prehend each idea separately in the abstract, but also
the manner in which they may possibly exist in
combination with each other.

"Something infinite," says Mr. Mill, "is a conception which, like
most of our complex ideas, contains a negative element, but which
contains positive elements also. Infinite space, for instance; is
there nothing positive in that? The negative part of this
conception is the absence of bounds. The positive are, the idea of
space, and of space greater than any finite space."--(P. 45.)

This definition of _infinite space_ is exactly that which Descartes
gives us of _indefinite extension_,--"Ita quia non possumus imaginari
extensionem tam magnam, quin intelligamus adhuc majorem esse posse,
dicemus magnitudinem rerum possibilium esse indefinitam."[AR] So too,
Cudworth,--"There appeareth no sufficient ground for this positive
infinity of space; we being certain of no more than this, that be the
world or any figurative body never so great, it is not impossible but that
it might be still greater and greater without end. Which _indefinite
increasableness_ of body and space seems to be mistaken for a _positive
infinity_ thereof."[AS] And Locke, a philosopher for whom Mr. Mill
will probably have more respect than for Descartes or Cudworth, writes
more plainly: "To have actually in the mind the idea of a space infinite,
is to suppose the mind already passed over, and actually to have a view
of all those repeated ideas of space, which an endless repetition can
never totally represent to it,--which carries in it a plain
contradiction."[AT] Mr. Mill thus unwittingly illustrates, in his own
person, the truth of Hamilton's remark, "If we dream of effecting this
[conceiving the infinite in time or space], we only deceive ourselves by
substituting the _indefinite_ for the infinite, than which no two notions
can be more opposed." In fact, Mr. Mill does not seem to be aware that
what the mathematician calls _infinite_, the metaphysician calls
_indefinite_, and that arguments drawn from the mathematical use of the
term _infinite_ are wholly irrelevant to the metaphysical. How, indeed,
could it be otherwise? Can any man suppose that, when the Divine
attributes are spoken of as infinite, it is meant that they are
indefinitely increasable?[AU]

[AR] _Principia_, i., 26.

[AS] _Intellectual System_, ed. Harrison, vol. iii., p. 131.

[AT] _Essay_, ii., 17, 7.

[AU] One of the a