and even in sciences so far as they are not
treated mathematically (say, Botany and Psychology); propositions that
merely tell us that something happens (as that _salt dissolves in
water_), or that something has a certain property (as that _ice is
cold_): as to these, it belongs to Logic to show how we may judge
whether they are true, or false, or doubtful. When propositions are
expressed with the universality and definiteness that belong to
scientific statements, they are called laws; and laws, so far as they
are not laws of quantity, are tested by the principles of Logic, if they
at all admit of proof.

But it is plain that the process of proving cannot go on for ever;
something must be taken for granted; and this is usually considered to
be the case (1) with particular facts that can only be perceived and
observed, and (2) with those highest laws that are called 'axioms' or
'first principles,' of which we can only say that we know of no
exceptions to them, that we cannot help believing them, and that they
are indispensable to science and to consistent thought. Logic, then, may
be briefly defined as the science of proof with respect to _qualitative_
laws and propositions, except those that are axiomatic.

Sec. 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, i