ries is forever limited by them. Kant himself
admits that it _can never be completed_, and is only potentially
infinite; actually, therefore, by his own admission, it is finite. But a
last term implies a first, as absolutely as one end of a string implies
the other; the only possibility of an unconditioned lies in Kant's first
alternative, and if, as he maintains Reason must demand it, she can not
hesitate in her decisions. That _number is a limitation_ is no new
truth, and that every series involves number is self-evident; and it is
surprising that so radical a criticism on Kant's system should never
have suggested itself to his opponents. Even the so-called _moments_ of
time can not be regarded as constituting a real series, for a series can
not be real except through its divisibility into members whereas time is
indivisible, and its partition into moments is a conventional fiction.
Exterior limitability and interior divisibility result equally from the
possibility of discontinuity. Exterior illimitability and interior
indivisibility are simple phases of the same attribute of _necessary
continuity_ contemplated under different aspects. From this principle
flows another upon which it is impossible to lay too much stress,
namely; _illimitability and indivisibility, infinity and unity,
reciprocally necessitate each other_. Hence the Quantitative Infinites
must be also Units, and the division of space and time, implying
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