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Considered absolutely and in the broadest sense of the term, unspecified plurality, hence intelligible only as opposed to some kind of unity. Often usage connotes, in addition to mere plurality, a collectivity or superior kind of unification embracing a plurality of more ultimate units, as when one speaks of "a multitude." The more properly metaphysical notion refers to a non-numerable plurality. This article discusses the origin of the notion, its various analogies, and its uses in philosophy and theology.

Origin. In the order of development of the various analogical uses of this term, the first refers to the kind of plurality that is grasped in immediate sense experience, such a rudimentary and ultimate experience that no further analysis seems capable of altering the basic content or interpretation. Prior to any notion of number, this plurality of material things is available to the sense of touch, to sight, and to hearing. The ability to grasp such a plurality as a collective set is sometimes referred to as number sense, but this precedes the formation of the number concept since number, taken concretely, is a measured material multitude. This prime analogate of multitude, pertaining to material entities only, manifests finer distinctions within it. Thus some pluralities are not perfect in the sense that their parts cannot be perfectly distinguished, e.g., the fingers of the hand, distinct yet joined. Again, some multitudes are irreducible, e.g., a group of men, whereas others are not, e.g., several pieces of wax that can be melted together to form one. This latter instance indicates that plurality is due to materiality, to quantity, and not to formal differences that characterize the individual members who constitute the multitude.

Analogies. Plurality requires some kind of distinction, for without distinction there is simple identity under which only unity can be found. Confining one's thought to perceptible, physical multitude, it makes little difference whether the elements of the collection be substantial individuals or mere parts, whether they be of the same type or species or simply diverse in kind. Almost any degree of physical separation or any kind of actual separation will suffice to found such a multitude, but some sort of dividedness based on the distinctions proper to quantified matter is required. Since distinction itself is based on some mode of opposition that sets one element over against another, the ultimate foundation of physical multitude can be found in the fact that in extended matter one part is not the other: "this here" is not "that there." This opposition, a difference in quantity, is sometimes called situation (situs ). The parts of such a quantitative multitude can be understood as units; and when the collection is compared to a representative unit, the number, or relative measure, of the collection can be determined. This kind of multitude is opposed to, and yet, in some way, composed of, units that can be signified by the numeral "1."

Following a somewhat similar line of development, it is possible to conceive of multitude in another, analogous, sense based on some mode of formal opposition. Consequent upon opposition, formal distinctions can be made, and thus division and plurality or multitude in a formal sense. This notion of multitude is often called transcendental and is opposed to transcendental unity or unity of being itself, since form is the principle of entitative unity. Aristotle distinguished four modes of formal opposition: contradiction, contrariety, privation, and relation. Any of these may found a formal distinction and hence transcendental multitude"transcendental" because not limited to any category but analogically common, as the term being is common. Clearly the notion of multitude changes as the basis of opposition changes, but in any case the correlative unity is a kind of nondividedness in being itself and hence not a standard for quantitative measure or enumeration. A formal, or transcendental, multitude cannot be counted in any sense of the term, whereas material, or quantitative, multitude is the proper subject of enumeration.

Philosophy and Theology. In philosophical thought the opposition between unity and multiplicity appears in many guises. The problem of the one and the many is one of the most fundamental metaphysical issues: how can being be one, i.e., common to all that is, and yet be the obvious multitude that it is? The Eleatics tended to regard multiplicity as an illusion of the senses (see greek philosophy). plato found a unity in the transcendent Idea in which the sensible multitude participates, and Aristotle resorted to a theory of analogy to preserve both undeniable facts. The solution of I. kant, unique in its time, required a synthesizing activity of the mind that alone could attain intelligible unity in phenomenal multiplicity by the imposition of its own categories and connectives. The same issue reappears in epistemology as a dispute between nominalism and realism, in the philosophy of logic as the problem of universals, in the philosophy of nature as the problem of monism versus pluralism, and in philosophical theology as pantheism versus monotheism. Even in the philosophical considerations of mathematics, which seems to concern itself with quantitative plurality, there is a reflection of the problem in questions about the formation of the number concept.

In theology the concept of transcendental multitude is quite important inasmuch as all distinction and hence plurality of nonmaterial being must be formal. Any speculation about the pluralities of angels involves transcendental multitude, and each angelic individual can be understood as formally distinguished from all others. Likewise, in Trinitarian theology, the divine Persons are distinguished by a relational opposition that is itself transcendental and so the multiplicity in the Persons must be analogically transcendental. Apparently the image-making power of the human mind and the necessity for material signification create the impression that such multiplicity is subject to counting.

Bibliography: d. j. b. hawkins, Being and Becoming (New York 1954), ch. 7. f. sladeczek, "Die spekulative Auffassung vom Wesen der Einheit in ihrer Auswirkung auf Philosophie und Theologie," Scholastik 25 (1950) 36188. d. garcia, "De Metaphysica multitudinis ordinatione et de tribus simpliciter diversis specibus ejusdem secundum divi Thomae principia," Divus Thomas, 3d series 31 (1928) 83109, 60738; 32 (1929) 4356.

[c. f. weiher]

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