PREFACE. 465 
cannot be altogether insignificant, neither can it degenerate into a toy, fit only for the 
amusement of idle curiosity. 
It may be said, indeed, that a mere notation can lead to no discoveries in Mental 
Science. ‘This is in one sense true, but may not the same be said with equal, nay, with 
greater propriety, of the different notations of Mathematics, Logic, and Chemistry? The 
arbitrary signs of Algebra and the Calculus, do not contain in themselves the elements 
of any new truth, but they furnish a concise and precise language, by means of which, the 
results of a long process of investigation may be briefly expressed, and employed as the 
basis for new researches. A system of symbols that should render similar aid to Ethical, 
Social, and Intellectual Science, could hardly fail to yield important advantages. 
A symbol in any case is not to be regarded as a box or wrapper in which some valu- 
able but unknown truth is hidden, but it may be properly employed to represent, in the 
simplest possible form, an analysis that has already been made, and to keep the pure, un- 
mixed results of that analysis so steadily in view, that they may be most conveniently 
used to facilitate farther investigation. Thus, although the Intellectual Symbols can 
convey very little meaning, until they are interpreted in familiar language, our operations 
with them may possibly lead us to reflect upon relations that had never before been ob- 
served, and by the study of these relations, new discoveries may be made. 
If I am right in supposing the eternal necessity of an entity of the same order as Space 
and Time, for which I have proposed the name of Position,* the steps which led to its dis- 
covery, will well illustrate my meaning. Many have supposed “formal conditions of ex- 
perience,” or “logical antecedents of phenomena,” different from Space and Time, but in 
every instance that has fallen under my notice, those conditions or antecedents have had 
either a subjective coloring, or a concrete reference. Take, for example, the ideas of per- 
sonality, substance, cause, finitude, and figure. If there had never been manifestation, 
' it is difficult to conceive either their necessary or their possible existence. But even if we 
suppose manifestation to be annihilated, Space, Time, and Position would still remain. 
Since most, if not all our ideas of the Objective are derived from the material world, 
and our ideas of the Subjective from our own activity and its results, the necessary involu- 
tion of space in the former, and of time in the latter, must have been evident to the ear- 
liest philosophical observers. But the necessity of a third form could never appear, until 
either the necessary triplicity of relativity, or the essential difference of relation from both 
the subjective and the objective, was perceived. The study of relativity led me to seek for 
the third formal condition, under which alone its triplicity was possible. Of my success 
in defining that condition by the sphere that I have assigned to Position, I must leave 
others to judge. 
* See Chapter XII. 
