nfinity 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, _inf