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Neuralgia [Gr. neuron, nerve, + algoV, pain]: Ger. Neuralgie; Fr. névralgie; Ital. neuralgia. A nervous disorder characterized by paroxysmal pain, which is usually along the distribution of one nerve, and unilateral, and which is not due to changes in the periphery of the nerve or to organic disease, but to nutritive or functional changes in the conditions of the nerves or to NEURITIS (q.v.).

Neuralgia is especially prone to occur in families of neurotic temperament. It is rare in early youth, largely confined to middle life, more frequent in women than in men, and is often induced by cold, exhaustion, overwork, worry, mental shock, lack of rest, and the strains accompanying periodic physical functions. The first attack quite generally comes on when the subject is in a condition of general or special debility. The attacks may appear suddenly and spontaneously, or may be preceded by a brief feeling of numbness or anaesthesia, by twitching, or by an indisposition which ushers in the nerve-pain at first in brief darts of minor intensity and then in more continuous but still periodic spasms of severe burning, boring, or shooting pains, until these in turn become less and less frequent, and leave the sufferer in an exhausted condition. Neuralgias are of an indefinite number of varieties, according to the nerves affected, the distinction between superficial and visceral neuralgias being a prominent one. Painful points which are sensitive to pressure are often present.

Literature: all the treatises on nervous diseases (e.g. GOWERS) contain adequate descriptions of neuralgia. For a special treatise see CHAPMAN Neuralgia (1873); and especially BERNHARDT, in Nothnagel's Spezielle Pathol. u Therapie, xi. Pt. II. 185-440; HALLION, in Traité de Méd. de Charcot, vi. (1895); BOULAY, in Manuel de Méd. de MM. Debove et Achardon; GROCCO, in Trat. ital. di Patol. e Terapia med. (1898). (J.J.)

Neurasthenia [Gr. neuron, nerve, + sqenoV, strength]: Ger. Neurasthenie; Fr. neurasthénie; Ital. neurastenia. In general, nervous debility or weakness (cf. NERVOUSNESS); but usually employed in a more special sense to indicate a pronounced degree and form of such weakness, with typical symptoms of a morbid character.

Historical. While the condition was in a measure known and partially described by older writers (Robert Whyte, 1765, Marshall, Darwin, Villemain, Jaeger, and others), its modern prominence dates from the writings of Bouchut (1860) and Beard (1868). The latter brought the term neurasthenia into general use, although it was employed in 1867 by Van Dusen, and occurs in Dunglison's Medical Dictionary of 1833 (Dercum). Of other names for the malady may be mentioned encephalasthenia (Althaus), the French nervosisme, cachexie, and the more popular terms, nervous prostration, nervous exhaustion, failure of brain power, pathological fatigue, morbid irritability.

Varieties. Neurasthenia is a symptom complex occurring, like hysteria, under the most varying circumstances, but so frequently alone that in a great majority of cases it may be recognized as a true idiopathic condition. In the ordinary typical cases the symptoms partake of a mental as well as a sensori-motor character, and this type has been termed cerebro-spinal. When the mental symptoms are particularly marked and the motor symptoms not prominent, the condition is by some termed cerebral neurasthenia (cerebrasthenia, encephalasthenia); while spinal neurasthenia (myelasthenia) is characterized by motor abnormalities, particularly by difficulty in walking, by a feeling of sinking of the limbs, by abnormal locomotor tendencies, &c. A specific sexual neurasthenia has been described by Beard, Krafft-Ebing, and others; gastric or dyspeptic neurasthenia (nervous dyspepsia) has received special attention (Glatz). Hystero-neurasthenia is an approximation of neurasthenical symptoms to a hysterical type -- a condition emphasized by French writers. Hereditary, traumatic, adolescent, neuralgic, and other forms of neurasthenia are mentioned in literature. In some cases it is difficult to distinguish neurasthenia from a mere pronounced temperamental peculiarity, or from rudimentary paranoia, or the prodromal symptom-complexes of other nervous and mental diseases (dementia praecox, general paralysis, paranoia). It seems best to regard the general difficulty as of one main type, with tendencies for certain groups of symptoms (motor, sensory, hypochondriacal, depressive, fatigue, &c.) to become specially emphasized. Of other maladies associated with neurasthenia, neuralgia and migraine are the most frequent.

Nature and Course. Neurasthenia is a functional disorder of the central nervous system. The nature of the disturbance which conditions the neurasthenic state is not known. Neurasthenia is, with few doubtful exceptions, of a chronic character; its onset is slow; the symptoms ensue in irregular sequence; they appear first in lighter and then in more cumulative form, and the entire attack often covers a period of many years. A marked characteristic is the fluctuation and recurrence of the symptoms both in shorter and longer periods, while moments of intense paroxysmal attacks are not uncommon. As the disease is often of long standing before treatment and recovery begin, so there is also a considerable period of convalescence, during which many of the typical neurasthenic symptoms persist. Not unfrequently some traces, like scars, remain almost indefinitely. The disorder is rarely fatal, nor is it prejudicial to longevity.

Aetiology. It cannot as yet be determined to what extent heredity, early development, and later influences tend to form peculiar 'neurasthenic' constitutions, the aggravation of which is known as constitutional chronic neurasthenia, with its exacerbations and special types; and also to what extent transitory debilitating conditions can produce the chronic exhaustion which is commonly termed nervous prostration or acquired neurasthenia. Speaking in general terms, we may recognize the hereditary predisposition as the most prominent aetiologically. Ziehen finds that a neurotic inheritance is traceable in 74 per cent. of all cases; that men are more liable to the disorder than women; that the years from twenty to thirty yield relatively the largest proportion of cases, and that 70 or 80 per cent. of cases occur between the ages of twenty and fifty years. Race and nationality, social status and mode of life, are of influence, but no exact relation has been determined. The effects of unhygienic conditions of life, of abnormalities of sexual life, of accidents, over-exertion, fright, and of ill health generally, and most frequently the accumulated strain of overwork under conditions of worry and stress, may be traced as causal factors. Professional brain-workers and those engaged in responsible and worrying positions are particularly disposed to the disorder. Neurasthenia has been characterized as the typical malady of modern civilization.

Symptoms. The symptoms of neurasthenia may be considered under the head of (1) mental attitude; (2) the subjective sensory and motor disturbances; (3) the physical condition. The great variability of the symptoms and their tendency to involve more than one of these factors must not be lost sight of. (1) Prominent mental symptoms are the difficulty in holding the attention for a protracted effort, a speedy fatigue, a diminished readiness for acquisition of new impressions, momentary states of confusion and distraction, mental restlessness and unsettlement, the persistence of unbidden thoughts, irregularity of memory, a lack of pleasure in ordinary occupation, irritability, excessive anxiety about small affairs, lack of self-control, an undue occupation with one's own bodily and mental condition, unreasonable fears and aversions, marked idiosyncrasies, and the like. Along with these there are often periods of intense depression (particularly in severe cases or where the disorder reaches its worst stages), occasionally leading to suicide.

This great variety of mental symptoms is more or less easily traced to states of fatigue and the irritability characteristic of certain phases of fatigue. The neurasthenic fears are characteristic, and often constitute the most distressing symptoms. Their unreasonableness is recognized by the patient; conduct is often carried out in opposition to them, but they always occasion anxiety, distress, and a feeling of impending calamity. Almost all the various PHOBIAS (q.v.) -- agoraphobia, claustrophobia, mysophobia, and so on -- have been noted in neurasthenia. Such hesitation in conduct may be properly viewed as a defect of will or irresolution. This is exhibited in the difficulty of maintaining the attention, the restlessness, the slow and weak attempts to throw off invalid habits, the dependence upon others, and the necessity of constant stimulation and encouragement. (2) Of first importance among the sensory symptoms are the paraesthesias, or abnormal sensations, and the characteristic pains. Such paraesthesias are difficult to describe. The patient complains of a feeling of tightness in the head, a feeling of heaviness, a feeling of inward pressure (this symptom, 'Kopfdruck,' Ziehen finds in 85 per cent. of all cases), a sense of confusion in orientation, and various forms of VERTIGO (q.v.). He is subject to various dull, aching pains, or fatigue pains as the result of slight exertions, while specific throbbing or piercing local pains in the head or spine are not uncommon. The tendency of such symptoms to fluctuate and to disappear under proper mental stimulation indicates their quasi-subjective (psychogenic) character. Disturbances of the specific sense-impressions is less common. Blurring of the images, as in protracted reading; difficulty in accommodation; buzzing, pulsating, or beating in the ears; tickling or itching in the skin, and local hyperaesthesias are frequently noted. Of motor disorders may be mentioned a muscular weakness often markedly felt, and which, probably in combination with a vaso-motor disorder, at times gives rise to a feeling of faintness and impending unconsciousness. Tests with the dynamometer indicate an abnormally early appearance of fatigue symptoms. Delicate co-ordinations are often affected; the handwritting loses in definition; slips of the tongue in speaking, twitching of the muscles, tremor, hoarseness, or a hollow sound of the voice, and motor restlessness are also common. Disorders in the reflex are frequently noted. The knee-jerk is apt to be exaggerated, or to present irregularity of action. In spinal neurasthenia motor disorders of locomotion are marked. (3) Bodily symptoms are not uncommon accompaniments of neurasthenic conditions, however insufficient in themselves for a diagnosis of neurasthenia. Anaemia is often present; the heart action may be irregular; digestive disturbances are quite common; the palms of the hand may perspire under unusual conditions; there may be a special sensitiveness to heat and cold and to changes of the weather; the respiration is often accompanied with effort, a sort of neurasthenic asthma; an explosive irritating cough may appear; a peculiar flushing of the skin when touched or stroked may be observed, while irregularities in the urine (oxaluria, phosphaturia, and excess of uric acids and urates) are particularly significant. Sexual  abnormalities, both as symptoms and as aetiological factors, are often present, and when prominent form the sexual type of neurasthenia. Irregularities of sleep, mostly insomnia, are the rule; even where the amount of sleep is sufficient it is apt to be interrupted and unrefreshing in character.

Interpretation. The keynote of neurasthenia is an inability to recuperate, due to a subjective disturbance of balance between efficiency and output of energy; hence the characteristic feeling of exhaustion, with the peculiar sensations of pains and fears, and the cumulative effect of irritability accompanying weakness and fatigue. Physically it becomes manifest, apart from excessive exhaustibility, in the prostration of the nutritional functions, and quite unusually in profound vaso-motor disorders. Neurasthenia thus illustrates the effects of a pathological fatigue, and illustrates as well the varied and widespread manifestations of such a fatigued condition. Neurasthenia further is peculiarly subjective (psychogenic) in many of its symptoms; such symptoms are not without objective basis, nor are they in any true sense feigned or assumed; but they are so markedly aggravated and made chronic by self-consciousness and worry and so generally subject to emotional influences as to suggest a quasi-subjective origin. Neurasthenia further illustrates the importance of the emotional factors in mental processes. It is mental worry rather than overwork that induces the fatigue or neurasthenia; it is the environment, free from anxiety, that is so much more difficult to procure than mere rest from exertion. The emotional factor conditions the fatigue potentiality of overwork; the emotional attitude often makes the distinction between work and recreation, and it is because this emotional attitude is so largely a matter of temperament that neurasthenia exists as a diathesis, even where it does not become developed as a specific disorder. In the disease itself the prominence of the emotions is exhibited most of all in the morbid fears and in the depression and irritability that in some cases constitute the most important symptoms.

The relation of neurasthenia to the conditions of modern existence, particularly in large cities, is doubtless an important one. The disease is not a new one, however, though brought into prominence by recent study. In the overwork of the schoolroom, in the stress and strain of youthful ambition, in the worry and competition of commercial enterprise, and cares of public life, the inconsiderate absorption of the scholar, the excessive demands of society, the hunger for wealth and station, the incessant wear and tear of a modern metropolis, and in other unwholesome influences, certainly lie the influences by which neurasthenia is propagated. The contrast between these conditions and those of a half-century or more ago may well explain the increased frequency of the disorder.

Literature: among earlier contributions: BOUCHUT, Du Nervosisme aigu et chronique (1859, 2nd ed. 1877); BEARD, Nerv. Exhaustion (1880); Amer. Nervousness (1881); and Sexual Neurasth. (1884); CORNING, Brain Exhaustion (1884). More recent: KRAFFT-EBING, Die Nervosität u. d. neurasth. Zustände (1895); F. C. MÜLLER, Handb. d. Neurasth., in Moebius, Neue Beitr., ii. 62-122; LOEWENFELD, Pathol. u. Ther. d. Neurasth. u. Hysterie (1894, with bibliog.); BINSWANGER, Die Pathol. u. Ther. d. Neurasth. (1896); GILLES DE LA TOURETTE, Les états neurasth. (1898); BOUVERET, La Neurasth. (2nd ed., 1891); LEVILLAIN, La Neurasth. (1891); GLATZ, Dyspepsie nerv. et Neurasth. (1898); KRAEPELIN, Psychiatrie (1898), ii. 45-56, 520-62; MOLL, Das nervöse Weib (1898); SCHRENK-NOTZING, Neurasth. (1894); ALTHAUS, Failure of Brain Power (1898); CULLERRE, Nervosisme et Neuroses (1887); BOREL, Nervosisme et Neurasth. (1894); DORNBLÜTH, Nervöse Anlage u. Neurasth. (1896). See also NERVOUSNESS. (J.J.)

Neuraxis [Gr. neuron, nerve, + axwn, axis]: Ger. Centralnervensystem; Fr. névraxe, axe cérébrospinal; Ital. neurasse. The cerebrospinal axis, or central nervous system, including the brain and spinal cord. Other terms used are myelencephalon, neuron, axion. (H.H.)

Neurility [Gr. neuron, nerve]. Sometimes used for nervous conduction. See NERVE STIMULATION AND CONDUCTION.

Neurite [Gr. neurithV]: Ger. Neurit (Rauber), Neuraxon (Kölliker); Fr. cylindre-axe; Ital. cilindrasse. The main or cellifugal process of a nerve-cell. Cf. DENDRITE, and NEUROCYTE.

The neurite, or 'axis-cylinder' process, is commonly more simple than the dendrite, though not devoid of collaterals, and ending sooner or later in free arborizations or an END-ORGAN (q.v.). (H.H.)

Neuritis [Gr. neurithV]: Ger. Nervenentzündung; Fr. névrite; Ital. neurite. An inflammatory condition of a peripheral nerve.

Severe functional disturbance, such as neuralgia, may occur without inflammation, but where acute or purulent neuritis occurs it may advance until DEGENERATION (q.v.) supervenes. The axis cylinder resists the longest, and may be regenerated after extensive destructive processes have taken place. Where the inflammatory changes are slight and chronic, the state is spoken of as chronic degenerative atrophy. Where various parts of the body are simultaneously affected the disease becomes a multiple neuritis. Alcoholic multiple neuritis is a common form of the latter, and this type may include sensory or motor fibres, or both. (H.H.)

Neuroblast [Gr. neupon, nerve, + blastoV, layer]: Ger. Neuroblast; Fr. neuroblaste; Ital. neuroblasto. An embryonic nerve-cell of the central nervous system; an immature NEUROCYTE (q.v.). Cf. NERVOUS SYSTEM (Histology). (H.H.)

Neurocyte [Gr. neuron, nerve, + kutoV, cell]: Ger. Neuron; Fr. neurone; Ital. neurone. The adult nerve-cell of whatever kind within the central system, together with all its appendages. A recent usage, however, applies the term to the cell-body to the exclusion of the appendages. The former is preferred. Cf. NEUROBLAST, and NEURONE.

The appendages are usually of two orders, DENDRITES (q.v.) and the NEURITE (q.v.). The latter may be secondarily provided with sheaths and other accessories. The stimulus normally enters through the dendrites and discharges through the neurite. Both neurite and dendrites break up at their termini into ARBORIZATIONS (q.v.). A variety of terms have been proposed for the unit of nervous structure. 'Ganglion cell' is inapt, for a ganglion, in strictness, is an extra-axial cell cluster. 'Neuron' (Waldeyer) is largely used, but aside from the matter of etymology, it has been used (Wilder) in the sense of the entire axial nervous system, as well as (Schäfer) for the NEURITE (q.v.) and a portion of the spinal cord (Kölliker). 'Neurodendron' has been recently substituted, but its etymology is ambiguous, and moreover not all neurocytes have dendrites. Analogy and recent usage favour the employment of the termination -cyte for mature cells and -blast for embryonic cells. See Fish, 'Terminology of the Nerve-cell,' J. of Compar. Neurol., iv (Sept., 1894). (H.H.)

The term NEURONE (q.v.) is, however, coming into very general use with this meaning, and may be made general without confusion with the shorter form neuron. See Barker, The Nervous System, 39 ff., for discussion and literary references. (J.M.B.)

Neuroglia [Gr. neuron, nerve, + glia, glue]: (same in the other languages). The non-nervous supporting framework of the central nervous system.

Two classes of cellular elements are usually included under the term: (1) true connective tissue, of mesodermal origin, brought into the central nervous system in small amounts chiefly with the blood-vessels, and (2) cells and fibres derived from the original ectodermal cells of the embryonic nerve-tube (see BRAIN, Embryology). The latter, or true neuroglia, is composed partly of these original epithelium cells, greatly modified, and partly of derivatives from them, which wander out into the brain substance and there give rise to fibres, which form a dense meshwork, within which the nervous elements are enclosed. Weigert claims that in the adult human brain the neuroglia fibres are entirely distinct from the neuroglia cells. According to Bevan Lewis the neuroglia cells may function as 'scavenger cells,' assisting in the elimination of effete material. If nerve tissue is destroyed by disease, its place is usually taken by neurologia.

Literature: W. L. ANDRIEZEN, Brit. Med. J. (July 29, 1893); F. W. EURICH, Studies on the Neuroglia, Brain, xx (1897); W. HIS, Arch. f. Anat. u. Physiol., Suppl. -Bd. (1890); A. V. KÖLLIKER, Handb. d. Gewebelehre des Menschen (6th ed.), ii. 136 (Leipzig, 1896); M. v. LENHOSSÉK, Der feinere Bau d. Nervensystems (Berlin, 1895); BEVAN LEWIS, A Textbook of Mental Diseases (2nd ed., Philadelphia, 1900); F. B. MALLORY, Centralbl. f. allg. Pathol. u. pathol. Anat., vi (1895); W. F. ROBERTSON, J. of Ment. Sci., x1iii (1897); RETZIUS, Biol. Untersuch. (1893); J. SCHAFFER, Arch. f. mikr. Anat., x1iv (1894); E. W. TAYLOR, A Contribution to the Study of Human Neuroglia, J. of Exper. Med., ii (1897); VIGNAL, Développement d. Éléments du Syst. nerv. (Paris, 1889); CARL WEIGERT, Abhandl. d. Senckenberg'schen Naturf. -Ges., xix (1895). (H.H.)

Neurology [Gr. neuron, nerve, + logoV, discourse]: Ger. Neurologie, Nervenlehre; Fr. neurologie; Ital. neurologia. The science of nervous structures and functions. The scope of neurology is limited by its subject-matter rather than its method, and may be correlated with the departments of myology and osteology, deriving its chief claim to recognition as an independent science from its direct bearing upon psychology and phylogeny.

Comparative Neurology is not merely that department of neurology which includes the system of the nervous system of inferior animals; the term especially designates that method of approaching the problems of nervous function which employs the combined biological procedures, such as embryology, histology, pathology, physiology, and life history, and applies the results from the lower groups in the interpretation of human neuroses. It is in this sense that the term is employed, e.g. in the Journal of Comparative Neurology. See further C. L. Herrick, 'The Problems of Comparative Neurology,' and 'Neurology and Psychology,' J. of Compar. Neurol., i (1891), and Morselli, Semej. malat. ment., ii (1895).

The Technology of Neurology is essentially that of modern biology at large. Nearly all the marvellous progress of the last decades can be traced directly to the effect of improved histological and experimental technique. The processes which are most essential are such as permit (1) the fixation, hardening, and preservation of tissues; (2) the sectioning, teasing, or isolation of the substance; (3) the staining, impregnation, and differentiation of the several elements. In the hardening processes (including fixation, &c.) the reagents most useful are chiefly such as contain, or are composed of, alcohol, chromic salts, corrosive sublimate, acetic acid, osmic acid, platinic chloride, formalin, &c. For purposes of sectioning, simple freezing or impregnation with a coagulable or solidifying mixture, such as paraffin, celloidin, gum, soap, &c., precedes the actual slicing with the microtome, after which the adhesive substance is dissolved and the section is prepared for preservation. Staining is sometimes accomplished prior to sectioning, but is often only possible after the delicate section has been glued by means of albumen, collodion, or the like to the glass slip to which it is permanently attached.

The staining reagents are innumerable, but among the most important are compounds of haematoxylin, and various aniline dyes which have selective affinities for various cells or parts of cells, and which react in a way determined by the relation between their own chemical condition and that of these organs. Staining intra vitam by means of methylene blue has become a technique by itself, and has yielded marvellously intricate and delicate pictures of the finest ramifications of nervous fibrils. This method has been especially fruitful in the study of the ultimate termini of the peripheral nerves.

Nissl has introduced a method of applying methylene blue to the cells of the central nervous system, which has been productive of great advancement of our knowledge of the alterations in internal structure which these cells undergo in different functional and pathological states.

The methods of Golgi, and other applications of the idea of precipitating silver or mercury salts within the cellular elements, have effected a revolution in our knowledge of the relations of cell with cell, and demonstrate the unsuspected extent of interrelation and association between centres.

Golgi's method was first published by its inventor as early as 1873, but was not brought into prominence until a decade later, when Golgi's great monograph on the finer anatomy of the nervous system appeared. And indeed this splendid work was ignored by the majority of European anatomists until Forel. His and others worked over the ground and correlated it with the current data of embryology and experimental neurology. Then the import of Golgi's discoveries was first made manifest, and all neurologists eagerly took up the method. Never before had it been possible to see a complete nerve-cell, for none of the older methods bring out the ultimate ramifications of the nervous processes. It now became possible to demonstrate that the nervous system is composed of cells, comparable in embryonic origin and adult structure to those of the other tissues of the body, and the implications of this discovery in physiology and pathology have been very far-reaching. >From it has grown the doctrine of the neurone as the structural and functional unit of the nervous system. The validity of the neurone theory and its enormous importance as a tool of research are in no wise dependent (as some seem to suppose) on the idea of the strict anatomical independence of the neurones in the adult body. That they are independent in embryonic origin is well established, but secondary fusions of various kinds may occur during development.

The haematoxylin-copper processes of Wiegert and Pal are still indispensable to a study of fibre-tracts. These methods rest upon the principle that the myelinic sheaths of the medullated nerves, after mordanting in a solution of chrome or copper and staining with haematoxylin, resist the action of a decolorizer longer than do the other tissues. All medullated fibres appear brilliant blue on a clear ground.

Also of great importance are the experimental degeneration methods. The first of these is Marchi's method. If the continuity of a tract is interrupted during life, either by disease or experimentally, degeneration of its fibres ensues (see DEGENERATION). Now, if the specimen is treated first with a solution of chromic salts and then with osmic acid, the degenerated fibres only are blackened by the osmium, and thus the injured tract can be differentiated and clearly followed. Marchi's method bring out the degenerated fibres only. If, now, the centres to which the injured nerve is related are examined by Nissl's method, the cells from which the degenerate fibres spring will show a characteristic 'Nissil degeneration' of their protoplasmic contents, and can thus readily be distinguished from other cells among which they may be mingled.

This principle is employed in the study of the degenerations produced by von Gudden's method, a method of determining the structure and functions of the brain by the removal of parts of the nervous system or sensory organs from a newborn animal, and the investigation of the consequent atrophic changes or secondary degenerations in later life. Upon this method, more than any other, we are dependent for exact knowledge of the ultimate courses of individual tracts in the intricate mazes of the higher centres.

Antiseptic methods permit an amount of operative interference impossible a few years since, and the progress of electrical mensuration is utilized in a study of conductivity and resistance. A statistical method applied to pathology and controlled by necropsy returns, and histological analysis, is daily contributing to our knowledge. The study of the results of FATIGUE in lower animals interprets the conditions encountered in diseased states of man.

Literature: for the detailed application of these methods, consult the technological manuals, especially LEE, The Microtomist's Vade-Mecum (4th ed., Philadelphia, 1896), and the works there referred to; also BEVAN LEWIS, The Human Brain, Histological and Coarse Methods of Research (1882); POLLOCK, Die Färbetechnik des Nervensystems (1897), also Eng. trans.; VAN GEHUCHTEN, Anat. du Syst. nerveux de l'Homme (3rd ed., 1901); DEJERINE, Anat. du Syst. nerveux. i (1896), ii (1901).

On the methylene blue method, see especially P. EHRLICH, Ueber die Methylenblaureaction der lebenden Nervensubstanz, Deutsche med. Wochensch., xii (1886); H. RIESE gives a general review of the method to date in the Centralbl. f. allg. Pathol. u. pathol. Anat., ii (1891); A. BETHE, Studien über das Centralnervensystem, Arch. f. mikr. Anat., x1iv (1895). For the list of the contributions to the cytology of the nerve-cell by F. NISSL and others who have used his method, see chap. x of BARKER'S The Nerv. Syst. and its Constituent Neurones (New York, 1899); also the extensive bibliography by SMITH ELY JELLIFFE in the Arch. of Neurol. and Psychopathol., i (1898). On the Golgi method consult GOLGI, collected works, translated into German as Untersuchungen über den feineren Bau des centralen u. peripherischen Nervensystems (Jena, 1894); an English translation of a part of this work is given by STRONG, under the title Review of the Golgi Method, in the J. of Compar. Neurol., vi (1896); A. HILL, The Chrome-silver Method, Brain, xix (1896); C. WEIGERT has given a comprehensive review in Merkel u. Bonnet's Ergebnisse d. Anat. u. Entwicklungsgeschichte, v (1896).

Neuronymy: the nomenclature of the nervous system. It is in a transition state, and the various methodical attempts to secure a uniformity and consistency of usage are, as yet, serving chiefly to call attention to the confusion still existing.

The ambiguity and confusion incident to independent naming of organs, and the use of discordant directional terms, has long been recognized, and individual attempts to remove the inconsistencies have been numerous. Owen, Henle, Parker, Schultze, and Wilder have contributed notably towards a systematic reform, though the immediate result of agitation in each case is to add to the existing confusion.

Most harmful is the ambiguity growing out of uncertainty as to the standard of reference in terms of direction and position, especially when the same relative positions are referred to both lower animals and man. Through the combined influence of F. E. Schultze and B. G. Wilder, we are now rapidly approaching substantial uniformity on the part of careful writers. Thus 'dorsal' and 'ventral' have very generally superseded 'anterior' and 'posterior,' and instead of 'in an anterior direction' or 'towards the front,' the majority of English writers employ the directive adverb 'ventrad,' though the too frequent use of the suffix '-ad' is offensive to many. 'Forward' or 'upward' as applied to a direction towards the cephalic extremity is replaced by 'cephalad,' 'frontal,' rostral,' 'capital,' 'acrad,' cranial,' and others, while nearly all writers employ 'caudal' or 'caudad' for the opposite direction. The terms 'proximal' and 'distal,' 'ental' and 'ectal,' 'peripheral' and 'central,' and their adverbs in '-ad,' are very generally used. 'Mesal' and 'lateral' seem to have been less generally acceptable. In Germany the mesal plane is termed sagittal.

In 1895 the results of the deliberations of the German Nomenclature Commission were published by William His. A commission of English anatomists failed to report in time to be incorporated, while the recommendations of the American committees were for the most part ignored. All these recent undertakings have in common a desire to restrict a single name to a single organ, and to employ directive and descriptive terms consistently for all subjects. The preference of the American committees for single-word terms (mononyms) where practicable, although recognized by a majority as desirable, has not thus far been widely adopted because of prejudice against barbaric combinations and in favour of adhering to historical priority. It is impossible in this place to go into details, and the reader is referred to the works cited below. The article by Wilder is the fullest recent discussion, accompanied by extensive comparative tables and a bibliography.

The immediate result of the discussion now in progress may be to prevent much laxity of usage due to carelessness, but unanimity may be long delayed.

Literature: P. A. FISH, The Terminology of the Nerve Cell, J. of Compar. Neurol., iv (1894); W. HIS, Vorschläge zur Eintheilung des Gehirns, Arch. f. Anat. u. Physiol., Anat. Abth. (1893); Die anatomische Nomenclatur, Nomina anatomica: Verzeichniss der von der Anatomischen Gesellschaft auf ihrer ix. Versammlung in Basel angenommen Namen. Eingeleitet und im Einverständniss mit dem Redactionsausschuss erläutert; ibid., Suppl.- Bd. (1895); W. KRAUSE, On Anatomical Nomenclature, Brit. Assoc. Rep. (1891); also Int. Monatssch. f. Anat. u. Physiol., ix (1892); T. JEFFREY PARKER, On the Nomenclature of the Brain and its Cavities, Nature, xxxv (1886); P. H. PYE-SMITH, Suggestions on some Points of Anatomical Nomenclature, J. of Anat. and Physiol., xii (1877); B. G. WILDER, neural Terms, International and National, J. of Compar. Neurol., vi. (Dec., 1896) 216-352; Proc. Assoc. of Amer. Anatomists, Tenth Session (1897), 27-60; C. L. and C. JUDSON HERRICK, Inquiries regarding Current Tendencies in Neurological Nomenclature, J. of Compar. Neurol., vii (March, 1898), embodying the results of an attempt to secure a consensus of views by means of a circular sent to neurologists in the interests of this work. (H.H.)

Neuromeres [Gr. neuron, nerve, + meroV, part]: Ger. Nervensegmenten; Fr. renflements métamériques de la moelle; Ital. neuromeri, neurotomi. Node-like and transitory dilatations of the medullary tube resembling the primitive segmentation (metameric) of the embryonic body.

Widely divergent views are held as to the significance of these structures, which can no longer be held to be artifacts. Recent observations tend to render doubtful the theories that this segmentation is wholly due to mesodermic influence or entirely a result of the proliferations at the root of the nerves. They have a constancy, moreover, indicating that they can hardly be accidents of growth.

Literature: B. H. WATERS, Primitive Segmentation of the Brain, Quart. J. Microsc. Sci., N. S., xxxiii (1892); W. A. LOCY, Contribution to the Structure and Development of the Vertebrate Head, J. of Morphol., xi (1895); NEAL, The Segmentation of the Nervous System in Squalus acanthias, Bull. Mus. Compar. Zool., xxxi. 7 (1898). The two last contain full bibliographies, in which consult especially the works of HOFFMANN, KUPFFER, BÉRANECK, VAN WIJHE, and FRORIEP. (H.H.)

Neuron [Gr. neuron, a nerve]: Ger. Neuron; Fr. and Ital. neurone. Originally employed in English for the central nervous system, or NEURAXIS (q.v.), but has of late come into general use as a name for the nerve unit (after Waldeyer). See NEURONE, and NEUROCYTE. (H.H.)

Neurone: for foreign equivalents see NEURON. The unit of nervous structure, NEUROCYTE (q.v.), or nerve-cell, a term free from the ambiguity attending the German form Neuron, and hence preferred by many of the most recent writers, especially in America. See L. F. Barker, The Nervous System (1899), chap. v. (H.H.)

Neuronymy: see NEUROLOGY.

Neuropathy [Gr. neuron, nerve, + paqeia, suffering]: Ger. Nervenleiden, Neuropathie; Fr. névropathie, affection (or maladie) nerveuse; Ital. neuropatia. An abnormal or diseased condition of the nervous system or some part of it. See NEUROSIS. (H.H.)

Neuropilem [Gr. neuron, nerve, + piloV, hair]: Ger. Neuropilem, Nervenfilz; Fr. (not in use -- Y.D.); Ital. neuropilema. A meshwork of nervous arborizations forming a system of intercommunication between various neurocytes; contrasted with neuroreticulum or histological plexus.

Modern research has made it increasingly evident that actual anatomical continuity between the terminal arborizations of centrifugal and centripetal systems is not necessary to nervous interchange. The methylene-blue method of Dogiel has, however, demonstrated association by continuity in the retina and skin, and it probably exists to a greater or less extent in the central system. (Cf. NERVOUS SYSTEM (Histology). (H.H.)

Neuroplexus: for foreign equivalents for PLEXUS, see that term. An interlacing meshwork of peripheral nerve-fibres (to be distinguished from a vascular plexus, or meshwork of capillaries). Cf. PLEXUS, and GANGLIOPLEXUS. (H.H.)

Neuropore [Lat. neuroporus]: Ger. Neuroporus; Fr. névropore; Ital. neuropore. The opening by which the cavity of the medullary tube communicates with the surface at its cephalic extremity; the morphological front of the brain (Kupffer).

The opening has been observed in several groups of fishes, and some indications of it are reported in certain higher animals, but they are transitory. The location of the neuropore is apparently midway of the lamina terminalis.

Literature: C. v. KUPFFER, Stud. z. vergleichenden Entwickelungsgesch. des Kopfes d. Kranioten, i (1893). Compare also the account of A. WILLEY, in Amphioxus and the Ancestry of the Vertebrates (1894). (H.H.)

Neurosis [Gr. neuron, nerve]: Ger. Neurose, Nervenbeschwerde; Fr. névrose; Ital. neurosi. (1) Any activity of a nervous structure as such.

It is, no doubt, true that nerve-cells participate in the vital processes common to all living structures, and there is undoubtedly a close connection between the nervous and non-nervous processes (cf. TROPHISM, and LIVING MATTER) which makes it difficult to separate the two classes. It might be well to limit 'neurosis' to the nervous processes which have an expression in consciousness, or, in other words, a corresponding 'psychosis.'

(2) A morbid or diseased condition of the nervous system. Functional neurosis is a morbid affection of the nervous system known only by its symptoms and without ascertained anatomical basis. It is doubtless true that an anatomical lesion of some kind does in each case exist, and the classification of diseases as organic and functional is but a concession to our ignorance. Cf. NEUROPATHY. (H.H.)

Neutrality (in law) [Lat. neutralis, through Fr.]: Ger. Neutralität; Fr. neutralité; Ital. neutralità. The relation to a belligerent power of another power which is at peace with each of the belligerents, and not an ally of either.

The neutral power is bound, by international law, to render no aid to either belligerent in its prosecution of the war. Its duties are not measured by its own municipal law. As to how far it should prevent its own subjects from giving such aid, the principles of international law are not settled. The United States and England incline to interfere less with the liberty of the citizen, in this respect, than the continental powers of Europe (see Davis, Int. Law, chap. xi). Neutrality Laws: the statutes of any particular state upon that subject. Armed neutrality: in which the neutral power arms to defend its neutral position against violence apprehended from, or offered by, a belligerent; in practice it is almost invariably the result of concerted action or alliances between several neutral powers (Woolsey's Int. Law, § 155). Permanent neutrality: the position of a state, like Switzerland, which by treaty with neighbouring powers stipulates never to declare war against them, except for a violation of her neutrality; they making corresponding promises. The United States have generally pursued a policy favourable to restricting within narrow limits the duties of neutrals (see Wharton's Int. Law Dig., chap. xxi).

The doctrine of neutrality is a modern one, and originated with the trading cities of the middle ages. Its outlines are sketched, though lightly, by Grotius, the neutral being described as medius (De Iure Belli et Pacis, III. i. 5, xvii. 3; cf. Vattel's Droit des Gens, Lib. III. chap. vii; Cobbett, Leading Cases in Int. Law, Pt. III). (S.E.B.)

New Academy: see PLATONISM, and SCHOOLS OF GREECE.

Newman, John Henry. (1801-90.) Educated at Ealing and at Trinity College, Oxford. Fellow of Oriel, 1823; took orders in the Anglican Church, 1824; vice-president of St. Alban's Hall, 1825-6; tutor of Oriel, 1826-32; a university preacher at Oxford, 1830; travelled in Italy and Sicily, 1832-3; Vicar of St. Mary's, Oxford, 1828-43; joined the Roman Catholic priesthood, 1845; established at Edgbaston a branch of the brotherhood of St. Philip Neri; lectured in 1850-1; was tried for libel and found guilty; was made Cardinal, 1879.

Newton, Sir Isaac. (1642-1727.) Attended school at Woolsthorpe, Lincolnshire, and at Grantham. Entered Trinity College, Cambridge, 1660, where the philosophy of Descartes was prominent. He became subsizar, 1661; scholar, 1664; B. A., 1665; junior fellow and M.A., 1667; senior fellow, 1668; Dr. Barrow's successor as Lucasian professor of mathematics, 1669. On account of the plague (1665), he moved to his country home at Woolsthorpe, where he studied gravity. Member of the Royal Society of London, 1672. Discovered the law of universal gravitation, 1682. Became M.P. for Cambridge, 1689. On account of impaired health, went to Kensington to live, 1725, and died there. He was buried in Westminster Abbey.

Newton's Law (of colour mixture): see VISION, X.

Nexus [Lat. nexus, a bond, from nectere, to bind, tie]: Ger. Nexus; Fr. nexus, lien: Ital. nesso. The mutual dependence of different elements of an ordered series upon one another; same as connection or relation, but containing in addition a suggestion of union into an ordered whole; most frequently used in the phrase 'Causal Nexus.' (J.D.)

Nicolai, Friedrich. (1733-1811.) A self-taught philosophical critic. Attended the orphanage at Halle and the Real-Schule at Berlin. Apprenticed to a bookseller at Frankfort-on-the-Odor, he learned English and Greek in leisure hours, and read notes on lectures by Baumgarten. In Berlin he studied Wolff. He was for twenty-three years an editor, first of the Library of Fine Arts (1757-9), and later of the Universal German Library.

Nicolas of Cusa (or Nicolaus Cusanus), Nicolaus Chrypffs (i.e., Krebs). (1401-64.) Received his first training at Deventer in the Society of the Brethren of the Common Life, founded by Geert de Groot. Studied law at Padua. Practised at Mainz (Mayence) until 1428, when he adopted the clerical profession. Deacon in Coblenz, 1431; member of the council of Basel, 1433; entrusted by Pope Eugenius IV with important commissions in France, in Constantinople, and at the Reichstag of Frankfort; appointed cardinal by Pope Nicholas V, 1448; bishop of Brixen, 1450. He made extended missionary journeys in Germany and the Netherlands, quarreled with Archduke Sigismund of Austria, and was thrown into prison. Many of his writings are still unprinted.

Nidus [Lat.]: same in the other languages. (1) A cluster of nerve-cells within the central nervous system. Sometimes used in place of the more common term NUCLEUS (q.v.), on account of the ambiguity of the latter.

(2) A point of infection or centre of origin for a pathological process.

Nidus avis: a depression in the side of the vermis on the ventral aspect of the cerebellum, in which one lobe of the cerebellar hemisphere (the amygdala) is lodged. (H.H.)

Nietzsche, Friedrich Wilhelm. (1844-1900.) Born in Saxony and educated for the ministry at Bonn and Leipzig. Abandoning the clerical profession, he accepted (1870) a professorship in philology at Basle. While at Basle he became the friend of Wagner, whose musical dramas has fascinated him from childhood. In 1876, however, his taste for Wagnerian opera changed to disgust and hatred. About this time also began the first stages of a mental malady which wrecked the later years of his life. In 1880 he resigned his professorship and lived in health resorts. His literary activity was incessant, but in 1889 he became hopelessly insane.

Night-blindness: Ger. Nachtblindheit; Fr. héméralopie; Ital. nittalopia. Unduly reduced vision in dim light or at night; it may vary in degree from slight discomfort to practical blindness.

The vision in daylight or strong light may remain nearly or quite normal. As a symptom it seems most usually associated with a form of intraocular disturbance (retinitis pigmentosa), while it occurs also as a specific disorder in cases of general malnutrition (anaemia, scurvy, fasting, &c.), and may then be regarded as a pathological exaggeration of the normal difficulty in vision in passing from a brightly illuminated to a dimly lit space. The opposite defect is termed day-blindness. Cf. HEMERALOPIA. (J.J.)

Nightmare [ME. nightemare]: Ger. Alpdrücken; Fr. cauchemar; Ital. incubo. A troubled dream, with a sense of oppression, fear, or terror.

The terror is often realized as the flight from a monster, the danger of an impending fall, the oppression of an horrible weight and the like. A sharp outcry or confused cry of alarm accompanies the nightmare. See DREAM. (J.J.)

Night-walker: Ger. Nachtwandler, Schlafwandler; Fr. somnambule; Ital. nottambulo. Literally one who walks at night; but equivalent to sleep-walker. See SOMNAMBULISM. (J.J.)

Nihil est in intellectuquod non prius fuerit in sensu [Lat.]. The motto of SENSATIONALISM (q.v.).

Nihil ex nihilo [Lat.]. Nothing comes from nothing. Scholastic negative statement of the law of causal dependence. See CAUSE. (J.M.B.)

Nihilism [Lat. nihil, nothing]: Ger. Nihilismus; Fr. nihilisme; Ital. nichilismo. A term somewhat loosely used, generally by the opponents of a system, to designate its supposed tendencies; namely, to destroy existence, truth, or knowledge. In its strictest sense it means the belief that nothing is, and hence no knowledge is, possible; or that truth in knowledge and obligation in morality have no objective reality. In its contemporaneous use it generally denotes a political or social doctrine rather than a strictly philosophic one; the idea that social progress is to be looked for only in the abolition of all existing social institutions and a return to political void (e.g. Spencer's 'Administrative Nihilism' -- Huxley); the extreme being ANARCHISM (q.v.).

This doctrine, however, is said to be derived from the emphasis laid on the negative in Hegel's dialectic, especially from the first categories of his Logic, in which the dialectical identity of being and non-being is asserted.

The first pure nihilist in philosophic theory was also the last, viz. the Sophist Gorgias of Leontium, who is reported to have taught: (1) that nothing exists; (2) that if anything did exist it would be unknowable; (3) if it existed and were knowable it could not be communicated. The doctrine thus stated has no modern supporters, but certain phases of the Buddhistic doctrine of NIRVANA (q.v.) and of Schopenhauer's doctrine of the annihilation of will might be termed nihilistic. It is generally used nowadays by realists to mark their opinion of the idealistic doctrine of the external world, or, in a similar controversial way, to denote the tendency of doctrines of philosophical scepticism, such as Hume's. Fichte's words, as quoted by Sir W. Hamilton (edition of Reid's Works, 129, note), are often used as a proof of the nihilistic character of idealism, but in fact are employed by Fichte to express simply the logical outcome of a partial stage of development, not as a statement of his whole system.

Literature: UEBERWEG, Hist. of Philos., i. 76-8; REID'S Works, 478; FICHTE, Sittenlehre, Werke, iv. 151. The dependence of Russian nihilism upon a development of Hegel's philosophy is asserted by KAUFMANN, Contemp. Rev., xxxviii. 913. (J.D.)

Nirvana [Sansk. nis, out, + vana, blowing]: Ger. Nirvâna; Fr. nirvana; Ital. nirvana. That state of blissful repose which the Hindu devotee realizes when, through the prescribed discipline of his religion, he has extinguished Karma or the principle of individual existence within him, and has thereby obtained deliverance from the doom of the Samsâra, or unending temporal cycle of deaths and reincarnations. See ORIENTAL PHILOSOPHY (India).

Nirvana in its primary meaning has no temporal reference, and hence is not a state to be attained only after death. Death belongs to the Samsâra and is bound up with Karma. Nirvana is the condition reached by the soul that has crucified Karma by renouncing the desire for individual existence. The whole world of individuality, including death, is a sphere of Maia or illusion. Nirvana is freedom from illusion, and on its positive side absorption into, identification with, the blessed life of Brahm the absolute. Negatively, Nirvana may be characterized as the cessation of the striving for individual existence. As to its positive significance, Brahmistic and Buddhistic thought seem to differ; the latter, emphasizing the deliverance which is effected in Nirvana, tends to regard it as little more than the negation of existence, while to the former it is the realization of a man's Atman, his true and infinite self. Rhys Davids, following the Buddhistic interpretation, represents the Nirvana of Buddhism as simply extinction, while Deussen, speaking from the point of view of earlier Brahmistic conceptions, represents it as the realization on the part of the infinite of 'its own all-pervading, eternal, almighty nature.'

Literature: DEUSSEN, Philos. of the Vedânta; MAX MÜLLER, Buddhist Nihilism, and art. on Buddhism in Encyc. Brit.; Concise Dict. of Religious Knowledge, art. 'India.' See the literature given under ORIENTAL PHILOSOPHY (India). (A.T.O.)

Nisus [Lat. nitor, to struggle, to strive]: same in the other languages. The inherent tendency in any process of change to strive against obstacles towards its appropriate end. Leibnitz uses it as a quasi-technical term. He denies the existence of mere capacity or potency, holding that reality always issues in act. This remains as nisus or active tendency when hindered from expressing itself. In modern physical terms, it is practically the equivalent of energy of position, ready to translate itself into kinetic energy (Leibnitz, New Essays, ii. chap. xxi. § 2, and On the Reform of Metaphysics).

Nisus formativus is the supposed tendency inherent in every embryonic organism to reproduce the form of its species -- a term of speculative biology. (J.D.)

Noctambulism [Lat. nox, night, + ambulatio, a walking about]: Ger. Nachtwandeln; Fr. noctambulisme; Ital. nottambulismo. Synonym of SOMNAMBULISM (q.v.).

Noetic [Gr. nohtikoV, from nohta, ideas which can be thought, not imaged, from nouV, reason]: Ger. noëtisch; Fr. intelligible; Ital. noetico. (1) Referring to concepts which originate in pure, that is, non-sensuous thought. In its more technical use, it excludes ideas arrived at from logical analysis of any sense material, or material imaginatively presented, and is confined to ideas supposed to be self-generated by reason. In a looser use, it denotes ideas freed from sensuous reference, independent of question as to mode of origin.

(2) Involving more or less cognitive process, as in the phrases 'noetic consciousness,' 'noetic SYNTHESIS' (q.v.). See also COGNITION.

The term anoetic is applied to consciousness, mental states, &c., which do not involve cognition, as, for example, hypothetical pure affection or conation. Cf. Stout, Analytic Psychol. (J.M.B.)

In accordance with their general philosophical presuppositions, the early Greek writers assumed that all distinctions in existence were the counterparts of distinctions in modes of knowing and vice versa. When it was seen that certain experiences appeared to have permanent and general validity, while others had to do with the particular and changing, the tendency was to assume a superior form of knowing -- reason -- and an inferior -- sense -- and to divide the objective spheres accordingly. Heraclitus and Parmenides contributed to the distinction, but we owe its sharp formulation to Plato. With reference to his theory of ideas, he marks off sharply the incorporeal world, topoV nohtoV, the world of conceptions, from the world which is seen, topoV aisqhtikoV, the world of perceptions. The first is the ultimate reality of which the second is but an image.

Aristotle, following Plato, uses the noun nohta to express the essence of real beings taken in their intelligible aspect, their capacity of being rationally apprehended. As the Neo-Platonists made much of the doctrine of NOUS (q.v.), so the adjective noetic played a large part in their system. The noetic cosmos (kosmoV nohtoV) expressed the fact that the nous includes within itself a complete system of forms and forces as its own distinctions. Cudworth revived the term with practically the Aristotelian meaning. Sir William Hamilton used it to designate knowledge originated within the mind.

Literature: PLATO, Rep., vi. 507 ff.; Phaedrus, 246 ff.; Phaedo, 100 D; Theaetetus, Symposium; ARISTOTLE, De Anima, III. iv. 12; PLOTNIUS, Enn., vi. 22; CUDWORTH, Eternal and Immutable Morality, Bk. II. i. 4, v. 2; HAMILTON, Lects. on Met., xxxviii. See also MARTINEAU, Types of Ethical Theory, 443-5. (J.D.)

Noise [OF. and ME. noyse and noise]: Ger. Geräusch; Fr. bruit; Ital. rumore. A sensation of hearing distinct from the sensation of tone; usually given as mixed noise and tone; characterized by intensity, duration, and pitch.

It is stimulated by air-vibrations of mixed or rapidly changing rates. It was formerly referred to the vestibule, but is now generally held to have its seat in the cochlea of the ear. Cf. Auditory Sensation under HEARING.

Literature: HELMHOLTZ, Sensations of Tone, 7, 8; EBBINGHAUS, Psychol., 283, 284. (E.B.T.- J.M.B.)

Nolition [Lat. nolle, to be unwilling]: Ger. Wider-Willkürhandlung (see below); Fr. nolition; Ital. nolizione (not in use -- E.M.) Negative VOLITION (q.v.) or the will not to do.

A term not in general use, but convenient. An act of nolition is CONTRA-VOLITIONAL (q.v.), and a decision of nolition is a Veto (see FIAT). 'Nolitio et aversio sensitiva non sunt actiones privitivae [unvolitional] sed positivae [contra-volitional]' (Ch. Wolff, Phil Pract., i. § 38, quoted by Eisler).

The German equivalent is suggested. Nolition is a form of Streben (conation) and also of Widerstreben (negative conation); but is confined to Willkürhandlung (volitional action) as narrower than Willenshandlung (voluntary action). (J.M.B., G.F.S.)

Nominal [Lat. nominalis, pertaining to a name]: Ger. nominal; Fr. nominal; Ital. nominale. Relating to a logical term, whether expressed in language or merely a concept of the mind, and not to anything real. Cf. NOMINALISM, and REALISM.

Nominal definition (definitio nominis): the declaration of the essence of a word or expression, that is, the necessary and sufficient conditions of its applicability, or the enumeration of marks which suffice, but do not more than suffice, to give the meaning of the term, understanding by the 'meaning,' not the whole idea it may convey, but so much as it would require to be intended to convey in order to be a suitable word. Leibnitz says, 'Habemus quoque discrimen inter definitiones nominales, quae notas tantum rei ab aliis discernendae continent, et reales, ex quibus constat rem esse possibilem, et hac ratione satisfit Hobbio, qui veritates volebat esse arbitrarias, quia ex definitionibus nominalibus penderent, non considerans realitatem definitionis in arbitrio non esse, nec quaslibet notiones inter se posse coninungi. Nec definitiones nominales sufficiunt ad perfectam scientiam, nisi quando aliunde constat rem definitam esse possibilem.' This mode of making the distinction has been approved by many nominalists, as J. S. Mill. It cannot satisfy the realists, who demand of the real definition that it should express the real generating nature of the real species which it defines. As for the possibility of the thing, if by that is meant logical possibility, the nominal definition suffices. If more than that is meant, it is out of the province of definition to prove or declare a thing to be possible; a 'problem' proves such possibility.

Nominal mode, in the doctrine of modals: a mode of a proposition expressed by an adjective, as 'Sortem currere est contingens.' (C.S.P.)

Nominalism [Lat. nominalis, from nomen, a name]: Ger. Nominalismus; Fr. nominalisme; Ital. nominalismo. The doctrine that universals have no objective existence or validity; in its extreme form, that they are only names (nomina, flatus vocis), that is, creations of language for purposes of convenient communication. See REALISM (1) for full account and history. (J.D.)

Nomology [Gr. nomoV, law, + logoV, doctrine]: for equivalents see the next topic. The science which investigates laws, as general psychology and general physics; contradistinguished from classificatory and explanatory science. Hamilton says, 'We have a science which we may call the nomology of mind -- nomological psychology' (Lects. on Met., vii). (C.S.P.)

Nomology (in law): Ger. Nomologie, Gesetzeslehre; Fr. nomologie; Ital. nomologia. Jural science; the science of the conformity of human actions to rules of conduct prescribed by law. 'Ethic is the science mainly of duties, while nomology looks rather to the definition and preservation of rights' (Holland, Jurisprudence, chap. iii. 25). The rules of conduct, with which it is conversant, are both those prescribed by the current standard of morality, and those of legislation (ibid. 26; Smith's Right and Law, § 51). (S.E.B.)

Non-A (in logic): same in the other languages. An expression occurring in the usual forms of statement of the principles of contradiction and excluded middle. It is a term which denotes whatever is supposed not to be denoted by A, and denotes nothing more. (C.S.P.)

Non-being: Ger. Nichtsciendes, Nichts (Nicht-sein); Fr. non-être (néant); Ital. non-essere. Literally, just the absence or negation of being; but in accordance with the Greek tendency to give (unconsciously) an objective meaning to all categories of thought, non-being (mh on, uh einai) was assumed as existent, until it became an object of dispute among philosophic schools as to whether non-being is or is not.

The Eleatics (Parmenides, 470 B.C.) who identified it with empty space, holding that everything must be full (or that all that is, is), denied its existence. The Atomists, however (Leucippus), needing a space for their discrete particles to move in, asserted that non-being (the VOID, q.v.) was as real as being (the atoms). Plato (denying empty space as a fact) assumed a relative world of non-being (the counterpart of ignorance) as the opposite of his ideas, and, interpreting it also as space, regarded it as the matrix out of which the world was created. In not dissimilar fashion the theological doctrine of the creation of the world 'out of nothing' tended to give non-being a quasi-existence, as at least the background of the divine operation. Aristotle attempted to give the term a dynamic interpretation. As all nature moves between the potential and the completed, the potential at once is and is-not. On one side, it is the medium, the matter, through which the form realizes itself; and it is also the restraint which prevents the full exhibition of form, and which is responsible for failures and deviations from the main line of development. In the Neo-Platonists, non-being becomes a highly important category. As empty space and as privation it was the responsible factor in the development of the purely physical world and also the cause of evil. It is the absolute opposite of pure being, which yet, just because it is non-being, reduces the manifestations of being to lower levels. However naïve the Greek formulation, it is obvious that through the use of this term there were gradually developed two of the most serious problems of philosophy: one on the side of cosmology, as to the existence of a vacuum; the other the metaphysical and ethical problem of the significance of the negative factor in the universe, of hindrance and imperfection. It is a metaphysical problem, as well as an ethical one, because the value of the concept of growth and development (of change which is qualitative) seems to imply a passage from the potential to the actual, or from (relative) non-being to being. The problem in the former sense was revived by Descartes and in the latter by Hegel. With Hegel, becoming (Werden), process, activity are the ultimate and absolute, and thus a negative factor is as necessary as is a positive. In the famous doctrine of the identity of being and non-being is contained the assertion that the immediate or 'first' being of anything negates itself, and thus passes away, and that this passing away turns out to be not complete disappearance, but a development of itself, and so a reconstitution of being upon a higher, more mediate (or significant) plane (cf. the recent development of the doctrine by Ormond, as cited below). Scotus and other mediaeval philosophers had already taught that since God creates the world out of nothing, nothing belongs to the essence of God.

Literature: PARMENIDES, v. 33, 35; ARISTOTLE, De Gen. et Corr., i. 8 (for Leucippus's doctrine), and also PLUTARCH, Adv. Coel., 4. 2; PLATO, Rep., v. 476-9, vi. 511; Timaeus; ARISTOTLE, Physics, iv. 2 (cf. ZELLER, Philos. d. Griechen, iii. 603-23); Met., Bk. XII; PLOTINUS, Enneads, iii. 6, 18; ST. AUGUSTINE, De Civ. Dei, xii. 2; SCOTUS, De div. Nat., iii. 19; HEGEL, Logic (lesser), §§ 87-8, and Werke, iii. 72-3 (larger logic); ORMOND, Basal Concepts in Philos. (1896). (J.D.)

Non compos mentis [Lat.]: Ger. same, or nicht dispositionsfähig; Fr. incapable, non compos sui; Ital. same, or non compos sui. Incapable through mental impairment or disease of conducting one's affairs; usually employed in a technical or legal sense; cf. COMPOS MENTIS. (J.J.)

Non-contradiction. The 'law' of non-contradiction' is another name for the principle of CONTRADICTION (q.v.). See also LAWS OF THOUGHT. (C.S.P.)

Non-ego: Ger. Nicht-ich; Fr. non-moi; Ital. non-io. The opposite of the Ego; the not-me; the external object; the external world. Cf. EGO.

The term is of especial significance, as a technical term, in the philosophy of Fichte; it represents the second positing (the anti-positing -- Entgegensetzen; see POSIT) of the Ego as that which limits and thereby stimulates and defines the more specific activity of the Ego. See Fichte, Werke, i. 101-5, and Fischer, Gesch. d. neueren, Philos., v. 438. (J.D.)

Nonsequitur [Lat. for 'it does not follow]'. A name which belongs to the slang of the universities for the fallacia consequentis (called by Aristotle o para to epomenon elegcoV, De Sophist. Elen., 167 b 1), which is, strictly speaking, a fallacy which arises from a simple conversion of a universal affirmative, or transposing a protasis and apodsis, or condition and consequent.

Thus Aristotle tells us that the Eleatic Melissus argued that the universe is ungenerated, since nothing can be generated by what does not previously exist. The universe, then, not being generated, had no beginning; and having no beginning, it is infinite. But, as Aristotle remarks, although everything generated has a beginning, it does not follow (non sequitur, ouk anagkh de touto sumbainein) that everything that has a beginning is generated. A fever, for example, is not generated. Such fallacies are extremely common. De Morgan (Formal Logic, 268) gives this example: 'Knowledge gives power, power is desirable, therefore knowledge is desirable.' But though whatever is desirable has some desirable effect, it does not follow that whatever has any desirable effect is desirable. An attack of yellow fever has the desirable effect of rendering it unlikely the patient will for a long time have another; still, it is not itself desirable.

But the majority of logicians not only confound this fallacy with the post hoc, ergo propter hoc, which Aristotle considers immediately after, but even define it as 'failure in the formal inadequacy of the reason' (Sidgwick, Fallacies, II. ii. 4), or as 'the introduction of new matter into the conclusion, which is not contained in the premises' (Hyslop, Logic, xviii. 2), or as 'the simple affirmation of a conclusion which does not follow from the premises' (De Morgan, loc. cit.), or as 'any argument which is of so loose and inconsequent a character that no one can discover any cogency in it' (Jevons, Lessons in Logic, xxi), or 'to assume without warrant that a certain conclusion follows from premises which have been stated' (Creighton, Introductory Logic, § 46). Very many logicians omit it altogether, which is better.

Aristotle, however, could not express himself more precisely: 'O para to epomenon elegcoV dia to oiesqai antistrefein thn akolouqhoin. That is, 'from thinking that the consequentia can be converted.' That is to say, thinking that because 'If A, then C,' therefore 'If C, then A.' Owing to the neglect of fallacies by the more scientific logicians, it is not easy to cite many who define the fallacy correctly. The Conimbricenses (than whom no authority is higher) do so (Commentarii in Univ. Dialecticam Arist. Stagir., In lib. Elench., q. i. art. 4); also Eustachius (Summa Philos., Tom. I, pars. III, tract. iii, disput. iii. 9. 3); also Cope, an admirable student of Aristotle, in his note on the Rhetorics, B. cap. xxiv. See also the Cent. Dict., under 'Fallacy.' (C.S.P.)

Non-voluntary: Ger. nicht-strebend; Fr. non-volontaire; Ital. (not in use). ACONATIVE (q.v.). See also ACTION.

Noology [Gr. nouV, reason, + logoV, theory]: Ger. Noologie; Fr. noologie; Ital. noologia (the equivalents are suggested). That part of philosophy which deals with intuitive truths of reason; as distinct from Dianoiology, which deals with truths discursively or demonstratively established.

A term suggested by Sir William Hamilton, Reid's Works, note A, § v, but having no currency. Hamilton probably derived it from Kant (Krit. d. reinen Vernunft, 643). It is used by Crusius for psychology. (J.D.)

Norm (and Normality) [Lat. norma, a carpenter's square, a rule]: Ger. Norm, Normalität; Fr. norme, normalité; Ital. norma, normalità. (1) A standard type or pattern from which continuous departures are possible in opposite directions. (C.S.P.)

(2) In natural science: the usual, in form, size, and function. Normality is conformity to that usual.

Fluctuations and deviations from normality, both physical and mental, constantly occur, and when within moderate limits are still considered normal; when exceeding such limits they gradually pass into the ABNORMAL (q.v.). For examples of the use of this conception in psychological discussions see Maudsley, Responsibility in Mental Disease. (J.J.)

Norm and Normative (in the moral sciences): Ger. normativ (normgebend); Fr. normatif; Ital. normativo. The principle, whether truth or mode of reality, which controls action, thought, and emotion, if these are to realize their appropriate ends; the end as law. The norm of thinking is truth; of emotion, the beautiful; of volition, the good. These principles (and their corresponding philosophic disciplines) are hence termed normative. The three normative sciences are thus logic, aesthetics, and ethics.

Reference to a norm may be roughly taken to discriminate the philosophic from the natural sciences. The latter aim simply to describe phenomena and explain them in terms of laws or principles homogeneous with the facts. The explaining principles are, moreover, mechanical, having to do with conditions of manifestation in time. In the philosophic sciences, facts are interpreted with reference to their meaning, or value -- their significance from the position occupied, or part played, by them in the total make-up of experience. The standpoint, moreover, is teleological, since the interest is not in the conditions of origin, but in the fulfilment of purpose in realizing their appropriate values. Whether this distinction is one of objective reality, or one of standpoint and method of treatment, is, however, itself a philosophic problem. According to some writers the distinction between concepts of origin and of value has a distinct ontological reference; according to others the significance is only methodological. That is to say, to the latter there are not two spheres, one of pure phenomena, the other of ends and values; but the distinction is one of standpoint for purposes of description and explanation. Cf. ORIGIN versus NATURE.

The term norm is closely related to the terms criterion and standard. Criterion applies, however, more definitely to the process of judgment; it is the rule or mode of control as employed to assist judgment in making proper discriminations. A criterion of beauty is the principle employed in arriving at correct estimates or appreciations; a norm of beauty controls (or is supposed to control) the facts themselves in their own meaning. The criterion thus has a more subjective connotation. The standard is the principle used to measure value, and to lay off a scale of values. The standard of beauty is that type or form to which the facts conform in the degree in which the term beautiful is applicable to them. It differs from the norm in that the objectively regulating character of the norm is not necessarily ascribed to it. It agrees with the criterion in referring especially to the process of judgment or evaluation, but differs in that it takes some objective form as its adequate embodiment or manifestation. The criterion is the deciding principle in forming judgments; the standard is the principle which gives content to the adequate judgment. The norm which regulates the value of the facts may also, of course, be the standard by which their relative worths are measured, and the criterion by which the individual is guided in arriving at a correct apprehension of these worths. (J.D.)

Normal (in economics) [Lat. normalis, from norma, a rule]: Ger. normal; Fr. normal; Ital. normale. (1) In the broad sense, action which conforms to observed economic laws. 'The course of action which may be expected under certain conditions from the members of an industrial group is the normal action of the members of that group' (Marshall).

(2) In the narrower sense, a normal adjustment is one which represents conditions of economic EQUILIBRIUM (q.v.), e.g. normal price.

The term normal price was brought into prominence, if not actually introduced, by Cairnes. 'A normal price is reached when the product has so adjusted itself to the demands of consumers that the market price affords the current rate of profit to the producer, who enjoys no extraordinary advantage. We may contrast market and normal price by saying that a market price is one at which, for the moment, the supply is equal to the demand; while a normal price is one at which, as long as the existing state of things continues, the production is likely to be equal to the consumption' (Hadley). Cf. SUPPLY AND DEMAND. (A.T.H.)

Normal (in law): Ger. regelrecht, normal; Fr. normal; Ital. normale. Pertaining to the ordinary individual. 'The rights of a child, a lunatic, or a corporation, are abnormal' (Holland, Jurisprudence, chap. ix. 119; xi. 144; xiv. 288).

Literature: for a discussion of the normal rules of human conduct see HEINECCIUS, Elementa iuris Naturae et Gentium, Lib. I. chap. i. § 4, and chaps. iii and iv. (S.E.B.)

Normal School: Ger. Lehrerseminar; Fr. école normale; Ital. scuola normale. An educational institution for the preparation of teachers, chiefly for elementary schools; a training college for teachers.

The work of well-equipped normal schools embraces three kinds of activity: (1) instruction in the theory of education as founded upon psychology, ethics, and sociology; (2) instruction in the subject-matter to be taught; (3) direct contact with the problems of teaching in a model or practice school. In thirty-two of the United States the normal school has become an integral part of the public school system.

Literature: see Reports of Normal School Section of the Nat. Educ. Assoc. in the 'Proceedings' from 1871 to the present; also art. on 'Normal Schools' in Johnson's Univl. Cyc., revised ed (C.DE G.)

Normal or Standard Stimulus: Ger. Normalreiz; Fr. excitant normal; Ital. stimolo normale. The stimulus taken as a standard in a series of experiments in which the stimulus is varied with reference to this standard. Cf. PSYCHOPHYSICAL MEASUREMENT METHODS. (J.M.B.)

Normative: see NORM.

Nota notae [Lat.]: The logical principle Nota notae est nota rei ipsius, that is, the predicate of the predicate is the predicate of the subject, which is laid down in several places by Aristotle as the general principle of syllogism. The principle passages are as follows: --

'When one thing is predicated of another as its subject, whatever is said of the predicate can also be said of the subject' (Categ., iii. 1 b 10).

'Whatever is said of the predicate will hold also of the subject' (Categ., v. 3 b 4).

'We say that something is predicated universally when nothing can be admitted as coming under the subject of which the predicate will not hold; and the same thing holds of negation' (1 Anal. pr., i. 24 b 28). The term nota notae is from the first words of the original of this passage.

'Of whatever the species is predicated, the genus is predicable' (Topics, D. i. 121 a 25).

Some writers (as Hamilton, Lects. on Logic, App. VI. ii) imagine a distinction between the nota notae and the dictum de omni. Some have been so extravagant as to attribute the former to Kant, in whose Falsche Spitzfindigkeit (1762, ii) it is very likely that the precise phrase 'nota notae est nota rei ipsius' first occurs, though similar phrases, such as 'cui convenient notae eidem quoque convenit nomen,' are common in Wolf's and other logics of the 18th century. But it is clear that in Aristotle's mind it was one principle, essentially that which De Morgan well called the principle of the 'transitiveness of the copula.'

Aristotle, in the last but one of the above passages, seems to regard the nota notae as following from the definition of universal predication. To say that 'Any S is P' is to say that of whatever S is true, P is true. This amounts to deriving the transitiveness of the copula from the transitiveness of illation. If from A follows B and from B follows C, then from A follows C. This, again, is equivalent to the principle that to say that from the truth of X follows the truth of the consequence that from Y follows Z, is the same as to say that from the joint truth of X and Y follows Z. (C.S.P.)

Note [Lat. nota, a mark, a sign]: Ger. (1) Klang, (2) Note, Tonzeichen; Fr. (1) son, (2) note; Ital. nota, suono. (1) A 'musical' or COMPOUND TONE (q.v.), as specifically determined in a musical scale. Cf. CLANG.

(2) The written or printed symbol of the musical tone. (E.B.T.- J.M.B.)

Note-blindness: Ger. Notemblindheit; Fr. cécité musicale (or notale); Ital. cecitàmusicale. An infrequent symptom in disorders of the aphasic type, in which there is a loss of the power to read musical notes; it is thus, in the realm of music, the analogue of ALEXIA (q.v.). Cf. AMUSIA, and SPEECH AND ITS DEFECTS. (J.J.)

Nothing (Hegel's Nichts): see HEGEL'S TERMINOLOGY, sub verbo. Cf. also NON-BEING.

Notion: Ger. Begriff (concept) Gedanke (thought; no exact equivalent, see below); Fr. notion; Ital. nozione. (1) Sometimes used generally for any kind of apprehension of an object rather than actual perception; but (2) it is better to restrict its application to that element in the apprehension of an object which does not consist in an image.

The general application of the word to any cognitive state is illustrated by the following passage from Reid (Works, Hamilton's ed., i. 289): 'The word notion, being a word in common language, is well understood. All men mean by it the conception the apprehension, or thought which we have of any object of thought. A notion, therefore, is an act of the mind conceiving or thinking of some object. The object of thought may be either something that is in the mind, or something that is not in the mind. It may be something that has no existence or something that did, or does, or shall exist. But the notion which I have of that object is an act of my mind, which really exists while I think of the object; but has no existence when I do not think of it.' The more restricted usage which we propose is suggested by Berkeley (Princ. of Human Knowledge, Pt. 1. § 142): 'We may not, I think, strictly be said to have an idea of an active being, or of an action, although we may be said to have a notion of them. I have some knowledge of my mind and its acts about ideas, inasmuch as I know or understand what is meant by these words, What I know, That I have some notion of. I will not say that the terms idea and notion may not be used convertibly, if the world will have it so, but yet it conduceth to clearness and propriety that we distinguish things very different by different names. It is also to be remarked that, all relations including an act of the mind, we cannot so properly be said to have an idea, but rather a notion of the relations and habitudes between things.'

Without committing ourselves to the statement that there are no ideas of relation or even of activity, we agree with Berkeley that some such distinction as he suggests would be very useful. All those modes of cognitive consciousness which are called by James 'psychic fringes,' 'feelings of tendencies,' 'sense of whence our thought is coming and whither it is going,' should be called 'notional' in accordance with the usage we recommend. Under the same head would be brought that 'understanding of the meaning of words' which seems independent of the mental imagery suggested by them. It should be noted that we do not wish to imply that notional consciousness ever exists in complete severance from mental imagery, though the imagery is often merely verbal. Nor do we, like Berkeley, simply identify idea and image. The idea must include an image: but it also includes whatever notional 'fringe' serves to give the image meaning or significance. Any object considered as an INTENT (q.v.) is necessarily an object of notional consciousness.

As to the German usage, Begriff has served, like concept in English, to cover the whole ground. Wundt (Grundriss d. Psychol., § 17, B) marks off the 'ideational elements,' calling them the Gesammtvorstellung; but it remains to find a term for the notional part. Possibly something might be said for the corresponding consciousness of intent. Both French and Italian admit a distinction of terms as suggested. (G.F.S. - J.M.B.)

Notion (Hegel's Begriff): see HEGEL'S TERMINOLOGY, VI, d.

Notochord [Gr. nwtoV, back, + cordh, string]: Ger. Rückensaite, Chorda, Wirbelsaite; Fr. corde dorsale, notocorde; Ital. notocorda. A rod of peculiar tissue constituting the primitive axial skeleton of vertebrates.

It begins immediately behind the pituitary body, and extends to the caudal extremity. It occurs as a permanent structure in fishes, and as a temporary one in the embryos of amphibia, reptiles, birds, and mammals, being functionally replaced in the adult of these forms by the vertebral column, which is evolved around the notochord. Comparative embryology has shown that it is a greatly modified epithelial band, which arises in the embryo from the median dorsal line of the entoderm, being in position and mode of development somewhat analogous to the ectodermal medullary canal, or primitive tubular nervous system.

Literature: MINOT, Human Embryol., 181; GEGENBAUR, Vergleichende Anat. d. Wirbelthiere (1898); R. WIEDERSHEIM, Compar. Anat. of Vertebrates (trans., 1897). (C.S.M.)

Noumenon, and -al [Gr. nooumenon, anything known, from noein, to perceive, know]: Ger. Noumenon (-al), DING AN SICH (q.v.); Fr. noumène (-al); Ital. numeno. The object of pure thought, or of rational intuition, free from all elements of sense. See PHENOMENON, and MUNDUS INTELLIGIBILIS.

Plato uses the term a number of times, but simply in connection with nouV and noein, as the intelligible, the things of thought, e.g. Parmenides, 132; Republic, vi. 508.

Kant uses the term generally as equivalent with thing-in-itself; that is, the thing, as not object of sense; and hence as something which can only be thought. But in his Dialectic he ascribes to thought, as over and above sensuous schematism, specific functions; namely, (1) to limit the world of sense and phenomena, by making us aware of a possible world of reality beyond; (2) to afford an ideal of totality, which can, indeed, never be realized, but which serves, none the less, as a standard to suggest and to regulate, so as to give the greatest possible completeness to experience. For this Kant uses, indeed, the term idea rather than noumenon, but as its basis of definition is exactly the same (the reference to reason transcending experience), it was impossible that the two should not be confused. Through the practical Reason, the world of Noumena, or Things-in-themselves, thus left open as a theoretical possibility, is found to be a practical reality in the consciousness of duty. And in the Critique of Judgment, the teleological principle lying at the basis of science mediates between the noumenal and the phenomenal, not indeed asserting the existence of the former, but treating the latter as if the noumenal were its ground. It was the aim of Fichte and of Kant's successors to combine systematically the objective sense of noumenon, the thing-in-itself, and the subjective -- the ideal of knowledge -- which Kant had brought together only in a confused way. Reinhold is conscious of this confusion, and accordingly carefully discriminates the thing-in-itself, as the source of the 'matter' of our perceptions, from the noumenon, as denoting the unrealizable ideals and problems which thought sets to experience. The thing-in-itself here has more kinship with phenomena than with noumena. See Kant, Critique of Pure Reason, 217-26, 249-52 (Max Müller's trans.); Proleg., §§ 44, 57 (in this latter, the three meanings of thing-in-itself, limit to sensibility, and ideal of rational completeness are practically identified); Critique of Practical Reason, Bk. I. chap. i. Pt. II; Critique of Judgment, 427-8 (Bernard's trans.). Kant seems to have used the term as equivalent to the ancient nohta, which was opposed to aioqhta. According to Vaihinger (Commentar zu Kant, 117) Kant was indebted especially to Sextus Empiricus. For Reinhold, see Erdmann, ii. 479. (J.D.)

Nous [Gr. nouV, reason, thought]: Ger. Nus (K.G.); Fr. intelligence; Ital. nous. Reason, thought, considered not as subjective, nor as a mere psychic entity, but as having an objective, especially a teleological, significance.

We owe the term, as a technical one, to Anaxagoras. He felt the need of a special principle to account for the order of the universe and so, besides the infinity of simple qualities, assumed a distinct principle, which, however, was still regarded as material, being only lighter and finer than the others. To it, however, greater activity was ascribed, and it acted according to ends, not merely according to mechanical impact, thus giving movement, unity, and system to what had previously been a disordered jumble of inert elements. It is probable, however, that he limited its importance to the stellar heavens; or, at least, used it only when mechanical principles failed. Diogenes of Apollonia identified nous with air, and extended its action to organic bodies. Plato generalized the nous of Anaxagoras, proclaiming the necessity of a rational (teleological) explanation of all natural processes, and making nous also a thoroughly immaterial principle. As the principle which lays down ends, nous is also the Supreme Good, the source of all other ends and aims; as such it is the supreme principle of all the ideas. It thus gets an ethical and logical connotation as well as a cosmological.

On the other hand, nous gets a psychological significance as the highest form of mental insight, the immediate and absolutely assured knowledge of rational things. (Knowledge and the object of knowledge are thus essentially one.) Here nouV is distinguished from dianoia (sometimes called episthmh, and sometimes tecnh), which is discursive knowledge, and hence dependent upon assumptions, which cease to be such (and hence are unproved hypotheses) until carried back to the self-evident things of reason. Aristotle continues this line of thought, and practically identifies nouV as the supreme end, and thus the unmoved mover, or source of all motion, with God, whose activity is nohoiV nohsewV, the thinking of thought; an expression which makes explicit and absolute the virtual assumption of Plato regarding the unity  of nouV as faculty of highest knowledge and the nohton as the supreme object of knowledge. This divine nous is transcendent, moving the world only teleologically, not immanently nor yet causally. As transcendent it is, while immanent in human beings, yet separable from the body (cwristoV) and, as such, imperishable. In man, however, the nouV assumes a dual form: the active (nouV poihtikoV), which is free and the source of all man's insight and virtue that links him to the divine (qewrein), and the passive (nouV paqhtikoV), which includes thoughts that are dependent upon perception, memory -- experience as mediated through any bodily organ. Some of the Peripatetic followers of Aristotle, such as Theophrastus and Strato, appear (like his later Arabian followers) to have denied the transcendence of nous, to have given it a material and sensuous colouring, and thus to have prepared the way for the Stoics. It is with the Neo-Platonists, however, that the conception of nous becomes all-important again. The Absolute is, indeed, above all distinctions, and so cannot be regarded as, in itself, conscious or as reason. But its first distinction is into nous on one side, and being on the other. Nous thus becomes the conception for the absolute reason and subject. Moreover, it possesses a dynamic and self-differentiating quality, and is thus plural (noi) as well as singular. As noi it is the source of all the dynamic principles which operate in the creation of the universe. With the Neo-Platonists the conception reaches its zenith. The distinction (of Kant, but particularly as used by Coleridge) of REASON from UNDERSTANDING (q.v.) may, however, be compared with it, but the modern distinction of the subjective from the objective inevitably gives reason a much more psychological sense than nous possessed with the ancients.

Literature: PLATO, Phaedo, 97; Republic, vi. 508; and Sophist, 254; ARISTOTLE, Metaphysics, i. 3, 984; SIMPLICIUS, Phys., 33, and 225 a; PLOTINUS, Enneads; ZELLER, Philos. d. Griechen, ii. 590-2, iii. 512, 528-9. (J.D.)

Novation (in law) [Lat. novatio, a renovation]: Ger. Umschaffung, Novation, Neuerungsvertrag; Fr. novation; Ital. novazione. The substitution, by mutual consent, of a new obligation for an old one.

It may be a new obligation of the same party, or an obligation of a third party. In either case the old obligation is extinguished. If the obligation of a third party be substituted, he must consent to the arrangement.

'Novatio est prioris debiti in aliam obligationem vel civilem vel naturalem transfusio atque translatio: hoc est, cum ex praecedenti causa its nova constituatur, ut prior perimatur. Novatio enim a novo nomen accepit, et a nova obligatione' (Dig., x1vi. 2, De Novationibus et Delegationibus). Cf. Gaius, Commentaries, iii. 176.

Literature: a compendious discussion of the subject is to be found in Holtzendorff's Encyc. d. Rechtsw., sub verbo. (S.E.B.)

Now: see PRESENT (specious), and TIME (perception of).

Nucleus [Lat. nucleus, a kernel]: Ger. (1) Zellkern, (2) Kern; Fr. noyau; Ital. nucleo. (1) The functional and structural centre of a CELL (q.v.). The structure which seems in some way to dominate the vital processes of the cell.

(2) Often used also for cell clusters within the central nervous system.

The second use of the term, though ambiguous, is strongly intrenched in the prevalent usage. Nidus and nidulus have been proposed instead.

With reference to their fibrous connections we distinguish nuclei of origin from terminal nuclei, the former originative, the latter receptive. Thus the primary nuclei of the motor nerves are nuclei of origin, those of the sensory nerves terminal nuclei with reference to those nerves. Practically every nucleus belongs to both classes, and will receive one or the other name according to whether the cellipetal or the cellifugal impulses are considered. (H.H.)

Nullibrists: Ger. Nullibristen (Eisler); (not in use in the other languages). A term applied to those who deny that the soul exists in space, since it is simple and immaterial.

Used by Henry More (Enchir. met., 27, 1). It has no currency. (J.D.)

Number [Lat. numerus, through the French]: Ger. Zahl; Fr. nombre; Ital. numero. How many; cf. NUMBER CONCEPT. (J.M.B.- G.F.S.)

(1) We think of certain designated things as constituting a 'group' or 'assemblage,' whenever, without ignoring the separateness of the things from one another, we separate them from all other things, not individually, but as a whole, and thus make them collectively a single object of our attention.

(2) Let us call two groups of things 'equivalent,' when it is possible to bring the elements of the one into a relation of one-to-one correspondence with the elements of the other.

Thus the groups of letters, A, B, C, D, and E, F, G, H, are equivalents, since by matching A with E, B with F, C with G, and D with H, we are able to set up a relation of one-to-one correspondence between them.

(3) We may think of all possible groups of things as distributed into classes of equivalent groups. A relation of one-to-one correspondence may be established between every two groups which belong to the same class, but not between two groups which belong to different classes.

The property which is common to all groups which belong to the same class, and which distinguishes the groups of one class from those of another class, is the number of things in a group, or its cardinal number. In other words:

The cardinal number of any group of distinct things is that property which is common to the group itself and every group which can be brought into a relation of one-to-one correspondence with it.

Thus the number of things in a group may be described as the fundamental 'invariantive' property of the group, that is, as the property which remains unchanged during all changes (transformations) to which the group may be subjected, except such as affect the distinctness of the things themselves or their common distinctness from all other things.

(4) A 'finite' group may be defined as a group which is equivalent to no one of its parts.

From this definition it follows that if the first of two finite groups be equivalent to a part of the second, the second cannot be equivalent to the first or to any part of the first.

Let M and N represent any two finite groups. It must be the case that --

either (i.) M is equivalent to N,
or (ii.) M is equivalent to a part of N,
or (iii.) N is equivalent to a part of M;

and, as we have just seen, these three cases are mutually exclusive.

In the case (i.) M and N have the same cardinal number. In the case (ii.) we say that the cardinal number of M is 'less than' that of N; in the case (iii.) that the cardinal number of M is greater than that of N.

(5) By starting with a group which contains but one thing, and repeatedly adding one new thing, we arrive at the following scheme of the cardinal numbers: --

(i.) The cardinal number of a group like I, which contains but a single element;

(ii.) The cardinal number of a group like II, obtained by adding a single element to a group of the first kind;

(iii.) The cardinal number of a group like III, obtained by adding a single element to a group of the second kind; and so on, indefinitely.

It can be shown to follow from (4) that every cardinal contained in this scheme is finite, that every finite cardinal is included in the scheme, and that no two of these cardinals are equal.

Moreover, as thus arranged, the cardinal numbers constitute a never-ending 'ordinal system,' each cardinal following every lesser and preceding every greater cardinal.

(6) If a relation of one-to-one correspondence can be set up between two groups, either group may be used as a 'numeral symbol' for the other; for the two groups have the same cardinal number, and, generally speaking, no other property in common.

The primitive numeral symbols were groups of fingers or of marks, such as I, II, III, . . . , standing in this relation of one-to-one correspondence to the groups which they represent numerically. These are natural or immediate numeral symbols, but they are serviceable for the smaller cardinals only. The more highly developed races have therefore devised various artificial methods of representing the cardinal numbers, by systems of numeral words, as 'one,' 'two,' 'three,' &c., or conventional symbols, as 1, 2, 3, &c. These are the so-called 'natural numbers.'

(7) Arranging these symbols in an order corresponding to that already given the cardinals themselves, we have the never-ending scheme: 1, 2, 3, 4, . . . , which is sometimes called the scale of the natural numbers.'

All relations of greater and less among the cardinals are indicated by the relative positions of the corresponding symbols in this scale.

(8) Arithmetic is concerned primarily with the relations which exist among the natural numbers, and with certain operations by which these numbers may be combined.

The operation which lies at the basis of arithmetic is 'counting.'

We count a group of things by bringing it into a relation of one-to-one correspondence with a group of fingers or with a part of the natural scale. The process leads to the knowledge of the cardinal number of the group by yielding a familiar symbol for this number -- in the one case a finger-symbol, in the other the last of the numeral words 'one,' 'two,' 'three,' &c., used in the count.

It can readily be shown to follow from the definition of finite group (4) that the result of counting such a group is independent of the order in which the count is made.

This may be regarded as the fundamental theorem of arithmetic. The various operations of arithmetic all stand in a more or less immediate relation to counting. Thus, addition is an abbreviated form of counting, and subtraction is the inverse of addition; multiplication is an abbreviated form of addition, and division the inverse of multiplication. We are speaking, of course, of the primary meanings of these operations, when both the numbers which they combine, and the results of the combinations, are natural numbers.

(9) Thus far we have been considering the natural numbers only. But the complete number-system of arithmetic, algebra, and analysis also includes several classes of 'artificial' numbers: the negative, fractional, irrational, and imaginary numbers. These numbers were invented to express relations not immediately expressible in terms of the natural numbers; but they may be defined independently of such relations, by generalizing the ordinal property of the natural number-system.

(10) First of all we enlarge the natural scale 1, 2, 3, . . . into a scale on which it is possible to count backward with the same freedom as forward, by inventing the new numbers: 0, -1, -2, &c., and placing 0 before 1, -1 before 0, -2 before -1, &c. The new numbers are thus defined ordinally, each being characterized by its position in the enlarged ordinal scale.

(11) Next we invent the fractions, defining them ordinally as follows:

Combine any live natural numbers a and b to form the symbol a/b. Read simply 'a over b.'

In particular, let a/1 = a.

Then, arrange all possible symbols of this form ordinally in accordance with the rule:

'a/b shall precede, follow, or coincide with c/d according as ad precedes, follows, or coincides with bc.'

The integral and fractional numbers, positive, negative, and 0, together constitute the 'rational' number system. This system possesses a property not belonging to the natural system: viz. between every two numbers of the system there are other numbers of the system.

(12) We can, in various ways, separate all the numbers of the rational system into two classes, C₁ and C₂, so related that --

(i.) Each number in C₁ is less than (i.e. precedes) every number in C₂.

(ii.) There is no greatest (last) number in C₁, and no least (first) number in C₂.

We obtain such a separation, for instance, if we assign to C₁ all numbers whose cubes are less than 2, and to C₂ all numbers whose cubes are greater than 2.

Corresponding to every such separation we invent a new number, called an irrational number (e.g. cube root of 2), assigning it a place after all numbers in C₁ and before all numbers in C₂, and so defining it ordinally.

The rational and irrational numbers together constitute the 'real' number system. This system is 'continuous'; see CONTINUITY (in geometry).

(13) Finally, we add to the number system a new unit i, such that i² = -1, and then create a new continuous ordinal system (the system of 'pure imaginary numbers') in which the relative positions of any two numbers ai and bi are the same as that of the numbers a and b in the system of real numbers.

The real and imaginary numbers are combined by 'addition' into numbers of the form a + ib, called 'complex numbers,' and the complete number-system of analysis consists of all possible numbers of this form.

(14) The operations by which the natural numbers may be combined have experienced a corresponding generalization. But the generalized addition and multiplication are, like the addition and multiplication of the natural numbers, characterized by conformity to the laws:

         a + b = b + a
a + (b + c) = (a + b) + c
              ab = ba
        a (bc) = (ab) c
  a (b + c) = ab + ac;

subtraction is still the inverse of addition, division the inverse of multiplication, &c.

(15) In conclusion, we may call attention to two further extensions of the number-concept:

(i.) By the creation of complex numbers involving other fundamental units than 1 and i (Hamilton's Quaternions, Grassmann's Ausdehnungslehre, &c.).

(ii.) By the creation of transfinite cardinal and ordinal numbers (Georg Cantor). (H.B.F.)

Literature: G. CANTOR, in Mathematische Annalen, x1vi. 489; DEDEKIND, Essays on Number (Eng. trans., 1901), comprising trans. of Irrationale Zahlen and Was sind und was sollen die Zahlen? (in which the cardinal attribute of number is derived from the ordinal attribute); in the same connection see papers by HELMHOLTZ and KRONECKER in the volume commemorative of the Zeller-Jubiläum; various articles in recent volumes of the Rev. de Mét. et de Mor., by COUTURAT, POINCARÉ, and others; PEIRCE, Proc. Amer. Acad. Arts and Sci., Sept. 10, 1867; and Amer. J. of Math., iv. 85 (1881); H. B. FINE, The Number System of Algebra; and College Algebra (1901); WALTER BRIX, Der mathematische Zahlbegriff, in Philos. Stud., v and vi. (H.B.F.- J.M.B.)

Number (in metaphysics). According to the Pythagoreans, numbers constituted the essence or reality of things. They were the first and ultimate elements out of which things are composed. Plato in his later doctrine (taught orally) seems to have called the Ideas numbers. The Neo-Platonists and Neo-Pythagoreans regarded metaphysical numbers as the archetypes of arithmetical numbers, and the animating principles of things. See ONE (the).

Nicholas Cusanus and the Platonists of the early Renaissance gave great place to number in their cosmologies, being clearly influenced by the new mathematical developments. The mystics have in all ages given importance to numbers and their relations, as either prototypes or symbols of the deepest things in experience. Three (the union of the odd and even), four (the first square), seven (the sum of four and three), twelve (the product of three and four) have been especially honoured. (J.D.)

Number Concept: Ger. Zahlbegriff; Fr. concept (or idée) de nombre; Ital. concetto di numero. The thought of plurality or manyness, abstracted from the particular determinations indicated by 'how many,' 'so many,' &c., and from any definite arrangement or order.

The number concept involves on this definition: (1) reference to a group of objects considered as having some sort of connection with one another; (2) complete abstraction from the characteristics which distinguish these objects from one another; (3) the thought of the objects as distinguishable and capable of being variously and indifferently grouped and arranged. (G.F.S.- J.M.B.)

This analysis of the number concept is in fundamental accord with the theory of NUMBER (q.v.). The apprehension of GROUP (q.v.) precedes that of number, and the comparison of groups gives the 'more' or 'less' which is the first stage in the genesis of the number concept (see below). It involves the notion of the substitution of equal groups for one another and of like individuals within the same group. The idea of one-to-one correspondence of the groups inter se is a second step, by which mere inequality of groups gives place to numerical more or less, expressed by units. The third stage or step is reached when the notion of substitution becomes that of rearrangement of neutral units within the group itself, together with possible interchange of units from group to group. This is made possible by abstraction from the concrete characters of the members of both groups. It is probable that in this latest stage the device of measurement enters; by it a single constant unit is held for one-to-one comparison with members of the group (or determines such units in a continuous magnitude). But the use of measurement involves the earlier stages of the number concept, since the unit of measurement is itself a numerical abstraction. For a theory which derives the number concept from a form of rudimentary measurement see McLennan and Dewey, as cited below.

Genetically, it is likely that the struggle to accommodate to situations involving groups of objects precipitates comparisons of quantity and size, and this in turn yields a rudimentary sense of number. The writer's child H. for a considerable period distinguished 'one' from 'too-free' (two-three: a general term for plurality), but did not further distinguish different cases of plurality. The conception of unity probably does not arise until from the treatment of various inequalities of groups (possibly the most favourable case is that of greater and smaller occurring together, with reference to a familiar group which lies between them) 'two' and 'three' are distinguished from each other and also from 'one.'

The necessity of abstracting from the concrete characters of objects is seen in the difficulty in counting found by primitive peoples who have no adequate abstract symbols. The fingers seem to have served as counting instruments in many cases and to have been represented in pictographic signs. Early peoples, however, seem to have reckoned, as in the payment of debts (expressed in number of objects, such as cattle), in kind -- sheep for sheep, oxen for oxen, &c. This shows the number concept still lacking in completeness; the one-to-one correspondence has been reached, but not the idea of abstract substitution of units as between different groups.

Literature: DEDEKIND, Was sind und was sollen die Zahlen?; RIEHL, Philos. Krit., II. i. 73; WUNDT, Logik, i. 468; SCHUPPE, Logik, 102; JERUSALEM, Die Urtheilsfunction, 254; McLENNAN and DEWEY, The Psychol. of Number. (J.M.B., G.F.S.)

Number Form: Ger. Zifferform; Fr. schème (or diagramme) numérique; Ital. schema numerale. The form of SYNAESTHESIA (q.v.) in which the digit numbers and their combinations are given a scheme or arrangement in space by a manner of imaging peculiar and necessary to the individual.

The term is extended also to similar forms for other series, such as the letters of the alphabet, the months of the year, &c. For illustrations see SYNAESTHESIA. (J.M.B.)

Numenius. Born in the latter half of the 2nd century A.D. in Apamea, Syria. A Neo-Pythagorean who prepared the way for Neo-Platonism.

Numerical [Lat. numerus, number]: Ger. Zahl- (in compounds, as Zahldifferenz); Fr. numérique; Ital. numerico, numerale. If two bodies move in the same orbit and differ in no respect but that of being at any one instant in different places, they are said to be numerically different. Whether or not it is quite accurate to say that they differ only in this, that there are two of them, it is sufficiently so to account for the origin of the phrase. Numerical difference is individual difference, apart from all qualitative unlikeness. Numerical identity is being strictly the same individual. Cf. the different topics IDENTITY, DIFFERENCE, and INDIVIDUAL.

This adjective in logical phrases usually translates the Greek ariqmw. Some writers have doubted whether the Greek word is here to be understood in an arithmetical sense, and have seemed to suspect that it was a relic of some original and different signification of the word. But this is hardly called for.

A numerically definite syllogism is one the force of which depends upon the relations of numbers; as 'Most of the men at a certain gathering wore dress-coats, and most of them had white neckties. Hence, some of those who wore dress-coats had white neckties.' (C.S.P.)

Nutrition [Lat. nutritio, a nourishing]: Ger. Ernährung; Fr. nutrition; Ital. nutrizione. (1) The series of vital processes by which living organisms transform food materials into the substances of their own bodies: anabolic processes. See ANABOLISM.

(2) Substances capable of thus being transformed into living tissues, nutriment. (C.F.H.)

Nyya Philosophy: see ORIENTAL PHILOSOPHY (India).

Nyctalopia: see HEMERALOPIA, DAY-BLINDNESS, and NIGHT-BLINDNESS.

Nymphomania [Gr. numfh, a nymph, a bride, + mania, madness]: Ger. Nymphomanie; Fr. nymphomanie; Ital. ninfomania. A morbid and uncontrollable sexual desire in woman (in man termed Satyriasis).

It appears as a symptom in various mental disorders, but particularly in acute mania, and at times forms the chief indication or the initial symptom of such disorder. Nymphomania refers particularly to the morbid passion for sexual intercourse, while Erotomania refers to the excessive mental concentration on ideas concerning love, courtship, and mating. (J.J.)