Page:Encyclopædia Britannica, Ninth Edition, v. 1.djvu/841

Rh A N A A N A 797 disregarding the various applied methods of the real sciences, or consciously excluding them as lying beyond the province of pure logic, would seek to reduce all scientific procedure to this kind of mental action, the attempt implies a deep misapprehension. It is one thing for the mind to have its subject of inquiry clearly and sharply defined apart from what else is given therewith, or again to have its existing knowledge always well in hand and sifted out to the uttermost; it is another thing for the mind to be making advances, to be passing out from the known to the unknown, or labouring to bring the unknown into relation with that which is known already. Condillac is the thinker who has most expressly made the attempt to bring all scientific method back to the conception of mere logical analysis, repeating it everywhere throughout his works. The sixteenth chapter of his unfinished treatise, the Langue des Calculs, may especially be noted in this respect; the more because he there endeavours to justify his developed expression for the procedure of all science that it consists in a continued substitution of identical pro positions by the actual solution of an algebraical problem. Simple, however, though the instance chosen is, he fails to make good his view, appearing to prove it only by leaving out the step of critical moment. To analysis and synthesis in the specially logical sense is undoubtedly related the distinction that logicians have made of analytic and synthetic method. Without stepping beyond the bounds of logic conceived as a formal doctrine, a fourth department, under the name of Method or Dis posing, may be added to the three departments regularly assigned Conceiving (Simple Apprehension), Judging, Reasoning; and this would consider how reasonings, when employed continuously upon any matter whatever, should be set forth to produce their combined effect upon the mind. The question is formal, being one of mere exposition, and concerns the teacher in relation to the learner. How should results, attained by continuous reasoning, be set before the mind of a learner 1 Upon a line representing the course by which they were actually wrought out 1 Or always in the fixed order of following from express prin ciples to which preliminary assent is required ] If the latter, all teaching becomes synthetic, and follows a pro gressive route from principles to conclusions, even when discovery (supposing discovery foregone) was made by analysis or regression to principles; of which expository method no better illustration could be given than the practice of Euclid in the demonstrations of his Elements. On the other hand, it may be said that the line of dis covery is itself the line upon which the truth about any question can best be expounded or understood, for the same reason that was found successful in discovery, namely, that the mind (now of the learner) has before it something quite definite and specific to start from ; upon which view, the method of exposition should be analytic or regressive to principles, at least wherever the discovery took that route. The blending of both methods, where possible, is doubtless most effective; otherwise it depends upon circumstances chiefly the character of the learner, but also the nature of the subject in respect of com plexity which should be preferred, when one alone is followed. The question of prime logical, or general, importance remaining is to determine the relation of Analysis and Synthesis as methods of real science, to the ground-processes of all reasoning, known since the days of Aristotle under the names of Induction and Deduction. Much difference of opinion has been expressed on this subject, not only because of the want of agreement as to what should be called analysis and synthesis, but also because of more fundamental disagreement regarding tba nature cf tLs inductive and deductive processes. It was remarked before as somewhat surprising, that Aristotle himself did not more expressly consider the relation, when we have seen that he was familiar with the process of geometrical analysis, under the very name. The distinction, however, upon which he lays so much stress throughout his works, between knowledge from principles, prior or better known by nature, and knowledge of or from facts, prior in experience or relatively to us, has generally- been understood to imply a connection of synthesis with deduction, of analysis with induction; so much so indeed, that synthetic and deductive method, analytic and induc tive method, have come to be used respectively almost as interchangeable terms. Nor, although Sir William Hamilton seems to wish to reverse the usual association of the terms, when he calls induction a purely synthetic pro cess, and declares it to be erroneously viewed as analytic (Metaphysics, i. p. 102), is he really at variance with the other authorities; his observation having a special reference which the others also might allow. But any such asso ciation seems to rest upon a misconception, not to be laid to the charge of Aristotle himself. In the sense of analysis and synthesis for which it is important to deter mine the relation, namely, when they are taken as the means of real discovery in science, the true view rather is that they are the different methods in which reasoning, whether inductive or deductive, must be applied for dis covering truth in the form of special or particular ques tions. Analysis, as well as synthesis, may proceed by way of deduction, as we have seen in the process of mathe matics; on the other hand, synthesis as applied in chemistry is as much an inductive act, being strictly experimental, as anything could well be. Induction and deduction are concerned about the relation of the particular and general in thought; analysis and synthesis about the relation of the known and the unknown. The two points of view are of course related to each other : analysis and synthesis, as practised by the human mind, either for purposes of science or in the affairs of life, cannot be worked except under those highest laws of the relation between the par ticular and general in thought which Aristotle s genius first was able to extract from the instinctive practice of human reason. But whether the processes are applied singly, or, for greater assurance, conjointly, it depends upon the matter of the inquiry under which laws those of induc tion or those of deduction they shall be worked; and in any case there is implied a peculiar intellectual attitude different from that of mere formal reasoning. It is the difference between the act of finding out and proving. If it should ever become possible to develop a logic of Dis covery, it must consist in the formulation of the processes of Analysis and Synthesis, conceived in the general sense attributed to them in the foregoing article. (o. c. E.) ANALYTIC JUDGMENTS have been distinguished under that name, in opposition to Synthetic, since the time of Kant. It was necessary, for the purposes of his critical inquiry into the principles of human knowledge, that he should carefully determine the character of those assertions which metaphysicians had so freely made respecting the supernatural, and he found them to be such that, while the predicate was added on to the subject, not involved in it, the connection was affirmed as necessary and universal. He therefore called them, as well as other assertions of like character in mathematics and pure physics, synthetic judg ments d priori, and the aim of his critical inquiry came to be the determining of the conditions under which such judgments were possible. Now, as differing from these, he noted two classes of judgments: (1), such as in the predi cate added indeed to the content of the subject, but only