ANALYSIS (Greek, ’αναλυσις [análysis]—dismantling)—a breaking down of a whole into its elements, most often non-uniform and non-integral elements; in terms of knowledge, examining something by breaking it down into component parts, distinguishing its primary elements, searching for the constitutive or conditioning elements, searching for causes, or arriving at principles. Sometimes analysis designates the result of these operations or even a scientific discipline; synthesis is the opposite of analysis and they are often complementary in investigative operations.
In ancient times Plato used analysis as a method. Aristotle also thought of analysis as a form of reasoning, and he called his logical works on the syllogism and demonstration the Analytics. Euclid developed analytic demonstration in geometry. In the Middle Ages analysis was called “modus (ordo) resolutionis” as opposed to “via compositionis”, and analytical demonstration (ratio analytica) was reasoning based on the premises specific to a particular science, as opposed to a demonstration that started from general principles (ratio logica). In modern times philosophers have understood the method of analysis in different ways. According to R. Descartes (and the authors of the Logique de Port-Royal), analysis is a type of reasoning for which rules have previously been provided.
Natural scientists (Galileo, I. Newton) connected the analytic method with induction and treated it as a way of invention, for drawing out the consequences from particular facts, and for forming hypotheses on the basis of particular facts. G. W. Leibniz thought of analysis as the basis epistemological thesis that every true proposition is analytic, that is, by defining its terms it may be reduced to an identically true proposition; all reasoning is analytic in character since it develops what is contained in the concepts of the premises. The empiricists recognized analysis as a natural and proper way to work in science (according to E. B. Condillac, analysis is also a cognitive method and the best method for presenting acquired knowledge; only analysis provides evidence in reasoning).
I. Kant distinguished between the analysis of concepts and the analysis of consciousness; he described an analytic judgment as one which in predication states only what is implied in the subject of a proposition, and he called the breaking down of human knowledge into purely mental elements the transcendental analytic. Hegel thought that analysis and synthesis were dialectically dependent upon one another. Analysis played an important role for E. Husserl and W. Wundt. Wundt regarded analysis as more valuable than synthesis and distinguished between elementary, causal, and logical analysis.
In twentieth-century science the value of analysis has been dependent upon the type of science: contemporary philosophy has an analytic character (the logico-semiotic analysis of language has sometimes replaced philosophical thought); in empirical psychology analysis is applied in statistical methods; in the natural sciences it is a basic method. Systems analysis arose in connection with the development of general systems theory (concerning social, political, and psychological systems). Analysis may be a purely mental operation or it may involve physical actions (manipulative analysis).
INTELLECTUAL ANALYSIS is studied in the methodology of the sciences. It is a method in which we proceed from that which is complex to that which is simple, from the particular to the general (hence it is identified with induction), from effect to cause, and from conclusions to their premises. Depending upon the object analyzed we may list the following forms of analysis: the analysis of concepts—breaking down concepts into their features; the analysis of truths—the rational justification of a thesis by seeking reasons equivalent to it, consequences or more generally formal connections (logical analysis); the analysis of problems—breaking down problems into simple questions, and solving problems by deducing conclusions that can be reduced to recognized truths; the analysis of facts—the investigation of phenomena while considering their genesis (genetic analysis), their structure (structural analysis), or the laws by which they function (functional analysis).
Intellectual analysis is applied in different fields: as an experimental method in psychology (factor analysis) where it consists in a collection of statistical operations that make possible the reduction of numerical variables that occur in tests, which in turn makes it easier to single out the factors that evoke correlations between elements of the variables (psychological analysis may have a specific character when it is connected with a particular trend, e.g., analytic psychology); the term “analysis” is used in the humanistic sciences more or less metaphorically: textual analysis, literary analysis, philological analysis, grammatical analysis, and historical analysis. In the humanities it designates operations (or their methods) for establishing or characterizing sources (an external or erudite critique), and a method for reading, interpreting, and evaluating information contained in a source (an internal critique).
In the mathematical sciences analysis is a broad area of higher mathematics based on the concepts of function, continuity, derivative, integer, and series, and it is chiefly comprised of differential and integral calculus. Analysis may also be a special section of mathematics: harmonic analysis (devoted to the development of functions for trigonometric series), numeric analysis (the theory of methods for approximate calculuses and their application), functional analysis which is concerned equally with problems from different domains of mathematics, analysis of permutations (this studies the degree of difference in the partial sets in which a general set is divided). The following forms of analysis may appear in philosophy: semiotic analysis—the investigation of the semiotic function of expressions in order to avoid errors as the causes of philosophical disputes or as the sources of linguistic abuses, or in order to construct a precise system of language; phenomenological analysis—the investigation of the elements and structure of a phenomenon that is known in an inspection, and the relations of the phenomenon t to other phenomena; and reflective analysis—the explanation of philosophical facts by indicating their causes, the reasons that show them to be free of contradiction.
MANIPULATIVE ANALYSIS is applied mainly in the natural sciences. It is dependent upon the character of the particular sciences. It includes the following: chemical analysis, which is understood as all operations aimed at investigating what substances form a compound (qualitative analysis) or in what quantities the substances occur in the compound (quantitative analysis); spectral analysis which is used in physics (determining a body’s chemical composition by lines and bands in its spectrum); physical-chemical analysis—the study of the relations between a body’s chemical composition and its physical properties; biological analysis—the study of an organism by the analysis of the particular organs considered in isolation.
Science also uses terms which originate from the term “analysis”: analytics—a part of logic (in Aristotle); a section of the philosophy of knowledge (in Kant). The adjective “analytic” is used to characterize the following: propositions (judgments), definitions, functions, language, method, the mind, and certain sciences. Analytic propositions are described as follows: (1) they are internally free of contradiction (the truth of an analytic proposition is guaranteed by the appropriate terminological conventions); (2) we recognize the truth of an analytic proposition only after we understood it (it is analytic quoad nos); (3) the analytic proposition can be fulfilled in any non-contradictory world (analytic quoad se); an analytic definition is formed when the content of the “definiendum” is taken apart; an analytic function is one that can be resolved into an exponential series. Analytic language is characterized by the fact that in it grammatical relations are indicated by auxiliary expressions (adjectives, articles), word-order, or intonation, whereas in a synthetic language grammatical relations are indicated by the forms of expressions.
Philosophical Analysis. A Collection of Essays, Ithaca 1950; M. Black, Problems of Analysis. Philosophical Essays, Ithaca 1954; H. Dingler, Analyse oder Synthese in der Philosophie der Wissenschaften?, Meth 6 (1954), 165–193; J. Hospers, An Introduction to Philosophical Analysis, Lo 1956, 19974; E. Poznański, Spór o analityczność [Dispute on what analysis is], SF 6 (1960) 4, 119–148; P. Ziff, Semantic Analaysis, It 1960, 19672; J. W. Yolton, Concept Analysis, KantSt 52 (1961), 467–484; J. Lechat, Analyse et synthèse, P 1962; S. Gorovitz, Philosophical Analysis. An Introduction to its Language and Techniques, NY 1965, 19793; R. Draper, H. Smith, Applied Regression Analysis, NY 1966; Philosophical Analysis and History, NY 1966; Problems and Methods in Analysis, I–II, Ox 1966; A. H. Smith, W. A. Albrecht, Fundamental Concepts of Analysis, EC 1966; E. M. MacKinnon, Analysis and the Philosophy of Science, IPhQ 7 (1967), 213–250; P. F. Lazarsfeld, J. N. Morgan, J. C. Selvin, IESS XV 411–436; A. Rapport, (et al.), IESS XV 452–495; L. Gabriel, Das Verhältnis der Synthese zur Analyse im integrativen Denken, in: Akten des XIV Internationalen Kongress für Philosophie, W 1968, II 369–372; G. Kung, Language, Analysis, and Phenomenological Analysis, ibid, II 247–253; D. Locke, The Necessity of Analytic Truths, Philosophy 44 (1969), 12–32; K. M. Sayre, Plato’s Analytic Method, Ch 1969; New Readings in Philosophical Analysis, NY 1972; S. Rosen, The Limits of Analysis, NY 1980, South Bend 19992; P. H. Byrne, Analysis and Science in Aristotle, Albany 1997; F. Jackson, From Metaphysics to Ethics. A Defence of Conceptual Analysis, Ox, NY 1998.