The aim of the analysis is to give us just conceptions, correct definitions, and true propositions. The process is slow, progressive, and endless. The problems are infinitely many, and it is necessary to select. Fortunately the solution of a few leads automatically to the solution of many others. Some of the greatest and most far-reaching scientific discoveries have been nothing else than a few correct definitions, a few just concepts and a few true propositions. Such, for example, was the work of Euclid, Newton and Leibnitz—a few correct definitions, a few just concepts, a few true propositions; but these have been extended and multiplied, sometimes by men of creative genius, and often almost automatically by men of merely good sense and fair talent.
The matter of definition, I have said, is very important. I am not now speaking of _nominal_ definitions, which for convenience merely give names to known objects. I am speaking of such definitions of phenomena as result from correct analysis of the phenomena. Nominal definitions are mere conveniences and are neither true nor false; but analytic definitions are definitive _propositions_ and are true or else false. Let us dwell upon the matter a little more.
In the illustration of the definitions of lightning, there were three; the first was the most mistaken and its application brought the most harm; the second was less incorrect and the practical results less bad; the third under the present conditions of our knowledge, was the “true one” and it brought the maximum benefit. This lightning illustration suggests the important idea of _relative_ truth and _relative_ falsehood—the idea, that is, of degrees of truth and degrees of falsehood. A definition may be neither absolutely true nor absolutely false; but of two definitions of the same thing, one of them may be truer or falser than the other.
If, for illustration’s sake, we call the first “truth” _A_, (alpha 1), the second one _A_2 (alpha 2), the third one _A_3 (alpha 3), we may suppose that a genius appears who has the faculty to surpass all the other relative truths _A_1, _A_2, _A_3, ... _A_n and gives us an absolute or final truth, VALID IN INFINITY (_A_infinity) say a final definition, that lightning is so ... and so ..., a kind of energy which flows, let us say, through a glass tube filled with charcoal. Then of course this definition would immediately make obvious what use could be made of it. We could erect glass towers filled with charcoal and so secure an unlimited flow of available free energy and our whole life would be affected in an untold degree. This example explains the importance of correct definitions.