absolute contradiction, is not even cogitable as an hypothesis.[220] "The word _infinite_, therefore, in mathematical usage, as applied to _process_ and to _quantity_, has a two-fold signification. An infinite process is one which we can continue _as long as we please_, but which exists solely in our continuance of it.[221] An infinite quantity is one which exceeds our powers of mensuration or of conception, but which, nevertheless, has bounds and limits in itself.[222] Hence the possibility of relation among infinite quantities, and of different orders of infinities. If the words _infinite, infinity, infinitesimal_, should be banished from mathematical treatises and replaced by the words _indefinite, indefinity,_ and _indefinitesimal_, mathematics would suffer no loss, while, by removing a perpetual source of confusion, metaphysics would get great gain." [Footnote 220: By the application of these principles the writer in the "North American Review" completely dissolves the antinomies by which Hamilton seeks to sustain his "Philosophy of the Conditioned." See "North American Review," 1864, pp. 432-437.] [Footnote 221: De Morgan, "Diff. and Integ. Calc." p. 9.] [Footnote 222: Id., ib., p. 25.] The above must be regarded as a complete refutation of the position taken by _Hume_, to wit, that the idea of nature eternally existing in a state of order, without a cause other than the eternally inherent laws of nature, is no more self-contradictory than the idea of an eternally-existing and infinite mind, who originated this order--a God existing without a cause. The eternal and infinite Mind is indivisible and illimitable; nature, in its totality, as well as in its individual parts, has interior divisibility, and exterior limitability. The infinity of God is not a _quantitative_, but a _qualitative_ infinity. The miscalled eternity and infinity of nature is an _indefinite_ extension and protension in time and space, and, as _quantitative_, must necessarily be limited and measurable, therefore _finite_. The universe of sense-perception and sensuous imagination is a phenomenal universe, a genesis, a perpetual becoming, an entrance into existence, and an exit thence; the Theist is, therefore, perfectly justified in regarding it as disqualified for _self-existence_, and in passing behind it for the Supreme Entity that needs no cause. Phenomena demand causation, entities dispense with it. No one asks for a cause of the _space_ which contains the universe, or of the Eternity on the bosom of which it floats. Everywhere the line is necessarily drawn upon the same principle; that entities _may_ have self-existence, phenomena _must_ have a cause.[223] [Footnote 223: "Science, Nescience, and Faith," in Martineau's "Essays," p. 206.]