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.

Sec. 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.