HOW A NUMBER MAY BE CALLED INFINITES
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; 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, 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. 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, “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.
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 outisde 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 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 Essence sence 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.