Infinity

“ Whatever the ultimate truth may be, whether we admit the abstract, absolute and perfect infinity—the changeless, immovable infinity which has attained perfection and which knows everything, to which our reason tends—or whether we prefer that offered to us by the evidence, undeniable here below, of our senses—the infinity which seeks itself, which is still evolving and not yet established—it behoves us above all to foresee in it our fate, which, for that matter, must, in either case, end by absorption in that very infinity. ”

“ Though our idea of infinity arise from the contemplation of quantity, and the endless increase the mind is able to make in quantity, by the repeated additions of what portions thereof it pleases; yet I guess we cause great confusion in our thoughts, when we join infinity to any supposed idea of quantity the mind can be thought to have, and so discourse or reason about an infinite quantity, as an infinite space, or an infinite duration. ”

“ There is an infinity greater than our domestic infinities. It will soon strike you when tramping that the word infinite does not always mean the same: there are grades in infinity and measures of the immeasurable. ”

“ I have even noticed that they place the infinite rather below than above the dimensions known to them. They judge a distance to be immense rather by their feet than by their eyes; infinity is bounded for them, not so much by what they can see, but how far they can go. ”

“ For, when we call them infinite, we have no other idea of this infinity but what carries with it some reflection on, and imitation of, that number or extent of the acts or objects of God’s power, wisdom, and goodness, which can never be supposed so great, or so many, which these attributes will not always surmount and exceed, let us multiply them in our thoughts as far as we can, with all the infinity of endless number. ”

“ OUR FATE IN THOSE INFINITIES 1 The first infinity, the ideal infinity, corresponds most nearly with the requirements of our reason, which is not a reason for giving it the preference. It is impossible for us to foresee what we shall become in it, because it seems to exclude any becoming. It therefore but remains for us to address ourselves to the second, to that which we see and imagine in time and space. ”

“ 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. ”

“ The distinction may seem trivial, but it is based upon an important difference between the infinity of space and time on the one hand, and the infinity of God on the other. Neither philosophy nor theology can afford to disregard the difference. Quantitative Infinity is illimitation by quantity. Qualitative Infinity is illimitation by degree. ”

“ Movement is attributed to infinity only to explain that the infinite has no permanency. Should we believe that the infinite exists on high in one only and single place, or that it arises there, and descends here below? ”

“ We have explained the idea of infinity in general, by the indeterminate conceptions of being and the negation of limit. In order to assure ourselves that the explanation is well grounded, and that we have pointed out the essential marks of the conception, let us examine whether their application to determinate objects corresponds to what we have established in general. ”

“ If, on the other hand, each part feels the entire object, and if each magnitude is divisible to infinity, the result is that, for a single object, there will be an infinity of sensations in each part of the soul; and, so much the more, an infinity of images in the principle that directs us. ”

“ 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 POSITIVE THEORY OF INFINITY The positive theory of infinity, and the general theory of number to which it has given rise, are among the triumphs of scientific method in philosophy, and are therefore specially suitable for illustrating the logical-analytic character of that method. ”

“ If the idea of infinity is what we have defined it to be, we may apply it to all objects of sensible intuition or of the pure understanding, and we shall obtain the results which we ought to obtain, including the anomalies already referred to. ”

“ It may give us some notion of infinity to remember that at this sixth step, having long surpassed all bounds of intuitive conception, we make no approach to a limit. Nay, were we to make a hundred such steps, we should be as far away as ever from actual infinity. ”

“ In a word, we are in an infinity that seems to have almost the same 211character and the same habits as that power in the midst of which we breathe and which, upon our earth, we call nature or life.
What will be our fate in that infinity? We are asking ourselves no idle question, even if we should unite with it after losing all consciousness, all notion of the ego, even if we should exist there as no more than a little nameless substance—soul or matter, we cannot tell—suspended in the equally nameless abyss that replaces time and space. ”

“ If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all. ”

“ The infinity of God is not a quantitative, but a qualitative infinity. The miscalled eternity and infinity of nature is an indefinite extension and protension in time and space, and, as quantitative, must necessarily be limited and measurable, therefore finite. ”

“ So is made a sort of infinity and eternity, not that any thing of these is infinite and eternal, but these finite entities are infinitely multiplied. ”

“ Nor is there any necessity to assume, as is done by a modern school of metaphysicians, a peculiar fundamental law of the mind to account for the feeling of infinity inherent in our conceptions of space and time; that apparent infinity is sufficiently accounted for by simpler and universally acknowledged laws. ”

“ Because it is eternal, and in this ever has delight, so that it enjoys happiness without end or [Pg 162] measure; and because, as it is finite in itself, so it may be infinite in the object.
Cic. What difference is there between the infinity of the object and the infinity of the potentiality?
Tans. This is finitely infinite, and that infinitely infinite. But to return to ourselves. ”

“ For that which we foolishly call vastness is, rightly considered, not more wonderful, not more impressive, than that which we insolently call littleness, and the infinity of God is not mysterious, it is only unfathomable, not concealed, but incomprehensible: it is a clear infinity, the darkness of the pure unsearchable sea. ”

“ Perfection is always infinite. We are this infinite already, and we are trying to manifest that infinity. You and I, and all beings, are trying to manifest it. ”

“ Infinity in relation to spaces is called immensity, and in relation to times eternity; and yet, notwithstanding these relations, there is nothing of space in God's immensity, and nothing of time in His eternity. 5. From very many objects in the world enlightened reason may discover the infinity of God the Creator. 6. Every created thing is finite; and the infinite is in finite things as in its receptacles, and in man as in its images. ”

“ THE PROBLEM OF INFINITY CONSIDERED HISTORICALLY It will be remembered that, when we enumerated the grounds upon which the reality of the sensible world has been questioned, one of those mentioned was the supposed impossibility of infinity and continuity. ”

“ 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. ”

“ Other modes in which the power of infinity is felt.to prove which I have brought it forward, will be as readily conceded, namely, the inherent power of all representations of infinity over the human heart ”

“ 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. ”

“ The universe infinite.Thus the infinity of extent is evidenced, first, by the teaching of sense, in the constant change which our circle of vision undergoes [Pg 183] as we move from one place to another. There always appears to be an ultimate limit, but no sooner do we move than the limit is seen to have been only apparent; so, it may be inferred, could we transfer ourselves with our senses to any of the distant stars, we should still seem to ourselves to be in the centre of a closed sphere,—the very same appearance which is presented to us on this earth. ”

“ 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. ”

“ The tremendous disintegrating force slackens in exact relation to the time which passes, so that the smaller the morsel the less the relative loss of mass. Here, then, is the Indefinite Regress. In the world of fact as well as of ideas we are dealing with aspects of Infinity. ”

“ If the infinity of the sea may call out thus, perhaps when a man is growing old, calls come to him, too, from another infinity still darker and more deeply mysterious; and the more he is wearied by life the dearer are those calls to him. ”

“ And why should we think our idea of infinite space requires the real existence of matter to support it, when we find that we have as clear an idea of an infinite duration to come, as we have of infinite duration past ? ”

“ The last proceeding of reason is to recognise that there is an infinity of things which are beyond it. ”

“ If there may be two or four things infinite after their kind, because not limited by anything of the same nature, are many infinites inconceivable? Moreover, when infinity is thus understood—and it can be understood when relating to God in no other way—the difficulty raised by the latter part of Mr. ”

“ That morning Camille’s brow had worn the halo of thoughts born of these researches during a night-time of painful struggle. Calyste was ever before her like a celestial image. The beautiful youth, to whom she had secretly devoted herself, had become to her a guardian angel. Was it not he who led her into those loftier regions, where suffering ceased beneath the weight of incommensurable infinity? and now a certain air of triumph about Beatrix disturbed her. No woman gains an advantage over another without allowing it to be felt, however much she may deny having taken it. ”

“ And these two being put together, are that infinite duration we call Eternity : which, as we turn our view either way, forwards or backwards, appears infinite, because we still turn that way the infinite end of number, i.e. ”

“ So that in fact we go through an infinite, [space] in an infinite [time] and not in a finite [time] , and we touch infinite things with infinite things, not with finite things.” Philoponus, a sixth-century commentator (R.P. 136A, Exc. Paris Philop. in Arist. Phys., 803, 2. Vit.) , gives the following illustration: “For if a thing were moved the space of a cubit in one hour, since in every space there are an infinite number of points, the thing moved must needs touch all the points of the space: it will then go through an infinite collection in a finite time, which is impossible.” ”

“ That all things may be resolved into their minima's, and what is beyond them, is nothing, and that there is one maximum, or biggest, which is the world, and what is beyond that, is Infinite. Truly, Madam, I must ingeniously confess, I am not so high learned, as to penetrate into the true sense of these words; for he says, they are both divisible, and indivisible, and yet no atomes, which surpasses my Understanding; for there is no such thing, as biggest and smallest in Nature, or in the Infinite matter; for who can know how far this World goes, or what is beyond it? ”

“ Is there an infinite beyond us? Is that infinite there, inherent, permanent; necessarily substantial, since it is infinite; and because, if it lacked matter it would be bounded; necessarily intelligent, since it is infinite, and because, if it lacked intelligence, it would end there? Does this infinite awaken in us the idea of essence, while we can attribute to ourselves only the idea of existence? ”

“ The study of this intellect at work, not merely in shoemaking, in anatomy, or in astronomy, but in all fields, in the infinite, of its life in the absolute, is the means by which the art of logic is acquired. It is true that the infinite exists only in finite parts, and you cannot conceive of the infinite directly, you can perceive it only in its parts. And in perceiving them you must always remember that every part is an infinite piece of the infinite universe. ”

“ 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. ”