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 wit 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 suppositious 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
