AXIOM, in philosophy, is such a plain,_ self-evident, and received notion, that it cannot he made more plain and evident by demonstration ; because it is itself better known than any thing that can be brought to prove it; as, that nothing can act where it is not ; that a thing can be, and not be, at the same time ; that the whole is greater than a part thereof; and that from no thing, nothing can arise. By axioms, called also maxims, are understood all common notions of the mind, whose evi dence is so clear and forcible, that a man cannot deny them, without renouncin; common sense and natural reason.
The rule whereby to know an axiom is this : whatever proposition expresses the immediate clear comparison of two ideas, without the help of a third, is an axiom. But if the truth does not appear from the immediate comparison of two ideas, it is no axiom.
These sorts of propositions, under the name of axioms, have, on account of their being self-evident, passed not only for principles of science, but have been sup posed innate, and thought to be the foun dation of all our other knowledge ; though, in truth, they are no more than identic propositions ; for to say that all right angles are equal to each other, is no more than saying that all right angles are right angles, such equality being im plied in the very definition. All conside rations of these maxims, therefore, can add nothing to the evidence or certainty of our knowledge of them : and how lit tle they influence the rest of our know ledge, how far they are from being the foundation of it, as well as of the truths first known to the mind, Mr. Locke, and
some others, have undeniably proved. According to Bacon, it is impossible that axioms raised by argumentation should be useful in discovering new works ; be cause the subtlety of nature far exceeds the subtlety of arguments ; but axioms, duly and methodically drawn from par ticulars, will again easily point out new particulars, and so render the sciences active.
The axioms in use being derived from slender experience, and a few obvious particulars, are generally applied in a cor responding manner. No wonder, there fore, they lead us to few particulars ; and if any instance, unobserved before, hap pen to turn up, the axiom is preserved by some trifling distinction, where it ought rather to be corrected.
AxTort is also an established principle in some art or science.
Thus, it is an established axiom in phy sics, that nature does nothing in vain ; so it is in geometry, that if to equal things you add equals, the sums will be equal It is an axiom in optics, that the angle of incidence is equal to the angle of reflec tion, &c. In which sense, too, the gene ral laws of motion are called axioms : it may be observed, that these particular axioms are but deductions from certain hypotheses.