ART. I. -- DIFFERENT KINDS OF METHOD.
100. There are two kinds of method, the Inventive and the Didactic. -- The mind first endeavors to find the truth, and afterwards to demonstrate it or communicate it to others. There must, therefore, be two methods: (1) that of invention, which guides the mind in its search after truth; (2) that of demonstration or doctrine, which guides it in imparting to others the truth that has been found.
101. The method of invention is of three kinds: 1. Rational or a priori; 2. Experimental or a posteriori; 3. Mixed. -- The a priori method seeks to discover truth by the sole light of reason, to the exclusion of experience; this is the method of German Idealism, which shapes facts to ideas and transforms the most absurd conceptions of the mind into realities. The a posteriori method is the reverse of the foregoing; it is exclusively adopted by the Sensist school and ends in materialism. The mixed method is a combination of the other two; it is the only sound philosophic method, as it brings to the aid of science all the means of acquiring knowledge. Although this is the only legitimate method, it is none the less true that the a priori method ought to predominate in mathematics, and the a posteriori method in the natural sciences.{1}
102. The method of demonstration or doctrine is of three kinds: 1. Deductive; 2. Inductive; 3. Mixed. -- The deductive method descends from axioms or principles to their consequences, from laws to phenomena. The inductive method is the reverse of the preceding and makes the mind of the learner pass through the same process as is followed in arriving at truth. The mixed method is a union of these two. The deductive method is the easiest, the inductive the most effectual; the mixed method, being adapted to the ordinary requirements of students, is the one most frequently followed.
ART. II. -- SPECIAL LAWS OF EACH METHOD.
103. The laws of the inventive method require: 1. A determination, at least vaguely, of the end in view; 2. An attentive examination of known truths; 3. A classification of these known truths; 4. A careful use of definitions and divisions; 5. Elimination of whatever is useless or foreign to the end in view; 6. An affirmation of things as certain or doubtful according as they are really certain or doubtful; 7. Care to avoid all rash induction; 8. Prudence to advance nothing resting on what is doubtful or on inconsistent hypotheses.
104. The laws of the didactic method require: 1. The use of clear terms fully explained and defined; 2. Care to take as a starting point only clear and evident principles; 3. A gradual advancement from one conclusion to another; 4. Care to avoid digressions which make us lose the concatenation of ideas.
{1} As to the founders of these schools and the tenets which they held, see Sensism, Transcendentalism, and the Scholastic Theory of the Origin of Ideas, Ideology, chap. ii.; also History of Philosophy, passim.