ANALYSIS AND SYNTHESIS. — A. (Gr. ἀνάλυσις from ἀναλυτός, synonymous with ἀνάγειν = resolvere) and s. (Gr. σύνοψις from συνο-ίσχυσις = compound) designate two opposite and correlative methods used in science, the first consisting in ascending from the compound to the simple and from the effect to the cause, the second in the inverse operation by which one passes from the simple to the compound and from the cause to the effect.
Historically, a. as a mathematical method is first attested in Plato, to whom its discovery is attributed, and is defined as a method by which “the object of inquiry is reduced to an accepted principle” (Proclus, In Euclidem, p. 211). This sense was substantially taken up by Descartes when he called a. the general algebraic calculus. This identification of a. with algebra has not entirely disappeared, even though a. (abbreviation of a. infinitesimalis) is now in mathematics a synonym for differential and integral calculus or higher algebra. Today, in philosophy and the sciences, we call a. any real or logical process by which a whole or compound, of whatever nature, is reduced to the simple and the less compound, generally to the principles on which it depends or from which it is constituted. This is the sense already found in Aristotle, whose two principal logical works are called precisely the Analytics, inasmuch as the syllogism and other complex modes of knowledge are resolved into their most elementary forms and into the principles from which they depend: “in quo ἀνάλυσις nihil aliud est quam quod compositum est, tanquam ad causas reducere... Ita in analyticis cognoscendi rationes ad primas quasi formas tanquam ad causas revocantur” (F. A. Trendelenburg, Elementa logicae aristotélae, 9th ed., Berlin 1892, p. 47). Consequently, wherever a similar resolutive and regressive process intervenes, there is a. Thus, to say nothing of a. in a material sense (e.g., chemical a., spectral a.), essentially analytical is the process by which a complex phenomenon, fact, or situation is resolved into its concomitant and determining elements and traced back to its conditions, laws, and causes. It matters little whether the fact or phenomenon or function be of a physical, physiological, or even psychic order, individual or collective: thus, the examination by Galileo of the oscillatory motion of the pendulum is a., as is the introspection of the psychologist into the phenomenon of fear, or the study of a case of collective hallucination, etc.
In the more strictly logical domain, a. concerns first of all concepts and judgments. As regards the concept, which is a logical whole, generally of polyvalent content, a. consists in resolving (thinking) it into those simpler notes that constitute its comprehension or objective content. Thus one proceeds by a. when, for example, the concept of science is resolved into its primary elements to arrive at a distinct definition. One also speaks, though less properly, of a. in relation to the extension of a concept: then a. is nothing but the division of the concept into the multiple subjects to which it is referable. Since the content and extension or universality of a concept stand in inverse ratio, it is clear that an a. with respect to the content of a concept will result in an increase, and hence in a certain synthesis, of its extension: inasmuch as the simpler notions derived from a. precisely because they are such will have a greater range of reference. Hence the fluctuations and sometimes inversions in terminology that are encountered among certain authors with regard to this particular logical field of application of a.
As regards the judgment, if it is considered in its psychological genesis, it generally implies an initial a., that is, the discernment of subject and predicate that the mind performs on the object of judgment before uniting them in synthesis by attribution. Then, in relation to the movement of thought occasioned by the mutual connection of judgments, a. consists, according to the sense clearly formulated by Alexander of Aphrodisias (In Analyt. prior., I, p. 7, 13-13, Berlin 1883), in ascending from consequences to principles: more specifically, in reducing a complex proposition or conclusion to a general principle that contains and justifies it, and which, while being more universal in its references, is simpler in its actual content. Thus, the process by which a particular truth is demonstrated by resolving it into a more immediate principle is always a., for example when the dishonesty of theft is proved by affirming it as a violation of justice.
As may be seen, a., from an originally rather restricted meaning, has assumed in logic a much broader and richer sense, coming to designate in its entirety the ascending and ontologically regressive process of the human mind from the multiple to the simple, from the concrete to the abstract, from the particular to the universal. The inductive method is consequently related to a., although globally, as it is used in the sciences, it also involves non-analytical moments, as when one proceeds, by way of deduction, to verify the hypothesis. The reference of scientific induction to a. is already clearly found in Newton (cf. Optice, Latin ed., London 1706, p. 347).
Opposite to a. is s., which, to restrict ourselves here to its use in the logical domain, designates precisely the inverse procedure of thought by which one proceeds from the parts to the whole, from the simple to the compound, from the universal to the particular, from the law, cause, or principle to the phenomenon, effect, or conclusion. Thus it is s. when one proceeds by deductive syllogistic reasoning from universal principles, simpler in notional content, to particular consequences governed by those principles; or when, from a law already established, one moves to the search in experience for new facts and phenomena suggested and explained by that law; or again when, from any norm, for example of ethics or aesthetics, one deduces in concreto what a human act must be in order to be called honest, or a work of art in order to be beautiful.
A. and s. thus adequately divide the logical processes of human thought: both useful, both
Both, necessary and each responding to the dimorphism of human knowledge directed toward empirical contingency and universal values, find greater or lesser employment in the various fields and objects of knowledge according to the different nature of the sciences, their degree of organization, and the mental disposition of individuals. Thus, while the natural sciences, in reducing and ordering 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 formulations remain—on the contrary, the philosophical and mathematical sciences abound more in synthesis. Moreover, analysis and synthesis are not two procedures that can be sharply separated, nor can any science entirely dispense with one or the other. When this occurs, deviations inevitably arise at the expense of the balance of thought and thus of truth. Analysis, as an instrument of discovery and concrete knowledge of nature, if cultivated exclusively, will reinforce the positivistic tendency in science; while synthesis, also a powerful means of progress and enrichment of thought, if completely detached from analysis, will wither into abstraction and a priorism. And while human thought universally begins with analysis—since what is manifold, concrete, and particular is first known to us through the senses, always more or less complex and in need of mental resolution—nevertheless, thought will not attain its natural development and completion unless it fertilizes the material derived from analysis with a synthesis marked by prudence and courage.
As in the construction of knowledge, so in its teaching: although it may be said that in many sciences synthesis, as a didactic method, offers undoubted advantages, it should 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, deriving from their fundamental meanings, also find other frequent applications that are easily grasped: one speaks, for example, of grammatical analysis, aesthetic analysis, philological analysis; of historical analysis and synthesis; of analytic and synthetic languages. One also speaks, with reference to mental types (as we have already hinted), of an analytic mind and a synthetic mind, according to whether individuals exhibit a predominance of concrete observation, intuition, and discernment, or instead a comprehensive, deductive, and logical spirit capable of general and unitary knowledge.