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Logic: Deductive and Inductive
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Publisher: Nishelle Books
Pages: 386
Weight: 1.13
Height: 0.80 Width: 6.00 Depth: 9.00
Language: English
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, in-
deed, every such proposition; for as to those that declare the equality or in-
equality 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 be-
longs to Logic to show how we may judge whether they are true, or false, or
doubtful. When propositions are expressed with the universality and defi-
niteness 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
3 CARVETH READ
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 qualitativelaws 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 neces-
sary 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 con-
ditions 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 Probabil-
ities (chap. xx.). To bring a proposition or an argument under them,
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