ADDITIONAL NOTES.

[a]Page 1.—“But others from opinion in conjunction with reason;”—which in the original is, τα δε και δοξῃ, μετα λογου. But Ocellus is not accurate in what he here asserts, as is evident from what Plato says in his Timæus. For the divine philosopher having, in the former part of this dialogue, proposed to consider “what that is which is always being, but is without generation, and what that is which is generated [or consists in becoming to be], but is never [really] being,” adds: “The former of these, indeed, is comprehended byintelligence in conjunction with reason, since it always subsists with invariable sameness; but the latter is perceivedby opinion in conjunction with irrational sense, since it is generated and corrupted, and never truly is.” Τι το ον μεν αει, γενεσιν δε ουκ εχον· και τι το γιγνομενον μεν, ον δε ουδεποτε· το μεν δη, νοησει μετα λογου περιληπτον, αει κατα ταυτα ον· το δ’αυ δοξῃ μετ’ αισθησεως αλογου, δοξαστον, γιγνομενον και απολλυμενον, οντως δε ουδεποτε ον. Plato, as is evident from what is said in the Introduction to this work, had seen this tract of Ocellus, and corrects him in what he here says, as he also did the opinions of other philosophers anterior to, or contemporary with him. For if Ocellus had spoken accurately, he should have said, “that he had learnt some things through clear arguments from nature herself, but others from opinion in conjunction with irrational sense.” For, as Proclus admirably demonstrates in his Commentary on the above passage from theTimæus of Plato, truly existing being is only to be apprehended by us through illuminations from an intellect superior to the human, in conjunction with the energy ofthe summit of our reasoning power; for such is the accurate meaning of λογος in this place. But opinion is a knowledge of sensibles conformable to reason, yet without being able to assign the cause of what it knows; and sense is an irrational knowledge of the objects to which it is passive, and the instrument of sense is passion only. See the first volume of my translation of the Commentaries of Proclus on the Timæus of Plato, p. 202, &c.

Ocellus adds, “that it is his intention [in this treatise On the Universe] to derive what isprobablefrom intellectual perception.” For in physiological discussions we must be satisfied with probability and an approximation to the truth. Hence, Proclus, in his Commentary on that part of the Timæus in which Plato says, “What essence is to generation, that truth is to faith,” admirably observes as follows: “The faith of which Plato now speaks is rational, but is mingled with irrational knowledge, as it employs sense and conjecture; hence, it is filled with much of the unstable. For receiving from sense or conjecture the ὁτι,or that a thing is, it thus explains causes. But these kinds of knowledge have much of the confused and unstable. Hence, Socrates, in the Phædo, reprehends sense in many respects, because we neither hear nor see anything accurately.

“How, therefore, can the knowledge which originates from sense possess the accurate and the irreprehensible? For the powers which use science alone, comprehend the whole of the thing known with accuracy; but those that energise with sense, are deceived, and deviate from accuracy, on account of sense, and because the object of knowledge is unstable. For, with respect to that which is material, whatcan any one say of it? since it is always changing and flowing, and is not naturally adapted to abide for a moment. But that which is celestial, in consequence of being remote from us, is not easily known, nor can it be apprehended by science, but we must be satisfied in the theory of it with an approximation to the truth, and with probability [instead of certainty]. For everything which is in place requires the being situated there, in order to a perfect knowledge of its nature. The intelligible, however, is not a thing of this kind, since it is not apprehended by us in place; for, wherever any one establishes his reasoning energy, there, truth being everywhere present, he comes into contact with it. But if it is possible to assert anything firm and stable about that which is celestial, this also is possible, so far as it participates of being, and so far as it can be apprehended by intelligence. For, if anything necessary can be collected concerning it, it is alone through geometrical demonstrations which are universal. But so far as it is sensible, it is difficult to be apprehended, and difficult to be surveyed.”—See the first volume of my translation of Proclus on the Timæus of Plato, p. 291.

In p. 293, he also observes, “that perfectly accurate arguments, and such as are truly scientific, are not to be expected in physical discussions, but such as are assimilated to them. It is besides this requisite to know, that as the world is mingled from physical powers, and an intellectual and divine essence; for “physical works, as the [Chaldean] Oracle says, co-subsist with the intellectual light of the father;” thus, also, the discussion of the world makes a commixture of faith and truth. For things which are assumed from sense participate largely of conjectural discussion; but things which commence from intelligibles, possess that which is irreprehensible, and cannot be confuted.” And,lastly, in p. 296, he adds, “that the want of accuracy in the theory of the images of being, arises from our imbecility; for, to the knowledge of them we require imagination, sense, and many other organs. But the Gods contractedly contain these in their unity and divine intellection; for, in sublunary natures, we are satisfied in apprehending that which, for the most part, takes place on account of the instability of their subject matter. But again, in celestial natures, we are filled with much of the conjectural, through employing sense and material instruments. On this account we must be satisfied with proximity in the apprehension, of them, since we dwell remotely at the bottom, as it is said, of the universe. This also is evident from those that are conversant with them, who collect the same things respecting them from different hypotheses; some things, indeed, through eccentrics, others through epicycles, and others through evolvents, [in all these] preserving the phænomena.”

Shuttleworth, in his Astronomy, has demonstrated that the celestial phænomena may be solved by the hypotheses of Ptolemy and Tycho Brahe, equally as well as by those of Copernicus. But astronomers of the present day, from not being skilled in the logic of Aristotle, are not aware that true conclusions may be deduced from false premises; and hence, because their theory solves the phænomena, they immediately conclude that it is true. Aristotle, in his Posterior Analytics, has incontrovertibly shown, that the things from which demonstrative science consists, must be necessarily true, the causes of, more known than, and prior to the conclusion. But where the premises of a syllogism are false, the conclusion is notscientifically, i. e.necessarily, true. Thus in the syllogism, Every stone is an animal;every man is a stone; therefore every man is an animal,—the conclusion is true, but notscientific.

Note to p. 14.—Ocellus is wrong in ascribing two powers only to each of the elements, instead of three, as is clearly shown by Proclus, in the following extract from his admirable Commentary on the Timæus of Plato. “There are some physiologists (says he) who ascribe one power to each of the elements; to fire indeed heat, to air frigidity, to water moisture, and to earth dryness; in so doing, entirely wandering from the truth. In the first place, because they subvert the world and order. For it is impossible for things to be co-adapted to each other, when they possess the most contrary powers, unless they have something in common. In the next place, they make the most contrary natures allied to each other, viz. the hot to the cold, and the moist to the dry[26]. It is necessary, however, to make things which are hostile more remote than things which are less foreign. For such is the nature of contraries. In the third place, therefore, the first two powers will have no sympathy whatever with the rest, but will be divulsed[27]from each other. For it is impossible to say what is common to humidity and frigidity. And in addition to all these things, as the elements are solids, they will not be conjoined to each other by any medium. It has however been shown that it is not possible for solids to be conjoined through one medium. Nor can they be conjoined without a medium. For this is alone the province of things that are perfectly without interval.

“But some others, as Ocellus, who was the precursor of Timæus, attribute two powers to each of the elements; tofire indeed heat and dryness; to air, heat and moisture; to water, moisture and coldness; and to earth, coldness and dryness. And these things are written by this man in his treatise On Nature. In what, therefore, do these err who thus speak? In the first place, indeed, wishing to discover the common powers in the elements, in order that they may preserve the co-arrangement of them with each other, they no more assign communion than separation to them, but equally honour their hostility and their harmony. What kind of world, therefore, will subsist from these; what order will there be of things which are without arrangement and most foreign, and of things which are most allied and co-arranged? For things which in an equal degree are hostile and peaceful, will in an equal mode dissolve and constitute communion. But this communion being similarly dissolved, and similarly implanted, the universe will no more exist than not exist. In the second place, they do not assign the greatest contrariety to the extremes, but to things most remote from the extremes; though we everywhere see, that of homogeneous natures, those which are most distant have the nature of contraries, and not those which are less distant. How likewise did nature arrange them, since they are most remote in their situation from each other? Was it not by perceiving their contrariety, and that the third was more allied than the last to the first? How, also, did she arrange the motions of them, since fire is most light and tends upward, but earth is most heavy and tends downward? But whence were the motions of them which are most contrary derived, if not from nature? If, therefore, nature distributed to them most contrary motions, it is evident that they are themselves most contrary. For as the motions of simple beings are simple, and those things are simple of which themotions are simple, thus also those things are most contrary of which the motions are most contrary. And this may occasion some one to wonder at Aristotle, who, in what he says about motion, places earth as most contrary to fire; but in what he says about powers, he makes the most remote of similar natures to be more friendly than those that are proximate, when they are moved with most contrary motions. For, as the elements have contrary places in their positions, as they have contrary motions in lations, as they have contrary powers, gravity and levity, through which motions subsist in their forms, thus also they have contrary passive qualities. Aristotle himself likewise manifests that earth is contrary to fire. For wishing to show that it is necessary there should be more bodies than one, he says: “Moreover, if earth exists, it is also necessary that fire should exist. For in things, one of the contraries of which naturally is, the other likewise has a natural subsistence.” So that neither was he able after any other manner to show that there are more elements than one, than by asserting that fire is contrary to earth.

“Further still, as the elements are solids, how can they be bound together through one medium? For this is impossible in solids, as we have before observed. Hence those who assert these things, neither speak mathematically nor physically, but unavoidably err in both these respects. For physical are derived from mathematical entities.Timæus therefore alone, or any other who rightly follows him, neither attributes one or two powers alone to the elements, but triple powers; to fire indeed tenuity of parts, acuteness, and facility of motion; to air, tenuity of parts, obtuseness, and facility of motion; to water, grossness of parts, obtuseness, and facility of motion; and to earth, grossness of parts, obtuseness, and difficulty of motion.But this is in order that each of the elements may have two powers, each[28]of which is common to the element placed next to it, and one power which is different, in the same manner as it was demonstrated in mathematical numbers and figures; this different power being assumed from one of the extremes; and also in order that earth, according to all the powers, may subsist oppositely to fire; and that the extremes may have two media, and the continued quantities two; the latter having solids for the media, but the former, common powers. For let fire indeed be attenuated in its parts, acute, and easily moved. For it has an attenuated essence, and is acute, as having a figure of this kind [i. e. a pyramidal figure], and on this account is incisive and fugitive[29], and permeates through all the other elements. It is also moved with facility[30], as being most near to the celestial bodies, and existing in them. For the celestial fire itself is moved with celerity, as is likewise sublunary fire, which is perpetually moved in conjunction with it, and according to one circle, and one impulse. Since, therefore, earth is contrary to fire, it has contrary powers, viz. grossness, obtuseness, and difficulty of motion, all which we see are present with it. But these being thus hostile, and being solids, are also similar solids. For their sides and their powers are analogous. For as the gross is to the attenuated, so is the obtuse to the acute, and that which is moved with difficulty, to that which is moved with facility. But those are similar solids of which the sides that constitute the bodies are analogous.For the sides are the powers of which bodies consist.Hence, as fire and earth are similar bodies, and similar solids, two analogousmedia fall between them; and each of the media will have two sides of the extremes situated next to it, and the remaining side from the other extreme. Hence, since fire has for its three physical sides the triple powers, tenuity, acuteness, and facility of motion, by taking away the middle power, acuteness, and introducing instead of it obtuseness, we shall produce air, which has two sides of fire, but one of earth, or two powers of fire, but one of earth; as it is fit that what is near should rather communicate with it, than what is separated in the third rank from it.

“Again, since earth has three physical powers, contrary to the powers of fire, viz. grossness of parts, obtuseness, and difficulty of motion; by taking away difficulty of motion, and introducing facility of motion, we shall produce water, which consists of gross parts, is obtuse, and is easily moved; and which has indeed two sides or powers common with earth, but receives one from fire. And thus these media will be spontaneously conjoined with each other; communicating indeed in twofold powers, but differing in similitude by one power; and the extremes will be bound together by two media. Each element also will thus be in a greater degree conjoined to, than separated from, the element which is near to it; and one world will be perfectly effected through all of them, and one harmonious order, through the predominance of analogy. Thus also, of the two cubes 8 and 27, the medium 12 being placed next to 8, will have two sides of this, but one side of 27. For 12 is produced by 2 × 2 × 3. But it is vice versâ with 18. For this is produced by 3 × 3 × 2. And the side of 27 is 3, in the same manner as 2 is the side of 8. The physical dogmas, therefore, of Plato, about the elements of the universe, accord with mathematical speculations.”

In the Introduction to my Translation of the Timæus of Plato, I have added the following numbers, for the purpose of representing this beautiful distribution of the elements, by Proclus, arithmetically.

Let the number 60 represent fire, and 480 earth; and the media between these, viz. 120 and 240, will correspond to air and water. For, as 60 : 120 :: 240 : 480. But 60 = 3 × 5 × 4, 120 = 3 × 10 × 4, 240 = 6 × 10 × 4, and 480 = 6 × 10 × 8. So that these numbers will correspond to the properties of the elements as follows:

Fire.3 × 5 × 4Subtle, acute, moveable.

Air.3 × 10 × 4 ::Subtle, blunt, moveable.

Water.6 × 10 × 4 :Dense, blunt, moveable.

Earth.6 × 10 × 8.Dense, blunt, immoveable.

“Hence,” Proclus adds, “these things being thus determined, let us physically adapt them to the words of Plato. We call a [physical] plane or superficies, therefore, that which has two powers only, but a [physical] solid that which has three powers. And we say, that if we fashion bodies from two powers, one medium would conjoin the elements to each other. But since, as we assert, bodies possess triple powers, they are bound together by two media. For there are two common powers of the adjacent media, and one power which is different. And the extremes themselves, if they consisted of two powers, would be conjoined through one medium. For let fire, if you will, be alone attenuated and easily moved; but earth, on the contrary, have alone grossness of parts and immobility. One medium, therefore, will be sufficient for these. For grossness of parts and facility of motion, andtenuity of parts and difficulty of motion, are all that is requisite to the colligation of both. Since, however, each of the elements is triple, the extremes require two media, and the things themselves that are adjacent are bound together through two powers. For solids, and these are things that have triple contrary powers, are never co-adapted by one medium.”

FOOTNOTES:[26]For το εναντιωτατα here, read τα εναντιωτατα, and for τῳ θερμον τῳ ψυχρῳ, read το θερμον, κ. τ. λ.[27]For απηρτημενα in this place, I read διῃρημενα.[28]For μιαν here, it is obviously necessary to read ἑκατεραν.[29]For ὑπατικον in this place, read ὑπακτικον.[30]Instead of ακινητον here, it is necessary to read ευκινητον.

[26]For το εναντιωτατα here, read τα εναντιωτατα, and for τῳ θερμον τῳ ψυχρῳ, read το θερμον, κ. τ. λ.

[27]For απηρτημενα in this place, I read διῃρημενα.

[28]For μιαν here, it is obviously necessary to read ἑκατεραν.

[29]For ὑπατικον in this place, read ὑπακτικον.

[30]Instead of ακινητον here, it is necessary to read ευκινητον.

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