wever great. When we dream of conceiving
an infinite regress of time, says Sir W. Hamilton, "we
only deceive ourselves by substituting the _indefinite_
for the infinite, than which no two notions can be more
opposed." This caution has not been attended to by some
later critics. Thus, Dr. Whewell (_Philosophy of
Discovery_, p. 324) says: "The definition of an infinite
number is not that it contains all possible unities; but
this--that the progress of numeration, being begun
according to a certain law, goes on without limit." This
is precisely Descartes' definition, not of the
_infinite_, but of the _indefinite_. _Principia_, i. 26:
"Nos autem illa omnia, in quibus sub aliqua
consideratione nullum finem poterimus invenire, non
quidem affirmabimus esse infinita, sed ut indefinita
spectabimus." An indefinite time is that which is
capable of perpetual addition: an infinite time is one
so great as to admit of no addition. Surely "no two
notions can be more opposed."

The cardinal point, then, of Sir W. Hamilton's philosophy, expressly
announced as such by himself, is the absolute necessity, under any system
of philosophy whatever, of acknowledging the existence of a sphere of
belief beyond the limits of the sphere of thought. "The main scope of my
speculation,"[Q] he says, "is to show articulately that we _must
believe_, as actual, much that we are unable (positively) _to conceive_
as even possible." It is, of course, beyond the range of such a
speculation, by itself, to enter on an examination of the positive
evidences in support of one form of belief rather than another. So far as
it aims only at exhibiting an universal law of the human mind, it is of
course compatible with all special forms of belief which do not
contradict that law; and none, whatever their pretensions, can really
contradict it. Hence the service which such a philosophy can render to
the Christian religion must necessarily, from the nature of the case, be
of an indirect and negative character. It prepares the way for a fair
examination of the proper evidences of Christianity, by showing that
there is no ground for any _a priori_ prejudice against revelation, as
appealing, for the acceptance of its highest truths, to faith rather than
to reason; for that this appeal is common to all religions and to all
philosophies, and cannot th