Analysis and Synthesis

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Transcriptions of the Greek νάλυσις, from ν and λύω, meaning resolution, and σύνθεσις, from σύν and τίθημι, meaning composition. Analysis and synthesis are methods of inquiry and processes of things. Logical statements of analysis and synthesis, therefore, reflect basic metaphysical and epistemological theories.

Greek Thought. epicurus, building on the atomic philosophy of democritus, rejected dialectic for a canonic of sensations, preconceptions, and passions. All man's notions are derived from sensations by contact, analogy, likeness, and synthesis (Diogenes Laertius, 10.3132). plato distinguished two methods in dialectic: division (διαίρεσις) and bringing together (συναγωγέ); and later commentators, such as Ammonius, proclus, and Diogenes Laertius, enumerate three or four dialectical methods that include "analysis" but not "synthesis."

Aristotle, who frequently contrasted the methods of Democritus and Plato, made use of both analysis (but not in the sense of dichotomous division) and of synthesis (but not in the sense of combination of atomic parts). Aristotle distinguishes between a mixture, or composition (σύνθεσις), and a compound, or combination (μίξις; Gen. et cor. 328a 517); but he also uses "synthesis" more broadly to include three kinds: compositions of elements in simple substances, compositions of simple substances in homoeomerous substances (bones, flesh, etc.), and compositions of these in more complex organic and inorganic bodies (Part. animal. 646a 1224; Topica 151a 2031). Thinking is true or false by a synthesis (or division) of objects of thought (Anim. 430a 26-b 4); synthesis and division are essential to truth and falsity, and nouns and verbs are related by synthesis and division in propositions (Interp. 16a 918). In general, a synthesis is a combination of parts in a whole, and its opposite is division rather than analysis. Analysis is resolution in two senses for Aristotle. In the Prior Analytics it is the resolution of all syllogisms to the perfect, or universal, syllogisms of the first figure (47a 25). In the Posterior Analytics it is the resolution of demonstrative syllogisms to true premises (78a 68). In the latter sense practical deliberation, like mathematical inquiry, is an analysis: what is sought is assumed and the means of achieving it are sought. What is last in the order of analysis is first in the order of genesis (Eth. Nic. 1112b 1124).

Commentators. Mathematical analysis is presented by Euclid, Pappus, and Proclus as Aristotle formulated it. Analysis is the method of assuming what is sought and tracing its consequences to something admitted to be true. These thinkers added, however, that synthesis is the contrary method of assuming that which is admitted to be true and tracing its consequences. Alexander of Aphrodisias attributes this geometrical conception of analysis and synthesis to Aristotle in his commentary on the Prior Analytics. Synthesis is the way from principles to that which is derived from the principles, and analysis is the return from the ends to the principles. Greek commentators tended to accept this interpretation, and it was reinforced by Galen's inclusion of analysis and synthesis among the methods of medicine. Cicero, on the other hand, distinguished two methods, "invention" and "judgment" and since the method of invention is developed in the Topics, the method of judgment was sought in the Analytics. After the translation of the Analytics and the Topics in the 12th century, the terms resolutio (analysis) and compositio (synthesis) took their places beside inventio and judicium in the interpretation of Aristotle's logic. thomas aquinas distinguishes three applications of these terms: (1) nouns and verbs are related in propositions by composition and division; (2) inferences involving certainty depend on judgment and are treated in the Analytics, those short of certainty depend on invention, and inventions concerned with probabilities are treated in the Topics; and (3) inference from experienced composites to simple principles is resolution, and inference from principles or simples to conclusions or composites is composition.

Renaissance and Modern Thought. During the Renaissance, problems of method assumed a central place in the arts and sciences and in logic. All the varieties of classifications of methods in logic and rhetoric, mathematics and medicine, science, practice, and the arts were brought into complex opposition. Two pairs of distinctionsanalysis and synthesis, and judgment and invention (or discovery)emerged as dominant, sometimes in opposition, sometimes merging. Peter ramus held that there is a single method and that invention and judgment are phases of its employment. His opponents, e.g., J. Schegk (151187) and J. zabarella, differentiated analysis and synthesis, resolution and composition. Basic issues of philosophy and scientific method were involved in the oppositions. Analysis and synthesis may be conceived in terms of parts and wholes or in terms of principles and conclusions. By the first approach analysis proceeds from wholes to parts, and synthesis arranges parts in wholes; by the second approach analysis proceeds from effects to causes, and synthesis from principles to conclusions. The first constitutes a single method in which discovery is a synthesis of elements analyzed, and knowledge is conceived as empirical and a posteriori; the second distinguishes two processes, the analytic discovery of causes and principles and the synthetic derivation of conclusions; knowledge is conceived as universal and a priori. These differences emerged in formulations of scientific method when F. bacon sought a method of discovery in topics or tables of observations and a synthesis in the increase and organization of the sciences, while R. descartes sought a method of discovery in the methods of mathematical analysis and a synthesis in mathematical deduction.

Differences of method underlie the treatment of simple, clear, and distinct ideas by the philosophers of the 17th and 18th centuries. I. Kant abandoned dogmatic philosophy for the methods of critical philosophy and emphasized the need to distinguish (as many philosophers beginning with Aristotle had) between analytic and synthetic as applied to propositions or judgments and analytic and synthetic methods. He argued against D. hume that significant, and therefore true, judgments must be synthetic and that mathematical truths are synthetic, not analytic; he also sought to establish synthetic judgments a priori in mathematics, physics, and ethics by deriving them from principles synthetically.

Contemporary Usage. The oppositions of analytic and synthetic in contemporary philosophy apply the same distinctions to experience, nature, phenomena, and language; and the prominence of "analysis" in many 20th-century philosophies is conditioned by the same contradictory oppositions of definition. The truths of mathematics are analytic in an "analysis" related to the language of the Principia Mathematica, and they are derived, as the truths of any formalized science can be, from logical primitives. The analysis of language may be of formal languages or of actual languages, and it may proceed by constructing operational rules of use and of interpretation or by uncovering meanings of basic terms and of their coherences and incoherences. Phenomenological and existential analysis, on the other hand, seeks to avoid deduction and returns at each point to direct experience of phenomena without abstract separation of language, thought, and thing. Mathematics, psychology, and all the special sciences are subject to the same phenomenological analysis, but for that reason analysis does not depend on the conclusions of any of the sciences. The analysis of the phenomenologically given may adumbrate a transcendent ontological reality, or it may proceed creatively and operationally to the discovery of ontological essences emergent from existences. In both forms of analysis there is a tendency to refute or destroy the errors of past philosophers. Error is a mistaken synthesis, but there are many forms of analysis and, therefore, many errors of analysis owing to the fact that by one analysis other analyses are frequently seen to be undetected syntheses.

See Also: deduction; induction.

Bibliography: s. caramella, Enciclopedia filosofica, 4 v. (Venice-Rome 1957) 1:18590. r. eisler, Wörterbuch der philsophischen Begriffle, 3 v. (4th ed. Berlin 192730) 1:4546, 3:20104. s. e. dolan, "Resolution and Composition in Speculative and Practical Discourse," Laval Théologique et Philosophique 6 (1950) 962. l. m. rÉgis, "Analyse et synthèse dans l'oeuvre de saint Thomas," Studia Mediaevalia in honorem A. R. P. Martin (Bruges 1948) 30330.

[r. mckeon]