ORDER

Few notions have both so rich a heritage of meaning and so clear an application to all fields of knowledge as does order. There are many myths of cosmic order and its polar opposite, chaos, and there is no great religion without some principle of order. If men do not worship the transcendent God of Genesis, who imposes arrangement, then they have an immanent principle of law and of right relation of thing to thing and person to person (ṛta in Sanskrit, dhamma in Pali, tao in Chinese, as well as the more familiar Greek notions associated with κόσμος, δίκη, μο[symbol omitted]ρα, θέμις, and νο[symbol omitted]ς). Until comparatively recent times order is not only always regularly associated with deity ("Order is Heaven's first law," A. Pope, Essay on Man, Ep. 4.49) but also always a virtue in man (according to W. Jaeger, cosmos "originally signifies right order in a state or other community"). As preserved in the expression "law and order," the orderly is the right way to behave, the disorderly is the wrong way. Order applies, then, not only to the lawful universe but to right action of man; order is also regularly associated with intelligibility. To order may mean to act regularly, or with system, i.e., to arrange acts by method. In the last meaning, to order is to strive toward a goal, and those things that serve to achieve a goal are said to be ordered to it. Aristotle's favorite example of an order is an army, but St. thomas aquinas uses an example of another kind of order, a heap of stones. Stones can scarcely be said to be led, or to be under a leader; nevertheless, even when placed by chance, there is a gradation from the topmost to the lowermost (In 5 meta. 13.939). Order, then, has many senses, and things ordered in one way may yet not be ordered in another.

Formal Analysis. Exact definition of order seems only to have been achieved by scholastic philosophy, and the recent elaboration by symbolic logic, largely in the 20th century, has served to reduce the ambiguity of the term (see logic, symbolic). The primitive notion, itself indefinable, is relation. Since relation is between things (in the most general sense, including terms of thought), order presupposes a plurality of things. A theorem common to both St. Thomas and such moderns as J. royce,A. N. whitehead, and B. russell is that one thing cannot be ordered. The most general definition of order is to be related in some definite way. One definite way in which things are related is a series; that is, one thing is prior to another. In spite of the many senses in which "this" may be prior to "that," it follows immediately that "that" is posterior to "this." Logicians say of two symbols that they are well ordered when it makes a difference which is to the right of the other. "Before" and "after" are of this type. St. Thomas's defining statement is:

The terms "before" and "after" are attributed according to the relation of some principle. Now order includes some mode of the "before" and "after." Hence, wherever there is a principle, it is necessary that there be also an order of some kind. [Summa theologiae 2a2ae, 26.1]

Order, then, is not meant absolutely, but always in some respect, or as Whitehead put it: "'Order' is a mere generic term: there can only be some definite specific 'order,' not merely 'order' in the vague" [Process and Reality (New York 1929) 128].

St. Thomas seems first to have made explicit what is shared by all serial orders and what differentiates one from another:

…the notion of order includes the notion of the prior and the posterior. Thus there can be said to be an order of things according to all those modes, spatial, temporal and all like others, according to which a thing can be said to be before another. [In one sent. 20.1.3.1]

The modern way of expressing such a relation is to call it asymmetrical. That is, if A is larger than B, then B cannot be larger than A, etc. In a familiar symbol, if A > B, then immediately it follows, B < A (in the example B is smaller than A ). There are also symmetrical relations, in which the relation, r, is such that A r B implies B r A. The most obvious example of a symmetrical relation is equality. It makes no difference whether it is said that A = B or B = A, for one follows necessarily from the other.

"The notion of order includes the notion of the prior and the posterior," said St. Thomas. The modern says that asymmetry is necessary to an ordering relationship, but that it is not sufficient. For in a series, say the stones piled one atop the other, there is the same relation "on top of" holding between the top and the middle, and between the middle and the bottom stone. The relationship is called transitive when there are three things so related that when A r B and B r C, then A r C. This is certainly the case for "earlier than in time," or "to the right of in space," or "larger than in quantity," etc. Now although, as has been seen, serial relations are transitive and asymmetrical, there are also relations that are transitive and symmetrical. To use the former example of equality, it is obvious that when A = B and B = C, then it must follow that A = C. The common notion of Euclid is that things equal to the same thing are equal to each other. Those who have developed the theory of order here being expounded consider the principle of ordering relations no less fundamental in human thought. Consider such a relation as "heavier than," says William james, and symbolizing the relation >, when a > b > c > d, then a > d. Evidently three terms are the minimal number for transitivity, and since there can be no maximum number of terms, the formal types of order are infinite.

The principle of mediate comparison is only one form of a law which holds in many series of homogeneously related terms, the law that skipping intermediary terms leaves relations the same. This axiom of skipped intermediates or of transferred relations occurs, as we soon shall see, in logic as the fundamental principle of inference, in arithmetic as the fundamental property of the numberseries, in geometry as that of the straight line, the plane and the parallel. It seems to be on the whole the broadest and deepest law of man's thought. [James, Principles of Psychology (New York 1890, 1950) 2:646]

Asymmetry and transitivity are not sufficient to define serial order. A third important factor to be made explicit, whether in the case of St. Thomas's rocks one atop another or James's objects of different weights, is that if any two are chosen, there is the relation "above" or the relation "heavier than," and either it or its opposite holds. Since by virtue of this property one can form a single system of the items, it is called connexity. It is found in the case of musical notes, where, because of the relation "higher than in pitch," one can construct scales. The beauty of this is obvious to anyone who reflects upon how he uses numbers, whether whole numbers or fractions. Of any two (different numbers, not equal one to the other), one is greater than the other, and occupies a unique place in the series called the order of magnitude.

The foregoing analyzes a common intuitive concept of order that is learned in the nursery: a place for everything and everything in its place. It would be false to argue that this is the only formal definition of order. One might, for example, define order as a relation that is aliorelative (or nonreflexive, i.e., not related to itself but to another), transitive, and connected, and deduce asymmetry. [A. N. Whitehead, "Mathematics," Encyclopaedia Britannica, 11th ed.; also in Essays in Science and Philosophy (London and New York 1948) 197]. It would be false to argue also that this definition fits all kinds of order. It applies only to series that are open, i.e., in which the same term does not recur. There are not only asymmetrical relations that are called orderly, but also all symmetrical relations, such as the many forms of balance in which an axis divides matching or balanced sides.

Historical Survey. The concrete kinds of order (as distinguished from the formal types of order) may best be sketched in terms of their exemplification in the history of thought.

To a great extent the Egyptians viewed their kingdom as an expression of an eternal and unchanging order. For the Babylonians there was a struggle to maintain order in the universe and in human affairs, and an element of risk. One way of reading history as reflected in men's concepts is to regard society itself, and man's arts and sciences, as efforts to overcome confusion, to respond to the threat of chaos. Since contemporary human society lives in a period of vast uncertainty, it tends to smile at the complacency of the Egyptians and to feel sympathetically the anxiety of the Babylonians. The facts seem to be that there are periods when questioning the eternal order, or its goodness, rises to prominence. In contrast to the serenity of aristotle is the restlessness of St. augustine (in the Confessions ). In contrast to the serenity of St. Thomas and dante is the uncertainty of william of ockham and his followers. Some of the Elizabethans express confidence in the hierarchical ordering, somewhat as conceived by St. Augustine in The City of God (Civ. 19.13), but the rise of mechanical science in the early 17th century is associated with the unrest of John donne ("’Tis all in peeces, all cohaerance gone"). Yet the mechanical order became itself the ground of confidence:

All nature is but art unknown to thee; All chance direction, which thou canst not see; All discord, harmony not understood; All partial evil, universal good. [A. Pope, Essay on Man, Ep. 1.10]

In contrast to the serenity of the post-Newtonian men of the Enlightenment is the emphasis on the arbitrary and willful ways of individual genius in the Romantic period. Man is most recently being deeply affected by the existentialists—S. A. kierkegaard, F. W. nietzsche, F. M. dostoevskii', and their followers—who tend not only to question any knowledge of a divine order but also to belittle knowledge of an order of nature, to scoff at the law of human institutions, even to exalt chaos above order.

To trace the history of order is to go to the heart of Greco-Roman, medieval, and modern thought. It is also to discover those experiments that, in both their successes and failures, are most valuable in framing an adequate philosophy.

Greek Thought. The Greek achievement is fourfold. To the pre-Socratics man is indebted for the discovery that he inhabits a cosmos. The Ionian naturalists tend to stress mechanical order; particularly democritus (and later epicurus and lucretius) would account for all qualitative differences by changes in spatial order (τάξις). anaxagoras counts this a failure to explain the "why" of order: the "how" alone lacks the purpose of intelligence (νο[symbol omitted]ς). pythagoras and the Pythagoreans stress an intelligible order of forms to account for the sensuous harmony, especially as musical instruments produce sounds by simple proportions of the lengths of strings or vibrating columns of air. plato and Aristotle, however differing in their theories of form, both account for the good and the beautiful as illustrations of order (see beauty). Thus is born the concept of good order (εὐταξία) that the Stoics stress, and a problem is set for St. Augustine: if everything that is has an order, and some things are bad, how can there be bad order? (see evil.) Plato and Aristotle achieve concepts of the ordering of men in society and of the succession of the orders of constitutions.

Medieval Thought. The Christian achievement of a philosophy of order is best studied by St. Augustine, particularly in his brilliant dialogue De ordine. The plurality of orders is illustrated in nature, in the arts, in language, and above all in the moral life, seen in the light of divine providence. Christian philosophy surpasses its pagan predecessors in richness; problems of great depth are explored and solved, and without these achievements the modern world cannot be imagined. One is the conception of all peoples as part of an evolving pattern in time. History is a succession of orders: a concept developed centuries later by G. vico and, most recently, by E. Voegelin's Order and History (Baton Rouge, LA 1956–). The second problem is that of the ultimate good of man. Salvation belongs to what is commonly called "the order of grace," and Christian philosophies of order stress a sharp break between the methods by which one knows the natural order and the supernatural order. No modern philosopher of order has stated this better than B. pascal in his fragmentary Pensées, which are worth reading on the three orders, any one irreducible to any other (history is neither nature, nor supernature, and is studied in a unique fashion).

Modern Thought. A great modern achievement is the understanding of the world of nature as a unitary order. How the new science was made possible by the medieval theological framework, which itself grew out of the ancient movements, is shown by Whitehead in Science and the Modern World (New York 1925): "There can be no living science unless there is a widespread instinctive conviction in the existence of an Order of Things, and, in particular, of an Order of Nature "(5). The world ruled by power that is all-extensive, down to the least detail, yet in principle intelligible, is the living faith of Christianity. This was lacking, Whitehead argues, in those regions where science did not arise. Order is coupled by the founders of modern philosophy with method, that is, regular procedure in investigating nature. A crucial question, particularly for modern empiricists (D. hume and his followers), is whether science can proceed without knowledge of an order of things and whether method is sufficient without metaphysical grounding. Modern metaphysics of order have been most various; doctrines of two orders ("order dualism"), an order of knowing and an order of being (R. descartes); or reduction of all orders to one logical order ("order monism" of B. spinoza). There are other forms of "order monism": one mechanical order (T. hobbes); one divine order (N. malebranche); one order of the mind, without a real material order (G. berkeley). There is also the view of mind imposing categorial order on otherwise chaotic sensations (I. kant), which might be called "order subjectivism." The later phases have stressed a recognition of change in species and chance as a factor in their development (C. R. darwin). Thus, as argued by A. O. Lovejoy in The Great Chain of Being (Cambridge, MA 1936), the hierarchical order persisting from the ancients into the schemes of the Enlightenment has been displaced, and a temporal and dynamic ordering prevails.

The present crisis was prepared by H. bergson and the pragmatists, such as James. Bergson denied any real chaos: disorder was merely frustration in not finding the order one had expected (Creative Evolution, tr. A. Mitchell, New York 1911). James came to doubt any real order: the world has any order one chooses to recognize in it: it is as beans spilled on the table: a person can see whatever patterns are of interest to him (Varieties of Religious Experience, New York 1902, 1963, etc.).

Contemporary Thought. Contemporary philosophies of order—not only pragmatist but also existentialist, positivist, and Marxist—are all reacting against hegelianism. The phrase that expresses "order-monism" in Royce is "one true Order of things" (The World and the Individual, New York 1900). Contemporary protests often take the form of extreme "order-dualism" or "order-pluralism." Philosophers who voice such protests assert confidently that there is no one final and eternal order; this ideal of one final order is mocked by L. wittgenstein as the search for a "crystal palace." The existentialists, following Dostoevskiῐ, who protested against cosmic order in the name of radical human freedom, tend toward acosmism: they tend to say that man alone is the only principle of order, and each individual man from moment to moment as his interests and tasks shift.

The great hope of some contemporaries (G. G. Grisez, I. Jenkins, and P. G. Kuntz, all somewhat close to Paul Weiss, Modes of Being, Carbondale, IL 1958) is that a new systematic understanding can be developed. The errors of the past have been the fallacious reduction of the cosmos to one mode of being or, on the other hand, the overstress on the discontinuity of orders. Stated positively, there are several modes of order. If the hope of these new systems is fulfilled, the universe can be understood as many orders together.

See Also: universe, order of; relation.

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[p. g. kuntz]