Why wouldst thou that God should in power, in act and in effect (which in him are identical) be determined as the limit of the convexity of a sphere, rather than that he should be as we may say the undetermined limit of the boundless? The limit I say, without limit, that I may differentiate the one infinity from the other. For He is the whole, comprehensive [26] and complete totality of the infinite, but the universe is the explicit though not the all-comprehensive totality (if indeed we may in any wise use the term totality where there is neither part nor boundary). Therefore the nature of the one doth comprehend boundaries; that of the other is bounded. And this is not the distinction between infinite and finite. The distinction is rather that the one is infinite, while the other doth limit according to the nature of the totality and of the whole being thereof. So that although it is entirely infinite, the infinity thereof is not completely comprehensive, for this would be repugnant to dimensional infinity.

The notion of infinity had long since been introduced into mathematics, but this infinity was what philosophers call a becoming; Mathematical infinity was only a quantity susceptible of growing beyond all limit; it was a variable quantity of which it could not be said that it had passed, but only that it would pass, all limits.

It is only by intuition that the infinite can be apprehended. But why is this? Why cannot the infinite be apprehended by concepts? To see this we must understand that the word "infinite," in the religious sense, has nothing at all to do with that sense of the word in which it is applied to space, time, and the number series. We may call this latter the mathematical infinite to distinguish it from the religious infinite. And it is the confusion between these two which misled us into the false trail of supposing that the infinity of God's mind refers to the amount of His knowledge and that the finitude of man's mind refers to his ignorance. The religious infinite, or in other words the infinity of God, means that than 'which there is no other. In this sense neither space nor time could be infinite, since space is an "other" to time, and time is an "other" to space.

Infinity, in its first form (the improper-infinite) presents itself as a variable finite [veranderliches Endliches]; in the other form (which I call the proper infinite [Eigentlich-unendliche]) it appears as a thoroughly determinate [bestimmtes] infinite.

And what does infinity mean to you? Are you not infinity and yourself?

A great deal of misunderstanding is avoided if it be remembered that the terms infinity, infinite, zero, infinitesimal must be interpreted in connexion with their context, and admit a variety of meanings according to the way in which they are defined.

The field of the finite is all that we can see, hear, touch, remember, and describe. This field is basically that which is manifest, or tangible. The essential quality of the infinite, by contrast, is its subtlety, its intangibility. This quality is conveyed in the word spirit, whose root meaning is "wind, or breath." This suggests an invisible but pervasive energy, to which the manifest world of the finite responds. This energy, or spirit, infuses all living beings, and without it any organism must fall apart into its constituent elements. That which is truly alive in the living being is this energy of spirit, and this is never born and never dies.

[B]ecause that which is finite is always bounded with reference to something... it is necessary that there should be no end... [N]umber also appears to be infinite, and mathematical magnitudes, and that which is beyond the heavens. And since that which is beyond is infinite, body also appears to be infinite, and it would seem that there are infinite worlds; for why is there rather void here than there? ...If also there is a vacuum, and an infinite place, it is necessary that there should be an infinite body: for in things which have a perpetual subsistence, capacity differs nothing from being. The speculation of the infinite is, however, attended with doubt: for many impossibilities happen both to those who do not admit that it has a subsistence, and to those who do. ...It is ...especially the province of a natural philosopher to consider if there be a sensible infinite magnitude.

This feature is reminiscent in my opinion, of certain features of some paintings, where each part reflects other parts and even the whole, with regard to colour, form, composition and other elements which go to make up the picture.

The above idea of the infinite shows already the breakdown of the notion that the world can be divided into separately existing parts. For already, even in this very simple view, an essential aspect of what each part is that it reflects the other parts.

The further extension of the idea of infinity to time leads to an even more radical change. Here, what is suggested is to reverse the usual idea of first imagining time and then saying that things exist and move in time. Rather, we begin with existence and process, and say that time is the order in this process. Thus we define each time concretely as the 'time when' such and such existed, or changed, and each position as the 'place where' it was etc. to carry such a view consistently, we should begin with the concept of totality, which is infinite and eternal. This includes all that there is, was and will be. If we knew this, we would all know reality. We would all know every concrete existent, every law(relationship) and the limits of every law. Of course, we can only select out certain aspects of this totality. Each science reflects some aspect, the arts another, the poet another and so on...

"Is there an infinite outside of us? Is this infinite, one, immanent, permanent; necessarily substantial, since it is infinite, and because, if matter were lacking in it, it would in that respect be limited; necessarily intelligent, because it is infinite, and since if it lacked intelligence it would be to that extent, finite? Does this finite awaken in us the idea of essence, while we are able to attribute to ourselves the idea of existence only? In other words, it is not the absolute of which we are the relative? At the same time, while there is an infinite outside of us, is there not an infinite within us? These two infinities, do they not rest superimposed on one another? Does the second infinite not underlie the first, so to speak? It is not the mirror, the reflection, the echo of the first, an abyss concentric with another abyss? Is this second infinite intelligent, also? Does it think? Does it love? Does it will? If the two infinities are intelligent, each one of them has a principle of will, and there is a "me" in the infinite above, as there is a "me" in the infinite below. The "me" below is the soul; the "me" above is God."

i manifestly understand that there is more reality in infinite than in finite substance, and that therefore the perception of the infinite in me must be in some way prior to that of the finite: the perception of god, in other words, prior to that of myself. for how could i possibly understand that i doubt, and that i desire, that is, that there is something lacking in me, and that i am not completely perfect, if there were no idea in me of a more perfect being, by comparison with which i could recognize my own shortcomings?

So far from holding God to be finite, I hold, and in the book clearly teach, that all minds are infinite (in the true qualitative sense of the word), and God preeminently so. (See my pp. 330 seq., 363, and 373). Eternity, self-existence, self-activity, freedom, and infinity are to me all interchangeable terms, and are so treated wherever they turn up in the course of the book. My reviewer falls into a non sequitur when he concludes that I make God finite because I make him one of a community of spirits, each absolutely real; not God's finitude, but his definiteness, is what follows from that. This confusion of the definite with the finite is very common, and is the explanation of two tendencies in sceptical thinking — the tendency to deny the personality of God, whose infinity is supposed to mean his utter indefiniteness, and the tendency, in recoil from the former, to assert God's finitude in order to save his personality, which of course must be definite. But the true infinite, as distinguished from the pseudo-infinite, the infinite of quality in contrast to the infinite of quantity, is entirely definite; more definite, indeed, than any finite can be.

The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.

Since the science of nature is conversant with magnitudes, motion, and time, each of which must necessarily be either infinite or finite...[we] should speculate the infinite, and consider whether it is or not; and if it is what it is. ...[A]ll those who appear to have touched on a philosophy of this kind... consider it as a certain principle of beings. Some, indeed, as the Pythagoreans and Plato, consider it, per se, not as being an accident to any thing else, but as having an essential subsistence... the Pythagoreans... consider the infinite as subsisting in sensibles; for they do not make number to be separate; and they assert that what is beyond the heavens is infinite; but Plato says that beyond the heavens there is not any body, nor ideas, because these are no where: he affirms, however, that the infinite is both in sensibles, and in ideas. ...Plato establishes two infinities, viz. the great and the small.