ANALYSIS AND SYNTHESIS. - A. (Gr. ἀνάλυσις from ἀναλύειν, synonymous with ἀνάγειν = resolvere) and s. (Gr. σύνθεσις from συν-τίθημι = compono) designate two opposed and correlative methods in use in science, the first consisting in ascending from the composite to the simple and from effect to cause, the second in the inverse operation by which one passes from the simple to the composite and descends from cause to effect.
Historically a., as a mathematical method, is attested for the first time in Plato, to whom its discovery is attributed, and is defined as a method by which "the object of inquiry is reduced to an admitted principle" (Proclus, In Euclidem, p. 211). A sense substantially taken up again by Descartes when he called a. algebraic calculation in general. This identification of a. with algebra has not entirely fallen away, even if by now more precisely a. (abbreviation of infinitesimal a.) is in mathematics synonymous with differential and integral calculus or higher algebra. Today, in philosophy and in the sciences, we call a. every process, real or logical, 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 which constitute it. A sense that is already Aristotle's, whose two principal books of logic are in fact called Analytics, insofar as the syllogism and other complex modes of knowledge are resolved into the most elementary forms and into 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 such a resolutive 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 by which a phenomenon, a fact, a complex situation is resolved into its concomitant and determining elements, and traced back to its conditions, its laws, its causes, is essentially analytical. It does not matter whether the fact or phenomenon or function is of a physical, physiological or even psychic order, 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 first elements in order to derive from them 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 can be referred. Since the content and the extension or universality of a concept stand in inverse ratio, it is clear that an a. as to the content of a concept will resolve into an increase, and therefore into a certain synthesis, of its extension: insofar as the simpler notions derived from the a., precisely because they are such, will have a greater breadth of reference. Hence the fluctuations and sometimes inversions in terminology that are found in certain authors, with regard to this particular logical field of application of a.
As for the judgment, if one regards it in its psychological origin, it involves most of the time 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 to which the mutual connection of judgments gives rise, a. consists, according to the sense already clearly formulated by Alexander of Aphrodisias (In Analyt. priora, I, p. 7, 13-15, Berlin 1883), in ascending from consequences to principles: more specifically, in tracing a proposition or conclusion of a complex order back to a general principle that contains and justifies it, and which, although more universal in its references, is simpler in its actual content. Thus the process by which one demonstrates a particular truth by resolving it into a more immediate principle is always a., for example when one proves the dishonesty of theft by affirming it as a violation of justice.
As can be seen, a., from a fairly narrow original meaning, has assumed in logic a much broader and denser 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, from the particular to the universal. It is to a. that the inductive method consequently appeals, although, taken as a whole, as it is used in the sciences, it also involves non-analytical moments, as when one proceeds, by way of deduction, to the verification of the hypothesis. The reference of scientific induction to a. is already clearly found in Newton (cf. Optice, Latin ed., London 1706, p. 347).
Opposed to a. is s. which, to restrict ourselves here to its employment in the logical field, designates precisely the inverse procedure of thought by which one goes from the parts to the whole, from the simple to the composite, from the universal to the particular, from the law, cause, principle, to the phenomenon, effect, conclusion. Thus the deductive syllogistic procedure is s. by which, from universal principles, simpler in notional content, one proceeds to particular consequences governed by those principles; or else, from a law already won one moves to the search, in experience, for new facts and phenomena suggested and explained by that law; or again, from any norm whatever, for example of ethics or aesthetics, one deduces in concrete terms 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. therefore adequately divide the logical processes of human thought: both useful, both necessary, both of them responding to the dimorphism of human knowledge, which is directed toward empirical contingency and toward 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 individual persons. Thus, while the natural sciences, in the reduction and ordering of the complex phenomenology of nature, are and must remain predominantly analytical, and all the more analytical the more uncertain and hypothetical their conclusions and their systematic results remain, on the contrary the philosophical and mathematical sciences abound more in synthesis. Moreover, analysis and synthesis are not two procedures separable with a clean cut, nor can one totally prescind from either in any science. When this happens, deviations inevitably occur 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 entrench science in positivism; and synthesis, likewise a powerful means of progress and enrichment of thought, if completely detached from analysis, will wither into abstractism and apriorism. And while universally human thought takes its start from analysis, since the multiple, the concrete, the particular is first known to us through the senses, always more or less complex, and therefore in need for us of a multiple mental resolution, nevertheless thought will not attain its natural development and complement except by fertilizing with a synthesis made of prudence and courage the material derived from analysis. As in the construction, so in the teaching of science: although it may be said that in many sciences, as a didactic method, synthesis presents undoubted advantages, nevertheless it should in every case be tempered by a wise employment 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 find other frequent applications of easy intuition: one speaks, for example, of grammatical analysis, of aesthetic analysis, of philological analysis; of historical analysis and synthesis; of analytic languages and synthetic languages. One also speaks, with reference to mental types, and we have alluded to this above, of analytic and synthetic intellect, according to whether there prevails in individuals the concrete spirit of observation, intuition and discernment, or instead the comprehensive, deductive and logical spirit, suited to general and unitary knowledge.
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Ugo Viglino