Logic | Page 5

as Euclid
does not try to prove that 'two magnitudes equal to the same third are
equal to one another,' so the Logician (as such) does not attempt to
prove the uniformity of causation and the other principles of his
science.
Even when our purpose is to ascertain some general truth, the results of
systematic inquiry may have various degrees of certainty. If Logic were
confined to strict demonstration, it would cover a narrow field. The
greater part of our conclusions can only be more or less probable. It
may, indeed, be maintained, not unreasonably, that no judgments
concerning matters of fact can be more than probable. Some say that all
scientific results should be considered as giving the average of cases,
from which deviations are to be expected. Many matters can only be
treated statistically and by the methods of Probability. Our ordinary
beliefs are adopted without any methodical examination. But it is the
aim, and it is characteristic, of a rational mind to distinguish degrees of
certainty, and to hold each judgment with the degree of confidence that
it deserves, considering the evidence for and against it. It takes a long
time, and much self-discipline, to make some progress toward
rationality; for there are many causes of belief that are not good
grounds for it--have no value as evidence. Evidence consists of (1)
observation; (2) reasoning checked by observation and by logical
principles; (3) memory--often inaccurate; (4) testimony--often
untrustworthy, but indispensable, since all we learn from books or from
other men is taken on testimony; (5) the agreement of all our results.
On the other hand, belief is caused by many influences that are not

evidence at all: such are (1) desire, which makes us believe in whatever
serves our purpose; fear and suspicion, which (paradoxically) make us
believe in whatever seems dangerous; (2) habit, which resists whatever
disturbs our prejudices; (3) vanity, which delights to think oneself
always right and consistent and disowns fallibility; (4) imitativeness,
suggestibility, fashion, which carry us along with the crowd. All these,
and nobler things, such as love and fidelity, fix our attention upon
whatever seems to support our prejudices, and prevent our attending to
any facts or arguments that threaten to overthrow them.
§ 3. Two departments of Logic are usually recognised, Deduction and
Induction; that is, to describe them briefly, proof from principles, and
proof from facts. Classification is sometimes made a third department;
sometimes its topics are distributed amongst those of the former two. In
the present work the order adopted is, Deduction in chaps. ii. to xiii.;
Induction in chaps. xiii. to xx.; and, lastly, Classification. But such
divisions do not represent fundamentally distinct and opposed aspects
of the science. For although, in discussing any question with an
opponent who makes admissions, it may be possible to combat his
views with merely deductive arguments based upon his admissions; yet
in any question of general truth, Induction and Deduction are mutually
dependent and imply one another.
This may be seen in one of the above examples. It was argued that a
certain metal must be copper, because every metal is copper that turns
green when dipped in vinegar. So far the proof appealed to a general
proposition, and was deductive. But when we ask how the general
proposition is known to be true, experiments or facts must be alleged;
and this is inductive evidence. Deduction then depends on Induction.
But if we ask, again, how any number of past experiments can prove a
general proposition, which must be good for the future as well as for
the past, the uniformity of causation is invoked; that is, appeal is made
to a principle, and that again is deductive proof. Induction then depends
upon Deduction.
We may put it in this way: Deduction depends on Induction, if general
propositions are only known to us through the facts: Induction depends

on Deduction, because one fact can never prove another, except so far
as what is true of the one is true of the other and of any other of the
same kind; and because, to exhibit this resemblance of the facts, it must
be stated in a general proposition.
§ 4. The use of Logic is often disputed: those who have not studied it,
often feel confident of their ability to do without it; those who have
studied it, are sometimes disgusted with what they consider to be its
superficial analysis of the grounds of evidence, or needless technicality
in the discussion of details. As to those who, not having studied Logic,
yet despise it, there will be time enough to discuss its utility with them,
when they know something about it; and as for those who, having
studied it, turn away in disgust, whether they are justified every man
must judge for himself,