Part 3

15. (From the above discussion about the intelligibility of numbers) let us now return to what we said in the beginning. The universal (Being) is veritable Essence, Intelligence, and perfect living Organism; and at the same time contains also all the living organisms. Our universe, which also is an organism, by its unity imitates so far as it can the unity of the perfect living Organism. I say, to the extent of its capacity, because, by its nature, the sense-world has departed from the unity of the intelligible world; otherwise, it would not be the sense-world. Moreover, the universal living Organism must be the universal Number; for if it were not a perfect number, it would lack some number; and if it did not contain the total number of living organisms, it would not be the perfect living Organism. Number therefore exists before every living organism, and before the universal living Organism. Man and the other living organisms are in the intelligible world; so far as they are living organisms, and so far as the intelligible world is the universal living Organism; for man, even here below, is a part of the living Organism, so far as itself is a living organism, and as the living Organism is universal; the other living organisms are also in the living Organism, so far as each of them is a living organism.

THE INTELLIGIBLE AS POTENTIAL AND ACTUALIZED IN THE SOUL.

Likewise, Intelligence, as such, contains all the individual intelligences as its parts.[35] These, however, form a number. Consequently, the number which is in the Intelligence does not occupy the first degree. So far as the number is in Intelligence, it is equal to the quantity of the actualizations of Intelligence. Now, these actualizations are wisdom, justice, and the other virtues, science, and all the (ideas) whose possession characterizes it as veritable Intelligence. (If then science exist in the Intelligence) how does it happen that it is not there in some principle other than itself? In Intelligence the knower, the known, and science are one and the same thing; and with everything else within it. That is why every (entity) exists in the intelligible world in its highest degree. For instance, within it, Justice is no accident, though it be one in the soul, as such; for intelligible entities are in the soul (only in) potential condition (so long as she remains no more than soul); and they are actualized when the soul rises to Intelligence and dwells with it.[36]

NUMBER AS THE UNIVERSAL BOND OF THE UNIVERSE.

Besides Intelligence, and anterior thereto, exists Essence. It contains Number, with which it begets (beings); for it begets them by moving according to number, determining upon the numbers before giving hypostatic existence to the (beings), just as the unity (of essence) precedes its (existence), and interrelates it with the First (or, absolute Unity). Numbers interrelate nothing else to the First; it suffices for Essence to be interrelated with Him, because Essence, on becoming Number, attaches all (beings) to itself. Essence is divided not so far as it is a unity (for its unity is permanent); but having divided itself conformably to its nature in as many things as it decided on, it saw into how many things it had divided itself; and through this (process) it begat the number that exists within itself; for it divided itself by virtue of the potentialities of number, and it begat as many (beings) as number comported.

THE GENERATION OF EVERYTHING REGULATED BY NUMBER.

The first and veritable Number is therefore the source and principle[21] of hypostatic existence for beings. That is the reason that even here below, the classified both discrete and continuous quantity[38] and, with a different number, it is some other thing that is begotten, or nothing more can be begotten. Such are the primary Numbers, so far as they can be numbered. The numbers that subsist in other things play two parts. So far as they proceed from the First, they can be numbered; so far as they are below them, they measure other things, they serve to enumerate both numbers and things which can be enumerated. How indeed could you even say "ten" without the aid of numbers within yourself?

DIFFICULTIES CONNECTED WITH THESE INTELLIGIBLE NUMBERS.

16. The first objection might be, Where do you locate, or how do you classify these primary and veritable Numbers? All the philosophers (who follow Aristotle) classify numbers in the genus of quantity. It seems that we have above treated of quantity, and classified both discrete and continuous quantity[38] among other "beings." Here however we seem to say that these Numbers form part of the primary Essences, and add that there are, in addition, numbers that serve for enumerations. We are now asked how we make these statements agree, for they seem to give rise to several questions. Is the unity which is found among sense-beings a quantity? Or is unity a quantity when repeated, while, when considered alone and in itself, it is the principle of quantity, but not a quantity itself? Besides, if unity be the principle of quantity, does it share the nature of quantity, or has it a different nature? Here are a number of points we ought to expound. We shall answer these questions, and here is what we consider our starting-point.

UNITY CONTAINED IN SENSE-OBJECTS IS NOT UNITY IN ITSELF.

When, considering visible objects, by which we ought to begin, we combine one (being) with another, as for instance, a horse and a dog, or two men, and say that they form two; or, when considering a greater number of men we say they are ten, and form a group of ten, this number does not constitute being, nor an (accident) among sense-objects; it is purely and simply a quantity. Dividing this group of ten by unity, and making unity of its parts, you obtain and constitute the principle of quantity (unity) for a unity thus derived from a group of ten.

NUMERALS PREDICATED OF THE MAN IN HIMSELF ARE ESSENTIAL.

But when you say that the Man considered in himself is a number, as, for instance, a pair, because he is both animal and reasonable, we have here no more than a simple modality. For, while reasoning and enumerating we produce a quantity; but so far as there are here two things (animal and reasonable), and as each of them is one, as each completes the being of the man, and possesses unity; we are here using and proclaiming another kind of number, the essential Number. Here the pair is not posterior to things; it does not limit itself to expressing a quantity which is exterior to essence; it expresses what is in the very being of this essence, and contains its nature.

COLLECTIVE NOUNS USED AS PROOF OF INDEPENDENT EXISTENCE.

Indeed, it is not you who here below produce number when you by discursive reason range through things that exist by themselves, and which do not depend for their existence on your enumeration; for you add nothing to the being of a man by enumerating him with another. That is no unity, as in a "choric ballet." When you say, ten men, "ten" exists only in you who are enumerating. We could not assert that "ten" exists in the ten men you are enumerating, because these men are not co-ordinated so as to form a unity; it is you yourself who produce ten by enumerating this group of ten, and by making up a quantity. But when you say, a "choric ballet," an "army," there is something which exists outside of these objects, and within yourself.[39] How are we to understand that the number exists in you? The number which existed in you before you made the enumeration has another mode (of existence) (than the number that you produce by enumeration). As to the number which manifests itself in exterior objects and refers to the number within yourself, it constitutes an actualization of the essential numbers, or, is conformable to the essential Numbers; for, while enumerating you produce a number, and by this actualization you give hypostatic existence to quantity, as in walking you did to movement.

THE NUMBER WITHIN IS THE NUMBER CONSTITUTIVE OF OUR BEING.

In what sense does the number which is within us (before we enumerate) have a mode (of existence) other (than the one we produce in enumeration)? Because it is the number constitutive of our being, which, as Plato says,[40] participates in number and harmony, and is a number and harmony; for the soul is said to be neither a body nor an extension; she therefore is a number, since she is a being. The number of the body is a being of the same nature as the body; the number of the soul consists in the beings which are incorporeal like souls. Then, for the intelligible entities, if the animal itself be plurality, if it be a triad, the triad that exists in the animal is essential. As to the triad which subsists, not in the animal, but in essence, it is the principle of being. If you enumerate the animal and the beautiful, each of these two in itself is a unity; but (in enumerating them), you beget number in yourself, and you conceive a certain quantity, the pair. If (like the Pythagoreans) you say that virtue is a group of four, or tetrad, it is one so far as its parts (justice, prudence, courage, and temperance) contribute to the formation of a unity; you may add that this group of four, or tetrad, is a unity, so far as it is a kind of substrate; as to you, you connect this tetrad with the one that is inside of you.[41]

HOW A NUMBER MAY BE CALLED INFINITE.[42]

17. As the reasons here advanced would seem to imply that every number is limited, we may ask in which sense may a number be said to be infinite? This conclusion is right, for it is against the nature of number to be infinite. Why do people then often speak of a number as infinite? Is it in the same sense that one calls a line infinite? A line is said to be infinite, not that there really exists an infinite line of this kind, but to imply the conception of a line as great as possible, greater than any given line. Similarly with number. When we know which is the number (of certain objects), we can double it by thought, without, on that account, adding any other number to the first. How indeed would it be possible to add to exterior objects the conception of our imagination, a conception that exists in ourselves exclusively? We shall therefore say that, among intelligible entities, a line is infinite; otherwise, the intelligible line would be a simple quantative expression. If however the intelligible line be not this, it must be infinite in number; but we then understand the word "infinite" in a sense other than that of having no limits that could not be transcended. In what sense then is the word "infinite" here used? In the sense that the conception of a limit is not implied in the being of a line in itself.

INTELLIGIBLE LINE POSTERIOR TO NUMBER, AND EXISTS IN THE INTELLIGIBLE.

What then is the intelligible line, and where does it exist? It is posterior to number[43]; for unity appears in the line, since this starts from the unity (of the point), and because it has but one dimension (length); now the measure of dimension is not a quantative (entity). Where then does the intelligible Line exist? It exists only in the intelligence that defines it; or, if it be a thing, it is but something intellectual. In the intelligible world, in fact, everything is intellectual, and such as the thing itself is. It is in this same world, likewise, where is made the decision where and how the plane, the solid, and all other figures are to be disposed. For it is not we who create the figures by conceiving them. This is so because the figure of the world is anterior to us, and because the natural figures which are suitable to the productions of nature, are necessarily anterior to the bodies, and in the intelligible world exist in the state of primary figures, without determining limits, for these forms exist in no other subjects; they subsist by themselves, and have no need of extension, because the extension is the attribute of a subject.

THE INTELLIGIBLE SPHERICAL FIGURE THE PRIMITIVE ONE.

Everywhere, therefore, in essence, is a single (spherical) figure,[44] and each of these figures (which this single figure implicitly contained) has become distinct, either in, or before the animal. When I say that each figure has become distinct, I do not mean that it has become an extension, but that it has been assigned to some particular animal; thus, in the intelligible world, each body has been assigned its own characteristic figure, as, for instance, the pyramid to the fire.[45] Our world seeks to imitate this figure, although it cannot accomplish this, because of matter. There are other figures here below that are analogous to the intelligible figures.

FIGURES PRE-EXIST IN THE INTELLIGIBLE.

But are the figures in the living Organism as such, or, if it cannot be doubted that they are in the living Organism, do they anteriorly exist in the Intelligence? If the Organism contained Intelligence, the figures would be in the first degree in the Organism. But as it is the Intelligence that contains the Organism, they are in the first degree in Intelligence. Besides, as the souls are contained in the perfect living Organism, it is one reason more for the priority of the Intelligence. But Plato says,[46] "Intelligence sees the Ideas comprised within the perfect living Organism." Now, if it see the Ideas contained in the perfect living Organism, Intelligence must be posterior to the latter. By the words "it sees" it should be understood that the existence of the living Organism itself is realized in this vision. Indeed, the Intelligence which sees is not something different from the Organism which is seen; but (in Intelligence) all things form but one. Only, thought has a pure and simple sphere, while the Organism has an animated sphere.[47]

INFINITY IN NUMBER ARISES FROM POSSIBILITY OF INCREASING GREATEST IMAGINABLE PHYSICAL NUMBER.

18. Thus, in the intelligible world, every number is finite. But we can conceive of a number greater than any assigned number, and thus it is that our mind, while considering the numbers, produces the (notion of the) infinite. On the contrary, in the intelligible world, it is impossible to conceive a number greater than the Number conceived (by divine Intelligence); for on high Number exists eternally; no Number is lacking, or could ever lack, so that one could never add anything thereto.

AS UNMEASURED THE INTELLIGIBLE NUMBER MIGHT BE CALLED INFINITE.

Nevertheless, the intelligible Number might be called infinite in the sense that it is unmeasured. By what, indeed, could it be measured? The Number that exists on high is universal, simultaneous one and manifold, constituting a whole circumscribed by no limit (a whole that is infinite); it is what it is by itself. None of the intelligible beings, indeed, is circumscribed by any limit. What is really limited and measured is what is hindered from losing itself in the infinite, and demands measure. But all of the intelligible (beings) are measures; whence it results that they are all beautiful. So far as it is a living organism, the living Organism in itself is beautiful, possessing an excellent life, and lacking no kind of life; it does not have a life mingled with death, it contains nothing mortal nor perishable. The life of the living Organism in itself has no fault; it is the first Life, full of vigor and energy, a primary Light whose rays vivify both the souls that dwell on high, and those that descend here below. This Life knows why it lives; it knows its principle and its goal; for its principle is simultaneously its goal. Besides, universal Wisdom, the universal Intelligence, which is intimately united to the living Organism, which subsists in it and with it, still improves it; heightening its hues as it were by the splendor of its wisdom, and rendering its beauty more venerable. Even here below, a life full of wisdom is that which is most venerable and beautiful, though we can hardly catch a glimpse of such a life. On high, however, the vision of life is perfectly clear; the (favored initiate) receives from Life both capacity to behold and increased vitality; so that, thanks to a more energetic life, the beholder receives a clearer vision, and he becomes what he sees. Here below, our glance often rests on inanimate things, and even when it turns towards living beings, it first notices in them that which lacks life. Besides, the life which is hidden in them is already mingled with other things. On high, on the contrary, all the (beings) are alive, entirely alive, and their life is pure. If at the first aspect you should look on something as deprived of life, soon the life within it would burst out before your eyes.

ESSENCE ALONE POSSESSES SELF-EXISTENCE.

Contemplate therefore the Being that penetrates the intelligibles, and which communicates to them an immutable life; contemplate the Wisdom and Knowledge that resides within them, and you will not be able to keep from deriding this inferior nature to which the vulgar human beings attribute genuine "being." It is in this supreme "Being" that dwell life and intelligence, and that the essences subsist in eternity. There, nothing issues (from Essence), nothing changes or agitates it; for there is nothing outside of it that could reach it; if a single thing existed outside of ("being"), ("being") would be dependent on it. If anything opposed to (essence) existed, this thing would escape the action of ("being"); it would no longer owe its existence to ("being"), but would constitute a common principle anterior to it, and would be essence. Parmenides[48] therefore was right in saying that the Essence was one; that it was immutable, not because there was nothing else (that could modify it), but because it was essence. Alone, therefore, does Essence possess self-existence. How then could one, to Essence, refuse to attribute existence, or any of the things of which it is an actualization, and which it constitutes? So long as it exists, it gives them to itself; and since it exists always, these things therefore eternally subsist within it.

THE POWER AND BEAUTY OF ESSENCE IS TO ATTRACT ALL THINGS.

Such are the power and beauty of Essence that it (charms and) attracts all things, holding them as it were suspended, so that these are delighted to possess even a trace of its perfection, and seek nothing beyond, except the Good. For Essence is anterior to the Good in respect to us (when we climb up from here below to the intelligible world). The entire intelligible world aspires to the Life and Wisdom so as to possess existence; all the souls, all the intelligences likewise aspire to possess it; Essence alone is fully self-sufficient.

SECOND ENNEAD, BOOK EIGHT.

Of Sight; or of Why Distant Objects Seem Small.[49]

(OF PERSPECTIVE.)

VARIOUS THEORIES OF PERSPECTIVE.

1. What is the cause that when distant visible objects seem smaller, and that, though separated by a great space, they seem to be close to each other, while if close, we see them in their true size, and their true distance? The cause of objects seeming smaller at a distance might be that light needs to be focussed near the eye, and to be accommodated to the size of the pupils[50]; that the greater the distance of the matter of the visible object, the more does its form seem to separate from it during its transit to the eyes; and that, as there is a form of quantity as well as of quality, it is the reason (or, form) of the latter which alone reaches the eye. On the other hand, (Epicurus) thinks that we feel magnitude only by the passage and the successive introduction of its parts, one by one; and that, consequently, magnitude must be brought within our reach, and near us, for us to determine its quantity.

QUALITY IS MORE ESSENTIAL THAN QUANTITY.

(Do objects at a distance seem smaller) because we perceive magnitude only by accident, and because color is perceived first? In this case, when an object is near, we perceive its colored magnitude; when at a distance, we perceive first its color, not well enough distinguishing its parts to gather exact knowledge of its quantity, because its colors are less lively. Why should we be surprised at magnitudes being similar to sounds, which grow weaker as their form decreases in distinctness? As to sounds, indeed, it is the form that is sought by the sense of hearing, and here intensity is noticed only as an accident. But if hearing perceive magnitude only by accident, to what faculty shall we attribute the primitive perception of intensity in sound, just as primitive perception of magnitude in the visible object is referable to the sense of touch? Hearing perceives apparent magnitude by determining not the quantity but the intensity of sounds; this very intensity of sounds, however, is perceived only by accident (because it is its proper object). Likewise, taste does not by accident feel the intensity of a sweet savor. Speaking strictly, the magnitude of a sound is its extent. Now the intensity of a sound indicates its extent only by accident, and therefore in an inexact manner. Indeed a thing's intensity is identical with the thing itself. The multitude of a thing's parts is known only by the extent of space occupied by the object.

DIFFERENCES OF COLOR AID IN THE PERCEPTION OF MAGNITUDE.

It may be objected that a color cannot be less large, and that it can only be less vivid. However, there is a common characteristic in something smaller and less vivid; namely, that it is less than what it is its being to be. As to color, diminution implies weakness; as to size, smallness. Magnitude connected with color diminishes proportionally with it. This is evident in the perception of a varied object, as, for instance, in the perception of mountains covered with houses, forests, and many other objects; here the distinctness of detail affords a standard by which to judge of the whole. But when the view of the details does not impress itself on the eye, the latter no longer grasps the extent of the whole through measurement of the extent offered to its contemplation by the details. Even in the case where the objects are near and varied, if we include them all in one glance without distinguishing all their parts, the more parts our glance loses, the smaller do the objects seem. On the contrary, if we distinguish all their details, the more exactly do we measure them, and learn their real size. Magnitudes of uniform color deceive the eye because the latter can no longer measure their extent by its parts; and because, even if the eye attempt to do so, it loses itself, not knowing where to stop, for lack of difference between the parts.

DISAPPEARANCE OF THE FORM IMPLIES THAT OF THE SIZE.

The distant object seems to us close because our inability to distinguish the parts of the intervening space does not permit us to determine exactly its magnitude. When sight can no longer traverse the length of an interval by determining its quality, in respect to its form, neither can it any longer determine its quantity in respect to magnitude.

REFUTATION OF ARISTOTLE'S "VISUAL ANGLE" THEORY.