The Infinite

“ The true idea of the Infinite is neither a negation nor a modification of any other idea. The Finite, on the contrary, is in reality the limitation or modification of the Infinite, nor is it possible, if we reason in good earnest, to conceive of the Finite in any other sense than as the shadow of the Infinite. ”

“ But the finite, as multiplied infinitely, 217 ages upon ages, spaces upon spaces, stars beyond stars, worlds beyond worlds, is a true expression of the Infinite Being. Does it follow, because the universe has no limits,--that it must therefore be eternal, immense, infinite as God himself? No; that is but a vain scruple, which springs from the imagination, and not from the reason. The imagination is always confounding what reason should ever distinguish, eternity and time, immensity and space, relative infinity and absolute infinity. The Creator alone is eternal, immense, absolutely infinite. ”

“ Can a stinted limited being imagine and invent the infinite, if there be no infinite at all? Our weak and short-sighted mind cannot of itself form that image, which, at this rate, should have no author. ”

“ Does this infinite awaken in us the idea of essence, while we can attribute to ourselves only the idea of existence? In other terms, is it not the absolute, of which we are only the relative?
At the same time that there is an infinite without us, is there not an infinite within us? Are not these two infinites (what an alarming plural!) superposed, the one upon the other? Is not this second infinite, so to speak, subjacent to the first? Is it not the latter’s mirror, reflection, echo, an abyss which is concentric with another abyss? Is this second infinity intelligent also? ”

“ During this Greek period the conception of Infinity took shape. The pre-Platonic notion, reproduced again later in the decline of Socratic theory by the Stoics, was that the Infinite was the aggregate of the Finite; the Platonic and Aristotelian theory, that, namely, of the most vigorous moment of Greek thought, was that the Infinite was more than the aggregate of the Finite; that it had a self-determined existence from which the Finite had been derived. Existence, as known to man, was treated as a compromise between the Finite and the Infinite. ”

“ But, apart from this need of thinking it, it exists, this ‘more than everything infinite,’ which has the power of presenting itself eternally; this ‘more,’ I say, exists in pure simplicity and invariability from the very beginning, and in all infinity it does not become more than this ‘more,’ nor does it become less. Nothing but its visibleness as more than the infinite—and in no other way can it become visible in its highest purity—creates the infinite and all that appears to appear in it. ”

“ Whence have we deduced the idea of the infinite, except from the principle that the finite supposes the infinite, that all finite and defective things, which we perceive by our senses and feel within us, are not sufficient for themselves, and suppose something infinite and perfect? ”

“ What is meant by a part of the Infinite? The Infinite is indivisible; there cannot be parts of the Infinite. The Absolute cannot be divided. What is meant therefore that all these sparks are from Him? ”

“ Thus, we see, that the idea of the infinite, is in the reach of the most common intellects, and expresses only what any person of ordinary understanding would say, even though he had never occupied himself with philosophical studies; that the idea of the infinite is in our understanding, as a constant type, to which all finite representations are unable to arrive. ”

“ If He, the Infinite one, who, veiled from thy sight, sits surrounded by the gleaming abysses, without bounds save such as Himself creates, were to lay bare to thy sight the immeasurability of infinity, and let Himself be seen of thee as he distributes the suns, the great spirits, the little human hearts, and our days, and a tear or two therein ”

“ When, in fact, people talk of the Infinite in Time and Space, they can point to one intelligible signification; as to the rest, this word is not a subject for scientific propositions, and the attempt at such can lead only to contradictions. The Infinite is a phrase most various in its purport: it is for the most part an emotional word, expressing human desire and aspiration; a word of poetry, imagination, and preaching, not a word to be discussed under science; no intellectual definition would exhibit its emotional force. ”

“ Powerful reasoner that you are, you do not need that I should prove to you that the Infinite must everywhere be like unto Itself, and that, necessarily, it is One. God alone is Infinite, for surely there cannot be two Infinities, two Ones. If, to make use of human terms, anything demonstrated to you here below seems to you infinite, be sure that within it you will find some one aspect of God. ”

“ Everything finite therefore is imperfect, every sensible world is imperfect, as good and evil, matter and form, light and darkness, joy and sadness concur in it, and all things everywhere are in alteration and movement; but all of them, in the infinite, are as in unity, truth, and goodness, and in this aspect the infinite is rightly called the universe.” [332] In the infinite, as we have learned from the Causa, all contraries are one. The universe is perfect, not because of its quantity, but because it contains all other things in it. ”

“ Therefore those who confound infinite knowledge of the Infinite, which appertains to the Infinite Being alone, with that subjectively finite knowledge of it which we all possess, display an unpardonable ignorance. This is our answer to those who object that Infinite, as one term, is unintelligible, and we see no necessity for classifying it with the impenetrable secrets with which science is confronted at every step. ”

“ The various series of causes and effects are partly contingent relatively to each other, and are partly themselves continued into the so-called Infinite, and thus contain in their content nothing but those situations and forms of existence of which each is finite in itself; and what ought to give stability to the connection of the series, the Infinite namely, is not only something above and beyond this world, but is a mere negative, the very meaning of which is relative merely, and is conditioned by what is to be negated by it, and is consequently for this very reason not negated. ”

“ But it means that, in even the most purely contingent-seeming soul, and in its apparently but Institutional and Historical assents and acts, there ever is, there can never fail to be, some, however, implicit, however slight, however intermittent, sense and experience of the Infinite, evidenced by at least some dissatisfaction with the Finite, except as this Finitude is an occasion for growth in, and a part-expression of, that Infinite, our true home. ”

“ At the outset of all investigation, we are forced to recognise that the only way we can approach conception of the Infinite is necessarily in the form of a negative, the negative applying to those things of which [Pg 108] we have cognisance; we carry our thought to the utmost limit possible with our present knowledge, and, when we have come to a standstill, we conceive the Infinite to be not that but something further on. ”

“ He is there. If the infinite had no person, person would be without limit; it would not be infinite; in other words, it would not exist. There is, then, an I. That I of the infinite is God.” ”

“ The examination of the idea of the infinite is of the highest importance, not only because we meet it in various sciences, the exact sciences among others, but because it is one of the principal characteristics by which we distinguish God from creatures. A finite God would be no God; an infinite creature would not be a creature. ”

“ For I have been hitherto apt to think that the great and inextricable difficulties which perpetually involve all discourses concerning infinity, – whether of space, duration, or divisibility, have been the certain marks of a defect in our ideas of infinity, and the disproportion the nature thereof has to the comprehension of our narrow capacities. For, whilst men talk and dispute of infinite space or duration, as if they had as complete and positive ideas of them as they have of the names they use for them, or as they have of a yard, or an hour, or any other determinate quantity ”

“ For, for our present purpose, the simple remark will suffice, that the power of infinity in itself, and the pursuit of the infinite, is properly natural to man, and a part of his very essence. All that is wrong in it, and the source of all its aberrations, is simply and entirely boundless excess. ”

“ The idea of the infinite does not consist in conceiving that another quantity may always be added to a given quantity, or that a perfection may be made more intense; this expresses only the possibility of a series of conceptions by which we endeavor to approach the absolute idea of the infinite. ”

“ The philosophy of the infinitesimal, as we have just seen, is mainly negative. People used to believe in it, and now they have found out their mistake. The philosophy of the infinite, on the other hand, is wholly positive. It was formerly supposed that infinite numbers, and the mathematical infinite generally, were self-contradictory. ”

“ Whatever may be the nature and perfection of our [Pg 270] idea of the infinite, it is certain that it involves something fixed, and common to all intelligences. We apply the idea to things of very different orders, and it is always understood in the same sense by all men. ”

“ That one Infinite is contained within another; I mean, the several sorts of Infinites, as Infinite in number, Infinite in duration; as also the Infinite degrees, motions, figures, sizes, compositions, divisions, &c. all which are contained in the Infinite body of Nature, which is the onely Infinite in quantity or substance, neither can the parts of Nature go beyond Infinite. ”

“ It is to be remedied not by giving up the idea of the Infinite but by ceasing to think of the Infinite as of a being endowed with a static perfection which the finite will merely reproduces, and definitely recognizing the forward effort of the finite as an essential element in Its self-expression. ”

“ From the sequential, time viewpoint, all reality has its origin in the infinite I AM, whose solitary existence in past infinite eternity must be a finite creature's premier philosophic postulate. The concept of the I AM connotes unqualified infinity, the undifferentiated reality of all that could ever be in all of an infinite eternity. ”

“ For you were pleased to mention, That you could not well apprehend, how it was possible, that many Infinites could be contained in one Infinite, since one Infinite takes up all Place Imaginary, leaving no room for any other; Also, if one Infinite should be contained in an other Infinite, that which contains, must of necessity be bigger then that which is contained, whereby the Nater of Infinite would be lost; as having no bigger nor less, but being of an Infinite quantity. ”

“ But it will be asked, May we not go on until at last we attain the possession of all knowledge? People do not realize what is meant by "the infinite," or they would not ask such questions. The infinite is that which is limitless and exhaustless. ”

“ To show in detail how all the evils we experience are subservient to the best conceivable scheme of the universe, would require that we should know the infinite design of God, that we should be able to picture the infinity of other possible worlds, and to institute a comparison between these infinite infinities. ”

“ Or, secondly, the infinite is not the finite, no longer in the sense of being more in quantity, but in the sense of being something else, which is different in quality. The infinite is not in the world of limited things; it exists in a sphere of its own. The mind (e.g.) is something beside the aggregate of its states. God is something beside the things of this world. This is the infinite believed in by abstract Duty. But here once more, against its will, infinite comes to mean merely finite. The infinite is a something over against, beside, and outside the finite ”

“ Thus on the subject of infinity it is impossible to avoid conclusions which at first sight appear paradoxical, and this is the reason why so many philosophers have supposed that there were inherent contradictions in the infinite. ”

“ We have reached the position that the finite as a whole and finite knowledge are incapable of grasping the Infinite in general, as well as the Infinite in the form it takes as absolute necessity, and also of comprehending the Infinite by the aid of the conceptions of contingency and finitude from which finite knowledge starts. ”

“ That the Infinite degrees of Infinite Matter are all Infinite: For, say you, the degrees of Matter cannot be Infinite, by reason there cannot be two Infinites, but one would obstruct the other. My answer is ”

“ What is positive, what negative, in our idea of infinite. The idea of infinite has, I confess, something of positive in all those things we apply to it. When we would think of infinite space or duration, we at first step usually make some very large idea, as perhaps of millions of ages, or miles, which possibly we double and multiply several times. All that we thus amass together in our thoughts is positive, and the assemblage of a great number of positive ideas of space or duration. ”

“ it became clear that to say, 'in infinite space and time everything develops, becomes more perfect and more complex, is differentiated', is to say nothing at all. These are all words with no meaning, for in the infinite there is neither complex nor simple, neither forward nor backward, nor better or worse. ”