PRINCIPUM, in general, is used for the cause, source, or origin of anything.

in human nature. See DISPOSITION.

in science, is a truth, admitted without proof, from which other truths are inferred by a chain of reasoning. Principles are of two kinds, primary and general; and to the last the name of axiom is usually given on account of their importance and dignity. An axiom or general principle, when the terms in which it is expressed are understood, must be a self-evident truth; but from its very nature it cannot be a final truth. Our first truths are all particular. A child knows that two particular lines, each an inch long, are equal to one another, before he has formed any general notions of length and equality. "Things equal to one another, and the same thing are equal to one another," is the first of Euclid's axioms; and an axiom it undoubtedly is, but to no man has it been a final truth. It is, if we may use the expression, a genus or class of truths, comprehending under it numberless individuals. Were a full-grown man introduced into the world, without a single idea in his mind, as we may suppose Adam to have been, he would instantly perceive, upon laying together three pieces of wood each a foot long, that they were all equal in length; and if he were to cut another to the same length with any one of them, he would find upon trial that it was of the same length with them all. After a few simple experiments of this kind, he would, by a law of human thought, infer, that all things equal in length or in any other dimension, to any one thing, are in that dimension equal to one another.

It was not therefore with such weakness as some have imagined, that Hobbes affirmed those propositions commonly called axioms, not to be primary but secondary principles. A primary principle deserves not the name of an axiom, as it is only a particular truth including in it no other truth. There is not one of Euclid's axioms which has not been the result of induction, though we remember not the time at which the induction was made. That the whole is greater than any of its parts is a general truth which no man of common sense can controvert; but every one discovered that truth by observing that his body was larger than his head, his foot, or his hand; that a mountain is larger than a mole-hill in the middle of it; and that a piece of timber measuring what is called a yard is longer than any one of the divisions marked upon it, and termed inches. The particular observations are made through the senses and treasured up in the memory; and the intellect, by its constitution, compares them together, marks in what they agree and disagree, and thence draws its axioms or general principles. He, therefore, who should admit the truth of an axiom, and deny the evidence of sense and perception, would act as absurdly as he who accepts payment in a bank-bill, and refuses it in the individual pieces of gold or silver which that bill represents. General axioms are of infinite use in the pursuits of science; but it is not because they create new truths; they only shorten the process in the discovery of such as might be found, with labour, through the medium of particular propositions. See Campbell's Philosophy of Rhetoric and Tatham's Chart and Scale of Truth.