See also:resolution of a whole into its component elements; opposed to synthesis, the combining of
See also: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
See also:sentence into subject, predicate,
See also:object, &c . (an exercise introduced into
See also:schools by J . D .
See also:Morell about 1852) ; so the analysis of a
See also:book or a lecture is a synopsis of the
See also:main points . The chief technical uses of the word, which retains practically the same meaning in all the sciences, are in (I) philosophy, (2)
See also:mathematics, (3) chemistry . (I) Logical analysis is the
See also:process of examining into the
See also: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
See also:Kant distinguished an analytic from a synthetic
See also: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
See also:term, and
See also:vice versa; the process of knowledge involves the two methods, analysis being the corrective of synthetic -empiricism .
In a wider sense the whole of formallogic is precisely the analysis of the
See also:laws of thought .
See also:Analytical psychology is distinguished from genetic and empirical psychology inasmuch as it proceeds by the method of introspective investigation of
See also:mental phenomena instead of by physiological or psycho-
See also:physical experiment . For the relation between analysis and synthesis on the one
See also:hand, and deduction and induction on the other, see INDUCTION . (2) In mathematics, analysis has two distinct meanings, conveniently termed
See also:ancient and
See also: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
See also:GEOMETRY.) Modern analysis is practically coeval with
See also: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;
See also:DIFFERENTIAL EQUATION; VARIATIONS, CALCULUS OF;
See also:FUNCTION; SPHERICAL HARMONICS; SERIES;
See also: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 sub-stances . (See CHEMISTRY, Analytical) .
ANALOGY (Gr. avaXo-yLa, proportion)
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