INTRODUCTORY


§ 1. Logic is the science that explains what conditions must be
fulfilled in order that a proposition may be proved, if it admits of
proof. Not, indeed, every such proposition; for as to those that declare
the equality or inequality of numbers or other magnitudes, to explain
the conditions of their proof belongs to Mathematics: they are said to
be _quantitative_. But as to all other propositions, called
_qualitative_, like most of those that we meet with in conversation, in
literature, in politics, 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_