(Lat. de ducere, to lead, draw out, derive from; especially, the
function of deriving truth from truth). The topic will be treated
in two sections:
I. As an argument or reasoning process: that kind of mediate
inference by which from truths already known we advance to a
knowledge of other truths necessarily implied in the former; the
mental product or result of that process.
II. As a method: the deductive method, by which we increase our
knowledge through a series of such inferences.
I. AS AN ARGUMENT OR REASONING PROCESS
The typical expression of deductive inference is the syllogism.
The essential feature of deduction is the necessary character of
the connexion between the antecedent or premises and the
consequent or conclusion. Granted the truth of the antecedent
judgments, the consequent must follow; and the firmness of our
assent to the latter is conditioned by that of our assent to the
former. The antecedent contains the ground or reason which is the
motive of our assent to the consequent; the latter, therefore,
cannot have greater firmness or certainty than the former. This
relation of necessary sequence constitutes the formal aspect of
deduction. It can be realized most clearly when the argument is
expressed symbolically, either in the hypothetical form:
1."If anything (S) is M it is P;
2.but this S is M;
3.therefore this S is P",
or in the categorial form,
1."Whatever (S) is M is P;
2.but this S is M;
3.therefore this S is P".
The material aspect of the deductive argument is the truth or
falsity of the judgments which constitute it. If these be certain
and evident the deduction is called demonstration, the
Aristotelian apodeixis. Since the conclusion is necessarily
implied in the premises, these must contain some abstract, general
principle, of which the conclusion is a special application;
otherwise the conclusion could not be necessarily derived from
them; and all mediate inferences must be deductive, at least in
this sense, that they involve the recognition of some universal
truth and do not proceed directly from particular to particular
without the intervention of the universal.
AS A METHOD
When, starting from general principles, we advance by a series of
deductive steps to the discovery and proof of new truths, we
employ the deductive or synthetic method. But how do we become
certain of those principles which form our starting-points?
We may accept them on authority as, for example, Christians
accept the deposit of Christian revelation on Divine authority and
proceed to draw out their implications by the deductive reasoning
which has shaped and moulded the science of theology.
Or we may apprehend them by intellectual intuition as self-
evident, abstract truths concerning the nature of thought, of
being, of matter, of quantity, number, etc., and thence proceed to
build up the deductive sciences of logic, metaphysics,
mathematics, etc. Down through the Middle Ages enlightened thought
was fixed almost exclusively on those two groups of data, both
sacred and profane; and that accounts for the fulness of the
scholastic development of deduction.
But besides being and quantity, the universe presents change,
evolution, regular recurrences or repetition of particular facts,
from the careful observation and analysis of which we may ascend
to the discovery of a third great class of general truths or laws.
This ascent from the particular to the general is called
induction, or the inductive or analytic method. Comparatively
little attention was paid to this method during the Middle Ages.
Apparatus for the accurate observation and exact measurement of
natural phenomena was needed to give the first real impetus to the
cultivation of the physical, natural, or inductive sciences. In
these departments of research the mind approaches reality from the
side of the concrete and particular and ascends to the abstract
and general, while in deduction it descends from the general to
the particular. But although the mind moves in opposite directions
in both methods, nevertheless the reasoning or inference proper,
employed in induction, is in no sense different from deductive
reasoning, for it too implies and is based on abstract, necessary
Transcribed by Rick McCarty
From the Catholic Encyclopedia, copyright © 1913 by the
Encyclopedia Press, Inc. Electronic version copyright © 1996 by
New Advent, Inc.
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