that we have of the one or of the number derives from the objects themselves, is a notion as much "a posteriori" as those of "that,"[25] "something," "crowd," "festival," "army," or of "multitude"; for, just as the manifold is nothing without the multiple objects, nor a festival without the men gathered to celebrate the religious ceremony, thus "the One" is nothing without the one object, when we posit the one, conceiving it alone, having made an abstraction of everything else. The partisans of this opinion will cite many examples of the same kind, as the "right hand side," "the upper part," and their contraries. What reality indeed (to speak as they do), can the "right hand side" possess outside of a person who stands or sits here or there[26]? The case is similar with "the upper side," which refers to a certain part of the universe, and the "lower side" to another.[27] Our first answer to this argument is that we will allow that there is a certain kind of existence in the things themselves of which we have just spoken; but that this mode of existence is not identical in all things, considered either in respect to each other, or each in respect to the One which is in all. Further, we intend to refute one by one these arguments that have been opposed to us.
THE NOTION OF THE SUBJECT ONE DOES NOT COME FROM THE SUBJECT ITSELF.
13. To begin with, it is unreasonable to insist that the notion of the subject one comes to us from the subject itself (which is one), from the visible man, for instance, or from some other animal, or even some stone. Evidently the visible man and the One are things entirely different, which could not be identified[28]; otherwise, our judgment would not be able (as it is) to predicate unity of the non-man. Besides, as the judgment does not operate on emptiness for the right side, and other such things, seeing a difference of position when it tells us that an object is here, or there; likewise, it also sees something when it says that an object is one; for it does not experience there an affection that is vain, and it does not affirm unity without some foundation. It cannot be believed that the judgment says that an object is one because it sees that it is alone, and that there is no other; for, while saying that there is no other, the judgment implicitly asserts that the other is one. Further, the notions of "other" and "different" are notions posterior to that of unity; if the judgment did not rise to unity, it would not assert either the "other" nor the "different"; when it affirms that an object is alone, it says, "there is one only object"; and therefore predicates unity before "only." Besides, the judgment which affirms is itself a substantial (being) before affirming unity of some other (being); and the (being) of which it speaks is one likewise before the judgment either asserts or conceives anything about it. Thus (being) must be one or many; if it be many, the one is necessarily anterior, since, when the judgment asserts that plurality is present, it evidently asserts that there is more than one; likewise, when it says that an army is a multitude, it conceives of the soldiers as arranged in one single corps. By this last example, it is plain that the judgment (in saying one body), does not let the multitude remain multitude, and that it thus reveals the existence of unity; for, whether by giving to the multitude a unity which it does not possess, or by rapidly revealing unity in the arrangement (which makes the body of the multitude), the judgment reduces multitude to unity. It does not err here about unity, any more than when it says of a building formed by a multitude of stones that it is a unity; for, besides, a building is more unified than an army.[29] If, further, unity inhere in a still higher degree in that which is continuous, and in a degree still higher in what is not divisible,[30] evidently that occurs only because the unity has a real nature, and possesses existence; for there is no greater or less in that which does not exist.
UNITY, THOUGH BY PARTICIPATION EXISTING IN SENSE-OBJECTS, IS INTELLIGIBLE.
Just as we predicate being of every sense-thing, as well as of every intelligible thing, we predicate it in a higher degree of intelligible things, attributing a higher degree (of substantiality) to the (beings that are veritable than to sense-objects), and to sense-objects than to other genera (of physical objects); likewise, clearly seeing unity in sense-objects in a degree higher than in the intelligible (essences), we recognize the existence of unity in all its modes, and we refer them all to Unity in itself. Besides, just as "being and essence"[31] are nothing sensual, though sense-objects participate therein, so unity, though by participation it inhere in sense-objects, is not any the less an intelligible Unity. Judgment grasps it by an intellectual conception; by seeing one thing (which is sensual) it also conceives another which it does not see (because it is intelligible); it therefore knew this thing in advance; and if judgment knew it in advance, judgment was this thing, and was identical with that whose existence it asserted. When it says, "a certain" object, it asserts the unity, as, when it speaks of "certain" objects, it says that they are two or more. If then one cannot conceive of any object whatever without "one," "two," or some other number, it becomes possible to insist that the thing without which nothing can be asserted or conceived, does not at all exist. We cannot indeed deny existence to the thing without whose existence we could not assert or conceive anything. Now that which is everywhere necessary to speak and to conceive must be anterior to speech and conception, so as to contribute to their production. If, besides, this thing be necessary to the hypostatic existence of every essence--for there is no essence that lacks unity--it must be anterior to being, and being must be begotten by it. That is why we say "an essence" instead of first positing "essence," and "a" only thereafter, for there must be "one" in essence, to make "several" possible; but (the converse is not true; for) unity does not contain essence, unless unity itself produce it by applying itself to the begetting of it.
Likewise, the word "that" (when employed to designate an object) is not meaningless; for instead of naming the object, it proclaims its existence, its presence, its "being," or some other of its kinds of "essence." The word "that" does not therefore express something without reality, it does not proclaim an empty conception, but it designates an object as definitely as some proper name.
UNITY ONLY AN ACCIDENT IN SENSE-THINGS, BUT SOMETHING IN ITSELF IN THE INTELLIGIBLE.
14. As to those who consider unity as relative, they might be told that unity could not lose its proper nature merely as a result of the affection experienced by some other being without itself being affected. It cannot cease being one without experiencing the privation of unity by division into two or three. If, on being divided, a mass become double without being destroyed in respect to its being a mass, evidently, besides the subject, there existed unity; and the mass lost it because the unity was destroyed by the division. So this same thing which now is present, and now disappears, should be classified among essences wherever it be found; and we must recognize that, though it may be an accident of other objects, it nevertheless exists by itself, whether it manifest in sense-objects, or whether it be present in intelligent entities; it is only an accident in posterior (beings, namely, the sense-objects); but it exists in itself in the intelligible entities, especially in the first Essence, which is One primarily, and only secondarily essence.
TWO IS NOT AN ADDITION TO ONE, BUT A CHANGE (REFUTATION OF ARISTOTLE).
The objection that unity, without itself experiencing anything, by the mere addition of something else, is no longer one, but becomes double, is a mistake.[32] The one has not become two, and is not that which has been added to it, nor that to which something has been added. Each of them remains one, such as it was; but two can be asserted of their totality, and one of each of them separately. Two therefore, not any more than "pair," is by nature a relation. If the pair consisted in the union (of two objects), and if "being united" were identical with "to duplicate," in this case the union, as well as the pair, would constitute two. Now a "pair" appears likewise in a state contrary (to that of the reunion of two objects); for two may be produced by the division of a single object. Two, therefore, is neither reunion nor division, as it would have to be in order to constitute a relation.
OBJECTS PARTICIPATE IN NUMBERS JUST AS THEY PARTICIPATE IN ALL INTELLIGIBLE ENTITIES.
What then is the principal cause (by virtue of which objects participate in numbers)? A being is one by the presence of one; double, because of the presence of the pair; just as it is white because of the presence of whiteness; beautiful, because of the presence of beauty; and just by that of justice. If that be not admitted, we shall be reduced to asserting that whiteness, beauty and justice are nothing real, and that their only causes are simple relations; that justice consists in some particular relation with some particular being; that beauty has no foundation other than the affection that we feel; that the object which seems beautiful possesses nothing capable of exciting this affection either by nature, or by acquirement. When you see an object that is one, and that you call single, it is simultaneously great, beautiful, and susceptible of receiving a number of other qualifications. Now why should unity not inhere in the object as well as greatness and magnitude, sweetness and bitterness, and other qualities? We have no right to admit that quality, whatever it be, forms part of the number of beings, whilst quantity is excluded; nor to limit quantity to continuous quantity, while discrete quantity is excluded from the conception of quantity; and that so much the less as continuous quantity is measured by discrete quantity. Thus, just as an object is great because of the presence of magnitude, as it is one by the presence of unity; so is it double because of the presence of being a pair, and so forth.[33] THE VERITABLE NUMBERS ARE INTELLIGIBLE ENTITIES.
Should we be asked to describe the operation of the participation of objects in unity and in numbers, we shall answer that this question connects with the more general problem of the participation of objects in intelligible forms. Besides, we shall have to admit that the decad presents itself under different aspects, according as it is considered to exist either in discrete quantities, or in continuous quantities, or in the reduction of many great forces to unity, or, last, into the intelligible entities to which we are later raised. It is among them, indeed, that are found the veritable Numbers (spoken of by Plato,[10]) which, instead of being considered as discovered in other (beings), exist within themselves; such is the Decad-in-itself, which exists by itself, instead of simply being a decad[34] composed of some intelligible entities.
NUMBER EXISTS BEFORE EVERY ANIMAL, AND THE UNIVERSAL ANIMAL.
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.
2. Some[51] hold that distant objects seem to us lesser only because they are seen under a smaller visual angle. Elsewhere[52] we have shown that this is wrong; and here we shall limit ourselves to the following considerations. The assertion that a distant object seems less because it is perceived under a smaller visual angle supposes that the rest of the eye still sees something outside of this object, whether this be some other object, or something external, such as the air. But if we suppose that the eye sees nothing outside of this object, whether this object, as would a great mountain, occupy the whole extent of the glance, and permit nothing beyond it to be seen; or whether it even extend beyond the sweep of the glance on both sides, then this object