d _absolute_ infinity. The
Creator alone is eternal, immense, absolutely infinite."[218]

[Footnote 217: "The infinite is distinct from the finite, and
consequently from the multiplication of the finite by itself; that is,
from the _indefinite_. That which is not infinite, added as many times
as you please to itself, will not become infinite."--Cousin, "Hist, of
Philos.," vol. ii. p. 231.]

[Footnote 218: Saisset, "Modern Pantheism," vol. ii. pp. 127, 128.]

The introduction of the idea of "the mathematical infinite" into
metaphysical speculation, especially by Kant and Hamilton, with the
design, it would seem, of transforming the idea of infinity into a
sensuous conception, has generated innumerable paralogisms which
disfigure the pages of their philosophical writings. This procedure is
grounded in the common fallacy of supposing that _infinity_ and
_quantity_ are compatible attributes, and susceptible of mathematical
synthesis. This insidious and plausible error is ably refuted by a
writer in the "North American Review."[219] We can not do better than
transfer his argument to our pages in an abridged form.

[Footnote 219: "The Conditioned and the Unconditioned," No. CCV. art.
iii. (1864).]

Mathematics is conversant with quantities and quantitative relations.
The conception of quantity, therefore, if rigorously analyzed, will
indicate _a priori_ the natural and impassable boundaries of the
science; while a subsequent examination of the quantities called
infinite in the mathematical sense, and of the algebraic symbol of
infinity, will be seen to verify the results of this _a priori_
analysis.

Quantity is that attribute of things in virtue of which they are
susceptible of exact mensuration. The question _how much_, or _how many_
(_quantus_), implies the answer, _so much_, or _so many_ (_tantus_); but
the answer is possible only through reference to some standard of
magnitude or multitude arbitrarily assumed. Every object, therefore, of
which quantity, in the mathematical sense, is predicable, must be by its
essential nature _mensurable._ Now mensurability implies the existence
of actual, definite limits, since without them there could be no fixed
relation between the given object and the standard of measurement, and,
consequently, no possibility of exact mensuration. In fact, since
quantification is the object of all mathematical operations, mathematics
may be not inaptly defined as _the science of the determina