Classics in the History of Psychology

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Definitions Ma - Md

Posted August 2001

M. The logical symbol for the MIDDLE TERM (q.v.). (J.M.B.)

m. v. Symbol for Mean Variation. See ERRORS OF OBSERVATION. (J.M.B.)

McCosh, James. (1811-95.) Educated at Glasgow and Edinburgh; ordained minister of the Church of Scotland, 1835; took part in the organization of the Free Church, and became professor of logic and metaphysics in Queen's College, Belfast, 1843; president of the College of New Jersey at Princeton, 1868; resigned, 1888. He belonged to the Scottish school of philosophers. cf. NATURAL REALISM.

Mackintosh, Sir James. (1765-1832.) Educated at King's College, Aberdeen, and at Edinburgh. Called to the bar at Lincoln's Inn, 1795; knighted in 1803; recorder of Bombay, 1804-6; judge of Vice-admiralty, 1806-11; returned to England, 1811, and entered Parliament, 1813; professor of law and general politics in Haileybury College, 1818-24; a commissioner of Indian affairs, 1830.

Macrocosm (and Microcosm) [Gr. makroV, great, and mikroV, small, + kosmoV, universe]; Ger. Makro-, Mikrokosmus; Fr. macro-, microcosme; Ital. macro-, microcosmo. The great world, macrocosm, applied to the universe, when contrasted with man, the microcosm or little world, the correlation of the two terms being at the same time intended to express an analogy between them.

The idea of such an analogy is present in the Aristotelian philosophy, and was developed by the Stoics in connection with their doctrine of pneuma, the divine reason, which is also the warm vital breath that animates and purposively pervades the universe. As the world -- soul to the world, so is the individual soul (which is a part of the universal soul) related to the body; and to the universal reason corresponds the rational or ruling part (to hgemonikon) of the individual soul. The doctrine played a great part in the speculations of the Renaissance thinkers, e.g. in Bruno, Paracelsus, Weigel, and Böhme. In man's nature is to be found the sum or 'quintessence' of the cosmical forces. Because he unites in his body the finest essence of all material things, man is able to understand the material world. As an intellectual being, he is at the same time of 'sidereal' origin, and therefore competent to understand the world of intellectual forms, while a 'spark' of the divine, infused into his nature, enables him to become conscious of God, whose image he is. Thus man knows the universe of being only so far as he is the universe, or contains within himself the principles of all that is. In Bruno's system, not man alone, but every monad or individual substance is an immediate manifestation of the infinite life, which thus individualizes and concentrates itself everywhere throughout the universe. Each monad is thus a 'mirror' or microcosm of the all. In the system of Leibnitz, the relation between the individual monad and the universe is similarly expressed. The idea that like is known by like is, of course, as old as Empedocles, of whose theory of perception it forms the central doctrine. Cf. MONAD. (A.S.P.P.)

Literature: see the citations in EISLER, Wörterb. d. philos. Begriffe, 'Mikrokosmus'; also FLEMING-CALDERWOOD, Vocab. of Philos., 'Microcosm.' LOTZE used the term as title of his general work Microcosmus. (J.M.B.)

Madness (and Madman) [Sansk. mod, to be drunk or mad]: Ger. Manie (Toller); Fr. folie (fou); Ital. follia, pazzia (pazzo, matto). A synonym of insanity, referring particularly to the disorder of reason or the uncontrollable emotion frequently characteristic of the insane state. Madman is also used as a synonym of lunatic. See INSANITY AND SANITY, MANIA, and FUROR. (J.J.)

Magic (1) and (2) Divination [Gr. magikh, magic, from Magoi, the priests of the Medes and Persians, and Lat. divinare, to foresee]: Ger. (1) Magie, Zauberei, (2) Eingebung; Fr. (1) magie, (2) divination; Ital. (1) magia, (2) divinazione. (1) A varied and extensive group of practices which appeal to supernal or supernatural agencies and illustrate SUPERSTITION (q.v.) reduced to practice.

Magical practices are found in almost all stages of primitive culture, and have a long and significant history in the chain of civilizations leading up to the present. While magical powers were in part derived from a deity or spirit, and were exercised like those of possession, a larger and more distinctive group of magical practices depended upon the discovery and interpretation of mystic correspondences which were occult or hidden from the popular ken. By the exertion of the will, by the careful observation of minute ceremonial rules, by the solemn enunciation of formulas and words, by the interpretation of the flight of birds or of the entrails of a beast, by casting dice and lots, by seeking the significance of personal peculiarities in a system of correspondences, and by a host of similar performances, the shaman or medicine man, the sorcerer or astrologer, the fortune-teller or exorcizer, tries to interpret the past and to influence the future, to control the forces of nature, to remove disease and evil, to bring on health and prosperity. Such proceedings are never wholly fanciful, but involve some far-fetched or misleading analogy, vague enough to permit of the adjustment of details to special cases, and yet imposing enough to impress the uncultured mind. In such practices are found some scraps of knowledge and logical tendencies which, after ages of tortuous progress, have often become the starting-points of true scientific knowledge. For the formulation of such procedure under psychological principles, based on ethnology, see Hirn as cited below.

The study of magic in primitive civilizations contributes much to the comprehension of the mental processes in undeveloped man; for it shows that in the attempt to regulate the actions of his own life, or to interpret the phenomena of nature about him, the appeal to magical hidden relations was the natural, normal process. Omens and portents, charms and fetiches, rites and offerings, divination and sorcery were the expressions of a desire for security and for wisdom. Interpretation based upon signs, omens, &c., is called prognosis.

The history of magic in written records can only be referred to in this connection as a vast storehouse for the study of the action of the human mind under impulses and tendencies in large part inhibited or transformed, but not without effect on current beliefs. With the growth of the art of writing and the beginnings of natural science, elaborate possibilities for occult rites and systems were laid open, which were utilized alike by Assyrian or Egyptian priests, and by mediaeval astrologers.

The practice of magic or sorcery frequently came into disrepute, and was prohibited by law or even punishable by death. The distinction between 'black magic' and 'white magic' grew up as the result of such interdiction. White magic included the production of illusions and entertaining applications of physical principles, and thus became the antecedent of modern legerdemain.

(2) Divination is that form of magic which utilizes knowledge derived from some super-human source, the knowledge being acquired by magical means.

Artificial divination is a widespread practice most largely represented in the culture stages above the lowest, though by no means absent in the lowest stages. The methods of divination and augury are almost unlimited, many of them depending on the interpretation by analogy or symbolism of the results of chance or of accidental details. Amongst natural forms of divination may be mentioned the appearances and cries of animals, dreams, configuration of hand and face, inspection of entrails, the fanciful appearance of flames of fire, or smoke, or ashes; the interpretation of charms, names and marks on the body, and so on. Over fifty terms ending in '-mancy' (divination) are cited in the literature of this topic. Of special and somewhat artificial devices invented for the purposes of divination, may be mentioned the setting up of sticks, to see whether they stand or fall, the spinning of a teetotum or similar contrivance, the throwing of dice and cards, the melting of lead or wax, pricking for texts in the Bible, and the divining rod. The last has had a specially interesting history, for which consult Barrett, Proc. Soc. Psych. Res., Oct., 1900.

Of all the systems of divination, astrology, which depends upon the prediction of the fortunes of the individual on the basis of the position of the celestial bodies at the moment of birth, has been the most elaborate and influential, and may be studied for the abundant illustrations which it offers of the mental attitude under which the processes of divination flourish. (J.J.)

From the standpoint of philosophy, it may be said that there is an element common to these various practices and superstitions by the presence of which they may be fitly described as magic. This element may be explained or set forth in detail, it can hardly be defined. The essential, or permanent, element common to all 'universes' of human experience of this sort has been most clearly elucidated by Bastian: 'Sorcery, or, in its higher expression, magic, marks the first dawning consciousness of mutual connection throughout nature, in which man, feeling himself part of the whole, thinks himself able to interfere for his own wishes or needs. So long as religion fills the whole horizon of culture, the vague groping of magic contains the first experiments which lead to the results of exact science. Magic is the physics of mankind in the state of nature. It rests on the beginning of induction, which remains without result only because in its imperfect judgments by analogy it raises the post hoc to the propter hoc.' A similar explanation is wrought out by F. B. Jevons (cited below, chap. iv). Magic, in other words, grows out of a theory of causation. And the business of philosophy is to set forth the factors in this theory, no matter how they, and other results or accompaniments, may alter, as they do alter in marvellous ways, throughout the numerous stages varying between lowest savagery, Persian and Babylonian culture, mediaeval prejudice, and modern superstition. (R.M.W.)

Literature: JEVONS, Introd. to the Hist. of Religion; BASTIAN, Rechtsalterthümer; WAITZ and GERLAND, Anthropologie d. Naturvölker; B. SPENCER, Australian Aborigines; TYLOR, Primitive Culture, and Early Hist. of Mankind; ELLIS, Polynesian Researches; CALLAWAY, Religious Syst. of the Amazulu; LENORMANT, Magie chez les Chaldéens, and Divination chez les Chaldéens; SAYCE, Hibbert Lects.; KING, Babylonian Magic and Sorcery; ROBERTSON SMITH, Religion of the Semites; WEBER and SCHNEDERMANN, Jüdische Theol.; EISENMENGER, Entdecktes Judenth.; LECLERQ, Hist. de la Divination dans l'Antiquité; BRECHER, Das Transcendentale, Magie u. magische Heilarten im Talmud; RHODE, Psyche; FARNELL, Cults of the Greek States; FRAZER, The Golden Bough (2nd ed., 1900); CICERO, De Divinatione; AUST, Die Religion d. Römer; MAURY, La Magie et l'Astrol.; BRAND, Pop. Antiq.; PETTIGREW, Superstitions of Med. and Surg.; MENIUS, De Exorcismo. For mediaeval magic, especially in its ecclesiastical aspects, see Herzog's Real-Encyc., art. Exorcismus. On the subject as a whole, TYLOR, Encyc. Brit., art. Magic; BLAVATSKY, Isis unveiled (an accredited manual of contemporary superstition); WHITE, Hist. of the Warfare of Sci. with Theol. (1897), chap. xii and elsewhere; LEHMANN, Aberglaube u. Zauberei (1898); RYDBERG, Magic of the Middle Ages (trans., 1879); CHEVREUL, La Baguette divinatoire (1884); FIGUIER, Le Mystère de la Science, 573-644; ELLWORTH, The Evil Eye (1895); P. CHRISTIAN, Hist. de la Magie; LANG, The Making of Religion; DE LA SAUSSAYE, Lehrb. d. Religionsgesch.; C. MEYER, Der Aberglaube des Mittelalters (1884); BAUDI DI VESME, Storia dello Spiritismo (1897-8); BERENGERFERAUD, Superstitions et Survivances; REGNAULT, La Sorcellerie (1897); SKEAT, Malay Magic (1900); HIRN, Origins of Art (1900), chap. xx. (R.M.W.- J.J.- L.M.)

Magnetic Stopper: see LABORATORY AND APPARATUS, III, B, (a), (8).

Magnetism: Ger. Magnetismus; Fr. magnétisme; Ital. magnetismo. See Magnetic Energy, under ENERGY.

Magnitude (extensive) [Lat. magnitudo, bulk, size]: Ger. Grösse; Fr. grandeur; Ital. grandezza. That which had dimensions or extension, as a line, a surface, or a solid; called also a geometric magnitude. In other branches of mathematics than geometry the word is replaced by QUANTITY (q.v.). (S.N.)

Magnitude (intensive): see QUANTITY.

Maimon, Salomon. (1753-1800.) A Jewish rabbi and philosopher, born in Lithuania.

Maimonides (Moses ben Maimon in Hebrew; Abu Imram Musa ibn Maimun ibn Abdallah in Arabic). (1131-1204.) Known among Christian writers as R. Moyses. Early studied the Bible and the Talmud, guided by his father; also mathematics, astronomy, and medicine. Born at Cordova, he, with his family, was banished for political and religious reasons. In 1159 they were in Fez, in 1165 in St. Jean d'Acre. He settled in Cairo, followed the jeweller's trade, and became famous for learning and medical skill.

Major [Lat. maior, greater]: Ger. Dur; Fr. majeur; Ital. maggiore. One of the two fundamental scales or keys of modern music. Expressed in 'whole tones,' it runs: 1, 1, 1-2, 1, 1, 1, 1-2. Cf. MINOR, and TRIAD.

This is the natural diatonic series, represented by the series of musical tones starting from C. It corresponds to the Greek Lydian, and the ecclesiastical Tonic. Cf. Helmholtz, Sensations of Tone, 274.

A major interval is that form of the interval which is greater by a semitone than its corresponding minor. A major chord is a chord containing the major third above the fundamental. A major tone is one the vibration ration of which is 8:9, as contrasted with the minor 9:10. Cf. Parry, in Grove's Dict. of Music, ii. 200. (E.B.T.)

Major and Minor (extreme, term, premise, satz, &c., in logic): Ger. Ober- and Unter- (Begriff, &c.); Fr. majeur and mineur; Ital. maggiore and minore. The subject and predicate of the conclusion of a syllogism are called the extremes (ta akra, by Aristotle), because they are only brought together by the agency of the third term, called, on that account, the middle term (o mesoV oroV, Aristotle). Of the two extremes, the one that is the predicate of the conclusion is called the major extreme (to meizon akron, Aristotle), because in a universal affirmative proposition (the typical formal proposition) its breadth is the greater, while the subject of the conclusion is the minor extreme (to elatton akron, Aristotle).

Whether the expressions major term and minor term, for the major and minor extremes, are grammatically accurate or not, they are consecrated by usage through the scholastic period. The major and minor premises are respectively those which contain the major and minor extremes. Aristotle (I. Anal. Pr., ix) calls the former h proV to meizon akron protasiV, 'the proposition about the major extreme.' (C.S.P.)

Majority (in law): see INFANT.

Make-believe: Ger. (1) Vortäuschen, bewusster Schein; Fr. (1) feinte, faux semblant; Ital. (1) finzione. (1) The indulgence in SEMBLANCE (q.v.) with consciousness of, or for the sake of, the effect upon another.

As is pointed out under semblance, that state of mind may involve self-illusion or not. In the higher forms of semblance, there is the keeping up of the artificial situation without self-illusion, but with direct reference to the effect upon an observer, a more or less explicit attempt to make another believe, and so to sham. It is recommended that the term make-believe be confined to this more particular aspect of the consciousness of semblance. The term sham -- especially the verbal forms (e.g. shamming) -- may well be used as a synonym. The shamming of disease and the symptomatic forms of deception in certain diseases, known as malingering, illustrate make-believe.

(2) The consciousness of unreality attaching to certain mental constructions, notably those of play and art. See SEMBLANCE (also for foreign equivalents), which is preferable to this broad meaning; and cf. ART AND ART THEORIES.

(3) Used in biology for the attitudes of feigning (e.g. the opossum's feigning death), a form of SEMBLANCE (q.v.) which is largely instinctive, and probably only slightly, if at all, conscious. (J.M.B., G.F.S.)

Male [Lat. masculus]: Ger. männlich; Fr. mâle; Ital. maschio. The primary meaning refers to the individual capable of producing spermatozoa or the homologous elements in the lower animals or in plants. By extension it is applied (1) to characteristics of a male individual, especially such as are sexually distinctive; (2) to the spermatozoa or other sexual elements produced by a male individual or the male gland of an hermaphrodite. Cf. SEX. (C.S.M.)

Malebranche, Nicolas. (1638-1715.) Born of a wealthy and respectable family. He was too poor in health to attend school. Studied theology at the Sorbonne. Read Descartes in 1664, and devoted himself to philosophy.

Malevolence (or Malice) [Lat. malevolentia]: Ger. Bosheit, Böswilligkeit; Fr. malice, méchanceté; Ital. malevolenza, cattiveria. The disposition to bring pain or misery to another or to take pleasure in it.

The nature of malevolence and the possibility of disinterested malevolence have been discussed by the English moralists. Hutcheson describes 'disinterested malice or delight in the misery of others' as the highest pitch of what we count vicious; and, according to Butler, 'the utmost possible depravity which we can in imagination conceive is that of disinterested cruelty.' At the same time, both doubt the possibility of its being genuinely disinterested. 'Human nature,' says Hutcheson, 'seems scarce capable of malicious disinterested hatred, or a sedate delight in the misery of others'; and Butler holds that 'as there is no such thing as self-hatred, so neither is there any such thing as ill-will in one man towards another, emulation and resentment being away.' By Bentham the 'pleasures of malevolence' are recognized as motives corresponding with the 'pleasures of benevolence.' Cf. MALICE (in law). (W.R.S.)

It is interesting to ask whether there is not an aesthetic factor in malevolence, as there is in most benevolence and sympathy. There can be no doubt that many of the actions ordinarily ascribed to malice are better explained from the elements of play and of the comic involved in the production of grotesque and unusual situations. The aesthetic motive described by recent writers (e.g. Groos) as 'pleasure in being a cause' enters into much that passes for malice, as in painful practical jokes, cruel wit, &c. Furthermore, the very fact that the pain -- and in cases of sympathy, the pleasure -- is in another, makes it possible to take a contemplative attitude towards it as towards the element of semblance (Schein), which in the aesthetic psychosis is contrasted with actual personal experience. It may be the writhing, not the pain, of the pinned-down insect that interests. Delight in the repulsive seems to have one element, at least, of aesthetic contemplation -- disinterestedness -- at its purest; and it is quite possible that disinterested malice springs from a similar root. It is interesting to note that we often take pleasure -- and it is quasi-aesthetic -- in certain of our own pains (cf. Hirn, Origins of Art, chap. v). (J.M.B.)

Literature: HUTCHESON, Inquiry, §§ 1 and 2; BUTLER, Sermons, pref. and i; BENTHAM, Princ. of Mor. and Legisl., chap. x; BAIN, Emotions and Will (3rd ed.), 66, 187 ff. (W.R.S.)

Malfeasance [Fr. malfaisance; from mal, evil, + faire, to do]: Ger. Missethat, Übelthat (that which is wrongfully done); Fr. méfait, méchanceté (that which is wrongfully done); Ital. misfatto. Doing wrongfully what could not be done rightfully; as distinguished from doing wrongfully what could be done rightfully, which is termed misfeasance, and from non-feasance, which is not doing what one has undertaken to do. Malfeasance, however, is often used inaccurately for misfeasance.

Malfaisance, in French, signifies a disposition to do ill to another; not the doing of ill. (S.E.B.)

Malice: see MALEVOLENCE.

Malice (in law): Ger. Bosheit; Fr. malice; Ital. malizia. The evil intent to do a wrongful act injurious to another. By a legal fiction, such an intent is sometimes imputed where it did not exist, and is then termed malice in law, as distinguished from malice in fact (see Markby, Elements of Law, §§ 686, 687).

Where one causes another to be prosecuted for an alleged crime, without reasonable cause, and the result is an acquittal, he is liable for a 'malicious prosecution,' and malice is implied, though there was none in fact. Malice is a necessary ingredient of the crime of murder, being styled in that connection malice aforethought or malice prepense. (S.E.B.)

Malthus' Law: Ger. Malthus'sches Gesetz; Fr. loi de Malthus; Ital. legge di Malthus. An alleged tendency of population to increase in geometrical progression while subsistence increases only in arithmetical progression. The former therefore tends to outstrip the latter, until the inadequacy of food supply brings disease and reduces numbers within the necessary limits. The principle is known as MALTHUSIANISM.

In the first edition (1798) of his Essay on the Principles of Population, Malthus stated the law substantially as here given. In subsequent editions he laid more relative stress on the possibility of 'preventive checks,' which should avoid the fatal geometrical increase, and thus preclude the need for the positive check of famine and disease. Modern critics have sometimes said that this amounts to an abandonment of the whole position; for these preventative checks, they claim, are so far automatic that the whole geometrical-progression theory falls to the ground. Other critics insist that the limitation of the food supply is not nearly so rigid as Malthus assumed. The principle of Malthus suggested to both Darwin and Wallace the 'struggle for EXISTENCE' (q.v.) in the animal world, upon which the law of NATURAL SELECTION (q.v.) was based (see Poulton, Charles Darwin, 46, 88, 89; and cf. EXCESS, and PRODIGALITY OF NATURE).

Literature: BONAR, Malthus and his Work; K. PEARSON, The Chances of Death, i. (A.T.H.)

Malthusianism: see MALTHUS' LAW.

Malum (in law) [Lat.]. Malum prohibitum: an act wrong because prohibited by positive law, though not necessarily bad in the view of moral reason or natural law. Malum in se: an act which is wrong in the view of reason or natural law. (S.E.B.)

Mammal [Lat. mammalis]: Ger. Säugethier; Fr. mammifère; Ital. mammifero. One of the Mammalia, the highest class of vertebrates, containing all the animals with milk glands (mammae) for the nourishment of the young during a variable period after birth. The mammals are all air-breathing, warm-blooded animals, with a more or less hairy covering, a four-chambered heart, a sinistral aorta, and a complete diaphragm separating the pleural and abdominal cavities. The four last characteristics distinguish them from all other vertebrates, the four-chambered heart of birds being dextral in plan.

The blood of adult mammals contains non-nucleated red corpuscles of smaller size than the red corpuscles of other vertebrates, which are invariably nucleated throughout life. The class is subdivided into three sub-classes: (1) the monotremes, of which the duck-bill or ornithorhynchus is the best-known representative; (2) the marsupials, of which the opossum and kangaroo are the most familiar types; and (3) the placental mammals, which include the majority of living forms, and with which man is classed in the order of PRIMATES (q.v.). The habit of nourishing the young after birth has been a chief factor in the evolution of family life, and is therefore intimately correlated with the development of the brain, the size and complexity of which is, from the biological standpoint, by far the most important characteristic of the Mammalia. The phylogenetic origin of the Mammalia has not been determined, but it seems probable that they arose from forms belonging to the amphibian type, although many authorities maintain that their immediate ancestors were reptilian. The earliest unquestionable mammalian fossils have been found in the Jurassic strata.

Literature: FLOWER and LYDDEKER, Mammals; FLOWER, Osteol. of the Mammalia; PARKER and HASWELL, Zoology, ii; LECHE, Säugethiere, in Bronn's Thierreich; see also the Roy. Nat. Hist.; BREHM, Thierleben. On the evolution of the mammals: WIEDERSHEIM, Der Mensch; HUBRECHT, Princeton Lectures; HAECKEL, System. Phylogenie; the Proceedings and reports in Nature of the Int. Zool. Cong. (1897) discussion on the origin of mammals. (C.S.M.)


Man (doctrine of, in theology): see ANTHROPOLOGY (theological).

Manes (or Manichaeus). (cir. 216-cir. 277 A.D.) Appeared in Babylon (242 A.D.) as a religious teacher. Being unsuccessful there he spent his life wandering. Like the Gnostics, he combined into a world conception elements taken from various sources. In place of Jewish monotheism he took Persian dualism as a foundation for MANICHAEISM (q.v.).

Mania [Gr. mania, madness]: Ger. Manie; Fr. manie; Ital. mania. Mental disease involving irresistable and uncontrollable or uncontrolled habit, desire, or craving, with unreasonable or inadequate motives. In psychiatry it is also used symptomatically -- to designate certain groups of symptoms.

I. Symptomatic usage. All the phases of general excitement bearing the feature of lack of control are loosely called mania, and when very marked, frenzy. One symptom-complex, which is frequently called mania, although there is no general excitement, and which presents imperative or dominant ideas or habits of conduct, is considered in the article MONOMANIA. True general maniacal excitement occurs in several well-distinguished forms: --

(1) As delirium (delirious mania): implying a maniacal delirium without any of the known somatic foundations for delirium, such as acute typhoid, acute articular rheumatism, pneumonia, grippe, &c.; but sometimes following these diseases or lasting longer than the fever, or coming on after profound exhaustion (collapse delirium) or without any adequate cause: all these forms of excitement are marked by hallucinations, confusion, and disorientation, and often violent raving. Unless exhaustion, injuries, or intercurrent diseases cause death, a favourable course is the rule. It is not always easy to distinguish this form from other delirious states -- phases of KATATONIA (q.v.), dementia praecox, manic-depressive insanity, &c.

(2) As an episode of the manic-depressive psychoses (Kraepelin): a typical condition of uncontrollable motor excitement, feeling of strength and well-being, and exhiliration, together with a characteristic flight of ideas and disorder of the stream of thought, with frequent rhyming and inability to keep to one topic or to keep in mind a true picture of the actual state of affairs, with great distractability and irritability of emotional tone, with isolated delusions and (rarely) hallucinations. The untiring activity of the patient usually appears quite spontaneous, though often poorly planned and rapidly shifting; it is varied, rich in all sorts of whims, and, although frequently theatrical, free from senseless stereotypy. The attack is frequently ushered in by depression; and occasionally excitement and depression vary in irregular or regular intervals, every other day or month, or with the seasons, or after intervals of normal health. The excitement of these forms is so characteristic that the term music is exclusively applied to it in distinction from the general term maniacal, used for all forms of excitement. For slight forms the term hypomania is used.

(3) As the onset of dementia praecox (hebephrenia or katatonia): the excited phases of the processes of deterioration of Kraepelin. This type is devoid of many of the expansive features of the manic excitement, and is characterized by monotonous, stereotyped manners, strained or forced actions, impulsive outbreaks, silly attitude, and often absurd delusions, frequently of a sexual or religious trend. Cataleptic episodes, hallucinations (God urging the patient to take certain attitudes, not to eat, &c.), and delusions of mysterious influences are quite common; with it all, the patient's mind is often remarkably clear.

(4) As the excitement of general paralysis: often difficult to recognize unless the manifestations or subject matter of the excitement become very absurd, as in MEGALOMANIA (q.v.), and the somatic symptoms (disorder of speech, &c.) are obvious.

(5) As a form of alcoholic insanity: protracted delirium tremens, with the typical hallucinations (snakes, small animals, the devil, &c.), with more or less marked fear; or alcoholic delusional insanity, with or without hallucinations of hearing, centring about persecution, jealousy, &c.

(6) As senile mania: episodes of excitement in senility, often merely states of confusion and bewilderment, or restlessness over delusions concerning property, &c.

(7) As episodes following epileptic attacks, or taking the place of epileptic attacks: equivalents of the characters of acute frenzy.

(8) Many statistics include as chronic mania excited cases of dementia or paranoic conditions.

II. As a name for real diseases or PSYCHOSES (q.v.) the use varies extremely. Those who classify the forms of insanity merely from the point of view of exaltation, depression, and intellectual disorders, remain on purely symptomatic ground and use in a descriptive and retrospective way, without any further discrimination, the expressions acute, sub-acute, recurrent and chronic mania, according to the form of onset, duration, and course, including all the above types with the exception of the alcoholic, paralytic, epileptic, and senile forms. Kraepelin has made it extremely probable that the periodic or recurrent manic attacks, varying with attacks of depression, and described under (2), form a characteristic disease-entity, the manic-depressive insanity, distinct from the processes of deterioration. This form rarely occurs once only, but usually recurs, or alternates with depression with varying intervals of the normal condition, and the patients rarely become permanently demented. Even after a large number of attacks complete recovery is possible. Such facts suggest the view that manic states are merely an expression of an as yet unknown disease-process, which may likewise express itself as an attack of melancholia, or any other equivalent of manic-depressive insanity, just as a convulsion or some equivalent state is an expression of epilepsy. The types included in this disease-entity are the manic forms, certain semi-delirious ones, certain stuporous and depressed ones, and certain paranoic episodes and mixed forms. For the other forms of excitement the term mania had better be avoided.

Interesting psychophysical experiments exist on the peculiarities of association, writing, and reaction-time, during mania.

Literature: MENDEL, Die Manie (1881); KRAEPELIN, Psychiatrie (1899), ii. 359-425, and Das manisch-depressive Irresein; O. HINRICKSON, Statistischer Beitrag zur Frage nach der Häufigkeit der einfachen acuten Manie im Verhältniss zu den periodischen Formen, Diss. Zürich (1897); ASCHAFFENBURG, Experimentalle Studien über Associationen, in Kraepelin's Psychol. Arb., i, ii; GROSS, ibid., ii. 485-567; CONOLLY, Mania, in Tuke's Dict. of Psychol. Med.; MacPHERSON, Mania and Melancholia, J. of Ment. Sci. (1891); W. WEYGANDT, Über die Mischzustände des manisch-depressiven Irreseins (München, 1899); PAHL, Ueber Häufigkeit und Verlauf der Manie nach den Boebachtungen in der psychiatrischen Klinik zu Freiburg i. B. in den Jahren 1887-95, Diss. Freiburg (1897); ERP TAALMAN KIP, Acute Manie, Allg. Zeitsch. f. Psychiat., 1iv. 119 (1897). (A.M.)

Manichaeism: Ger. Manichäismus; Fr. manichéisme: Ital. manischeismo. The doctrine of MANES (q.v.). A dualistic system in which two co-ordinate principles of good and evil, symbolized by light and darkness, are represented as engaging in an eternal conflict in the world and in the nature of man; the struggle in man's nature taking the form of a contest between flesh and spirit, in which the triumph of spirit is to be secured by the practice of a rigorous discipline.

The system of Manes was a modification of the old Persian dualism, the modifying elements being derived from Buddhism and Syrian Gnosticism, with some ideas borrowed from Christianity. While the motive of it was religious, it aimed rather at knowledge than moral purity, and was essentially a form of gnosis. It had a wide following, and powerfully influenced some of the greatest thinkers of the time, notably St. Augustine, who continued under its influence for several years, but finally rejected it and became its most uncompromising foe. Most of the essential features of Manichaeism are found in the older system of Zoroaster.

Literature: F. C. BAUER, Manichäisches Religionssystem; MOSHEIM'S and GEISLER'S Eccles. Histories; McCLINTOCK and STRONG, Schaff-Herzog Cyc. of Eccles. Lit. (A.T.O.)

Manifestation (in theology) [Lat. manifestatio]: Ger. Offenbarung; Fr. manifestation; Ital. manifestazione. The self-revelation of the Deity to man, in and through nature or consciousness, by ordinary or super-ordinary agencies.

The term is used more especially of God's revelation of his nature and will in his Son Jesus Christ, and in the work of the Holy Spirit; also in the Holy Scriptures, which are a revelation of his will, according to Christian teaching.

Literature: see REVELATION. (A.T.O.)

Manifoldness (or Assemblage): see MATHEMATICS.

Mankind [ME. mankinde]: Ger. Menschheit; Fr. homme, humanité; Ital. genere umano, umanità. The human race considered collectively.

The study of mankind has led to the formulation of the general science of ANTHROPOLOGY (q.v.), while at the same time other sciences with other primary purposes yield much valuable knowledge concerning man, his position in nature, and his occupations, endowments, and history. The specific study of the races of mankind becomes the purpose of ETHNOLOGY and ETHNOGRAPHY (q.v.). See also RACE. Many important anthropological and ethnological works bear the title 'History of Mankind'; such as that by Ratzel (3 vols., trans. from 2nd ed., 1896-8). The term 'Natural History of Man' (e.g. the works of Prichard, 2 vols., 4th ed., 1855; Wood, 1868-70, edited by Kingsley, 1885) is used in the same sense. The mental and moral life of mankind is treated by the sciences of PSYCHOLOGY, ETHICS, HISTORY, SOCIOLOGY, &c. (see those terms). (J.J.)

Mansel, Henry Longueville. (1820-71.) Educated at Merchant Taylors' School and at St. John's College, Oxford. He was an Oxford fellow in 1842; ordained priest in the Anglican Church in 1845; reader in moral and metaphysical philosophy, Oxford; Bampton Lecturer, 1858; Waynflete professor of philosophy, 1859; Regius professor of ecclesiastical history and canon of Christ Church, 1867; dean of St. Paul's, 1868. He was born at Cosgrove, Northamptonshire, and died at London, England.

Many: see ONE AND MANY, and cf. NUMBER (different articles).

Marcus Aurelius Antoninus. (121-180 A.D.) A prominent Stoic philosopher. Adopted as a son by Emperor Antoninus Pius in 138 A.D. As emperor he was engaged in frequent wars. In 175 he visited Egypt and Syria. He founded a chair of philosophy in Athens for each of the sects -- Stoic, Platonic, Peripatetic, and Epicurean.

Mare clausum and Mare liberum [Lat.]. Mare clausum: a sea closed, by authority of a particular sovereign claiming special privileges or rights in it, to general navigation. Mare liberum: a sea open to navigation by all, freely. Such, it is now universally conceded, are the high seas.

'Et quidem naturali iure communia sunt omnium haec: aer, aqua profluens, et mare, et per hoc littora maris' (Inst. of Just., ii. 1, de rerum divisione, 1). A contrary view was supported by the popes in the middle ages, and by Spain and Portugal, claiming exclusive rights by discovery and under papal decrees over the western and southern seas. English jurists in the 17th century, while disputing those claims, set up a claim of English sovereignty as to the northern seas (see Selden, Mare Clausum, 1635, and Grotius, Mare Liberum, 1609). Russia made a similar claim as to the North Pacific as late as the beginning of this century, on the ground of riparian ownership (see Davis, Int. Law, 43).

Literature: WHARTON, Int. Law, Dig. i. § 26; WOOSLEY, Int. Law, § 55; WHEATON, Elem. of Int. Law, chap. iv. (S.E.B.)

Margin of Cultivation: Ger. Kulturgrenze (K.G.); Fr. marge de culture (L.M.); Ital. limite di coltivazione. The point at which, either on account of distance from market or lack of natural advantages, the value of the products of land barely covers the expense of producing them.

It was by assuming a point of this kind that Ricardo laid the basis of his theory of economic rent. If the demand was such as to necessitate the use of a certain piece of land in supplying a market, the price must be made high enough to cover the expense of production on this land. If other land was better located or more fertile, it would afford the owner a surplus above expenses equal to its advantages over land at the margin of cultivation. (A.T.H.)

Marginal Increment: Ger. Grenz- (in combination), marginal; Fr. élémentaire (marginal); Ital. incremento marginale. A very small variation in an economic quantity. If the quantity is regarded as changing discontinuously, the term corresponds to finite difference in physics; if it is regarded as changing continuously, it corresponds to differential. See CALCULUS.

It has gradually been discovered that equilibrium in economics, no less than in physics, depends upon differential equations, and may be explained more satisfactorily by differential analysis than by mass analysis pure and simple.

The beginning of this analysis is seen in Ricardo. He rejected Smith's proposition that there is in each community an average rate of rent which the price of food must cover. He showed that, theoretically and to a large extent in practice, the land in use actually varies from a high degree of fertility and productiveness to a low degree. The land which it just pays to cultivate represents, according to Ricardo, the 'margin of cultivation.' The price of the products must just pay wages and profits on this land, otherwise it will go out of use; it cannot be more than this, or some worse land will come into use. Thus the price of the product is a function not of the average productivity of land in use, but of the marginal productivity; and rent is not, as Smith thought, a determining element in price, but a differential gain. Walker applied the same analysis to profits, showing that that part of profit which was due to human skill rather than to capital invested was subject to the same laws as the rent of land; that there was a margin of skill, at which an employer could just maintain himself and no more; that the price of products must, in general, cover wages and interest at this margin; and that surplus profit was a differential gain no less than surplus rent.

The analysis of the effect of marginal utility upon demand came later than the analysis of the effect of marginal expense upon supply. The observed rule that increased quantities consumed in a given time produced diminished increments of pleasure or pain was applied by Gossen (1854), Jevons (1871), and Menger (1871) to show what limits were set to the possibility of marketing products, and, consequently, to the cost which could be incurred for that purpose. Marshall further showed that the consumers, to whom the products had a utility higher than that at the margin, obtained a differential gain analogous to that of the landowners, which he called CONSUMER'S RENT (q.v.).

If we represent quantities produced and consumed on an axis OX, and prices, which may serve as representative of enjoyment or sacrifice, on an axis OY, we shall find that the quantity marketed, Oq, will normally be produced at a marginal expense qx, equal to the marginal utility to the man who is just willing to buy it. In other words, the sacrifice to the last producer just balances the advantage (OPHELIMITY, q.v.) to the last consumer. But some producers have such advantages in location or skill that their actual expense is much less than qx, going down as low as Oc. Competition, by allowing them to receive the market price for their products, gives them an advantage cxp in the form of rent or profits. And some consumers have a similar advantage in utility, which may go as high as Oq. Competition, by allowing them to get their products at the market price, gives them a similar advantage nxp, which we may call consumer's rent.

In this apparently very beautiful analysis there is a fallacy. The whole theory of utility to the consumer as commonly stated is based upon increasing rapidity of stimulus, i.e. rates of production. The Ricardian law of rent and the whole analysis of cost to producers is based upon the need of increasing quantity of production -- more appliances at the old rate of speed. We are really putting two curves into the same figure, which are radically different in their principles of construction. It is too early to say how far this difficulty vitiates our analysis of the subject of consumer's rent.

Literature: IRVING FISHER, Bibliog. of Mathematical Economics, appended to the volume of Cournot; RAND, Bibliog. of Economics. Cf. the literature of ECONOMIC SCIENCE. (A.T.H.)

Marginal Utility: see FINAL UTILITY.

Marheineke, Philipp Konrad. (1780-1846.) Educated at Göttingen. Professor of theology at Erlangen, 1805; at Heidelberg, 1807; at Berlin, 1811, where he was pastor of Trinity Church.

Mark [AS. mearc, a bound]: Ger. Merkmal; Fr. marque, attribut; Ital. segno (contrassegno), nota. To say that a term or thing has a mark is to say that of whatever it can be predicated something else (the mark) can be predicated; and to say that two terms or things have the same mark is simply to say that one term (the mark) can be predicated of whatever either of these terms or things can be predicated.

The word translates the Latin nota. It has many practical synonyms, such as quality, mode, attribute, predicate, character, property, determination, consequent, sign. Most of these words are sometimes used in special senses; and even when they are used in a general sense, they may suggest somewhat different points of view from mark. (C.S.P., C.L.F.)

A great oversight which had vitiated the entire discourse of logicians about marks, and had prevented them from fully understanding what marks are, was corrected by Augustus de Morgan when he observed that any collection whatever of individuals has some mark common and peculiar to them. That it is so will appear when we consider that nothing prevents a list of all the things in that collection from being drawn up. Now, the mere being upon that list, although it has not actually been drawn up, constitutes a common and peculiar mark of those individuals. Of course, if anybody tries to specify a number of individuals that have no common and peculiar mark, this very specification confers upon their common and peculiar mark a new degree of actuality.

On the other hand, if two marks are common and peculiar to precisely the same collection of things, they may, for the ordinary purposes of formal logic, be looked upon as the same mark. For it is indifferent to formal logic how objects are marked, whether in a simpler or more complex way. We may, therefore, regard the two marks as constituting together a single mark. Marks, after all, are not the object of logical study; they are only fictitious aids to thought. (C.S.P.)

Market [AS. market]: Ger. Markt; Fr. marché; Ital. mercato. A place where prices are determined by competition and made to equalize demand with supply. An extension to modern conditions of the ideas of the mediaeval market or fair.

It makes no difference whether the goods are actually exposed for sale, as in the mediaeval markets, or largely bought and sold on the basis of warrants and telegraphic orders, as in the produce exchanges of to-day. The essential thing is that different buyers and sellers shall know something about one another's transactions, so that the individual buyer need not pay more than the prevailing rate, nor the individual seller be forced to accept less than the prevailing rate.

There may be different markets for the same article in the same place. The prices in the wholesale market may be determined by one set of conditions, and those in the retail market by another. (A.T.H.)

Marriage [Lat. maritus, husband, through Fr.]: Ger. Ehe; Fr. mariage; Ital. matrimonio. Any more or less permanent union of the sexes that is sanctioned by the community.

The earliest sanction is no more than a vague general approbation. Later sanctions have explicit legal expression, and assume the form of severe penalties for disobedience of legal prohibitions. The use of the term marriage by many ethnologists, including Westermarck (Hist. of Human Marriage), to designate any union of the sexes, sanctioned or not sanctioned, including the mating of animals, is erroneous. The correct use was indicated by J. F. McLennan in the correspondence with Charles Darwin, reproduced in McLennan's Studies in Ancient History, second series. McLennan held that polyandry was the first form of marriage, as distinguished from mere mating. Slowly and by many tentative experiments society has arrived at monogamous marriage of individuals not within the first and second degrees of consanguinity, by prohibiting, successively, incest, polyandry, polygamy, and bigamy. The marriage laws of Europe and America still bear the impress of the deliberations of the Council of Trent. (F.H.G.)

Literature: McLENNAN and WESTERMARCK, as cited (the latter having an extensive bibliography); STARCKE, The Primitive Family. See also under FAMILY. (J.M.B.)

Marsilius Ficinus: see FICINO, MARSIGLIO.

Martineau, James. (1805-1900.) An English writer in moral and religious philosophy. Of Huguenot ancestry, he was born in Norwich. He attended successively the Norwich Grammar School, Lant Carpenter's private school at Bristol, and a school for engineers at Derby. Changing his plans, he studied theology for five years at Manchester College, situated at that time at York. Admitted to preach, 1827; ordained in Dublin, 1828, he moved to Liverpool. In 1839 he took a prominent part in the Liverpool Controversy, and in 1840 he was appointed professor of mental and moral philosophy in Manchester New College, a position which he held until 1885.

Martyr, Justin: see JUSTIN MARTYR.

Mass [Lat. missa, dismissal]: Ger. Messe; Fr. messe; Ital. messa. The Sacrament of the Eucharist as administered in the Roman and Greek Churches, in which, through the separate consecration of the bread and wine, the sacrifice of Christ is exhibited and the real body of Christ are received in the communion.

There are several species of Masses, as High Mass, which is accompanied with chant, incense, and the assistance of deacon and subdeacon; Low Mass, which lacks these accompaniments; Requiem Mass, celebrated for the dead; and Pontifical Mass, celebrated by the bishop.


Mass (in physics) [Lat. massa, a lump}; Ger. Masse; Fr. masse; Ital. massa. The quantity of matter in a body, as measured by the amount of its inertia or the amount of force necessary to produce in it a given motion in a given time, it being entirely free to move in the direction of the force.

The weight of the body at a given place is equally a measure of its mass, and the only measure that can be readily applied in practice. Experiment shows the results of the two measures to be identical, since weight, or gravity, and inertia have the same ratio for all substances. All bodies retain their mass unchanged, whatever transmutations they may undergo. (S.N.)

Material. MATTER (q.v.), or, as adjective, belonging to or composed of matter. See also MATTER AND FORM, and cf. topics in FORM and FORMAL. (J.M.B.)

Material Fallacy. This term originated with Whately (Encyc. Metropolitana, i. 218 b). Whately's material fallacies are those in which the conclusion does follow from the premises. Therefore, excluding the multiple interrogation, which is no syllogism, of the rest of Aristotle's thirteen, only the ignoratio elenchi and the petitio principii are material. Cf. FALLACY (also for foreign equivalents).

Aldrich had modified Aristotle's division into fallacies in dictione and fallacies extra dictionem; making a division into Sophismata in forma argumenti (sicubi conclusio non legitime consequatur ex praemissis), and Sophismata in materia argumenti (sicubi legitime non tamen vere concludere videatur syllogismus). Under the latter head he placed the ignoratio elenchi, the non causa pro causa, the non sequitur, and the petitio principii. Whately's distinction is -- whether from a theoretical or a practical point of view -- by far the most important that can be drawn among fallacies; so that besides the reason of priority, which ought itself to be final, the needs of the logician forbid us to depart from Whately's definition. Some logicians do not admit material fallacies among the number of fallacies, but consider them to be faults of method (Hamilton, Lects. on Logic, xxvi; Ueberweg, Syst. d. Logik, §§ 126, 137). E.E. Constance Jones (Elements of Logic as a Science of Propositions, § xxvi) reduces them to formal fallacies. Hyslop (Elements of Logic, chap. xvii) uses the term material fallacy, quite unjustifiably, to include all fallacies due to something in the matter of reasoning. (C.S.P.)

Material Logic: Ger. materielle Logik; Fr. logique matérielle; Ital. logica materiale. Formal logic classifies arguments by producing forms in which, the letters of the alphabet being replaced by any terms whatever, the result will be a valid, probable, or sophistic argument, as the case may be; material logic is a logic which does not produce such perfectly general forms, but considers a logical universe having peculiar properties.

Such, for example, would be a logic in which every class was assumed to consist of a finite number of individuals; so that the syllogism of transposed quantity would hold good. In most cases material logic is practically a synonym of applied logic. But a system like Hegel's may also properly be termed material logic. The term originated among the English Occamists of the 14th century, who declared Aristotle's logic to be material, in that it did not hold good of the doctrine of the Trinity. (C.S.P.)

Materialism [Lat. materialis, material]: Ger. Materialismus; Fr. matérialisme; Ital. materialismo. That metaphysical theory which regards all the facts of the universe as sufficiently explained by the assumption of body or matter, conceived as extended, impenetrable, eternally existent, and susceptible of movement or change of relative position.

Matter in motion is held to be the fundamental constituent or ultimate fact of the universe; and all phenomena, including the phenomena of consciousness, are reduced by the theory to transformations of material molecules. As Paulsen points out, the reduction of psychical processes to physical is the special thesis of materialism.

The atomism of Leucippus and Democritus is the first formulation of a definitely materialistic system. It is true that in all the theories of the PRE-SOCRATICS (q.v.) the principle of explanation is materialistically conceived, but this is due to the fact that the contrast between matter and spirit had not yet been fully realized. Hence it is customary to apply the term HYLOZOISM (q.v.) to the earliest Greek speculations. But even where the principle of explanation appears most abstract and idealistic, as in the Being of Parmenides, it is found on closer scrutiny that the definition of Being as 'a finite, spherical, motionless plenum' implies the unchallenged identification of being with sensible reality. Hence it has been argued by Burnet (cf. Early Greek Philos., 192-5) that 'Parmenides is not, as some have said, the father of idealism; on the contrary, all materialism depends on his view of reality.' As a matter of fact, the atoms of Leucippus and Democritus correspond exactly to the Eleatic definition of Being. But Parmenides had brought philosophy to an impasse through the impossibility of deducing from his immovable one the phenomena of actual experience. The atomists solve this difficulty by placing Non-being or the void alongside of the Eleatic plenum, the latter conceived, however, not monistically, but pluralistically. 'Leucippus,' according to Aristotle's account (Gen. Corr., A. 8. 324 B, 35 ff.), 'thought he had a theory which was in harmony with sense-perception, and did not do away with coming into being and passing away, nor motion, nor the multiplicity of things. . . . For, said he, that which is, strictly speaking, real is an absolute plenum, but the plenum is not one. On the contrary, there are an infinite number of them, and they are invisible owing to the smallness of their bulk. They move in the void (for there is a void), and by their coming together they effect coming-into-being; by their separation, passing-away.' The atomists, as Lange says, were the first to fix the definition of matter and consciously to derive the totality of phenomena solely from matter so conceived. In the form given to it by Democritus, adopted (with a slight modification) by Epicurus and clothed in poetry by Lucretius, the materialistic theory undergoes little change in ancient times. Its characteristic features are (1) the reduction of all qualitative differences to quantitative, namely, to differences in the size, form, arrangement, and situation of the individual atoms, and (2) the denial of intelligent purpose or final cause. The origin of the world-structure from the clash of moving atoms is held to be fully explained by mechanical necessity (anagkh). Of the origin of motion no account is given: it is apparently considered as equally primordial with the existence of the atoms themselves. But the velocity of the atoms is made to depend on the size or mass of the atoms, whence arise those clashings and interferences which sift out the atoms of different kinds, and, by the separations and combinations produced, give rise in process of time to the existing cosmic system. Epicurus adopted the materialism and atomism of Democritus, but modified the principle of natural necessity by ascribing to the atoms (which he conceived as falling through infinite space) a power of voluntary deviation from the direct line of descent, explaining thereby the origin of the clashings and whirling movements from which the ordered system of things took its rise. The Stoics, as the great teleologists of the ancient world, with their pantheistic doctrine of the world-reason, stand at the opposite extreme from the pure atomism of the Epicureans; yet both schools are completely materialistic in their theoretical conceptions. The Stoics go so far as to declare that even the qualities, forces, and relations of things are 'bodies,' and the creative reason is conceived (after Heraclitus) as a warm vital breath penetrating all things and constituting their active principle.

The materialism of Epicurus was revived at the beginning of modern philosophy by Gassendi, who, however, reconciled the theory with orthodox Catholicism by making God the creator of the atoms. About the same time Hobbes defined philosophy as the theory of body and motion, laying down explicitly that 'all that exists is body, all that occurs motion.' But philosophy is concerned, according to Hobbes, only with phenomena or things that appear as generated. Hence God, as ungenerated, is excluded from its scope, and philosophy (which is thus used as equivalent to natural science) has nothing to do with matters of faith. Hence, although Hobbes banishes final causes from philosophy, and gives a completely materialistic account of the relation of body and mind, he can hardly be classed as a materialist in the full philosophical sense of the word; he himself claimed to be an orthodox member of the Church of England. The anthropological materialism, which is so uncompromisingly taught by Hobbes, appears in several successive English thinkers, who combine it with a theistic or deistic theory of the universe as a whole. Even Locke, while holding that matter must have been created, and that it is in itself devoid of consciousness (and even perhaps of any active power), designedly leaves the immateriality of the soul an open question, 'it being, in respect of our notions, not much more remote from our comprehension to conceive that God can, if he pleases, superadd to matter a faculty of thinking than that he should superadd to it another substance with a faculty of thinking' (Essay, iv. 3, 6). Hartley's doctrine of association is expressed in terms of movements in the brain, and his disciple, Priestley, avowedly held the soul to be material, treating psychical phenomena as consisting literally in the material motions of the brain.

It was in France in the 18th century that the great modern development of philosophical materialism took place in the writings of Lamettrie and the ENCYCLOPEDISTS (q.v.). Baron d'Holbach's Système de la Nature, published in 1770, represents the culmination of the movement. After the succession of idealistic systems in Germany in the end of the 18th and the beginning of the 19th century, materialism began, partly by way of reaction, to raise its head again about the middle of the century. Moleschott, Vogt, and Büchner may be mentioned as leaders. Büchner's Kraft und Stoff, although crude and vague and of no real philosophical significance, is a fair type of the popular materialistic arguments and conclusions in the second half of the century, seeing that it has passed through sixteen or more editions since its publication in 1855, and has been translated into thirteen foreign languages. The concentration of mental energy on the problems of science, and the great advance of the biological sciences in particular, have given a materialistic colouring to much recent speculation that would decline to identify itself with dogmatic materialism. The agnosticism of Huxley and of Herbert Spencer might be instanced as acknowledging in theory the co-equal rights of mind and matter, but in practice laying the stress of explanation upon the material side. Materialism as a dogmatic system hardly survives in philosophical circles, although, in alliance with secularism and socialism, it is no doubt influential among certain sections of the working-classes, and often forms the creed of the half-educated specialist. The place of materialism has been taken by scientific MONISM (q.v.), which, however, in some of its representatives, seems often to be but slightly differentiated from the materialism which it has superseded.

'Ethical materialism' (Lange) and 'practical materialism' (Külpe) are terms used to denote the temper of mind which sees in the acquisition of wealth, material comfort, and sensuous pleasure the only reasonable objects of human endeavour. Lange, in his great work, considers dogmatic materialism to be impossible after the epistemological criticism of Kant, but regards it as a regulative principle of scientific inquiry. The chief epistemological, metaphysical, and scientific arguments against materialism (as well as the considerations on which it is based) are discussed by Lange and are summarized in Flint, Paulsen, and Külpe.

The term materialist is stated by Eucken (Grundbegriffe der Gegenwart, 97) to have been first used by Robert Boyle in his work on The Excellence and Grounds of the Mechanical Philosophy, 1674. Idealist and materialistic appear frequently in Wolff as the two varieties of monist (monism being here opposed to dualism).

Literature: LANGE, Hist. of Materialism (Eng. trans.); FLINT, Antitheistic Theories, lects. ii-iv and notes 5-19; PAULSEN, Einleitung in die Philos., 63-90; KÜLPE, Einleitung in die Philos., 127-37 (who distinguishes the different logical forms of materialism). See also PAUL JANET, Le Matér. contemporain (6th ed.). Recent materialistic views in psychology are expounded by BALDWIN, Recent Discussion in Materialism, Presb. and Ref. Rev., i. (1890) 357. Cf. also the Encyclopedias, sub verbo; and BIBLIOG. B, 2, e. (A.S.P.P.)

Mathematical Economics: Ger. mathematische Oekonomik; Fr. économie mathématique; Ital. economia matematica. The development of notations and functions which serve to connect our experience with regard to balance of motives with our observation as to quantities of wealth; thus enabling the study of either set of phenomena to be used to explain the others quantitatively.

The differential equations of economics are mostly in terms of motive, the integrals mostly in terms of wealth.

The pioneer in mathematical economics was Cournot; his work has been extended by Dupuit and by Marshall. The efforts of v. Thünen were less permanently fruitful than those of Cournot. See SUPPLY AND DEMAND.

Another line of thought, first developed by Gossen, and afterwards (non-mathematically) by Menger, was made an instrument of powerful analysis by Jevons, and by the Austrian school after him (see MARGINAL INCREMENT). Among more recent mathematical economists we may note Anspitz and Lieben, Edgeworth, Fisher, and Pareto.

As Cohn well observes, mathematical methods in economics must not be confounded with statistical ones. The latter represent the extreme of concreteness, the former the extreme of abstraction. (A.T.H.)

Mathematical Logic: Ger. (1) Logik der Mathematik; Fr. (1) logique des mathématiques; Ital. (1) logica della matematica. (1) The logical analysis of mathematics. (C.S.P.)

(2) SYMBOLIC LOGIC (q.v.).

Literature (to 1): the logic of arithmetic is treated by DEDEKIND in his Was sind und was sollen die Zahlen? (Eng. trans. in Essays on Number, 1901). See also the ninth lecture of the third volume of SCHRÖDER, Logik; and FINE, Number System of Algebra. For the logic of the calculus, see the second edition of JORDAN, Cours d'Analyse; also CLIFFORD, Theory of Metrics, in his Mathematical Papers; WEBER, Algebra; and the papers of G. CANTOR, some of which are contained in the Acta Mathematica, ii, and subsequent ones in the Mathematische Annalen, 15, 17, 20, 21, 23, 46, 49. LISTING'S papers on topical geometry are two, one in the Gött. Abhand., the other in the Gött. Nachr. Several of RIEMANN'S papers are valuable in a logical point of view. See also CAUCHY, Théorie des Clefs. PETERSEN, Methods and Theories, shows how to solve problems in elementary geometry. Cf. MATHEMATICS. (C.S.P.)

Mathematics [Gr. maqhmatikh, from maqhmata, things learned]: Ger. Mathematik; Fr. mathématiques; Ital. matematica. A science of abstract relationships. These are by no means exclusively quantitative. The projective properties of curves, for instance, of which an example is given below, are purely positional. And the whole of analysis may be presented in the form of an abstract calculus of symbols to which no meaning of any kind need be assigned, the operations themselves being defined by certain formal laws, as addition by the laws a + b = b + a and (a + b) + c = a + (b + c). (J.M.B.- H.B.F.)

'Any conception which is definitely and completely determined by means of a finite number of specifications, say by assigning a finite number of elements, is a mathematical conception. Mathematics has for its function to develop the consequences involved in the definitions of a group of mathematical conceptions' (Chrystal) combined with certain fundamental principles, or axioms and postulates. (C.L.F., F.F.)

One of the most distinctive characteristics of mathematics is the extreme definiteness of the conceptions with which it deals. They admit of exact definition by a limited number of marks.

The more fundamental of these conceptions correspond immediately to things and relations among things in the external world, from which, in fact, they have been derived by a process of abstraction. Such are the conceptions of cardinal numbers and of the ordinal arrangement of the cardinal numbers on which arithmetic is based (see NUMBER); the conceptions of point, line, &c., and of such fundamental relations as that two points determine a right line, &c., which lie at the basis of geometry.

It is the function of mathematics to make the simplest possible selection of such of these primary conceptions as are mutually independent, and by combining them and generalizing them, to create a body of more complex conceptions which have intrinsic interest and beauty and a value for the furtherance of the science itself or for the study of other positive sciences. The extraordinary developments of the number-concept will serve as a familiar illustration to the extent to which the process of generalization is carried in mathematics.

For the investigation of these complex relationships, it must also invent an adequate symbolism.

It is customary to call those sciences 'mathematical' in which there exist, among the results of observation, certain fundamental relations so simple and definite that they can be represented with advantage by mathematical conceptions, and to denominate the disciplines which grow out of the mathematical discussion of these conceptions the 'applied mathematics.' Strictly speaking, geometry itself is a branch of the applied mathematics.

Very characteristic of the modern mathematics is the prominence of the notions: manifoldnesses or assemblages of actual or ideal elements of some kind, e.g. of points, lines, or surfaces; the transformations or substitutions by which the elements of two assemblages may be brought into definite relations of correspondence; and the invariantive properties of assemblages, i.e. the properties which remain unchanged by given groups of transformations. In fact, to such an extent do these notions, in some form or other underlie the various branches of mathematics, that it is almost admissible to define mathematics as the science of assemblages.

To cite one or two illustrations: --

(1) The simplest class of assemblages are finite groups of distinct things. The invariantive property of such a group is its cardinal number -- the property which remains unchanged by every 'transformation,' which merely changes the arrangement of the things in the group or replaces them, one for one, by other things.

(2) Every functional relation (see FUNCTION) between two variables y and x, say y = x2, is a relation of correspondence between two number-assemblages -- the values of x, on the one hand, and those of y on the other.

(3) In the study of a curve by the analytic method, we substitute for the curve itself the assemblage which consists of all the points upon it. The equation of the curve, y = f(x), is merely a statement of the relation of correspondence into which this assemblage can be brought to another point assemblage -- that which consists of all points on the x axis. And the equation y = f(x) serves this purpose, because, before undertaking the study of the particular curve, we set up a definite relation of one-to-one correspondence between the assemblage of all the points of the plane and the assemblage of all possible pairs of real values of the variables x and y. Cf. IMAGING.

(4) We can transform an algebraic curve whose equation is f (x, y) = 0 into an endless variety of other curves by substituting for x and y, in the equation  f (x, y) = 0, various functions of these variables.

But there is a group of such substitutions distinguished from all others by the fact that they leave invariant the 'order' of the curve f (x, y) = 0, that is, the greatest number of points in which it can be cut by a right line. This is the group of 'linear' substitutions, defined by all possible equations of the form

The curve has other properties which also remain invariant by this group of substitutions. Thus, if the equation f (x, y) = 0 be of the second degree, it will ordinarily represent a 'proper' conic, that is, an ellipse, hyperbola, or parabola; but it may also represent a pair of intersecting straight lines, which may be characterized as a conic possessing a 'singular point' -- the point of intersection of the lines. The presence or absence of such a singular point in the conic f (x, y) = 0 is an invariantive property of this curve with respect to the group of linear substitutions; that is, if f (x, y) = 0 be a proper conic, so will every conic be into which it can be transformed by a substitution of this group; if it be a pair of right lines, so will every conic be into which it can be transformed by a substitution of the group.

We may add that the properties of a curve which remain thus unchanged by linear transformation are called its 'projective' properties; those which do not, its 'metrical' properties.

Literature: CLIFFORD, Essays and Addresses; KLEIN, Lectures on Mathematics; POINCARÉ, papers in the Monist and Rev. de Mét. et de Mor. (1898-1901); RUSSELL, The Foundation of Geometry; MACH, papers in the Monist (1899-1901). (H.B.F.)

Matriarchate [Lat. mater, Gr. mhthr, mother, + arcoV, leader, ruler]: Ger. Mutterrecht, Matriarchat; Fr. matriarcat; Ital. matriarcato. A family, clan, or tribe ruled by a woman or by women.

This term was introduced into ethnology by Backofen (Das Mutterrecht), and was adopted by E. B. Tylor and others. There is no proof that a matriarchate has ever existed, so-called matriarchal groups being probably merely METRONYMIC (q.v.). 'Children took the name of mothers. . . . This is really the origin of the so-called matriarchate, in which the mother had in fact no power, but gave her name to her child.' (G. Bertin, J. of the Anthropol. Inst., xviii. 271). (F.H.G.)

Matronymic: see METRONYMIC.

Matter: see EXTERNAL (different topics), BELIEF, EPISTEMOLOGY, PHILOSOPHY, and the following topics.

Matter (in physics) [Lat. materia, stuff]: Ger. Materie; Fr. matière: Ital. materia. The substance of which the sensible universe seems to us to be composed.

Its existence is manifested by an infinite variety of ever-changing phenomena, which we may consider as growing out of the direct or indirect action of matter upon our organs of sense. Thus, when we feel the object, we conceive it to act directly upon the nerves of sensation; when we see it, the action is that of light, and is therefore indirect. What differentiates matter from the phenomena or actions of which alone we are directly conscious is its permanence. The object which I call a chair presents itself to my senses in a great variety of more or less complex combinations, according to the point from which I view it or the way I touch it. If I leave the room in which it is placed, these phenomena cease entirely. From the fact that I can reproduce them at pleasure by going where the chair is -- that by assuming the existence of the matter composing the chair as a reality, independent of my own existence, I can account in a very simple way for an infinitely complex series of experiences which could not be reduced to law in any other way -- we have the strongest ground for our belief in the real existence of matter.

What attributes are we justified in assigning to this reality? We answer: those attributes which are necessary to account for the phenomena, and no others. Two associated attributes which are essential to our conception of matter are EXTENSION (q.v.) and IMPENETRABILITY (q.v.). Matter occupies space; two portions of matter cannot occupy the same position in space at the same time.

Such is our primary conception: but experience leads us to doubt whether these qualities are absolute. If we hold a lump of sugar in water, we find that the water penetrates the sugar. We account for this by saying that the matter of the sugar is not a plenum; that there are unoccupied spaces between the particles, into which the water penetrates. But if we admit that the lump which seems to us a plenum -- a continuous space-filling mass -- is not such, where shall we stop? What space is really occupied by the ultimate parts of the mass?

This question gives rise to the hypothesis of Boscovich -- that matter is composed of points endowed with inertia and certain powers of mutual attraction and repulsion. As two particles or atoms are brought closer, a distance is reached at which the mutual repulsion increases without limit as the distance is lessened, so that the two points cannot be brought into absolute coincidence by any amount of force.

This hypothesis is far from accounting for all the molecular phenomena of matter, cohesion, &c., but its elimination of extension and impenetrability as primary attributes is a distinctive step forward. To compare this and the natural conception, I hold a billiard ball in my hand. If I squeeze the ball, it resists. I conceive of the ball as filling a certain space, and passively resisting my effort to put my hand into the same space. But what I really feel, and all that I really feel , is a repulsive force between the matter of the ball and that of my hand. The latter presses the ball; by the law of action and reaction the ball equally presses the hand; the pressure is all that I feel, and pressure is only a force. How it happens that we posit a passive space-filling substratum when we feel only a force is an interesting question of genetic psychology; perhaps it is because the passive form of the conception is the easier one, and does not involve any use of the law of action and reaction. The vital point is that the attributes of impenetrability and extension become apparent or secondary ones.

Atoms. The ancient doctrine that matter is not infinitely divisable, but is composed of minute parts called atoms, which remain unchanged through all the chemical and physical processes to which matter can be subjected, seems to be justified by the great mass of facts which make up our chemistry and physics. The attributes of atoms are conceived of as, in themselves, invariable, though possibly subject to differences of manifestation under different surrounding conditions.

From this point of view every atom of the same kind of matter, or of the same chemical element, must have the same mass. A series of numbers proportional to the masses of different kinds of atoms are called the atomic weights. For example, if we take the mass of an atom of hydrogen as unity, then that of an atom of oxygen will be about 8, of carbon about 6, &c. These numbers are only relative, since nothing is known of the absolute mass of any one atom. Cf. CHEMICAL SYNTHESIS. For the atom in philosophy, see MONAD.

Molecules. Most substances with which we are familiar are compounded of various elements: hence these smallest portions must be capable of subdivision into these elements, and therefore cannot be atoms. These smallest portions, portions which cannot be divided without changing the chemical properties of the compound, are called molecules. The distinction between an atom and a molecule is that the latter is subject to division, while the former is not.

Elements are the different kinds of matter which cannot be decomposed, and which therefore make up the substance of the material universe. From a purely logical point of view, the distinction between an element and a compound would seem to be relative to our knowledge at the moment. Possibly many of what we call elements are compounds which we have not succeeded in decomposing; and the idea that all matter may be of one kind, and all atoms be really molecules made up of different arrangements of one kind of primaeval atoms, has been widely entertained, and may be well founded. But it is a significant fact in this connection that no progress is being made in the way of decomposing the accepted elements. In no case has a substance accepted in our modern chemistry as an element been decomposed or transformed into another. The distinction between elements and compounds is therefore a real one in kind, whether, in the absolute sense, an atom is or is not a compound. (S.N.)

Matter and Form: Ger. Materie (Stoff) und Form; Fr. la matière et la forme; Ital. materia e forma. The word matter (Lat. materia, which was used to translate the Gr. ulh) is often employed where the more appropriate Greek word would be swma, corpus, body; or to upokeimenon, subjectum, or even h npostasiV, translated person in theology. Form (Lat. forma, used to translate the Gr. morfh and eidoV, though the latter is more exactly represented by species) is often employed where schma, figure, or tupoV, shape, would be near equivalents. The Greek expressions morfh, paradeigma, eidoV, idea, to ti esti, to ti hn einai are pretty nearly synonymous.

The distinction of matter and form was first made, apparently, by Aristotle. It almost involves his metaphysical doctrine; and as long as his reign lasted, it was dominant. Afterwards it was in disfavour; but Kant applied the terms, as he did many others drawn from the same source, to an analogous but widely different distinction. In many special phrases the Aristotelian and Kantian senses almost coalesce, in others they are quite disconnected. It will, therefore, be convenient to consider: (1) the Aristotelian distinction; (2) the Kantian distinction; and (3) special applications.

The Aristotelian distinction. Not only was the distinction originated by Aristotle, but one of the two conceptions, that of matter, is largely due to him. Indeed, it is perhaps true that the Greek word for matter in the sense of material, ulh, was never understood in that general sense before Aristotle came to Athens. For the first unquestionable cases of that meaning occur in certain dialogues of Plato, concerning which -- though there are no dates that are not open to dispute -- it seems to the present writer that it is as certain as any such fact in the history of Greek philosophy that the earliest of them was written about the time of Aristotle's arrival. It is true that, as Aristotle himself says, matter was the earliest philosophical conception. For the first Ionian philosophers directed their thoughts to the question what the world was made of. But the extreme vagueness of the notion with them is shown by their calling it h arch, the beginning, by the nonsense of the question, and by many more special symptoms. If the philosophical conception of matter distinguished the metaphysics of Aristotle, that of Plato had been no less marked by its extraordinary development of the notion of form, to which the mixed morality and questioning spirit of Socrates had naturally led up; the morality, because the form is the complex of characters that a thing ought to have; the questioning, because it drew attention to the difference between those elements of truth which experience brutally forces upon us, and those of which reason persuades us, which latter make up the form. But Aristotle's distinction set form, as well as matter, in a new light.

It must not be forgotten that Aristotle was an Asclepiad, that is, that he belonged to a family which for generation after generation, from prehistoric times, had had their attention turned to vital phenomena; and he is almost as remarkable for his capacity as a naturalist as he is for his incapacity in physics and mathematics. He must have had prominently before his mind the fact that all eggs are very much alike, and all seeds are very much alike, while the animals that grow out of the one, the plants that grow out of the other, are as different as possible. Accordingly, his dunamis is germinal being, not amounting to existence; while his entelechy is the perfect thing that ought to grow out of that germ. Matter, which he associates with stuff, timber, metal, is that undifferentiated element of a thing which it must possess to have even germinal being. Since matter is, in itself, indeterminate, it is also in itself unknowable; but it is both determinable by form and knowable, even sensible, through form. The notion that the form can antecede matter is, to Aristotle, perfectly ridiculous. It is the result of the development of matter. He looks upon the problem from the point of view of a naturalist. In particular, the soul is an outgrowth of the body.

The scholastics, who regarded Aristotle as all but infallible, yet to whom the ideas of a naturalist were utterly foreign, who were thoroughly theological in their notions, admitted that the soul was a form. But then, they had great difficulty with those opinions of their master which depended upon his conceiving of matter as more primitive than form. Their notions of form were rather allied to those of Plato. The mode of being that, in some sense, anteceded individual existence, they would have held to be one in which there was form without matter, if awe of Aristotle had not caused them to modify the proposition in one way or another. A question, for example, which exercised them greatly was, how the form was restricted to individual existence? For Aristotle there could not be any such question, because he did not conceive of a form taking on individuality, but of an undifferentiated matter taking on, or rather developing, form, and individuality, perhaps, with it (412 a, 7).

The Kantian distinction. Aristotle refuses to consider any proposition as science which is not universal. He does not go so far as to say that all knowledge involves synthesis, but he often approaches doing so. In particular, he holds that matter is something in itself beyond our knowledge, but the existence of which has to be assumed in order to synthetize the opposites that are involved in all change. He expressly defines that as the function of the conception of matter. With Kant, the view that all knowledge involves synthesis -- various acts of synthesis one over another -- is vastly more developed; and he, too, employs the terms matter and form as called for by such synthesis. But it is curious that while with Aristotle it is matter that is the quasi-hypothesis imported into the facts that the mind may synthetize, with Kant, on the other hand, it is form which performs this function. The matter of cognition consists of those elements which are brutally and severally forced upon us by experience. By the form he means the rational or intelligible elements of cognition, which he wishes, as far as possible, to regard as independent contributions of the mind itself, which we have no right to suppose are duplicated by anything corresponding to them in the thing. For the Aristotelian, all pure matter is exactly alike, equally devoid of all predicates, while the forms make all the variety of the universe. For the Kantian, on the other hand, matter is the manifold, while the pure forms are the few different modes of unity. Nevertheless, the Kantians -- indeed, Kant himself (see the Critic of the Pure Reason, 1st ed., 266) -- argued that they were using the terms in their old and accepted sense. What enabled them to give some speciousness to their contention was the circumstance that during the full century and more of neglect of the Aristotelian doctrine that had intervened, certain secondary senses of the term matter, especially that of corporeal matter, and that of a species of corporeal matter, had become relatively prominent.

Special senses. Although there is only one first or primary matter, absolutely indeterminate, yet Aristotle often uses the term in a modified sense as that which is relatively indeterminate; so that the last or second matter is the same as the form. But these phrases are also used in quite other senses, which need not here be specially noticed. Matter being taken relatively, the same thing can have this or that as its matter in different respects; and so matter is distinguished into materia ex qua, in qua, and circa quam. Materia ex qua is the material; silver is the materia ex qua of a dime. Materia in qua is the subject in which the form inheres; materia circa quam is the object. Aquinas illustrates the distinction by virtue, which is a form, and, as such, has no materia ex qua; but it has a subject in which it inheres and an object upon which it is exercised. Aquinas introduced the term signate matter. Matter of composition, or proximate matter, is that of which a thing consists; matter of generation, or remote matter, that from which it is developed, as a seed or egg.

The varieties of form are so numerous that they may best be taken in alphabetical order.

Absolute form: form abstracted from matter.

Accidental form: an accident, or that the presence of which constitutes an accident; as music is the accidental form of the musician.

Advenient form: a form subsequent to the final form.

Apprehended form = apprehended SPECIES (q.v.).

Artificial form: a form superinduced by art.

Assistant form: an agent aiding in the realization of a form, especially of that whose essential character is to move; as the angel who turns the heavens round once every twenty-four hours, or the captain of a ship.

Astral form. According to Gilbert (De Magnete), phenomena of electricity are produced by a material effluvium, while the action of a magnet takes place directly at a distance. Whatever it may be then which constitutes the magnetic field, not being matter, must be called form. Gilbert names it forma prima radicalis et astralis.

Common form: a form belonging to a species.

Completive form: used by Aquinas in the sense of the last of the series of forms which gradually bring a thing to fully developed existence. By Aristotle called last form.

Composite form: the form of a collective whole, so far as it is different from its parts.

Corporeal form: a form of a corporeal nature. This is used by Aquinas, Summa Theol., pars I. qu. 1xv. art. 4. See Material form.

Disponent form: a form rendering matter apt to receive another, principal, form. Thus, dryness in wood disposes it to receive combustibility.

Elementary form: one of the four combinations of hot and cold with moist and dry which were supposed to characterize the four elements.

Exemplar form: an idea.

Final form: see Completive form.

General form: the form of a genus; as we should now say a generic form.

Immaterial form: a form which neither depends upon matter while it is being made nor after it is made; a term employed in the theological doctrine of creation.

Incorruptible form: a form not subject to corruption.

Individual form: in one of the theories of individuation, was a form which by existing in matter acquired the power of individuating another form.

Informant form: a form which is a part of the thing of which it is the form.

Inherent form: a form which can only exist in a state of inherence in matter.

Intellective form: the mind as form.

Intelligible form: see Sensible form.

Intermediate form: a form having a middle position between an elementary and a completive form.

Material form: a term of Scotus, who defines it as follows: 'Formam materialem dico esse omnem illam, quae ex natura sua necessario inclinatur naturaliter, ut sit actus materiae, sive sit substantialis, sive accidentalis' (Op. Oxon., IV. i. 1); 'Ideo dici potest tertio modo.' But elsewhere (ibid., 1 Post. qu. ii.) he distinguishes two senses of the term: 'Forma materialis potest intelligi dupliciter. Uno modo dicitur, quae educitur de potentia materiae, vel quia utitur organo corporeo in operando: et isto modo forma intellectiva non est forma materialis. Alio modo dicitur forma materialis, quia perfectio materiae, et isto modo anima intellectiva est forma materialis, ideo aliquam variationem potest accipere a materia, quam perficit, quia ex materia et forma fit vere unum.' Perhaps the most accessible book from which to gain a hint of the nature of the difficulty which gives rise to this distinction is Bridges' edition of what is called The Opus Majus of Roger Bacon, ii. 507-11, cap. ii.

Mathematical form: an object of mathematical contemplation, and the result of mathematical abstraction.

Metaphysical form: form in the philosophical sense.

Native or natural form, forma in natura exsistens, forma naturae, form of a nature, is a term going back to John of Salisbury (Opera, ed. Giles, v. 92), and closely connected, if not synonymous, with material form. Certain questions started by Aristotle in Book V of the Metaphysics (of which there is an admirable periphrastic translation by Grote, Aristotle, 2nd ed., 619 ff.) gave rise to discussions in which the doctrine was compared with Christian beliefs; and the natural form plays a considerable part in such discussions.

Bacon adopted the term forma naturae. He did not grossly depart from the received meaning of the term, but owing to his occupying himself with inquiries quite antipodal to those of the scholastics, the two parties did not understand one another. Bacon means the physical explanation of a phenomenon, its occult modus operandi. Among the followers of Bacon we, at first, hear a great deal about forms. Boyle wrote whole books about them. But the distinction of matter and form was not calculated to further such inquiries as theirs. It is adapted to expressing phenomena of life. It might be twisted to such a purpose as Gilbert put it to (see Astral form), but it was not suited to the mechanical philosophy of Boyle, and only led to wordy and fruitless discussions.

Participate form: a form considered as it is united with matter.

Preparatory form: a term used by Boyle where disponent form would be more technical. He says, 'The preparatory form is but (if I may so speak) a harbinger that disposes the matter to receive a more perfect form, which, if it be not to be succeeded by any other more noble, is entitled the specific form of that body; as in the embryo, the vegetative and the sensitive soul is but preparatory to the rational, which alone is said to be the specific form of man' (Free Considerations about Subordinate Forms).

Physical form: such forms as may form the object of physical inquiries. Of course, the term was very differently understood during scholastic times and in the 17th century. But the above definition covers both uses.

Primary form. There is no such well-recognized term of metaphysics; but a remark of William Gilbert leads us to suppose that medical men attached some meaning to it.

Principal form is that which per se constitutes a species. Called also specific form.

Radical form: see Astral form.

Sensible form. Though it chances that Aristotle nowhere distinguishes morfh into aisqhth and nohth, yet his followers did. Sensible forms are those which the outward senses distinguish; intelligible are those which the intellect alone can distinguish.

Significate form: a Thomistic term, a form distinguished by a name.

Simple form: form without matter. 'Forma simplex, quae est purus actus, est solus deus,' says St. Thomas.

Specific form: see Principal form.

Subsistent form: a form capable of existing separate from matter, as Aquinas holds that the angels and departed spirits are.

Substantial form: a form which constitutes a nature, i.e. a species or genus. Thus, the accidental form of a musician is music; but his substantial form is the rational soul which makes him a man. When men's thoughts became turned from theology to the investigation of physics, those who were animated by the new spirit found themselves confronted with objections based upon allegations of substantial forms. That these substantial forms, so used, were merely a hindrance to the progress of science, was quite plain to them. But the objections were urged with a logical accuracy, born of centuries of study, with which the new men were utterly incapable of coping. Their proper course would have been quietly to pursue their own inquiries, and leave the theologians to square their results with philosophy as best they could. But circumstances did not permit this. The theologians had the popular intelligence and the arm of power on their side; and when an apparent opposition arose, they naturally exerted themselves to put it down. Thus, the innovators were led to protest against these senseless and harmful substantial forms; and they had to formulate their objections to them -- a business for which they were entirely unfitted. But since the discoveries of the physicists were plainly adding to man's knowledge and power, while their antagonists were simply obstructive, the former soon carried the day in the general opinion of mankind. The history proves that there was something vicious about the theological application of substantial forms; but it in no degree goes to show that the physicists accurately defined the objection to that application. In reviewing the arguments at the present day, when the position of the mechanical philosophers is becoming almost as obsolete as that of the scholastic doctors, we first note that when the new men denied that the substantial forms were 'entities,' what they really had in mind was, that those forms had not such a mode of being as would confer upon them the power dynamical to react upon things. The Scotists, for it was they upon whom, as being in possession of the universities, the brunt of the battle fell, had in fact never called the substantial forms 'entities, 'a word sounding like a Scotistic term, but in fact the mere caricature of such a term. But had they used the word, nothing more innocent than the only meaning it could bear for them could be imagined. To call a form an 'entity' could hardly mean more than to call it an abstraction. If the distinction of matter and form could have any value at all, it was the substantial forms that were, properly speaking, forms. If the Scotists could really specify any natural class, say man -- and physics was at that time in no condition to raise any just doubt upon that score -- then they were perfectly justified in giving a name to the intelligible characteristic of that class, and that was all the substantial form made any pretension to being. But the Scotists were guilty of two faults. The first -- great enough, certainly, but relatively inconsiderable -- was often referred to, though not distinctly analysed and brought home to them. It was that they were utterly uncritical in accepting classes as natural, and seemed to think that ordinary language was a sufficient guarantee in the matter. Their other and principal fault, which may with justice be called a sin, since it involved a certain moral delinquency, was that they set up their idle logical distinctions as precluding all physical inquiry. The physicists and Scotists, being intent upon widely discrepant purposes, could not understand one another. There was a tolerably good excuse for the physicist, since the intention of the Scotist was of an abstract and technical kind, not easily understood. But there was no other excuse for the Scotist than that he was so drugged with his metaphysics that ordinary human needs had lost all appeal to him. All through the 18th century and a large part of the 19th, exclamations against the monstrousness of the scholastic dogma that substantial forms were entities continued to be part of the stock-in-trade of metaphysicians, and it accorded with the prevalent nominalism. But nowadays, when it is clearly seen that physical science gives its assent much more to scholastic realism (limited closely to its formal statement) than it does to nominalism, a view of the history more like that here put forward is beginning to prevail.

In the following terms, mostly Kantian, prepositional phrases express the qualifications.

Form of corporeity: a very common term of scholasticism, originating with Avicenna, and used by Aquinas (Summa Theol., pars i. cap. 1xvi. art. 2), but more particularly by Scotus (in his great discussion Opus Oxon., IV. dist. xi. 9. 3, beginning 'De secundo articulo dico') and by all his followers. The point is, that the rational soul, being purely spiritual, cannot confer corporeity upon the human body, but a special form, the form of corporeity, is requisite. Suarez and others, generally Thomists, as well as Henry of Ghent, denied this on the ground that a species has but one form. Thus a great metaphysical dispute arose. It sprung from the study of the doctrine of transubstantiation. See Cavellus, Suppl. ad quaest. Scoti in De Anima, disp. i, which is in the Lyons ed. of Scotus, tom. ii.

Form of cognition, in Kant's doctrine, is that element of knowledge which the matter of experience must assume in order to be apprehended by the mind. Kant seems to have been thinking of legal forms which must be complied with in order to give standing before a court. So an English sovereign, in order to be crowned, must, as a 'matter of form,' swear to an intensity of loathing for Romish dogmas which he probably regards with great coolness. Kant's definitions are chiefly the following: --

'In the phenomenon, that which corresponds to the impression of sense, I call the matter of it; while that which constitutes the fact that manifoldness of the phenomenon is intuited as ordered in certain relations, I call the form of the phenomenon' (Krit. d. reinen Vernunft, 1st ed., 20).

'All cognition requires a concept, be it as imperfect and dark as you will; and this, in respect to its form, is always a universal which serves as a rule' (ibid., 106).

'The transcendental unity of the synthesis of the imagination is the pure form of all possible cognition, through which, consequently, all objects of possible experience must a priori be represented' (ibid., 118).

'There are two factors in cognition; first, the concept by which any object is thought -- that is, the category; and secondly, the intuition by which that object is given. For if the concept had had no corresponding intuition, it would be a thought, no doubt, as far as its form goes; but having no object, no cognition whatsoever [he means, whether true or false] of anything would be possible by it; since, so far as I should know, there would be nothing, and perhaps could be nothing, to which such a concept would be applicable' (2nd ed. of the Deduction of the Categories, § 22).

'It is not more surprising that the laws of phenomena in nature must agree with the understanding and its a priori form, i.e. with its power of combining any manifold, than that the phenomena themselves must agree with the a priori form of sensuous intuition. For just as phenomena have no existence in themselves, but are merely relative to the mind, as having senses, so laws do not exist in the phenomena, but are merely relative to the mind in which the phenomena inhere, that mind exercising understanding' (and see the rest of this passage, ibid., § 26).

Form of forms. Francis Bacon says 'the soul may be called the form of forms,' which would be a pretty conceit, were it not plagiarized from the serious doctrine of Aristotle: o nouV eidoV eidwn (432 a, 2).

The terms matter and form are used in certain peculiar ways in logic. Speaking materialiter, the matter of a proposition is said to be its subject and predicate, while the copula is its form. But speaking formaliter, the matter of a proposition is, as we familiarly say, the 'matter of fact' to which the proposition relates; or as defined by the scholastics, 'habitudo extremorum adinvicem.' The second tractate of the Summulae of Petrus Hispanus begins with the words: 'Propositionum triplex est materia; scilicet, naturalis, contingens, et remota. Naturalis est illa in qua praedicatum essentia subiecti vel proprium eius; ut, homo est animal; vel, homo est risibilis. Contingens est illa in qua praedicatum potest adesse et abesse subiecto praeter subiecti corruptionem; ut, homo est albus, homo non est albus. Remota est illa in qua praedicatum non potest convenire cum subiecto; ut, homo est asinus.'

Of a syllogism, the proximate matter is the three propositions; the remote, the three terms. The form, which ought to be the ergo, by the same right by which the copula is recognized as the form of the proposition, is said to be 'apta trium propositionum dispositio ad conclusionem ex praemissis necessario colligendam.' But Kant, in the Logik by Jäsche, § 59, makes the premises the matter, and the conclusion the form. (C.S.P.)

Maxim (in ethics) [Lat. maxima sententia, opinion of greatest weight]: Ger. Maxime; Fr. maxime; Ital. massima. (1) Any important principle for the regulation of conduct.

(2) A technical term in Kant's ethics: a practical principle regarded by the agent as valid for his own will.

In this latter sense a maxim is distinguished from a practical law. The latter is regarded as objectively valid, or valid for the will of every rational being. Morality consists, according to Kant, in the objective law becoming also the subjective maxim of the will; and his moral imperative is accordingly expressed in the terms, 'Act so that the maxim of thy will can always at the same time hold good as a principle of universal legislation.' Cf. Kant, Krit. d. prakt. Vernunft, Pt. I. Bk. II. chap. i. §§ 1 and 7. (W.R.S.)

Maxim (in logic). A widely received general assertion or rule.

The earliest writers, so far as has been shown, to use maxima as a substantive were Albertus Magnus and Petrus Hispanus. The former (Post. Anal., lib. I. cap. ii) makes maximae constitute the seventh of thirteen classes of propositions which may be accepted, though they are uncertain, so that they differ widely from dignitates, or axioms. He says, 'Maximae propositiones opinantur esse quae non recipiuntur nisi in quantum sunt manifestae. Et putat vulgus commune et alii simplices et non periti quod sint primae ex sui veritate communicantes omnem intellectum; sicut est ista propositio, Mendacium est turpe,' &c. Hamilton quotes, but gives an unverifiable reference to, a sentence in which Albertus makes maxima another name for a dignitas. Petrus Hispanus (Summulae, v) says, 'Maxima est propositio qua non est altera prior neque notior'; and he divides commonplace into two kinds, called Maxim and Difference of Maxim. This phraseology was so generally followed that it is surprising that Prantl's attribution of it to Albert of Saxony (who simply copies the Summulae here, almost verbatim) should have found any acceptance. Blundevile and other early writers of logic in English take the word from the Summulae. It was also adopted into English law. The meaning now tends to return to that used by Albertus. Kant (Krit. d. reinen Vernunft, 1st ed., 666) defines a maxim of reason as a subjective principle derived not from the character of the object, but from the interest of reason in such perfection of cognition as may be possible; and in the Critic of the Practical Reason he endeavours to make out something analogous in that sphere. In the Logik by Jäsche (Einleitung III) he defines a maxim as an inward principle of choice between different ends. (C.S.P.)

Maxim (legal): Ger. Rechtsregel, Grundsatz; Fr. maxime de droit; Ital. massima giuridica. The sententious expression of an established rule of law in a short form, which has become authoritative by long use and general approval; a legal axiom. Such a maxim has the force of law, e.g. 'Causa proxima, non remota, spectatur.'

The use of maxims is common to all systems of jurisprudence. The leading collection is the title of the Digest of Justinian, De diversis regulis iuris antiqui, L. 17. See Phillimore's Principles and Maxims of Jurisprudence; Brown's Maxims of English Law; and Bouvier's Law Dict., sub verbo. The latter contains about 1000 maxims, of which, say, 100 are in daily use in English and American courts. (S.E.B.)

Maximum Happiness: see GREATEST HAPPINESS.

Maximum Sensation: see LIMITS OF SENSATION.


Mazdeism [from Ahura Mazda]. Zoroastrianism. See ORIENTAL PHILOSOPHY (Persia).