — still the Infinite is inadmissible. For the nature and essence of these atoms is all the same, though they are different from each other in figure and arrangement; accordingly the motion of all must be the same: if one is heavy or centripetal, all must be so alike; if one is light or centrifugal, all must be so alike. But either of these motions would imply the existence of centre and periphery; which does not consist with an infinite whole. In the Infinite, there is neither centre nor periphery; no terminus prefixed either for upward or downward motion; no own place either for centripetal or centrifugal matter. Therefore in an infinite universe, there can be no motion at all (ss. 18, 19).

CH. 8. — There cannot be more than one Kosmos. All things both rest and are moved, either by violence, or according to nature. In that place to which it is carried by nature, it also rests by nature: in that place to which it is carried by violence, it rests by violence. If the current which we see towards the centre is by violence, the opposite current must be natural; if earth is carried by violence from thence hitherward, its natural current must be from hence thitherward; and, if being here it rests without violence, its current towards here must be a natural one. For there is one only which is natural. Now, if there be many Kosmi, they must be alike in their nature, and must be composed of the same bodies, having the same nature and powers — fire, earth, and the two intermediate elements: for, if the bodies here are not the same as those in other Kosmi — if the same names are given in an equivocal sense and do not connote the same specific attributes — the name Kosmos must be equivocal also, and there cannot be many true or real Kosmi, in the same sense. To the parts or elements of each Kosmos, therefore, the centripetal and centrifugal currents are natural; for the simple currents are limited in number, and each element is so named as to connote one of them specially; and, if the currents are the same, the elements must also be the same everywhere. If there were another Kosmos, the earth in that would tend towards the centre of our Kosmos, and the fire in that would tend towards the periphery of our Kosmos. But this is impossible; since in that case the earth in that Kosmos would run away from the centre of its own Kosmos, and the fire therein would run away from its own periphery. Either we must not admit the same nature in the simple elements of the numerous Kosmi; or, if we do admit it, we must recognize only one centre and one periphery. This difficulty prevents our recognizing more than one Kosmos (ss. 1-6).

It is unphilosophical to affirm that the nature of these simple elements becomes changed according as they are more or less distant from their own places. The difference is at best one of degree, not one of kind. That they are moved, we see plainly; there must therefore be some one current of motion natural to them. Accordingly every portion of the same element (or of elements the same in kind) must tend towards the same numerical place — towards this actual centre (πρὸς τόδε τι μέσον), or that actual periphery; and, if the tendency be towards one centre specie, but towards many centres numero, because particulars differ numero alone, and not specie, still the attribute will be alike in all, and will not be present in some portions, absent in others: I mean that, if the portions of this Kosmos are relative to each other, those in another Kosmos are in the like condition, and what is taken from this Kosmos will not be different from what is taken from the corresponding elements of any other Kosmos. Unless these assumptions can be overthrown, it is indisputably certain that there can be only one centre and one periphery; by consequence therefore, only one Kosmos and not more (ss. 7-10).

There are other reasons to show that there is a given terminus for the natural current both of fire and of earth. A thing moved, speaking generally, changes from something definite into something else definite; but there are different species of such change: the change called getting-well is from sickness to health; that called growth is from the little to great; that called local movement is from a terminus to another terminus, and local movements are specifically different from each other, according as the terminus a quo and the terminus ad quem is defined in each. The terminus is always a known and definite point: it is not accidental, nor dependent upon the arbitrium of the mover. Fire and earth therefore do not move on to infinity, but to definite points in opposite directions; and the local antithesis is between above and below: these are the two termini of the respective currents. Earth is carried with greater velocity, the nearer it approaches to the centre; fire is carried with greater velocity, the nearer it approaches to the periphery. This shows that its current does not stretch to infinity; for its velocity would then increase infinitely. Earth is not carried downward by the force of any thing else, nor fire upwards: not by any violence, nor by squeezing out (ἐκθλίψει), as some say. If this were so, a larger quantity of earth would move downward, and a larger quantity of fire upward, more slowly than a smaller. But the reverse is what occurs: the larger quantity of earth moves downward more rapidly than the smaller; if its motion had been caused by violence or by squeezing out, such motion would have slackened as it became more widely distant from the moving force (ss. 11-14).

We may deduce the same conclusion from the reasonings of the First Philosophy, also from the fact of circular motion which of necessity is constant both here and everywhere. Further, it is clear that there can be only one Kosmos; for, as there are three bodily elements, so there are three special places of such elements: one the undermost, at the centre; another the uppermost, at the periphery, revolving in a circular orbit; the third, in the intermediate place between the two, being the light or floating element (τὸ ἐπιπόλαζον); for, if not there, it must be outside of the Kosmos, which is impossible (ss. 15, 16).

CH. 9. — We must however now examine some reasons, which have been alleged to prove the contrary; and which seem to show, not only that there are many Kosmi, but even that there must be many, and that the hypothesis of one single Kosmos is inadmissible. It is urged that in all aggregates, natural as well as artificial, the Form by itself is one thing, and the Form implicated with Matter is another. When we declare the definition of a sphere or a circle, we do not include therein gold or brass, for this makes no part of the essence: if we mention these metals, it is when we cannot conceive or grasp anything beyond the particular case; for example, if we have one particular circle before us. Nevertheless, even here the circle in the abstract is one thing, and this particular circle is another: the first is the Form by itself, the last is the Form along with Matter, one among particular objects. Now, since the Heaven is perceivable by sense, it must be one among particular objects; for every thing perceivable is implicated with Matter. As such, it is this Heaven: to be this Heaven (Form along with Matter) is one thing; to be the Heaven simply and absolutely (Form without Matter) is another. Now, wherever there is Form, there either are or may be many distinct particulars; whether we admit (with Plato) that the Forms exist separately, or not. In all things where the Essence is implicated with Matter, we see that the particular manifestations are many and of indefinite number. Upon this reasoning therefore, there are or at least may be many Heavens: the supposition that there can be no more than one, is inadmissible (ss. 1-2).

But we must see how far this reasoning will hold. That the Form without Matter differs from the Form with Matter, is perfectly true. But this does not show that there must be many Kosmi; nor can there be many, if this one Kosmos exhausts all the matter that exists. If the matter of man were flesh and bone, and if a single man were formed, including all flesh and all bone indissolubly united; there could not possibly exist any other man; and the like is true about other objects; for, where the essence is implicated with an underlying matter, no object can come into existence unless some matter be furnished. The Kosmos, or Heaven, is a particular object, composed partly out of appropriate matter: but if it absorbs all the appropriate matter, no second Kosmos can come to pass. We shall now show that it does include all the appropriate matter (ss. 3-5).

The word Heaven has three different senses. 1. It means the essence of the extreme periphery of the universe, or the natural body which is there situated: we call this highest and farthest place Heaven, where we suppose all the divine agency to be situated (ἐν ᾧ τὸ θεῖον πᾶν ἱδρῦσθαί φαμεν). 2. It means the body continuous (τὸ συνεχὲς σῶμα) with the extreme periphery of the universe, wherein are contained Sun, Moon, and some of the Stars (Planets); for these we affirm to be in the Heaven. 3. In a third sense, it means the body circumscribed (περιεχόμενον) by this extreme periphery: for we usually call the Whole and the Universe, Heaven. — These being the three senses of Heaven, the Whole circumscribed by the extreme periphery must by necessity consist of all the natural and perceivable body existing, since there neither is nor can be any such outside of the Heaven. For, if there were any such outside of the Heaven, it must be either one of the elements or a compound thereof — either by nature or contrary to nature. For we have shown that each of the three elements — the circular, the centrifugal, and the centripetal — has its own special place by nature; and that, even if the place in which it now is were not its natural place, that place would be the natural place of another one among the three; for, if a place be contrary to nature in reference to one, it must be conformable to nature in reference to another. Neither of these three elements therefore can be outside of the Heaven, nor, of course, any of their compounds. And there exists no other body besides these; nor can there exist any other (ss. 6, 7).

We see therefore plainly that there neither is nor can be any mass of body (σῶματος ὄγκον) outside of the Heaven; and that the Heaven comprehends all matter — all body natural and perceptible. So that there neither are, nor ever have been, nor ever can be, many Heavens: this one is unique as well as perfect. Nor is there either place, or vacuum, or time, outside of the Heaven. There is no place or vacuum; because, if there were, body might be placed therein; which we have shown to be impossible. There is no time; because time is the number of motion, and there can be no motion without some natural body; but there cannot exist any extra-celestial body. Neither, therefore, are the things outside of the Heaven in place, nor is there time to affect them with old age, nor do they undergo change of any kind. They are without any change of quality and without susceptibility of suffering; they remain, throughout the entire Æon, in possession of the best and most self-sufficing life. The word Æon is a divine expression proposed (θείως ἔφθεγκται) by the ancient philosophers: they call the Æon of each creature that end which circumscribes the natural duration of the creature’s life. Pursuant to this same explanation, the end of the whole Heaven — the end comprising all time and the infinity of all things — is Æon, so denominated ἀπὸ τοῦ ἀεὶ εἶναι, immortal and divine. From this is suspended existence and life for all other things; for some closely and strictly, for others faintly and feebly. For it is a doctrine often repeated to us in ordinary philosophical discourse (ἐν τοῖς ἐγκυκλίοις φιλοσοφήμασι) respecting divine matters — that the Divine, every thing primary and supreme, is by necessity unchangeable; and this confirms what has been just affirmed. For there exists nothing more powerful than itself which can cause it to be moved (if there were, that would be more divine); nor has it any mean attribute; nor is it deficient in any of the perfections belonging to its nature. Its unceasing motion too is easily explained. For all things cease to be moved, when they come into their own place; but with the circular or revolving body the place in which it begins and in which it ends is the same (ss. 8-10).

CH. 10. — We shall next discuss whether the Kosmos be generable or ungenerable, and perishable or imperishable; noticing what others have said on the subject before. All of them consider the Kosmos to be generated: but some think it (although generated) to be eternal; others look upon it as perishable, like other natural compounds; others again — Empedokles and Herakleitus — declare it to be generated and destroyed in perpetual alternation. Now to affirm that it is generated and yet that it is eternal, is an impossibility: we cannot reasonably affirm any thing, except what we see to happen with all things or with most things; and, in the case before us, what happens is the very reverse of the foregoing affirmation, for all things generated are seen to be destroyed. Again that which has no beginning of being as it is now — that which cannot possibly have been otherwise previously throughout the whole Æon — can never by any possibility change; for, if it could ever change, there must exist some cause, which, if it had existed before, would have compelled what is assumed to be incapable of being otherwise, to be otherwise. To those who say that the Kosmos has come together from materials previously existing in another condition, we may reply: If these materials were always in this prior condition and incapable of any other, the Kosmos would never have been generated at all; and, if it has been generated, we may be sure that the antecedent materials must have been capable of coming into another condition, and were not under a necessity to remain always in the same condition; so that aggregations once existing were dissolved, and disgregations brought into combination, many times over before the present Kosmos; at least they possibly may have been so: and this is enough to prove that the Kosmos is not indestructible (ss. 1-3).

Among those who maintain the Kosmos to have been generated yet to be indestructible, there are some who defend themselves in the following manner. They tell us that the generation of which they speak is not meant to be affirmed as a real past fact, but is a mere explanatory or illustrative fiction, like the generation of a geometrical figure, introduced to facilitate the understanding by pupils. But such an analogy cannot be admitted. For in geometry the conclusions are just the same, if we suppose all the figures existing simultaneously; but it is not so with the demonstrations which they tender about the generation of the Cosmos, where the antecedent condition and the consequent condition are the reverse of each other. Out of disorder (they tell us) things came into order: these two conditions cannot be simultaneous; generation must be a real fact, and distinction of time comparing the one condition with the other; whereas in geometrical figures no distinction of time is required (ss. 4-6).

To assume alternate generation and dissolution, over and over again, is in fact to represent the Kosmos as eternal, but as changing its form; as if you should suppose the same person to pass from boyhood to manhood and then back again from manhood to boyhood — calling that by the name of generation and destruction. For, if the elements come together, the aggregation resulting will not be accidental and variable but always the same, especially upon the assumptions of these philosophers. So that, if the whole Kosmos, remaining continuous, is sometimes arranged in one way, sometimes in another, it is these arrangements which are generated and destroyed, not the Kosmos itself (ss. 7, 8).

Total generation, and total destruction without any renovation, of Kosmos might be possible, if there were an infinity of Kosmi, but cannot be possible with only one; for anterior to the moment of generation there existed the antecedent condition, which, never having been generated, could not be destroyed (s. 9).

There are some who think (with Plato in Timæus) that the non-generable may yet be destroyed, and that the generated may be indestructible. We have combated this opinion on physical grounds, respecting the Heaven specially. We shall now treat the subject upon universal reasonings (i.e., belonging to Logic or Metaphysics — πρὸς οὓς φυσικῶς μὲν περὶ τοῦ οὐράνου μόνον εἴρηται· καθόλου δὲ περὶ ἅπαντος σκεψαμένοις, ἔσται καὶ περὶ τούτου δῆλον — s. 10).

CH. 11. — In this reasoning, the first step is to point out that Generable and Non-Generable, Destructible or Indestructible, are words used in many different senses, which must be discriminated (πολλαχῶς λεγόμενα). If a man uses these words in an affirmative proposition without such discrimination, his affirmation is indeterminate; you cannot tell in which of their many different senses he intends to affirm. Non-Generable means: (1) That which now is, having previously not been, even though without either generation or change, as, to touch or to be moved; for, according to some persons, touching or being moved are not cases of generation; you cannot become touching, or become moved; you are moved, or you are not moved; you touch, or you do not touch (οὐ γὰρ εἶναι γίνεσθαί φασιν ἁπτόμενον, οὐδὲ κινούμενον. He means, I presume, that to touch, and to be moved, are instantaneous acts, though how they can be said to occur ἄνευ μεταβολῆς, I do not see.). It means: (2) That which, though capable of coming to pass or of having come to pass (ἐνδεχόμενον γίνεσθαι ἢ γενέσθαι), nevertheless is not; for this too is non-generable, since it might have come to be. Again, it means: (3) That which cannot by possibility sometimes exist, sometimes not exist. Impossible has two meanings: (1) That of which you cannot truly say that it might be generated (ὅτι γένοιτ’ ἄν); (2) That which cannot be generated easily, or quickly, or well (καλῶς). So also the Generable (τὸ γεννητόν) means: (1) That which, not existing previously, afterwards exists at one time and not at another, whether generated or not (he seems here to point to τὸ ἅπτεσθαι or τὸ κινεῖσθαι); (2) The possible, whether it be the strictly possible, or the easily possible; (3) That of which there is generation out of the nonexistent into existence, whether it now does actually exist, or may exist hereafter. The Destructible and Indestructible (φθαρτὸν καὶ ἄφθαρτον) have similar differences of meaning (ss. 1-6).

If we say that a man can raise a weight of 100 pounds, or march 100 stadia, we speak always with reference to a certain extreme, meaning to imply that he can also raise a weight of 50, 40, 30 pounds, and that he can also walk 50, 40, 30 stadia. If we say that he cannot raise a weight of 100 pounds, we mean to imply, Ã fortiori, that he cannot raise a weight of 110 pounds. In regard to sight and hearing, the case is opposite; he who can see a small object, can certainly see a large one; he who can hear a faint sound, can certainly hear a loud one. But he who can see a large object, is not necessarily able to see a small one; he who can hear a loud sound, is not necessarily able to hear a faint one. In sight and hearing, superior power is indicated by the less including the greater; in motion, by the greater including the less (ss. 7-8).

CH. 12. — If there are some things capable both of existence and of nonexistence, we must define on which falls the major portion of time; for, if we cannot in either case define the time, and can only say that it is greater than any assumed length of time and never less than any assumed length, — the same thing will be capable both of existence and of non-existence for an infinite time; which is an impossibility. We must take our departure from this principle: Impossibility is one thing, Falsehood another. Both the impossible and the false are, however, either conditional (as when it is said to be impossible that the triangle should have its three angles equal to two right angles, if such and such things are granted, and that the diameter should be commensurate with the periphery, if such and such positions were true), or absolute. But there are matters absolutely false, which are not absolutely impossible. When you are standing, I affirm that you are sitting: this is absolutely false, but not absolutely impossible. On the other hand, if I affirm that you are at the same time sitting and standing, or that the diameter is commensurable with the periphery, the proposition is not merely absolutely false, but absolutely impossible. An assumption simply false is not the same thing as an assumption absolutely impossible: from an impossible assumption there follow other impossibilities. The power of sitting or standing means that you can do either one at any given time — one at one time, the other at another; but not that you can do both at the same time. But, if any thing has throughout an infinite time the power of doing more things than one, it must have the power of doing more things than one at the same time; for this infinite time comprehends its whole existence. Accordingly, if any thing existing for an infinite time is nevertheless destructible, this means that it has the possibility not to exist. This being a possibility, let us imagine it realized: then the thing in question will both exist actually for an infinite time and yet not exist; which is a consequence not only false, but impossible, and thus proves the premiss assumed to be impossible (i.e., that a thing existing for an infinite time is nevertheless destructible). We thus see that what exists always is absolutely indestructible (ss. 1-3). It is also ungenerable; for, if generable, there will be a possibility that at some time or other it did not exist. That is generable, which may possibly have not existed at some anterior time, finite or infinite: so that, if τὸ ἀεὶ ὄν cannot possibly not exist, it cannot be generable. Now that which is always possible to exist, has, for its correlate negative (ἀπόφασις), that which is not always possible to exist; and that which is always possible not to exist, has, for its contrary, that which is not always possible not to exist. These two negatives must of necessity be true of the same subject: there must be something of which we may truly say — It has no possibility always to exist — It has no possibility always not to exist. This therefore is something intermediate between that which always exists, and that which always exists not, viz., That which may exist and may not exist (καὶ εἶναι μέσον τοῦ ἀεὶ ὄντος καὶ τοῦ ἀεὶ μὴ ὄντος, τὸ δυνάμενον εἶναι καὶ μὴ εἶναι); for both the negative predicates will find application, if it do not exist always. The possible to exist, and the possible not to exist, must therefore be the same thing — a mean between the two above-mentioned extremes (ss. 4, 5).

After a long metaphysical deduction, occupying from sections 6 to 17, Aristotle proceeds as follows.

We may also discern in the following manner that nothing which has been once generated, can continue indestructible; nothing which is ungenerable and which always existed heretofore, can ever be destroyed. For it is impossible that any thing which arises spontaneously (ἀπὸ τοῦ αὐτομάτου) can be either indestructible or ungenerable. The Spontaneous, and the Casual (τὸ ἀπὸ τῆς τύχης), are in antithesis to the always or the most frequently Ens or Fiens (παρὰ τὸ ἀεὶ καὶ τὸ ὡς ἐπὶ τὸ πολὺ ἢ ὂν ἢ γινόμενον — s. 18); but that which has existed for an infinite or a very long tine, must belong to this last category. Accordingly, such things must by nature sometimes exist, sometimes not exist. In them, both sides of the contradiction are alike true, owing to the matter of which they are composed: they exist, and they do not exist. But you cannot say with truth now that the thing exists last year; nor could you say last year that it exists now. Having once been non-existent, it cannot be eternal for future time; for it will still possess in future time the possibility of non-existence, yet not the power of non-existing at the moment when it does exist, nor with reference to last year and to past time; there being no power bearing upon past time, but only on present and future time. (Sections 21 and 22 are hardly intelligible to me.)

On physical grounds also it appears impossible that what is eternal in the past should be destroyed afterwards, or that what did not exist at some former time should afterwards be eternal. Those things which are destructible, are all of them generable and changeable (γεννητὰ καὶ ἀλλοιωτὰ πάντα). Those things which exist by nature, are changed by their opposites and by their component materials, and are destroyed by the same agencies (s. 23).

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