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Analysis (ἀνά="up" or "back", and λύειν, "to loose") means a separation; it is the taking apart of that which was united, and corresponds exactly to the Latin form "resolution" (re + solvere). Its opposite is synthesis (σύν, "together", and τιθέναι, "to put", hence, a "putting-together", a "composition"). According to this etymology, analysis, in general, is the process by which anything complex is resolved into simple, or, at least, into less complex parts or elements. This complex may be:
(1) In the case of a concrete object, we must distinguish three degrees of analysis. Sometimes a real separation or isolation is effected. To resolve a chemical compound into its elements, or white light into the elementary colours, to dissect an organism, to take a machine to pieces, is to proceed analytically. But frequently actual isolation is impossible. Thus the factors of a movement or of a psychological process cannot be set apart and studied separately. If the process occurs at all, it must be a complex one. We may, however, reach an analytical result by means of different successive syntheses, i. e. by variations in the grouping of the elements or circumstances. In order to ascertain the individual nature of any determined element, factor, or circumstance, it is maintained in the state of permanency, while the accompanying elements, factors, or circumstances are eliminated or changed; or, on the contrary, it may be eliminated or modified, while the others remain constant. The four methods of induction belong to this form of analysis. It is also in a large measure the method of psychological experiment and of introspective analysis. Finally, it may be impossible to effect any real dissociation of a concrete thing or event, either because it cannot be reached or controlled, or because it is past. Then mental dissociation and abstraction are used. In a complex object the mind considers separately some part or feature which cannot in reality be separated. Analogy and comparison of such cases with similar instances in which dissociation has been effected are of great value, and the results already ascertained are applied to the case under examination. This occurs frequently in physical and psychological sciences; it is also the method used by the historian or the sociologist in the study of events and institutions.
(2) When the complex is an idea, analysis consists in breaking it up into simpler ideas. We are in the abstract order and must remain therein; consequently, we do not take into consideration the extension of an idea, that is, its range of applicability to concrete things, but its intension, or connotation, that is, its ideal contents. To analyze an idea is to single out in it other ideas whose ideal complexity, or whose connotation is not so great. The same must be said of analytical reasoning. The truth of a proposition or of a complex statement is analytically demonstrated by reverting from the proposition itself to higher principles, from the complex statement to a more general truth. And this applies not only to mathematics, when a given problem is solved by showing its necessary connection with a proposition already demonstrated, or with a self-evident axiom, but also to all the sciences in which from the facts, the effects, and the conditioned we infer the law, the cause, and the condition. Principle, law, cause, nature, condition, are less complex than conclusion, fact, effect, action, conditioned, since these are concrete applications and further determinations of the former. A physical law, for instance, is a simplified expression of all the facts which it governs. In one word, therefore, we may characterize analysis as a process of resolution and regression; synthesis, as a process of composition arid progression.
The confusion that has existed and still exists in the definition and use of the terms analysis and synthesis is due to the diverse natures of the complexes which have to be analyzed. Moreover, the same object may be analyzed from different points of view and, consequently, with various results. It is especially important to keep in mind the distinction between the connotation and the denotation of an idea. As the two vary in inverse ratio, it is clear that, in an idea, the subtraction of certain connotative elements implies an increase in extension. Hence connotative analysis is necessarily an extensive synthesis, and vice versâ. Thus, if my idea of a child is that of "a human being under a certain age", by connotative analysis I may omit the last determination "under a certain age"; what remains is less complex than the idea "child", but applies to a greater number of individuals, namely to all human beings. In order to restrict the extension to fewer individuals, the connotation must be increased, that is, further determinations must be added. In the same manner, a fact, when reduced to a law, either in the physical, the mental, or the historical order, is reduced to something which has a greater extension, since it is assumed to rule all the facts of the same nature, but the law is less complex in connotation, since it does not share the individual characters of the concrete events.
The necessity of analysis comes from the fact that knowledge begins with the perception of the concrete and the individual, and that whatever is concrete is complex. Hence the mind, unable to distinctly grasp the whole reality at once, must divide it, and study the parts separately. Moreover the innate tendency of the mind towards unification and classification leads it to neglect certain aspects, so as to reach more general truths and laws whose range of application is larger. The relative usefulness of analysis and synthesis in the various sciences depends on the nature of the problems to be solved, on the knowledge already at hand, on the mind's attitude, and on the stage of development of the science. Induction is primarily analytic; deduction, primarily synthetic. In proportion as a natural science becomes more systematic, i. e. when more general laws are formulated, the synthetic process is more freely used. Previous analysis then enables one to "compose", or deduce future experience. Where, on the contrary, the law has to be discovered, observation and analysis are dominant, although, even then, synthesis is indispensable for the verification of hypotheses. Some sciences, such as Euclidean geometry, proceed synthetically, from simple notions and axioms to more complex truths. Analysis has the advantage of adhering more strictly to the point under investigation; synthesis is in danger of going astray, since from the same principle many different conclusions may be drawn, and a multitude of real or possible events are governed by the same law. For this same reason, however, synthesis, in certain sciences at least, is likely to prove more fruitful than analysis. It also has the advantage of starting from that which has a natural priority, for the conditioned presupposes the condition. When the result is already known, and the relation between a principle and some one conclusion thus ascertained, synthesis is a great help in teaching others. In synthesis the strictness of logical reasoning is required. Accuracy and exactness in the observation of phenomena, attention to all their details, the power of mental abstraction and generalization are qualities indispensable in the analytic process.
The literature of analysis includes all works on logic and on the methods of the sciences. We give only some few references. DUGALD STEWART, Philosophy of the Human Mind, P. II, iv, § 3; WUNDT, Logik (2d ed., Stuttgart, 1895), II, i; DUHAMEL, Des méthodes dans les sciences de raisonnement (Paris, 1865-73); BAIN, Logic, P. II, Induction (2d ed., London, 1873); ROBERTSON, art. Analysis in Encyclopœdia Britannica, 9th ed. - On psychological analysis, see, among others, ROYCE, Outlines of Psychology, iv, §§ 40-47 (New York, 1903).