LINGUISTIC REVISION 97
possible. This method is of extreme usefulness in mathematics, and seemingly can be applied to life also.
If we compare the three systems of Aristotle, Euclid, and Newton, designated, A, E, N, respectively, in Fig. 1, with the non-aristotelian, non-euclidean and non-newtonian systems, designated, a very
important fact should be noticed; namely, that thetrilogy is more general than AEN.
This fact has far-reaching semantic and practical consequences and perhaps can be best explained by the aid of a diagram. We see that the trilogy includes the AEN
trilogy as a particular case, from which it follows that all those readers who are already re-educated to the new s.r, have less
difficulty in understanding the older AEN, simply because the older systems are only
particular cases of the new. But this is not so with those readers
who still have the old AEN s.r; they have to enlarge their limited point of view, grasp more than they knew before, and so will have serious semantic difficulties for a while, and, perhaps, become impatient or even angry. With the understanding of this larger generality of the new , perhaps a great deal of this semantic futile unpleasantness can be eliminated.
I know of no better example to illustrate this than to refer the reader to a little elementary book, Debate on the Theory of Relativity, published by the Open Court Co., Chicago.2 It is really interesting to watch how good-natured the einsteinists are as compared with the new-tonians. This book is suggested because it is elementary, extremely instructive, and very well worth reading. But the whole literature of euclideanism, non-euclideanism, newtonianism and non-newtonianism gives ample proof of the above statements. What kind of verbal flowers the aristotelians will throw to the non-aristotelians remains to be seen; but some verbal and semantic uproar can be expected.
It should be expected that this widening of horizons can only be attained, after all, with difficulty, because it requires an alteration of habitual reactions, from one-, two-, and three-valued to oo-valued new s.rusually not easy to achieve. But there seems little doubt that the future depends on it, and so we shall not be able to escape it indefinitely.
As we usually fail to make allowances for the 'emotional' aspects of 'intellectual' pursuits, let me once more point to the fact that even purely 'intellectual' achievements have their 'emotional' components and these