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  Formalism is an exclusive concentration on form or forms, in any field from religion to science, from social behaviour to the arts.

In the criticism of fine art, formalism was a movement which flourished in the early part of this century, and then again from the 1960s onwards, in the work of such writers as Clement Greenberg. It offers a corrective to the obsessive interest in authenticity and individuality of connoisseurs, who label anything they are unable positively to identify as either ‘after X’, ‘School of X’ or a forgery. Formalism treats the characteristic appearance of, for example, Romantic painting, as an expression of ‘a way of seeing’ special to that period. It seeks to subsume the many different stylistic expressions of a period into a kind of meta-style, a dominant mode of seeing whose validity is confirmed by examples of the art of the period in question. There are two main problems: first, that this stance is too narrow to encompass a complete explanation of the meaning of any given work of art, and second, that only those works which support the formalist construction are considered important, the rest tending to be marginalized—a formalist equivalent of the connoisseurs\' ‘inauthentic’ label. Nonetheless, formalism was and is a salutary discipline, and was an important component in the development of modernism at the beginning of this century, when the notion was prevalent that artistic styles could be codified, and when artists themselves were more fascinated by such programmes and ‘isms’ than in almost any other period in history.

In literature, formalism was a critical theory developed in immediately post-Revolutionary Russia, by a group of writers and academics led by Roman Jakobson. The basic idea was that ‘literature’, as distinct from any other kind of writing, is achieved by the use of certain artificial formal devices, specific to it alone. For the original formalists, this theory had political and social overtones as well as literary: the structures of written communication were directly relevant to the objectives of such communication. In particular, the Formalists said that ‘literature’ never depicts reality in a straightforward way, but always mediates, organizes and presents it by the use of language, ‘defamiliarising’ it in the process. The idea of ‘defamiliarization’ (in Russian stranenie, ‘making strange’) interested later literary theorists, particularly Jacques Derrida and his followers: it is, precisely, the creative process which deconstruction sets out to investigate and sidestep.

In mathematics, formalism is a school of thought that all work in mathematics should be reduced to manipulations of sentences of symbolic logic, using standard rules. It was the logical outcome of the 19th-century search for greater rigour in mathematics. Programmes were established to reduce the whole of known mathematics to set theory (which seemed to be among the most generally useful branches of the science). First attempts to do this included those of Bertrand Russell and A.N. Whitehead in Principia Mathematica (1910), and the later Hilbert Programme. It was hoped that such programmes would be the culmination of all mathematics, not only setting the discipline on a strong formal foundation, but making it possible to write out a proof or disproof of any formal sentence totally mechanically. In other words, every mathematical result would be known or not known. Kurt Gödel, however, proved this impossible with his Incompleteness Theorem, dooming Hilbert\'s programme as unattainable (see Gödel\'s incompleteness theorem), and formalism is today something of a back-water in mathematical philosophy. Mathematicians tend to avoid the complication of constantly working in formal symbols, and to work informally—though arguments should be capable of being backed up with their formal versions if required.

In music, formalism is the use of specific musical forms—for example, fugue, passacaglia and ritornello—to give external order to works whose main intellectual rationale comes from something else. Thus, romantic symphonists, drawing the threads of their works together in last movements, often treated non-fugal material in the manner of fugue. Christian church composers, faced with the task of giving musical coherence to settings of enormously long liturgical statements such as the Gloria or Dies Irae, often used fugal or sonata techniques, sometimes to the point where musical logic, and attractiveness, obliterated the original devotional function of the work. Opera composers, from Purcell (in Dido and Aeneas) and Mozart (in his act-finales) to Verdi (in Falstaff) often underlaid emotional and dramatic flow with such forms as chaconne or fugue. Twelve-note composers (for example Berg in Wozzeck, Schoenberg in his concertos and chamber works, or Webern in almost every piece) used 18th-century forms to give a sense (real or ironical) of familiar order to work which was otherwise radical and innovatory: a process analogous to, if subtler than, the collage-like use of 18th-century forms by neoclassical composers. PD MG KMcL SMcL

See also axiomatization.Further reading Cedric Greenberg, Art and Culture.



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