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the representation of some body of knowledge—such as the arguments, proofs, or classification and information-gathering procedures of a scientific theory—as a formal system, or calculus.
Formalization is based on definite abstractions, idealizations, and artificial symbolic languages. It is used not only in mathematics (seeFORMALISM, MATHEMATICAL) but also in those sciences that have a sufficiently sophisticated mathematical apparatus. Formalization involves a strengthening of the role of formal logic as the foundation of theoretical sciences; the heightened rule of formal logic is necessitated by the insufficiency of formalized theories based on an intuitive belief that a certain line of reasoning is in accord with rules of logic learned through an acquired capacity for correct thinking. Only elementary theories with a simple logical structure and a small stock of concepts can be completely formalized; examples are elementary geometry in mathematics and the propositional calculus and the restricted (first-order) predicate calculus in logic. In principle, if a theory is complex, it cannot be completely formalized (seeCOMPLETENESS and META-THEORY).
Formalization permits the systematization, refinement, and methodological clarification of the content of a theory. Moreover, through formalization the interrelationships between the theory’s various assertions can be ascertained. Formalization also makes possible the identification and formulation of unresolved problems.
Formalization as a cognitive device, particularly formalization in the narrow mathematical sense, bears a relative character in the sense that a theory can be simultaneously both the means of formalization (of some other theory or domain of phenomena) and the object of formalization (in a more formal theory). Thus, traditional “formal” logic is a formalization with respect to the set of relationships of human thought reflected in it; with respect, however, to its own (axiomatic) formalization it constitutes a meaning-based theory of formalization.
REFERENCESTarski, A. Vvedenie v logiku i metodologiiu deduktivnykh nauk. Moscow, 1948. (Translated from English.)
Kleene, S. C. Vvedenie v metamatematiku. Moscow, 1957. Subsec. 15. (Translated from English.)
Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. Introduction (Translated from English.)