Note P — PREFACE

See Discussions, p. 29. Of course by this is not meant that no duration can be conceived except in a duration equally long—that a thousand years, e.g., can only be conceived in a thousand years. A thousand years may be conceived as one unit: infinity cannot; for an unit is something complete, and therefore limited. What is meant is, that any period of time, however long, is conceived as capable of further increase, and therefore as not infinite. An infinite duration can have no time before or after it; and thus cannot resemble any portion of finite time, however 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.”