Let us begin, then, at once, with that merest of words, “Infinity.” This, like “God,” “spirit,” and some other expressions of which the equivalents exist in all languages, is by no means the expression of an idea—but of an effort at one. 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.