ANALYSIS (Gr. ἀνὰ and λύειν, to break up into parts), in general, the resolution of a whole into its component elements; opposed to synthesis, the combining of separate elements or minor wholes into an inclusive unity. It differs from mere “disintegration” in proceeding on a definite scientific plan. In grammar, analysis is the breaking up of a sentence into subject, predicate, object, &c. (an exercise introduced into English schools by J. D. Morell about 1852); so the analysis of a book or a lecture is a synopsis of the main points. The chief technical uses of the word, which retains practically the same meaning in all the sciences, are in (1) philosophy, (2) mathematics, (3) chemistry.
(1) Logical analysis is the process of examining into the connotation of a concept or idea, and separating the attributes from the whole and each other. It, therefore, does not increase knowledge, but merely clarifies and tests it. In this sense Kant distinguished an analytic from a synthetic judgment, as one in which the predicate is involved in the essence of the subject. Such judgments are also known as verbal, as opposed to real or ampliative judgments. The processes of synthesis and analysis though formally contradictory are practically supplementary; thus to analyse the connotation is to synthesize the denotation of a term, and vice versa; the process of knowledge involves the two methods, analysis being the corrective of synthetic empiricism. In a wider sense the whole of formal logic is precisely the analysis of the laws of thought. Analytical psychology is distinguished from genetic and empirical psychology inasmuch as it proceeds by the method of introspective investigation of mental phenomena instead of by physiological or psycho-physical experiment. For the relation between analysis and synthesis on the one hand, and deduction and induction on the other, see Induction.
(2) In mathematics, analysis has two distinct meanings, conveniently termed ancient and modern. Ancient analysis, as described by Pappus, related chiefly to geometrical problems, and is the method of reasoning from the solution, as taken for granted, to consequences which are known to be true, whereas synthesis reasons from known data to the solution. (See Geometry.)
Modern analysis is practically coeval with Descartes, the founder of “analytical geometry,” although the calculus of general quantities had previously been termed analysis. Many mathematical subjects are now included under this name, and are treated in the following articles:—Geometry, Analytical; Infinitesimal Calculus; Differential Equation; Variations, Calculus of; Curve; Surface; Function; Spherical Harmonics; Series; Fourier’s Series; Groups, Theory of; Probability.
(3) In Chemistry, the word analysis was introduced by Robert Boyle to denote the determination of the composition of substances. (See Chemistry, Analytical).