ing only, viz., that of mathematical continuity. In this sense continuity is essentially a property of ordered series. The new realists suppose continuity of this kind to be typical of experience. Mr. Russell,[1] for example, asserts that the particular degree of continuity known as 'compactness' is sufficient to describe the continuity of experience. A compact series is one in which to any term there is no next term, that is one in which, if any two terms be selected, it is possible to find other terms between them. The number of terms of such a series is, of course, infinite. The view we are considering regards the objective side of experience as a compact series of sense-data.
The correctness or falsity of the view just stated hinges entirely upon the fact that a series consists of terms, and that however many terms there are, and of whatever magnitude they may be, they are discrete, each existing per se. Hence, if sense-data form a compact series, we must consider them to consist in an infinite number of separate members, each of indefinitely short duration. So much seems to be admitted by Mr. Russell. Yet again the point is overlooked that sense-data, though absolute and objective for the individual to whom they are presented, are relative and subjective from a universal standpoint. The separation of subject and object is still artificial. All that the theory under consideration has any right to assert is that the introduction of the notion of compact series is one of the most adequate ways of dealing with the unique continuity of experience considered objectively in abstraction. No doubt results based on analysis on these lines will be sensibly accurate when tested by experience; but this simply follows from the fact that the original constructions of compact series are sensibly accurate to the same order. It cannot be true, however, that experience is really composed in part of such a series of sense-data, for, as we have seen, the members of a compact series, in spite of their infinitude, are each a definite separate entity. The question might be raised as to whether such a series could have anything but an abstract existence. For example, we may write down any member of the compact series of rational fractions, but it is difficult to see how
- ↑ Op. cit., Lect. V.
