It stands for the possible attempt at an impossible conception. Man needed a term by which to point out the direction of this effort – the cloud behind which lay, forever invisible, the object of this attempt. A word, in fine, was demanded, by means of which one human being might put himself in relation at once with another human being and with a certain tendency of the human intellect. Out of this demand arose the word, “Infinity;” which is thus the representative but of the thought of a thought.
As regards that infinity now considered – the infinity of space – we often hear it said that “its idea is admitted by the mind – is acquiesced in – is entertained – on account of the greater difficulty which attends the conception of a limit.” But this is merely one of those phrases by which even profound thinkers, time out of mind, have occasionally taken pleasure in deceiving themselves. The quibble lies concealed in the word “difficulty.” “The mind,” we are told, “entertains the idea of limitless, through the greater difficulty which it finds in entertaining that of limited, space.” Now, were the proposition but fairly put, its absurdity would become transparent at once. Clearly, there is no mere difficulty in the case. The assertion intended, if presented according to its intention and without sophistry, would run thus: – “The mind admits the idea of limitless, through the greater impossibility of entertaining that of limited, space.”
It must be immediately seen that this is not a question of two statements between whose respective credibilities – or of two arguments between whose respective validities – the reason is called upon to decide: – it is a matter of two conceptions, directly conflicting, and each avowedly impossible, one of which the intellect is supposed to be capable of entertaining, on account of the greater impossibility of entertaining the other. The choice is not made between two difficulties; – it is merely fancied to be made between two impossibilities. Now of the former, there are degrees – but of the latter, none: – just as our impertinent letter-writer has already suggested. A task may be more or less difficult; but it is either possible or not possible: – there are no gradations. It might be more difficult to overthrow the Andes than an ant-hill; but it can be no more impossible to annihilate the matter of the one than the matter of the other. A man may jump ten feet with less difficulty than he can jump twenty, but the impossibility of his leaping to the moon is not a whit less than that of his leaping to the dog-star.
Since all this is undeniable: since the choice of the mind is to be made between impossibilities of conception: since one impossibility cannot be greater than another: and since, thus, one cannot be preferred to another: the philosophers who not only maintain, on the grounds mentioned, man’s idea of infinity but, on account of such supposititious idea, infinity itself– are plainly engaged in demonstrating one impossible thing to be possible by showing how it is that some one other thing – is impossible too. This, it will be said, is nonsense; and perhaps it is: – indeed I think it very capital nonsense – but forego all claim to it as nonsense of mine.
The readiest mode, however, of displaying the fallacy of the philosophical argument on this question, is by simply adverting to a fact respecting it which has been hitherto quite overlooked – the fact that the argument alluded to both proves and disproves its own proposition. “The mind is impelled,” say the theologians and others, “to admit a First Cause, by the superior difficulty it experiences in conceiving cause beyond cause without end.” The quibble, as before, lies in the word “difficulty” – but here what is it employed to sustain? A First Cause. And what is a First Cause? An ultimate termination of causes. And what is an ultimate termination of causes? Finity – the Finite. Thus the one quibble, in two processes, by God knows how many philosophers, is made to support now Finity and now Infinity – could it not be brought to support something besides? As for the quibblers —they, at least, are insupportable. But – to dismiss them: – what they prove in the one case is the identical nothing which they demonstrate in the other.
Of course, no one will suppose that I here contend for the absolute impossibility of that which we attempt to convey in the word “Infinity.” My purpose is but to show the folly of endeavoring to prove Infinity itself or even our conception of it, by any such blundering ratiocination as that which is ordinarily employed.
Nevertheless, as an individual, I may be permitted to say that I cannot conceive Infinity, and am convinced that no human being can. A mind not thoroughly self-conscious – not accustomed to the introspective analysis of its own operations – will, it is true, often deceive itself by supposing that it has entertained the conception of which we speak. In the effort to entertain it, we proceed step beyond step – we fancy point still beyond point; and so long as we continue the effort, it may be said, in fact, that we are tending to the formation of the idea designed; while the strength of the impression that we actually form or have formed it, is in the ratio of the period during which we keep up the mental endeavor. But it is in the act of discontinuing the endeavor – of fulfilling (as we think) the idea – of putting the finishing stroke (as we suppose) to the conception – that we overthrow at once the whole fabric of our fancy by resting upon some one ultimate and therefore definite point. This fact, however, we fail to perceive, on account of the absolute coincidence, in time, between the settling down upon the ultimate point and the act of cessation in thinking. – In attempting, on the other hand, to frame the idea of a limited space, we merely converse the processes which involve the impossibility.
We believe in a God. We may or may not believe in finite or in infinite space; but our belief, in such cases, is more properly designated as faith, and is a matter quite distinct from that belief proper – from that intellectual belief – which presupposes the mental conception.
The fact is, that, upon the enunciation of any one of that class of terms to which “Infinity” belongs – the class representing thoughts of thought– he who has a right to say that he thinks at all, feels himself called upon, not to entertain a conception, but simply to direct his mental vision toward some given point, in the intellectual firmament, where lies a nebula never to be resolved. To solve it, indeed, he makes no effort; for with a rapid instinct he comprehends, not only the impossibility, but, as regards all human purposes, the inessentiality, of its solution. He perceives that the Deity has not designed it to be solved. He sees, at once, that it lies out of the brain of man, and even how, if not exactly why, it lies out of it. There are people, I am aware, who, busying themselves in attempts at the unattainable, acquire very easily, by dint of the jargon they emit, among those thinkers-that-they-think with whom darkness and depth are synonymous, a kind of cuttle-fish reputation for profundity; but the finest quality of Thought is its self-cognizance; and, with some little equivocation, it may be said that no fog of the mind can well be greater than that which, extending to the very boundaries of the mental domain, shuts out even these boundaries themselves from comprehension.
It will now be understood that, in using the phrase, “Infinity of Space,” I make no call upon the reader to entertain the impossible conception of an absolute infinity. I refer simply to the “utmost conceivable expanse” of space – a shadowy and fluctuating domain, now shrinking, now swelling, in accordance with the vacillating energies of the imagination.
Hitherto, the Universe of stars has always been considered as coincident with the Universe proper, as I have defined it in the commencement of this Discourse. It has been always either directly or indirectly assumed – at least since the dawn of intelligible Astronomy – that, were it possible for us to attain any given point in space, we should still find, on all sides of us, an interminable succession of stars. This was the untenable idea of Pascal when making perhaps the most successful attempt ever made, at periphrasing the conception for which we struggle in the word “Universe.” “It is a sphere,” he says, “of which the centre is everywhere, the circumference, nowhere.” But although this intended definition is, in fact, no definition of the Universe of stars, we may accept it, with some mental reservation, as a definition (rigorous enough for all practical purposes) of the Universe proper– that is to say, of the Universe of space. This latter, then, let