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. 184.108.40.206]
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.
Bibliography: m. j. adler, ed., The Great Ideas: A Syntopicon of Great Books of the Western World, 2 v. (Chicago 1952); v.2, 3 of Great Books of the Western World, see index. g. giannini, Enciclopedia filosofica, 4 v. (Venice-Rome 1957) 3:1062–67. Paulys Realenzyklopädie der klassischen Altertumswissenschaft, ed. g. wissowa, et al. 18.1 (1931) 930–936. j. royce, j. hastings, ed., Encyclopedia of Religion & Ethics, 13 v. (Edinburgh 1908–27) 9:533–540. American Catholic Philosophical Association. Proceedings of the Annual Meeting 17 (1941) 1–52. e. cassirer, Logos, Dike, Kosmos in der Entwicklung der griechischen Philosophie (Göteborg 1941). w. w. jaeger, Paideia: The Ideals of Greek Culture, tr. g. highet, v.1 (2d ed. New York 1945). h. krings, Ordo: Philosophische-historische Grundlegung einer abendländischen Idee (Halle 1941). augustine, Ordine, ed. and tr. r. p. russell as Divine Providence and the Problem of Evil (New York 1942), also in Writings of St. Augustine (The Fathers of the Church: A New Translation, ed. r. j. deferrari 1; 1948) 239–332. l. r. ward, God and World Order (St. Louis 1961). j. m. ramirez, De ordine Placita quaedam Thomistica (Salamanca 1963). h. meyer, Thomas von Aquinas: Sein System und seine geistesgeschichtliche Stellung (2d ed. Paderborn 1961). b. coffey, "The Notion of Order according to St. Thomas Aquinas," The Modern Schoolman 27 (1949) 1–18. e. a. pace, "The Concept of Order in the Philosophy of St. Thomas," The New Scholasticism 2 (1928) 51–72. h. a. rommen, The Natural Law: A Study in Legal and Social History, tr. t. a. hanley (St. Louis 1947). c. i. lewis, Mind and the World Order (New York 1929; pa. 1956). w. d. oliver, Theory of Order (Yellow Springs, OH 1951). j. d. wild, Human Freedom and Social Order: An Essay in Christian Philosophy (Durham, NC 1959). c. j. schneer, The Search for Order (New York 1960). a. d. ritchie, Studies in the History and Methods of the Sciences (Edinburgh 1958). e. heimann, Freedom and Order (New York 1947). h. kuhn, "Le Concept de l'ordre," Greg 43 (1962) 254–267. g. g. grisez, "Sketch of a Future Metaphysics," The New Scholasticism 37 (1964) 310–340. i. jenkins, "The Matrix of Positive Law," Natural Law Forum 6 (1961) 1–50. p. g. kuntz, "Modes of Order," Review of Metaphysics 16 (1962–63) 316–345; "Mythical, Cosmic, and Personal Order," ibid. 718–748; "Order in Language, Phenomena, and Reality: Notes on Linguistic Analysis, Phenomenology, and Metaphysics," Monist 49 (1965) 107–136.
[p. g. kuntz]
or·der / ˈôrdər/ • n. 1. the arrangement or disposition of people or things in relation to each other according to a particular sequence, pattern, or method: I filed the cards in alphabetical order. ∎ a state in which everything is in its correct or appropriate place: she tried to put her shattered thoughts into some semblance of order. ∎ a state in which the laws and rules regulating the public behavior of members of a community are observed and authority is obeyed: the army was deployed to keep order. ∎ the overall state or condition of something: the house had just been vacated and was in good order. ∎ a particular social, political, or economic system: if only the peasantry would rise up against the established order the social order of Britain. ∎ the prescribed or established procedure followed by a meeting, legislative assembly, debate, or court of law: the meeting was called to order. ∎ a stated form of liturgical service, or of administration of a rite or ceremony, prescribed by ecclesiastical authority. 2. an authoritative command, direction, or instruction: he was not going to take orders from a mere administrator| the skipper gave the order to abandon ship. ∎ an oral or written request for something to be made, supplied, or served: the company has won an order for six tankers. ∎ a thing made, supplied, or served as a result of such a request: orders will be delivered the next business day. ∎ a written direction of a court or judge: a judge's order forbidding the reporting of evidence. ∎ a written direction to pay money or deliver property. 3. (often orders) a social class: the upper social orders. ∎ Biol. a principal taxonomic category that ranks below class and above family. ∎ a grade or rank in the Christian ministry, esp. that of bishop, priest, or deacon. ∎ (orders) the rank or position of a member of the clergy or an ordained minister of a church: he took priest's orders. See also holy orders. ∎ Theol. any of the nine grades of angelic beings in the celestial hierarchy. 4. (also Order) a society of monks, priests, nuns, etc., living according to certain religious and social regulations and discipline and at least some of whose members take solemn vows: the Franciscan Order. ∎ hist. a society of knights bound by a common rule of life and having a combined military and monastic character. ∎ an institution founded by a monarch for the purpose of conferring an honor or honors for merit on those appointed to it. ∎ the insignia worn by members of such an institution. ∎ a Masonic or similar fraternal organization. 5. [in sing.] used to describe the quality, nature, or importance of something: with musical talent of this order, von Karajan would have been a phenomenon in any age. 6. any of the five classical styles of architecture (Doric, Ionic, Corinthian, Tuscan, and Composite) based on the proportions of columns, amount of decoration, etc. ∎ any style or mode of architecture subject to uniform established proportions. 7. Mil. equipment or uniform for a specified purpose or of a specified type: drill order. ∎ (the order) the position in which a rifle is held after ordering arms. See order arms below. 8. Math. the degree of complexity of an equation, expression, etc., as denoted by an ordinal number. ∎ the number of differentiations required to reach the highest derivative in a differential equation. ∎ the number of elements in a finite group. ∎ the number of rows or columns in a square matrix. • v. 1. give an authoritative direction or instruction to do something: [tr.] she ordered me to leave | [with direct speech] “Stop frowning,” he ordered | the court ordered that the case should be heard at the end of August | [tr.] her father ordered her back home the judge ordered a retrial. ∎ [tr.] (order someone around/about) continually tell someone in an overbearing way what to do. ∎ command (something) to be done or (someone) to be treated in a particular way: he ordered the anchor dropped. 2. [tr.] request (something) to be made, supplied, or served: my friend ordered the tickets last week| I asked the security guard to order me a taxi | [intr.] Are you ready to order, sir? 3. [tr.] arrange (something) in a methodical or appropriate way: all entries are ordered by date | [as adj. in comb.] (-ordered) her normally well-ordered life. PHRASES: by order of according to directions given by the proper authority: he was released from prison by order of the court. in order 1. according to a particular sequence. 2. in the correct condition for operation or use. 3. in accordance with the rules of procedure at a meeting, legislative assembly, etc. ∎ appropriate in the circumstances: a little bit of flattery was now in order. in order for so that: employees must be committed to the change in order for it to succeed. in order that with the intention; so that: she used her mother's kitchen in order that the turkey might be properly cooked. in order to as a means to: he slouched into his seat in order to avoid drawing attention to himself. of the order of 1. approximately: sales increases are of the order of 20%. 2. Math. having the order of magnitude specified by. on order (of goods) requested but not yet received from the supplier or manufacturer. on the order of 1. another term for of the order of (sense 1) above. 2. along the lines of; similar to: singers on the order of Janis Joplin. Order! a call for silence or the observance of prescribed procedures by someone in charge of a trial, legislative assembly, etc. order arms Mil. hold a rifle with its butt on the ground close to one's right side. order of battle the units, formations, and equipment of a military force. orders are orders commands must be obeyed, however much one may disagree with them. out of order 1. (of an electrical or mechanical device) not working properly or at all. 2. not in the correct sequence. 3. not according to the rules of a meeting, legislative assembly, etc. ∎ inf. (of a person or their behavior) unacceptable or wrong: he's getting away with things that are out of order. to order according to a customer's specific request or requirements: the sweaters are knitted to order.DERIVATIVES: or·der·er n.
In most religions the world is believed to be an embodiment of divine wisdom. Paradoxically, the divine is both present (immanent) and absent (transcendent). This paradox is expressed in a hierarchy of degrees of manifestation of divine wisdom, each representing a kind of order. Further, both the natural and the moral order are seen as normative. In the Abrahamic religions order is created and, therefore, dependent on the creator. Since order is a manifestation of divine wisdom, it reveals knowledge about God. Accordingly, the created order has been seen as a unity in diversity, a machine, a work of art, or an embodiment of reason, beauty, and goodness. Disorder invaded the natural and the moral order, which require re-creation. In the Gnostic religions, however, disorder originates from an evil creator who battles a good redeemer. In response, the early Christian theologian Irenaeus (c. 130–200) emphasized that the creator and redeemer are one God who controls disorder and restores order. John Calvin (1509–1564) added that the created order required constant divine support to protect it from collapse into disorder: It could not exist independently. In contrast, for the theologian John Haught (1942–), disorder is the price God paid to grant freedom and independence to the created order.
Kinds and hierarchy of order
Science, philosophy, and theology recognize different kinds of order, as well as an order for the different kinds of order:
- One kind of inanimate order concerns energy. It refers to interactions with irreversible cause and effect relationships (heat melts ice).
- The order of life involves complexity. A complex sequence of molecules (DNA) carries information, which is transmitted from parent to offspring in a causal genetic relation. Mutations are not directed by the environment or the needs of the organism. This random order of mutation and the nonrandom order of natural selection produces organisms that are adapted to their environment.
- The order of reasoning involves the self-reflective awareness of norms for making distinctions, such as the principle of identity and the principle of the excluded third, as well as norms for correct arguments.
- The spiritual order concerns one's relationship with the divine. It is often characterized as a form of love, as it is, for example, in Hinduism and in the Abrahamic religions. These kinds of order represent ways in which entities exist, as well as ways in which people experience them.
The kinds of order are integrated in a hierarchy of order. In living things, the order of complexity, such as that of DNA, requires the order of energy with its chemical interactions, but chemical interactions do not require the complexity of living things. In a scientific explanation, the order of reasoning requires the order of sensation, but sensation does not require knowledge. In religious faith, the spiritual order of love requires the order of reasoning with its distinctions, but not vice versa. Thus, any kind of order is a necessary but insufficient condition for a higher kind of order. The complete hierarchy of kinds of order is found in persons and includes number, space, motion, interaction, life, sensation, perception, reasoning, human relations, lingual expression, legality, morality, and spirituality. Further, the order of life is not reducible to the order of energy. Nor can reasoning be reduced to sensation, or love to reasoning.
Entities can be ranked according to their highest kind of order, producing a hierarchy of entities. Chemical reactions exchange energy, but they do not transmit information to offspring. Plants transmit information to offspring, but they do not have knowledge. Animals have knowledge, but no spirituality as people do. Thus, the highest order in which entities function is the order of energy for chemical reactions, the order of life for plants, the order of knowledge for animals, and the order of love for people.
Order in the science-religion dialogue
One necessary condition for a mutual relevance of scientific and religious perspectives on order is that it is interpreted as divine action in the world. This, however, is not sufficient because a religiously interpreted order can be explored in science apart from its religious meaning (methodological atheism). Or the creator may be seen as utterly other than the created order so that what is known about nature is irrelevant for what could be known about God and vice versa (Eastern Orthodoxy, voluntarism in Western Christianity and Islam).
One sufficient condition for mutual relevance is that religious views of natural order serve in science as presupposition, sanction, motive, criterion for theory choice, criterion for the choice of kinds of explanation (regulative principle), or as part of explanations (constitutive principle), and vice versa. The rejection by Albert Einstein (1879–1955) of the probabilistic view of quantum physics was regulated by his belief that "God does not play dice." In reverse, the switch from a fixed to an evolving order of nature has motivated the development of evolutionary theologies and has constituted new conceptions of God, creation, divine grace, divine power, and redemption. For instance, instead of conceiving of divine power as a coercive force it is seen as persuasive love because divine love implies giving the universe the freedom to produce itself. Here, the biological idea of random mutation has been translated into the religious idea of a nature free from divine coercion.
A different type of sufficient condition is met in reductionism. In it a scientific definition of order is generalized into a metaphysical ideal of order. For instance, the empiricists as well as the neo-positivists reduced the cognitive order to the order of sensation. Since God cannot be known by sensation, knowledge of God is not possible and religion is reduced to belief without grounds in knowledge. This places knowledge and belief in different categories preventing a cognitive relationship between them. Similarly, biologist Edward O. Wilson (1929–) replaced a spiritual description of God as a being independent of matter with a naturalistic description: God is nothing but an objectification of the imagination. This was his way of including God in a kind of order that science can deal with by gathering empirical evidence. By redescribing God, sociobiology changed the content of religious belief and theology.
A third kind of sufficient condition is satisfied when a reduced view of order functions as religion (scientism). Biology functioned as (anti-)religion when biologists Jacques Monod (1910–1976) and Richard Dawkins (1941–) interpreted the randomness of mutations to mean that there is neither God nor purpose or when Wilson wrote that scientific materialism and evolutionism are his substitute religion in which the purpose of life is to promote evolutionary progress. This substitute religion motivated his re-description of God and, thereby, constituted the content of sociobiological explanations of religion. Here, science as a substitute religion influences religion.
See also Hierarchy; Nature
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jitse m. van der meer
1. In Classical architecture the elements making up the essential expression of a columnar and trabeated structure, including a column with (usually) base and capital, and entablature. There are eight distinct types of Classical Order:Greek Doric, Roman Doric, Greek Ionic, Roman Ionic, Greek Corinthian, Roman Corinthian, Tuscan (also known as the Gigantic Order), and Composite, although before the systematic rediscovery of Greek architecture in C18 the canonical 5 Orders (Tuscan, Roman Doric, Roman Ionic, Roman Corinthian, and Composite) were accepted, codified by Alberti, and illustrated by Serlio in 1537. The Greek Doric Order has no base, and sometimes (as in the Paestum Orders of Doric) the entasis is exaggerated and the capital is very large, with a wide projection over the shaft; the Ionic Order has variations in the design of its base (Asiatic and Attic types) and capital (especially in relation to angle, angular, and Bassae capitals where the problem of the corner volute is dealt with in different ways); and the Greek Corinthian capital (e.g. C4 BCChoragic Monument of Lysicrates, Athens) is taller and more elegant than its Roman counterpart. In London, Kent, and Sussex there is a unique type of English Ionic capital known as the Ammonite Order. See Agricultural, American, Ammonite, Britannic, Composite, Corinthian, Doric, Giant, Ionic, and Tuscan Orders.
2. Romanesque and Gothic arched opening consisting of several layers of arched openings usually with colonnettes, each smaller than the layer in front, and forming an Order Arch.
J. Curl (2001);
Lewis & Darley (1986);
C. Normand (1852)
Direction of a court or judge normally made or entered in writing, and not included in a judgment, which determines some point or directs some step in the proceedings.
The decision of a court or judge is made in the form of an order. A court may issue an order after a motion of a party requesting the order, or the court itself may issue an order on its own discretion. For example, courts routinely issue scheduling orders, which set the timetable and procedure for managing a civil lawsuit. More substantive orders, however, typically are made following a motion by one of the parties.
A motion is an application for an order. The granting or denying of a motion is a matter of judicial discretion. When a motion is granted, the moving party (the party who requests the motion) is ordinarily limited to the relief requested in the application. Although no particular form is required, a court order granting a motion should be sufficiently explicit to enable the parties to do whatever is directed. Though a court is not obligated to issue an opinion, in most cases a party is entitled to have the reasons for the decision of the court stated in the order. The order must be consistent with the relief requested in the motion, and it should set forth any conditions on which relief is awarded.
In trial courts the attorney for a party who obtains a favorable ruling usually has the responsibility of writing a proposed order. A copy of the proposed order is furnished to the other party so that he or she can propose amendments to it. It is then presented to the court for settlement and approval. Courts are free, however, to modify proposed orders or to write their own order. Appellate courts routinely write their own orders.
To take effect, an order must be entered, filed, or incorporated into the minutes of the court. An entry or filing must be made with the court administrator within the prescribed time limits.
Aside from scheduling orders and other orders that deal with the administration of a case, there are several general categories of orders. An interlocutory order is an order that does not decide the case but settles some intervening matters relating to it or affords some temporary relief. For example, in a divorce case, a judge will issue an interlocutory order that sets the terms for temporary child support and visitation rights while the case is pending.
A restraining order may be issued upon the filing of an application for an injunction forbidding the defendant to do the threatened act until the court has a hearing on the application. These types of orders are also called temporary restraining orders (TROs), because they are meant to be effective until the court decides whether to order an injunction. For example, if a neighborhood association seeks to prevent a land developer from cutting down a stand of trees, the association would seek an injunction to prevent the cutting and a TRO to forbid the developer from removing the trees before the court holds a hearing. If the association did not request a TRO, the developer could legally cut down the trees and effectively render the injunction request moot.
A final order is one that terminates the action itself or finally decides some matter litigated by the parties. In a civil lawsuit, the plaintiff may make many allegations and legal claims, some of which the court may dispose of during the litigation by the issuance of an order. When the court is ready to completely dispose of the case, it enters a final order. As part of the final order, the court directs that judgment be entered, which authorizes the court administrator to close the case in that court.
1. A means of indicating the way a function varies in magnitude as its argument tends to some limits, usually zero or infinity. More precisely if there is some constant K such that |f(x)| ← K φ(x)
for all x ≥ x1, then we say that f(x) is order φ(x) as x tends to infinity, and we write f(x) = O(φ(x))
For example, 100x2 + 100x + 2 = O(x2) as x → ∞
then we write f(x) = o(g(x))
For example, x = o(x2) as x → ∞
Both these notations are statements about maximum magnitude and do not exclude f from being of smaller magnitude. For example, x = O(x2)
is perfectly valid, but equally x = O(x)
then we write f(x) ≊ k g(x) as x → a
For example, 10x2 + x + 1 ≊ 10x2 as x → ∞
The term order and the O notation is used in numerical analysis, particularly in discretization methods. In ordinary differential equations, if h denotes the stepsize, then a method (or formula) has order p (a positive integer) if the global discretization error is O(hp). This means that as the step size h is decreased, the error goes to zero at least as rapidly as hp. Similar considerations apply to partial differential equations. High-accuracy formulas (order up to 12 or 13) are sometimes used in methods for ordinary differential equations. For reasons of computational cost and stability, low-order formulas tend to be used in methods for partial differential equations.
The term is also used to refer to the speed of convergence of iteration schemes, for example Newton's method for computing the zero of a function f(x). Subject to appropriate conditions, Newton's method converges quadratically (or has order of convergence 2), i.e. an approximate squaring of the error is obtained in each iteration.
2. Another name for operation code.
A. rank of angels; grade in the Christian ministry; (gen.) rank, grade; monastic society or fraternity XII (o. of chivalry, etc. XIV); (archit.) system of parts in established proportions XVI; (math.) degree of complexity of form; higher group of animals, etc. XVIII;
B. sequence, disposition; method of procedure or action XIV (in o. to, take o. XVI); condition of observance of law and usage XV;
C. regulation, direction, mandate XVI. ME. ordre — (O)F. ordre, earlier ordene — L. ōrdinem, nom. ōrdō row, etc., rel. to ōrdīrī begin, ōrnāre ADORN.
Hence orderly arranged in or observant of order XVI; charged with the conveyance or execution of orders XVIII (o. man, officer, †sergeant, hence as sb., by ellipsis). So ordinal †(rare) regular, orderly XIV; (of numbers) XVI; (nat. hist.) pert. to an order XIX. — late L. ōrdinālis. ordinal sb. book of the order of divine service XIV; form of ordination XVII. — medL. ōrdināle, n. sg. of ōrdinālis. ordinance A. (arch.) regular arrangement; authoritative direction; prescribed usage XIV; B. †provision, supply; spec. military supplies (now ordnance) XIV. — OF. ordenance (now ordonnance) — medL. ōrdinantia, f. ōrdināre ORDAIN. ordinand one about to be ordained. XIX. ordinary A. (eccl. and leg.) one having immediate jurisdiction or authority in juridical matters; B. book of divine service; C. sb. uses of the adj. from XVI. — AN., OF. ordinarie (later and mod. ordinaire) — medL. ōrdinārius, and in n. sg. ōrdinārium. So adj. belonging to the regular order or course; having regular jurisdiction XV; of the usual kind XVI. — L. ōrdinārius orderly, usual; see -ARY. ordination XV. — (O)F. or L., f. ordināre ORDAIN. ordnance XVII (see ORDINANCE). ordonnance systematic arrangement. XVII. — F., alt. of OF. ordenance, after F. ordonner.
The term order is one of the seven major classification groups that biologists use to identify and categorize living things. These seven groups are hierarchical or range in order of size. Order is at the exact middle of the seven groups, located between class and family. The classification scheme for all living things is: kingdom, phylum, class, order, family, genus, and species.
Organisms in the same order are much closer to each other, genetically and on the evolutionary scale, than are those in the larger group called class. For example, although all animals in the class Mammalia produce milk for their young, those in the order Carnivora eat meat, while others in the order Insectivora eat insects. A house pet like a dog (Carnivora) is distinguished by its eating habits and preferences from a mole (Insectivora), although both are in the same class.
The order names of plant groups generally use the suffix -ales (e.g., Rosales), while the order names of animals usually end with an -a (e.g., Carnivora). In practical terms and in most scientific discussions, the order of an organism is seldom considered. Rather, the more specific terms of family, genus, and species are used.
order paper in the United Kingdom and Canada, a paper on which the day's business for a legislative assembly is entered; in the House of Commons, members traditionally wave their order papers to signify support for a speaker.