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See R. A. Eberle, Nominalistic Systems (1970).
nominalism(PHILOSOPHY) the doctrine that ‘universal’ concepts which define general classes of things (e.g. redness, roundness) cannot be conceived of as having ‘real existence’ in the way that individual things exist (compare ESSENTIALISM).
a philosophical doctrine according to which the names of properties, classes, and relationships are not “proper names” (that is, names of individual, unique “essences,” real or ideal) but “common names,” that is, variables, for which the names of unique essences may be substituted. (For example, the name “person” may be replaced by the names “Peter,” “Paul,” “Anna,” “Mary,” and so forth.) In other words, common names are not applied to a class of things “as a whole” but to each thing in a particular grouping (plurality), which is called a class but which cannot be equated with a thing or substance. Classes exist not as things but as mental images or abstractions.
Because they may be used with reference to many things, the names for characteristics, classes, and relationships are also called universals. According to nominalism, universals are the names of names and are not essences (as in scholastic realism) or concepts (as in conceptualism). “If we say that a living being, a stone, a spirit, or anything else is a universal, this should not be understood as meaning that a man or a stone are universals, but only that the corresponding words (living being, stone, and so forth) are universals—that is, names common to many things. The concepts (conceptus), however, which correspond to these things in our minds are only images and phantasms (imagines et phantasmata) of various living beings and other things” (T. Hobbes, Izbr. proizvedeniia, vol. 1, Moscow, 1964, p. 66).
The sources of nominalism are found in antiquity. Its first representatives in the early classical period were Antisthenes and Diogenes of Sinope, who were opponents of Plato’s “world of ideas” and who made the nominalist point of view the foundation of ethics. Martianus Capella, a philosopher of the late classical period, expounded logic from a nominalist viewpoint.
The terms “nominalism” and “nominalists” were first used in the early Middle Ages, when nominalism emerged as a reaction against the rationalistic mysticism of the Neoplatonists. The nominalist interpretation of certain theological dogmas by Berengarius of Tours and Roscelin met with the disapproval of the church, and nominalism was condemned at the Council of Soissons (1092). However, this did not halt the development of nominalist ideas, which continued in the late Middle Ages in philosophical anthropology (Henry of Ghent), psychology (Alfred de Sereshel [Alfred dem Engländer]), and logic (Peter of Spain, William of Ockham, and J. Buridan). At that time nominalism grew into a philosophy of experimental science, breaking away from Scholasticism (Nicolaus of Autrecourt and Nicote Oresme). As V. I. Lenin pointed out, the struggle between the medieval nominalists and realists is, in many respects, analogous to the struggle between the materialists and idealists (Poln. sobr. soch., 5th ed., vol. 25, p. 37).
During the Renaissance, a period marked by a preference for experience over scholastic abstractions, nominalism found many supporters (including L. Valla, J. L. Vives, and Nizolius). In the modern era, nominalism usually took the form of sensationalism, represented, on the one hand, by T. Hobbes, J. Locke, and the French materialists, and on the other hand, by G. Berkeley and D. Hume. The principles of the semiotic doctrine characteristic of modern nominalism were established during this period. Among these principles is the assertion that the meaning of an abstraction is not free of its context. Abstractions are to be regarded as “symbolic fictions,” as terms whose meaning is determined by their context and whose use serves as a shorthand method of formulating completely intelligible assertions about real objects, especially when there are an infinite number of them. The correct use of abstractions for the convenient expression of specific facts depends on the ability to exclude them from any context, thereby proving their freedom from contradictoriness by finding an appropriate empirical model (the process of verification).
The idea of the exclusion of abstractions has become central to modern mathematical nominalism—a particular outlook on the foundations of mathematics. Mathematical nominalism originated in the early 20th century in Poland (S. Leśniewski, L. Chwistek, T. Kotarbiñski, and A. Tarski, for example), the USA (N. Goodman, W. Quine, L. Henkin, and R. Martin), and elsewhere in response to the revival of Platonism in the concepts of set theory, particularly the unlimited introduction of abstractions as essences (the principle of abstraction), which leads to paradoxes. The mathematical nominalists made a number of attempts to construct a mathematics without paradoxes, based on formal systems (formal languages), the terms of which can be used to express many mathematical abstractions and thus to exclude them by substituting an appropriate “linguistic model.”
The logic underlying these systems may be understood in the spirit of the nominalist tradition: only entities that can be perceived by the senses exist (“originally,” “of themselves,” outside of thought and speech). Only they (their proper names or descriptions) can be the meanings of the objective variables of logical language, forming the true “universe of discourse” (the objective realm) of any scientific theory. Therefore, from the viewpoint of nominalism, the only acceptable logic is a narrow calculus of predicates (hence the logic of predicates). To some extent, the nominalist program is justified by Craig’s theorem, according to which abstract terms can be excluded from the language of a scientific theory (W. Craig, “On Axiomatizability Within a System,” Journal of Symbolic Logic, 1953, vol. 18). However, the full practical realization of the nominalist program appears to be impossible.
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M. M. NOVOSELOV