laws and propositions, except those that are axiomatic.

§ 2. Proof may be of different degrees or stages of completeness.
Absolute proof would require that a proposition should be shown to agree
with all experience and with the systematic explanation of experience,
to be a necessary part of an all-embracing and self-consistent
philosophy or theory of the universe; but as no one hitherto has been
able to frame such a philosophy, we must at present put up with
something less than absolute proof. Logic, assuming certain principles
to be true of experience, or at least to be conditions of consistent
discourse, distinguishes the kinds of propositions that can be shown to
agree with these principles, and explains by what means the agreement
can best be exhibited. Such principles are those of Contradiction (chap.
vi.), the Syllogism (chap. ix.), Causation (chap. xiv.), and
Probabilities (chap. xx.). To bring a proposition or an argument under
them, or to show that it agrees with them, is logical proof.

The extent to which proof is requisite, again, depends upon the present
purpose: if our aim be general truth for its own sake, a systematic
investigation is necessary; but if our object be merely to remove some
occasional doubt that has occurred to ourselves or to others, it may be
enough to appeal to any evidence that is admitted or not questioned.
Thus, if a man doubts that _some acids are compounds of oxygen_, but
grants that _some compounds of oxygen are acids_, he may agree to the
former proposition when you point out that it has the same meaning as
the latter, differing from it only in the order of the words. This is
called proof by immediate inference.

Again, suppose that a man holds in his hand a piece of yellow metal,
which he asserts to be copper, and that we doubt this, perhaps