§ 1. Scientific Processes.

81. I. The Function of Definition. -- To define is to say what a thing is. -- Definition has a twofold function:

(1) The accessory function of clarifying concepts by resolving things that are to be known into their elements, so as to obtain a better light on them.

(2) The essential function of laying the foundations of science.

Just as not everything can be demonstrated, so not everything can be defined. Passing from analysis to analysis, we must sooner or later end with notions not susceptible of analysis. Such are the notions of unity and of number, the basis of arithmetic. These notions furnish the materials of the definitions, or first principles, on which the whole science rests, as a building rests on its foundations.^{1}

{1} "The principles of the sciences are indemonstrable definitions. The definition manifests what a thing is; thus mathematics lays down as principles what unity is, what an uneven number is, and so on." Aristotle, Posterior Analyt., II, 3.