UNITY

Unity, or oneness, is generally regarded as the attribute of a thing whereby it is undivided in itself and yet divided from others. Since it is an ultimate philosophical notion, it cannot be defined strictly, i.e., in terms that are better known; it is also somewhat ambiguous in meaning. As an abstract noun it refers to a property or character common to everything that can be said to be and in this sense is enumerated among the transcendentals; as a concrete noun it refers to a unity, i.e., to some one thing. The diversity of usage can be traced back to early Greek thought.

Among the pre-Socratics, parmenides noted that the cosmos exists or simply is. He held that whatever is constitutes the realm of being, since he could not think that what is, is not. If all is being, there is nothing that is not being. Being becomes thus self-identical; it is one. A follower of Parmenides, zeno of elea, thereupon developed the paradoxes of the many. The "many," in his view, were also "ones" as parts or units of a quantitative whole, or as constitutive of plurality. The resulting positions, namely, that unity is a property of what is and that a unity is part of a whole, are respectively linked to the abstract and the concrete meaning. Although the parallel is not absolute, the abstract meaning envisages all being as participating in unity or as having the common character of unity, while the concrete meaning has reference to the parts of a whole.

In view of the influence of history on the development of this concept, we shall outline how unity is treated first in the works of Plato, Aristotle, and Plotinus; then in the medieval tradition as exemplified by St. Thomas Aquinas; and finally in modern thought, with particular emphasis on its role in recent mathematics.

Classical Thinkers. While aware of Parmenides's statement that whatever is, is one, plato understood "whatever is" as divided into this and that being. In his doctrine of forms (ίδέαι), a form expresses being as a nature, a type; and forms are stable, necessary natures. Changing things are intelligible insofar as they participate in some form, or unchanging nature. Plato thus stresses a plurality of natures. He raises the question whether this "many" can be reduced to anything more ultimate, and suggests, in the Republic, a reduction to the good. The Good, for him, is above natures or forms and is not strictly a form itself. Yet Plato makes no clear reduction of the Good to the One. His plurality of kinds of being, it should be noted, is not Zeno's plurality of units. Nor is his "one" a mathematical form, because Plato distinguishes mathematical forms from forms as natures. Forms as natures are of one specific kind, while there can be many instances of a mathematical form. Such instances resemble Zeno's idea of unity.

Stressing the origin of knowledge, Aristotle bases his theory of cognition on the plurality of sensible particulars. This plurality includes not only groups containing many instances of one kind, as many sheep, but also many classes or many different kinds, as men and animals. The Aristotelian view recognizes both the Platonic forms of nature and so the unity of being as self-identical, as well as Zeno's unity or part that is constitutive of a plurality (cf. Meta. 1001a ff., 1052a ff.).

The outstanding exponent of neoplatonism, plotinus, posits the principle that unity precedes multiplicity (Enneades 5.1.5). Thus, for him, all plurality must be reduced to the One. The One or Unity is consequently above being, and all else is one by participation. Plotinus's One expresses intense, unique perfection rather than the totality of the cosmos.

Thomistic Analysis. St. thomas aquinas further explains the unity of a nature or kind, and unity as one of many, through corresponding concepts associated with plurality or multitude: to the first corresponds transcendental multitude; to the second, numerical multitude.

Unity and Existence. Some Thomists maintain that St. Thomas gave new meaning to both unity and multitude by interpreting these concepts existentially (see existential metaphysics). When St. Thomas speaks of being, in this view, he means it primarily not as nature or intelligible content but as act of existence (In 1 Sent. 25.1.4; Summa theologiae 1a, 3.3–4). To say that a thing is, is to say that it is one; but it is one not primarily from what it is but rather through its act of existence. It is created to be a kind, and is not to be regarded as something that is already a kind and then given existence. As with both Plato and Aristotle, for St. Thomas unity does not add any reality to being; it is only the negation of division. Thus "one" means "undivided being," and this in the sense of an existent or a possible existent (ST 1a, 11–14). To see the unity of a thing stemming from its manner of existence and not primarily from its nature as expressed through its definition allows such Thomists greater leeway in admitting unities of all sorts. For example, the parasitic plant is what it is only in a close conjunction with its host. Its unity taken from the point of view of its manner of existence includes this relationship, whereas from the point of view of "ideas" or definition it seems to exclude it.

St. Thomas contrasted unity with plurality in two ways: first, with different kinds of being, and secondly, with instances of the same kind. Among different kinds of being each could be said to be itself and not other. Each would be an existent individual. Unity here is not a property or characteristic of the thing in any accidental sense, but rather a transcendental property expressing the very being of the thing. Many such existents form a multitude, and here each being holds a determinate grade in being. St. Thomas refers to such a multitude as transcendental (ST 1a, 30.3); the best example is found in the realm of spiritual being. In this sense angel is not strictly a common noun, since there is nothing univocally common to Michael, Gabriel, Raphael, etc.

Unity and Number. Other instances occur in the material universe, which evidently is a quantitative whole constituted of many things as parts. It is this unity that St. Thomas considers the basis of number, for such parts or units are univocally alike, except for the fact that they are different parts of a whole or units of a group. They constitute a numerical multitude.

The first meaning of unity, as a transcendental property interchangeable with being, is not the basis of number, nor does it suggest any mathematical connotations. Like Plotinus, however, St. Thomas sees the necessity of reducing even transcendental multitude to unity. The many existents must be caused by the Pure Act of Existence that is Unique (see pure act). The Unique is one only in an analogical sense.

The distinction between numerical and transcendental unity is important for guarding the distinction between metaphysics and mathematics. For example, the principle of identity interpreted in metaphysical terms does not express a pure equality or a logical identity as in abstract mathematics (see identity, principle of). The distinction also enables the theologian to eliminate all mathematical connotations from his analogical use of terms, as, for example, when he speaks of the Trinity as one God in three Divine Persons. Mystery as this is, it becomes absolutely contradictory if it is thought of strictly in mathematical terms.

Descartes and Leibniz. The revival of mathematics and of Platonic and Neoplatonic currents in the 17th century centered the attention of modern philosophy on unity. Primarily interested in mathematics and then in its philosophical foundations, R. descartes sought not just the fundamental existent, the ego, but also clear and distinct ideas or simple natures as ultimates. He did not, however, clearly distinguish the unity of the ego in metaphysics from the unity studied in mathematics. His simple natures thus remain unclear. (Cf. Regulae; Meditations. )

For G. W. von leibniz, unity is the theme of his philosophy. His basic notion is the monad. "It is only indivisible substances and their different states which are absolutely real" (Correspondence with Arnauld ). "If there were no true one, then every true being would be eliminated" (Correspondence with De Volder ). The "true one" he likens to a spiritual soul. He was also a competent mathematician and a forerunner of much that is contemporary. While attempting to define unity and number in The Art of Combination, he says that unity is a notion abstracted from one being, whereas whole number is the idea of whole or totality formed by consideration of many unities—a description that suggests the notion of set or class as used in modern mathematics. Unity, he holds, is the simplest notion; while number is a more complex notion presupposing unity; and part or fraction is more complex than either since it presupposes both.

Unity in Mathematics. Modern mathematics begins with the notion of set as containing one or more members or as being null or empty; it also employs the idea of one set succeeding another. With these notions it defines the cardinal and ordinal numbers, including one. The procedure may be explained through the simple example of counting. If a shepherd wishes to count his sheep, he can match a stick or bead to each member of his flock and so establish a one-to-one correspondence between the units of the two groups, which indicates that both groups have the same number. The stick or bead can be refined to a stroke, or replaced by a symbol, or simply be considered as an element of a group or set, having the features of a unit with no character other than being matchable with other units or elements of another set or group. Since it is only after the operation of matching that both groups are said to have the same number, the idea of number is seen as subsequent to the idea of the unit-element.

Mathematicians, trying to define their basic terms logically, establish a distinction between "one" as a unit or member of a class and the "number one." They define the number one as the set of all those sets that contain only one member. This set of sets, however, is the result of the operation of forming a one-to-one correspondence among the member sets, and this operation presupposes "one" in the sense of unit or member. The last-named unit is what St. Thomas considered as the basis of his numerical multitude.

Since the number one presupposes an operation or relation established between sets and their unit members, the modern mathematician does not think in terms of substance, as does the philosopher, but rather in terms of relation. The result is that the notion of unity as employed in the mathematical sciences becomes even more distinct from unity as it is metaphysically understood.

Unity in Other Disciplines. Of the three fundamental ideas of unity, namely, that of number, that of unit-element of sets, and that of the existent, the last or transcendental notion of unity is the most important. This unity is exemplified for man, who does not have direct experience of the spiritual, in the unity of higher living organisms and especially in the living rational person. Such organisms can be said to guard their unity as they guard their life.

The biological theory of organic evolution questions, for the modern mind, the concept of unity of natures. And as evolution has been extended to explain the entire material universe, the seeming progressive development from the simple to the complex modifies not only the unit-substance notion but also the concept of "this" being as distinct from "that" being. In fact, the very idea of substance seems to be negated by modern science. Perhaps this is an instance where the scientist intimates to the philosopher the importance of noting a particular manner of existence before making any attempt at definition. Even though the mode of existence of beings in evolution may have a strongly relational character, this does not eliminate the termini of such relations. From the outset these are the factors through whose interaction evolution comes about. As such their "unit" character is reexpressed whenever different, more or less stable levels are reached in the development through interaction. Since scientists study nature through its action and connections, their method does not lend itself to grasping substance in its unity. Moreover, since, as a general rule, they treat their data mathematically, relational aspects inevitably predominate in their analyses.

Analogous to the living organism with its integral coordination and functional unity is society, exemplified in the family or the nation. The Church is such a society, but one whose unity is so marked that it approximates the unity of a spiritual person. It is in this sense that unity is spoken of as one of the marks of the Church (see unity of the church).

See Also: individuality; individuation; monism.

Bibliography: l. de raeymaeker, The Philosophy of Being, tr. e. h. ziegelmeyer (St. Louis 1954). Enciclopedia filosofica, 4v. (Venice-Rome 1957) 4:1395–1406. p. foulquiÉ and r. saint-jean, Dictionnaire de la langue philosophique (Paris 1962). e. h. gilson, The Unity of Philosophical Experience (New York 1937). r. eisler, Wörterbuch der philosophischen Begriffe, 3 v. (4th ed. Berlin 1927–30) 1:307–313. j. r. newman, The World of Mathematics, 4 v. (New York 1956). r. a. di nardo, The Unity of the Human Person (CUA Philosophical Studies 199; Washington 1961). l. oeing-hanhoff, Ens et unum convertuntur (Beiträge zur Geschichte der Philosophie und Theologie des Mittelalters [Münster 1891– ] 37.3; Münster 1953).

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