ANALYSIS AND SYNTHESIS. — A. (Gr. ἀνάλυσις from ἀναλύειν, syn. ἀνάγειν = resolvere) and s. (Gr. σύνθεσις from συν-τίθημι = compono) designate two opposed and correlative methods used in science, the first consisting in ascending from the composite to the simple and from effect to cause, the second in the inverse operation whereby one passes from the simple to the composite and descends from cause to effect.
Historically, a. is attested for the first time, as a mathematical method, in Plato, to whom its discovery is attributed, and is defined as a method by which “the object of inquiry is referred back to an admitted principle” (Proclus, In Euclidem, p. 211). This meaning was substantially taken up by Descartes when he called a. algebraic calculation in general. This identification of a. with algebra has not entirely disappeared, although today, more precisely, a. (abbreviation of a. infinitesimal) is in mathematics synonymous with differential and integral calculus, or higher algebra. Today, in philosophy and the sciences, we call a. every real or logical process by which a whole or composite, of whatever nature, is reduced to the simple and the less composite, generally to the principles on which it depends or that constitute II. This is already Aristotle’s meaning, whose two principal books of logic are precisely called the Analytics, since the syllogism and other complex modes of knowledge are resolved into the most elementary forms and the principles on which they depend: “in quo ἀναλύειν nihil aliud est quam quod compositum est, tanquam ad causas redigere... Ita in analytici cognoscendi rationes ad primas quasi formas tanquam ad causas revocantur” (F. A. Trendelenburg, Elementa logicae aristoteliae, 9th ed., Berlin 1892, p. 47). Consequently, wherever a similar resolving and regressive process occurs, there is a. Thus, not to speak of a. in the material sense (e.g. chemical a., spectral a.), the process is essentially analytical whereby a phenomenon, a fact, or a complex situation is resolved into its concomitant and determining elements and referred back to its conditions, its laws, and its causes. It does not matter whether the fact, phenomenon, or function is physical, physiological, or even psychic in nature, individual or collective: thus Galileo’s examination of the oscillatory motion of the pendulum is a., just as the psychologist’s introspection of the phenomenon of fear is a., or the study of a case of collective hallucination, etc.
In the more strictly logical field, a. concerns first of all concepts and judgments. As for the concept, which is a logical whole, generally of polyvalent content, a. consists in resolving it (thinking it) into those simpler notes that constitute its comprehension or objective content. Thus one proceeds by a. when, for example, one resolves the concept of science into its primary elements in order to derive from them a distinct definition. One also speaks, though less properly, of a. with regard to the extension of a concept: in that case a. is nothing other than the division of the concept among the multiple subjects to which it can be referred. Since the content and the extension or universality of a concept stand in inverse proportion, it is clear that an a. with regard to the content of a concept will result in an increase, and therefore in a certain synthesis, of its extension: insofar as the simpler notions derived through a., precisely because they are such, will have a wider range of reference. Hence the fluctuations and sometimes reversals in terminology found among certain authors concerning this particular logical field of application of a.
As for the judgment, if it is considered in its psychological genesis, it most often involves an initial a., that is, the discernment of subject and predicate that the mind performs in the object of the judgment before uniting them in synthesis through attribution. Then, in relation to the movement of thought generated by the mutual connection of judgments, a., according to the meaning already clearly formulated by Alexander of Aphrodisias (In Analyt. priora, I, p. 7, 13-15, Berlin 1883), consists in ascending from consequences to principles: more specifically, in referring a proposition or conclusion of a complex order to a general principle that contains and justifies it and that, although more universal in its references, is simpler in its actual content. Thus the process is always a. whereby a particular truth is demonstrated by resolving it into a more immediate principle, for example when the dishonesty of theft is proved by affirming it to be a violation of justice.
As can be seen, a., from an originally rather restricted meaning, has acquired in logic a much broader and more substantial sense, coming to designate as a whole the ascending and ontologically regressive process of the human mind from the multiple to the simple, from the concrete to the abstract, and from the particular to the universal. The inductive method consequently appeals to a., although, taken globally, as it is used in the sciences, it also involves non-analytical moments, as when one proceeds deductively to verify the hypothesis. The reference of scientific induction to a. is already found clearly in Newton (cf. Optice, Latin ed., London 1706, p. 347).
Opposed to a. is s., which, restricting ourselves here to its use in the logical field, designates precisely the inverse procedure of thought whereby one proceeds from the parts to the whole, from the simple to the composite, from the universal to the particular, and from the law, cause, or principle to the phenomenon, effect, or conclusion. Thus the syllogistic deductive procedure is s., whereby, from universal principles, simpler in notional content, one proceeds to particular consequences governed by those principles; or one moves from a law already established to the search, in experience, for new facts and phenomena suggested and explained by that law; or again, from any norm, for example one of ethics or aesthetics, one deduces concretely what a human act must be in order to be called honest, or what a work of art must be in order to be beautiful.
A. and s. therefore adequately divide the logical processes of human thought: both useful, both
necessary, each responding to the dimorphism of human knowledge, directed toward empirical contingency and universal values, find in the various fields and objects of knowledge greater or lesser employment, according to the different nature of the sciences, their degree of organization, and the mental disposition of individual persons. Thus, while the natural sciences, in reducing and arranging the complex phenomenology of nature, are and must remain predominantly analytical—and all the more analytical the more uncertain and hypothetical their conclusions and systematic results remain—philosophical and mathematical sciences, on the contrary, make greater use of synthesis. Moreover, analysis and synthesis are not two procedures that can be sharply separated, nor can any science wholly dispense with either one or the other. Whenever this occurs, deviations inevitably arise at the expense of the balance of thought, and therefore of truth: analysis, a fruitful instrument of invention and concrete knowledge of nature, if cultivated exclusively, will harden science into positivism; and synthesis, likewise a powerful means of progress and enrichment of thought, if completely detached from analysis, will wither into abstractionism and apriorism. And although human thought universally begins with analysis, since what is first known to us through the senses is the manifold, the concrete, and the particular—always more or less complex and therefore requiring, for us, a multiple mental resolution—it will nevertheless attain its natural development and fulfillment only by fructifying the material obtained through analysis with a synthesis combining prudence and courage. As in the construction, so also in the teaching of science: although it may be said that in many sciences synthesis, as a didactic method, offers undoubted advantages, it should nevertheless in every case be tempered by a judicious use of analysis, which is better suited to the formation and development of the scientific inventive spirit.
Analysis and synthesis, by derivation from their fundamental meaning, also have other frequent applications that are easy to understand: for example, one speaks of grammatical analysis, aesthetic analysis, and philological analysis; of historical analysis and synthesis; of analytic languages and synthetic languages. With reference to mental types, as we have mentioned above, one also speaks of an analytical mind and a synthetic mind, according to whether there predominates in individuals the concrete spirit of observation, intuition, and discernment, or, instead, the comprehensive, deductive, and logical spirit, suited to general and unified knowledge.