Dagobert D. Runes, Dictionary of Philosophy, 1942.
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Machiavellism: A political principle according to which every act of the state (or statesman) is permissible -- especially with reference to foreign relations -- which might be advantageous for one's own country. The word refers to Niccolo di Bernardo Machiavelli, born May 3, 1469 in Florence, died June 22, 1527. Author of Discorsi sopra la prima deca di Tito Livio (Discourses about the first ten books of Titus Livius), Il Principe (The Prince). -- W.E.
Macrocosm: (vs. Microcosm) The universe as contrasted with some small part of it which epitomizes it in some respect under consideration or exhibits an analogous structure; any large "world" or complex or existent as contrasted with a miniature or small analogue of it, whether it be the physical expanse of the universe as against an atom, the whole of human society as against a community, district, or other social unit, or any other large scale existent as contrasted with a small scale representation, analogue, or miniature of it; sometimes God as against man, or the universe as against man; or God or the universe as against a monad, atom, or other small entity. -- M.T.K.
Madhva: An Indian dualistic philosopher of the 13th century A.D., a Vedantist and Vishnuite who held that world and soul, as well as the highest reality are entities different in their essence, and non-commutable. -- K.F.L.
Madhyamaka: Another name for the Buddhist school of Sunyavada (s.v.), so-called because it assumes a middle path (madhyama) between theories clinging to the knowableness of the noumenal and the sufficiency of the phenomenal. -- K.F.L.
Maecenatism: Patronage of the arts (from Maecenas, the patron of Horace and Virgil). -- L.V.
Mahabharata: (Skr. "the great [war of the] Bharatas"). An Indian epic of 100,000 verses, ascribed to Vyasa, incorporating many philosophical portions, such as the Bhagavad Gita (q.v.) -- K.F.L.
Mahabhuta: (Skr.) A physical element; in the Sarikhya (q.v.) one of the five gross elements contrasted with the tanmatras (q.v.). -- K.F.L.
Mahat: (Skr. great, mighty) The first great principle produced by prakrti (q.v.) according to the Sarikhya (q.v.), ideation, spirit, Idea. -- K.F.L.
Mahatma, mahatman: (Skr. great soul) Term of respect, as applied to Gandhi, for instance. In philosophy, the super-individual or transcendental self, or the Absolute. -- K.F.L.
Mahayana Buddhism: "Great Vehicle Buddhism", the Northern, Sanskrit, Tibetan, and Chinese form of Buddhism (q.v.), extending as far as Korea and Japan, whose central theme is that Buddhahood means devotion to the salvation of others and thus manifests itself in the worship of Buddha and Bodhisattvas (q.v.). Apart from absorbing beliefs of a more primitive strain, it has also evolved metaphysical and epistemological systems, such as the Sunya-vada (q.v.) and Vijnana-vada (q.v.). -- K.F.L.
Maieutic: Adjective derived from the Greek maia, midwife; hence pertaining to the art of assisting at childbirth, and to the positive aspect of the Socratic method. Socrates pretended to be a midwife, like his mother, since he assisted at the birth of knowledge by eliciting correct concepts by his process of interrogation and examination. -- J.J.R.
Maimon, Moses ben: (better known as Maimonides) (Abu Imram Musa Ibn Maimun Ibn Abdallah) (1135-1204) Talmud commentator and leading Jewish philosopher during the Middle Ages. Born in Cordova, left Spain and migrated to Palestine in 1165 and ultimately 1160, settled in Fez, N. Africa, whence he settled in Fostat, Egypt. His Guide for the Perplexed (More Nebukim in Heb.; Dalalat al-hairin, in Arab.) contains the summa of Jewish philosophic thought up to his time. It is written in the spirit of Aristotelianism and is divided into three parts. The first is devoted to the problems of Biblical anthropomorphisms, Divine attributes, and exposition and criticism of the teachings of the Kalam; the second to the proof of the existence of God, matter and form, creatio de novo, and an exposition of prophecy; the third to God and the world including problems of providence, evil, prescience and freedom of the will, teleology, and rationality of the precepts of the Torah. Maimonides exerted great influence not only on the course of subsequent Jewish speculation but also on the leaders of the thirteenth century scholastic philosophy, Albertus Magnus and Thomas Aquinas. -- M.W.
Maimon, Salomon: (1754-1800) A Jewish philosophical writer, versed in rabbinical literature, in whom Kant found his acknowledged most astute critical opponent. He wrote historical works on philosophy, attempted to expound a system of symbolic logic, and originated a speculative monism which influenced the leading Post-Kantians. -- H.H.

Works: Versuch einer Transzendentalphilosophie, 1790-92; Versuch einer neuen Logik oder Theorie des Denkens, 1794.

Maine de Biran, F. P. Gonthier: (1766-1824) French philosopher and psychologist, who revolted against the dominant sensationalistic and materialistic psychology of Condlllac and Cabanis and developed, under the influence of Kant and Fichte, an idealistic and voluntaristic psychology. The mind directly experiences the activity of its will and at the same time the resistance offered to it by the "non-moi." Upon this basis, Maine de Biran erected his metaphysics which interprets the conceptions of force, substance, cause, etc. in terms of the directly experienced activity of the will. This system of psychology and metaphysics, which came to be known as French spiritualism, exerted considerable influence on Cousin, Ravaisson and Renouvier. His writings include: De la Decomposition de la Pensee (1805); Les Rapports du Physique et du Moral de l'Homme (1834); Essai sur les Fondements de la Psychologie (1812); Oeuvres Philosophiques, ed. by V. Cousin (1841). -- L.W.
Major premiss: See figure (syllogistic).
Major term: (Gr. meizon horos) That one of the three terms in a syllogism which appears as predicate of the conclusion; so called by Aristotle because in the first, or perfect, figure of the syllogism it is commonly the term of greatest extension, the middle term being included in it, and the minor term in turn coming under the middle term. See Aristotelianism; Logic, formal, § 5. -- G.R.M.
Malebranche. Nicolas: (1638-1715) Was bom in Paris and, on his maturity, embraced the doctrines of the Cartesian school. Like Geulincx, he was particularly interested in the problem of mind-body relation which he interpreted in the spirit of occasionalism. Believing that the mind and body cannot possibly interact, he concluded that God enacts bodily movements "on occasion" of corresponding mental processes. In general, he believed that God works in all things and is the only real cause of events. -- R.B.W.

Main works:

Recherche de la verite, 1674-5;
Conversations Chretiennes, 1676;
Traits de la Nature et de la Grace, 1680;
Traite de Morale, 1683;
Entretiens sur la metaphysique et la religion, 1688;
Traite de l'Amour de Dieu, 1697;
Reflexions sur la premotion physique, 1714.

Malevolence: Ill or evil will or disposition -- the will or disposition to do wrong or to harm others. The vice opposed to the virtue of benevolence or good will. -- W.K.F.
Mana: An impersonal power or force believed to reside in natural objects contact with which infixes benefits of power, success, good or evil. A belief held by the Melanesians. -- V.F.
Manas: (Skr.) Mind, mentality, the unifying principle involved in sensation (cf. indriya), perception, conation, conception, always thought of in Indian philosophy as a kinetic entity, will and desire being equally present with thinking. -- K.F.L.
Manicheism, a religio-philosophical doctrine which spread from Persia to the West and was influential during the 3rd and 7th century, was instituted by Mani (Grk. Manes, Latinized: Manichaeus), a Magian who, upon conversion to Christianity, sought to synthesize the latter with the dualism of Zoroastrianism (q.v.), not without becoming a martyr to his faith. To combat the powers of darkness, the mother of light created the first man. As Buddha (q.v.) and Zoroaster he worked illumination among men ; as Jesus, the Son of Man, he had to suffer, become transfigured and symbolize salvation by his apparent death at the cross; as spirit of the sun he attracts all connatural light particles to himself. But final salvation from the throes of evil demons is accomplished by ascetic living, reminding of the Hindu code of ethics (see Indian Ethics), and belief in Mani as the prophesied paraclete (John 14.16-17). Revived once more in the Occident during the crusades by the Cathari. -- K.F.L.
Manifold of Sense: (A.S. manig, many + feold, fold) The sensuous ingredients of experience (colors, sounds, etc.) considered as a multiplicity of discrete items. See I. Kant, Critique of Pure Reason, A. 77-9-B. 102-5. -- L.W.
Mantra: (Skr.) Pious thought couched in repeated prayerful utterances, for meditation or charm. Also the poetic portion of the Veda (q.v.). In Shaktism (q.v.) and elsewhere the holy syllables to which as manifestations of the eternal word or sound (cf. iabda, vac, aksara) is ascribed great mystic significance and power. -- K.F.L.
Many questions: The name given to the fallacy -- or, rather, misleading device of disputation -- which consists in requiring a single answer to a question which either involves several questions that ought to be answered separately or contains an implicit assertion to which any unqualified answer would give assent. -- A. C.
Many-valued logic: See propositional calculus, many-valued.
Marburg School: Founded by Herman Cohen (1842-1918) and Paul Natorp (1854-1924) and supported by Ernst Cassirer (1874-), the noteworthy historian of philosophy, and Rudolf Stammler (1856-1938), the eminent legal philosopher, the school revived a specialized tendency of critical idealism. Stress is laid on the a priori, non-empirical, non-psychological and purely logical of every certain knowledge. Cohen and Natorp register an emphatic opposition to psychologism, and sought to construct a system upon pure thought on the basis of Kant and the Kantian reconstruction of Platonism. The logical and a priori in aesthetics, ethics, psychology and law is, being also independent of experience, the essential basis of these fields. Cf. Natorp, Kant u.d. Marburger Schule, 1915. -- H.H.
Marcus Aurelius: (121-180 A.D.) The Roman Emperor who as a Stoic endowed chairs in Athens for the four great philosophical schools of the Academy, the Lyceum, The Garden and the Stoa. Aurelius' Stoicism, tempered by his friend Fronto's humanism, held to a rational world-order and providence as well as to a notion of probable truth rather than of the Stoic infallibilism. In the famous 12 books of Meditations, the view is prominent that death was as natural as birth and development was the end of the individual and should elicit the fear of no one. His harsh treatment of the Christians did not coincide with his mild nature which may have reflected the changed character of Stoicism brought on by the decadence of Rome.

Cf. Meditations (Eng. tr. of Ta Eis Heauton) of A. -- M.F.

Maritain, Jacques: (1882-) Was born in Paris, educated at the Lycee Henri IV and the Sorbonne, where he studied with H. Bergson. He was converted to Catholicism in 1906. Then he studied biology with H. Driesch for two years, and the philosophy of St. Thomas with Father Clerissac. He became an ardent advocate of Thomistic philosophy, stressing its applicability to modern problems. He was a professor at the Institut Catholique (1914) and the Institute of Med. Studies, Toronto (1933), but is now lecturing in the U. S. Chief works: Philos. Bergsonienne (1914), Distinguer pour Unir (1932), Sept Lecons sur l'Etre (1934). G. B. Phelan, Jacques Maritain (N. Y., 1937). -- V.J.B.
Marx, Karl: Was born May 5, 1818 in Trier (Treves), Germany, and was educated at the Universities of Bonn and Berlin. He received the doctorate in philosophy at Berlin in 1841, writing on The Difference between the Democritean and Epicurean Natural Philosophy, which theme he treated from the Hegelian point of view. Marx early became a Left Hegelian, then a Feuerbachian. In 1842-43 he edited the "Rheinische Zeitung," a Cologne daily of radical tendencies. In 1844, in Paris, Marx, now calling himself a communist, became a leading spirit in radical groups and a close friend of Friedrich Engels (q.v.). In 1844 he wrote articles for the "Deutsch-Französische Jahrbücher," in 1845 the Theses on Feuerbach and, together with Engels, Die Heilige Familie. In 1846, another joint work with Engels and Moses Hess, Die Deutsche Ideologie was completed (not published until 1932). 1845-47, Marx wrote for various papers including "Deutsche Brüsseler Zeitung," "Westphälisches Dampfbot," "Gesellschaftsspiegel" (Elberfeld), "La Reforme" (Paris). In 1847 he wrote (in French) Misere de la Philosophie, a reply to Proudhon's Systeme des Contradictions: econotniques, ou, Philosophie de la Misere. In 1848 he wrote, jointly with Engels, the "Manifesto of the Communist Party", delivered his "Discourse on Free Trade" in Brussels and began work on the "Neue Rheinische Zeitung" which, however, was suppressed like its predecessor and also its successor, the "Neue Rheinische Revue" (1850). For the latter Marx wrote the essays later published in book form as Class Struggles in France. In 1851 Marx did articles on foreign affairs for the "New York Tribune", published The 18th Brumaire of Louis Bonaparte and the pamphlet "Enthülungen über den Kommunistenprozess in Köln." In 1859 Marx published Zur Kritik der politischen Okonomie, the foundation of "Das Kapital", in 1860, "Herr Vogt" and in 1867 the first volume of Das Kapital. In 1871 the "Manifesto of the General Council of the International Workingmen's Association on the Paris Commune," later published as The Civil War in France and as The Paris Commune was written. In 1873 there appeared a pamphlet against Bakunin and in 1875 the critical comment on the "Gotha Program." The publication of the second volume of Capital dates from 1885, two years after Marx's death, the third volume from 1894, both edited by Engels. The essay "Value Price and Profit" is also posthumous, edited by his daughter Eleanor Marx Aveling. The most extensive collection of Marx's work is to be found in the Marx-Engels Gesamtausgabe. It is said by the Marx-Engels-Lenin Institute (Moscow) that the as yet unpublished work of Marx, including materials of exceptional theoretical significance, is equal in bulk to the published work. Marx devoted a great deal of time to practical political activity and the labor movement, taking a leading role in the founding and subsequent guiding of the International Workingmen's Association, The First International. He lived the life of a political refugee in Paris, Brussels and finally London, where he remained for more than thirty years until he died March 14, 1883. He had seven children and at times experienced the severest want. Engels was a partial supporter of the Marx household for the better part of twenty years. Marx, together with Engels, was the founder of the school of philosophy known as dialectical materialism (q.v.). In the writings of Marx and Engels this position appears in a relatively general form. While statements are made within all fields of philosophy, there is no systematic elaboration of doctrine in such fields as ethics, aesthetics or epistemology, although a methodology and a basis are laid down. The fields developed in most detail by Marx, besides economic theory, are social and political philosophy (see Historical materialism, and entry, Dialectical materialism) and, together with Engels, logical and ontological aspects of materialist dialectics. -- J.M.S.
Marxism: The philosophical, social and economic theories developed by Karl Marx and Friedrich Engels. A concise statement of the general Marxist position is to be found in the Communist Manifesto.

The philosophical aspect of Marxism is known as dialectical materialism (q.v.); in epistemology it adopts empiricism; in axiology, an interest theory of value strongly tinged, in places, with humanitarianism. The social theory of Marxism centers around the concepts of basic (but not complete) economic determinism (q.v.), and the class character of society. In economics it maintains a labor theory of value (q.v.) which involves the concept of surplus value (q.v.) in the capitalistic mode of production. Upon the basis of its analysis of capitalism, Marxism erects the ethical conclusion that capitalism is unjust and ought to be supplanted by socialism. It predicts for the more or less immediate future the decay of capitalism, an inevitable and victorious revolution of the workers, and the establishing of socialism under the dictatorship of the proletariat. It looks forward to the ultimate goal of the "withering away of the state" leading to a classless society, communistic in economy and self-regulatory in politics. -- M.B.M.

Material a priori: (in Max Scheler) Intuitively given essences (relation of ideas). -- P.A.S.
  1. A proposition about the existent or the real: that only matter (q.v.) is existent or real; that matter is the primordial or fundamental constituent of the universe; atomism; that only sensible entities, processes, or content are existent or real; that the universe is not governed by intelligence, purpose, or final causes; that everything is strictly caused by material (inanimate, non-mental, or having certain elementary physical powers) processes or entities (mechanism); that mental entities, processes, or events (though existent) are caused solely by material entities, processes, or events and themselves have no causal effect (epiphenomenalism); that nothing supernatural exists (naturalism); that nothing mental exists;
  2. a proposition about explanation of the existent or the real: that everything is explainable in terms of matter in motion or matter and energy or simply matter (depending upon conception of matter entertained); that all qualitative differences are reducible to quantitative differences; that the only objects science can investigate are the physical or material (that is, public, manipulable, non-mental, natural, or sensible);
  3. a proposition about values: that wealth, bodily satisfactions, sensuous pleasures, or the like are either the only or the greatest values man can seek or attain;
  4. a proposition about explanation of human history: that human actions and cultural change are determined solely or largely by economic factors (economic determinism or its approximation);
  5. an attitude, postulate, hypothesis, assertion, assumption, or tendency favoring any of the above propositions; a state of being limited by the physical environment or the material elements of culture and incapable of overcoming, transcending, or adjusting properly to them; preoccupation with or enslavement to lower or bodily (non-mental or non-spiritual) values.
Confusion of epiphenomenalism or mechanism with other conceptions of materialism has caused considerable misunderstanding. -- M.T.K.
Materialization: (in Scholasticism) The function of matter when it receives form and with it constitutes a body, as distinguished from information, which is the function of form when it perfects the matter united to it so as to constitute a specific body. -- H.G.
Materially: (in Scholasticism) A predicate is said to belong to a subject materially when it belongs to it by reason of its matter or subject -- but formally when it belongs to it by reason of its form, e.g. fire is materially wasteful or destructive, but formally warm. -- H.G.
Material Mode of Speech: A description introduced by Carnap and based upon his distinction between "object-sentences" and "syntactical sentences". A sentence is syntactical if it can be translated into (is materially equivalent to) another sentence of the same language which refers only to signs or formal properties of and relations between signs. All non-syntactical sentences are said to be object sentences.

In a fully symbolized language (a "calculus") any sentence can be assigned to one of these classes by inspecting the formal properties of the sentence-token. In a "natural" language such as English, the formal properties of a sentence-token may indicate that it is an object-sentence when it is in fact syntactical. Such a sentence (also said to be quasi-syntactical) is expressed in the material mode of speech. When translated into an overtly syntactical sentence it is then said to be expressed in the formal mode of speech.

R. Carnap, Logical Syntax of Language, 284 ff. (for a more exact account). -- M.B.

Mathematics: The traditional definition of mathematics as "the science of quantity" or "the science of discrete and continuous magnitude" is today inadequate, in that modern mathematics, while clearly in some sense a single connected whole, includes many branches which do not come under this head. Contemporary accounts of the nature of mathematics tend to characterize it rather by its method than by its subject matter.

According to a view which is widely held by mathematicians, it is characteristic of a mathematical discipline that it begins with a set of undefined elements, properties, functions, and relations, and a set of unproved propositions (called axioms or postulates) involving them; and that from these all other propositions (called theorems) of the discipline are to be derived by the methods of formal logic. On its face, as thus stated, this view would identify mathematics with applied logic. It is usually added, however, that the undefined terms, which appear in the role of names of undefined elements, etc., are not really names of particulars at all but are variables, and that the theorems are to be regarded as proved for any values of these variables which render the postulates true. If then each theorem is replaced by the proposition embodying the implication from the conjunction of the postulates to the theorem in question, we have a reduction of mathematics to pure logic. (For a particular example of a set of postulates for a mathematical discipline see the article Arithmetic, foundations of.)

There is also another sense in which it has been held that mathematics is reducible to logic, namely that in the expressions for the postulates of a mathematical discipline the undefined terms are to be given definitions which involve logical terms only, in such a way that postulates and theorems of the discipline thereby become propositions of pure logic, demonstrable on the basis of logical principles only. This view was first taken, as regards arithmetic and analysis, by Frege, and was afterwards adopted by Russell, who extended it to all mathematics.

Both views require for their completion an exact account of the nature of the underlying logic, which, it would seem, can only be made by formalizing this logic as a logistic system (q. v,). Such a formalization of the underlying logic was employed from the beginning by Frege and by Russell, but has come into use in connection with the other -- postulational or axiomatic -- view only comparatively recently (with, perhaps, a partial exception in the case of Peano).

Hilbert has given a formalization of arithmetic which takes the shape of a logistic system having primitive symbols some of a logical and some of an arithmetical character, so that logic and arithmetic are formalized together without taking logic as prior; similarly also for analysis. This would not of itself be opposed to the Frege-Russell view, since it is to be expected that the choice as to which symbols shall be taken as primitive in the formalization can be made in more than one way. Hilbert, however, took the position that many of the theorems of the system are ideale Aussagen, mere formulas, which are without meaning in themselves but are added to the reale Aussagen or genuinely meaningful formulas in order to avoid formal difficulties otherwise arising. In this respect Hilbert differs sharply from Frege and Russell, who would give a meaning (namely as propositions of logic) to all formulas (sentences) appearing. -- Concerning Hilbert's associated program for a consistency proof see the article Proof theory.

A view of the nature of mathematics which is widely different from any of the above is held by the school of mathematical intuitionism (q. v.). According to this school, mathematics is "identical with the exact part of our thought." "No science, not even philosophy or logic, can be a presupposition for mathematics. It would be circular to apply any philosophical or logical theorem as a means of proof in mathematics, since such theorems already presuppose for their formulation the construction of mathematical concepts. If mathematics is to be in this sense presupposition-free, then there remains for it no other source than an intuition which presents mathematical concepts and inferences to us as immediately clear. . . . [This intuition] is nothing else than the ability to treat separately certain concepts and inferences which regularly occur in ordinary thinking." This is quoted in translation from Heyting, who, in the same connection, characterizes the intuitionittic doctrine as asserting the existence of mathematical objects (Gegenstände), which are immediately grasped by thought, are independent of experience, and give to mathematics more than a mere formal content. But to these mathematical objects no existence is to be ascribed independent of thought. Elsewhere Heyting speaks of a relationship to Kant in the apriority ascribed to the natural numbers, or rather to the underlying ideas of one and the process of adding one and the indefinite repetition of the latter. At least in his earlier writings, Brouwer traces the doctrine of intuitionism directly to Kant. In 1912 he speaks of "abandoning Kant's apriority of space but adhering the more resolutely to the apriority of time" and in the same paper explicitly reaffirms Kant's opinion that mathematical judgments are synthetic and a priori.

The doctrine that the concepts of mathematics are empirical and the postulates elementary experimental truths has been held in various forms (either for all mathematics, or specially for geometry) by J. S. Mill, H. Helmholtz, M. Pasch, and others. However, the usual contemporary view, especially among mathematicians, is that the propositions of mathematics say nothing about empirical reality. Even in the case of applied geometry, it is held, the geometry is used to organize physical measurement, but does not receive an interpretation under which its propositions become unqualifiedly experimental or empirical in character; a particular system of geometry, applied in a particular way, may be wrong (and demonstrably wrong by experiment), but there is not, in significant cases, a unique geometry which, when applied in the particular way, is right.

M. Bocher,
The fundamental conceptions and methods of mathematics, Bulletin of the American Mathematical Society, vol. 11 (1904), pp. 115-135.
J. W. Young,
Lectures on Fundamental Concepts of Algebra and Geometry, New York, 1911.
Veblen and Young,
Projecthe Geometry, vol. 1, 1910 (see the Introduction).
C. I. Keyser,
Doctrinal functions, The Journal of Philosophy, vol. 15 (1918), pp. 262-261.
G. Frege,
Die Grundlagen der Arithmetik, Breslau, 1884; reprinted, Breslau, 1934.
G. Frege,
Grundgesetze der Arithmetik, vol. 1, Jena, 1893, and vol. 2, Jena, 1903.
B. Russell,
The Principles of Mathematics, Cambridge, England, 1903; 2nd edn., London, 1937, and New York, 1938.
B. Russell,
Introduction to Mathematical Philosophy, London, 1919. - --
R. Carnap,
Die logizistische Grundlegung der Mathematik, Erkenntnis, vol. 2 (1931), pp. 91-105, 141-144, 145.
A. Heyting,
Die intuitionistische Grundlegung der Mathematik. ibid., pp. 106-115.
J. v. Neumann,
Die formalistische Grundlegung der Mathematik, ibid., pp. 116-121, 114-145, 146, 148.
R. Carnap,
The Logical Syntax of Language, New York and London, 1937.
L. E. J. Brouwer,
Intuitionisme en Formalisme, Groningen, 1912 ; reprinted in Wiskunde, Waarheid, Werkelijkheid, Groningen, 1919; English translation by A. Dresden, Bulletin of the American Mathematical Society, vol 20 (1913) pp. 81-96.
H. Weil,
Die heutige Erkenntnislage in der Mathematik, Symposion, vol. 1 (1926), Pp. 1-32.
D. Hilbert,
Die Grundlagen der Mathematik, Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität, vol. 6 ( 1928), pp. 65-85 ; reprinted in Hilbert's Grundlagen der Geometrie, 7th edn.
A. Heyting,
Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, Berlin, 1934.
H. Poincare,
The Foundations of Science, English translation by G. B. Hilsted, New York, 1913.
E. Nagel,
The formation of modern conceptions of formal logic tn the development of geometry, Osiris, vol. 7 (1939), pp. 142-224.
A. N. Whitehead.
An Introduction to Mathematics, London, 1911, and New York, 1911.
G. H. Hardy,
A Mathematician's Apology, London, 1940.


Moritz Cantor,
Vorlesungen über Geschichte der Mathematik, 4 vols., Leipzig, 1880-1908; 4th edn., Leipzig, 1921.
Florian Cajori,
A History of Mathematics, 2nd edn., New York and London, 1922.
A History of Elementary Mathematics, revised edn., New York and London, 1917.
A History of Mathematical Notations, 2 vols., Chicago, 1928-1929.
D. E. Smith,
A Source Book in Mathematics, New York and London, 1929.
T. L. Heath,
A History of Greek Mathematics, 2 vols., Oxford, 1921.
Felix Klein,
Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert, 2 vols., Berlin, 1926-1927.
J. L. Coolidge,
A History of Geometrical Methods, New York, 1940.

Mathesis universalis: Universal mathematics. One major part of Leibniz's program for logic was the development of a universal mathematics or universal calculus for manipulating, i.e. performing deductions in, the universal language (characteristica universalis). This universal language, he thought, could be constructed on the basis of a relatively few simple terms and, when constructed, would be of immense value to scientists and philosophers in reasoning as well as in communication. Leibniz's studies on the subject of a universal mathematics are the starting point in modern philosophy of the development of symbolic, mathematical logic. -- F.L.W.
Matrix: See Logic, formal, § 3.
Matrix method: Synonymous with truth-table method, q.v. -- A.C.
  1. That the defining characteristic of which is extension, occupancy of space, mass, weight, motion, movability, inertia, resistance, impenetrability, attraction and repulsion, or their combinations; these characteristics or powers themselves; the extra-mental cause of sense experience; what composes the "sensible world"; the manipulate; the permanent (or relatively so); the public (accessible to more than one knower, non-pn'vate);
  2. the physical or non-mental;
  3. the physical, bodily, or non-spiritual; the relatively worthless or base;
  4. the inanimate;
  5. the worldly or natural (non-supernatural);
  6. the wholly or relatively indeterminate; potentiality for receiving form or what has that potentiality; that which in union with form constitutes an individual; differentiating content as against form; the particular as against the universal;
  7. the manifold of sensation; the given element in experience as against that supplied by mind;
  8. that of which something consists; that from which a thing develops or is made;
  9. the first existent or primordial stuff;
  10. what is under consideration.
Philosophers conceive matter as appearance or privation of reality, as one or the only reality; as the principle of imperfection and limitation, as potentially or sometimes good; as substance, process, or content; as points, atoms, substrata, or other media endowed with powers mentioned above. -- M.T.K.
Matter, prime: (Scholastic) Though the notion of prime matter or hyle is not unknown to the Schoolmen previous to the 13th century, a consistent philosophical view has been developed only after the revival of Aristotelian philosophy. In accordance with the Stagirite, Aquinas considers prime matter as pure potentiality, lacking all positive characteristics. Matter becomes the principle of individuation; by being united to matter, the form is "contracted", that is narrowed from its universal and specific being to existence in a particular. Consequently, individuality is denied to the Angels who are free of matter, subsistent forms; every angel is a species of his own. The individuating principle is, however, not prime matter as such but materia signata quantitate; this means that a still indefinite relation to quantity is added. What is now commonly called matter is defined by Aquinas as materia secunda; the material thing owes its existence to the information of prime matter by a substantial form. -- R.A.
Maxim, ethical: In general any rule of conduct which an individual may adopt, or which he may be advised to follow as a good guide for action, e.g., Descartes' maxim to try always to conquer himself rather than fortune. The formulation of such rules is often recommended as a help in deciding what to do in particular cases, especially if time is short, in resisting temptation, etc. Kant held (1) that each voluntary act proceeds according to a maxim or "subjective principle of action," e.g., in breaking a promise one has as one's maxim, "When it is to my advantage, I will make a promise and not keep it," (2) that one can tell whether an act is right or not by asking whether one can will its maxim to be a universal law. -- W.K.F.
Maya: (Skr.) The power of obscuring or state producing error and illusion; the "veil" covering reality, the experience of manifoldness when only the One is real; natura naturans; appearance or phenomenon, as opposed to reality and noumenon. A condition generally acknowledged in Indian philosophy and popular Hindu thinking due to the ascendency of the Vedanta (q.v.) which can be overcome principally by knowledge or insight. See Jnana. -- K.F.L.
McDougall, William: (1871-1938) Formerly of Oxford and later of Harvard and Duke Universities, was the leading exponent of purposive or "hormic" (from Gr. horme, impulse) psychology. "Purposive psychology . . . asserts that active striving towards a goal is a fundamental category of psychology, and is a process of a type that cannot be mechanistically explained or resolved into mechanistic sequences." Psychologies of 1930, p. 4. In his epoch-making book, Introduction to Social Psychology (1908), McDougall developed a purposive theory of the human instincts designed to serve as an adequate psychological foundation for the social sciences. His social psychology listed among the primary instincts of man: flight, repulsion, curiosity, self-abasement, self-assertion and the parental instinct. McDougall's teleological theory is psychological rather than metaphysical, but he believed that the psychological fact of purpose was a genuine instance of teleologilcal causation. (Modern Materialism and Emergent Evolution, 1929.) He was also led by his psychological studies to adopt a metaphysical dualism and interactionism which he designated "animism." See Body and Mind, 1911. -- L.W.
Mead, George Herbert: (1863-1931) Professor of Philosophy at Chicago University. One of the leading figures in the Deweyan tradition. He contributed an important article to the volume, Creative Intelligence. He emphasized the relationship between the individual and his formulation and testing of hypotheses, on the one hand, as against the organic relationship of the individual with the society which is responsible for him. -- L.E.D.

Main works: Philosophy of the Present, 1932; Mind, Self, and Society, 1934; Movements of Thought in the Nineteenth Century, 1936; Philosophy of the Act, 1938.

  1. In general, that which in some way mediates or occupies a middle position among various things or between two extremes. Hence (especially in the plural) that through which an end is attained; in mathematics the word is used for any one of various notions of average; in ethics it represents moderation, temperance, prudence, the middle way.
  2. In mathematics:
    1. The arithmetic mean of two quantities is half their sum; the arithmetic mean of n quantities is the sum of the n quantities, divided by n. In the case of a function f(x) (say from real numbers to real numbers) the mean value of the function for the values x1, x2, . . . , xn of x is the arithmetic mean of f(x1), f(x2), . . . , f(xn). This notion is extended to the case of infinite sets of values of x by means of integration; thus the mean value of f(x) for values of x between a and b is ∫f(x)dx, with a and b as the limits of integration, divided by the difference between a and b.
    2. The geometric mean of or between, or the mean proportional between, two quantities is the (positive) square root of their product. Thus if b is the geometric mean between a and c, c is as many times greater (or less) than b as b is than a. The geometric mean of n quantities is the nth root of their product.
    3. The harmonic mean of two quantities is defined as the reciprocal of the arithmetic mean of their reciprocals. Hence the harmonic mean of a and b is 2ab/(a + b).
    4. The weighted mean or weighted average of a set of n quantities, each of which is associated with a certain number as weight, is obtained by multiplying each quantity by the associated weight, adding these products together, and then dividing by the sum of the weights. As under A, this may be extended to the case of an infinite set of quantities by means of integration. (The weights have the role of estimates of relative importance of the various quantities, and if all the weights are equal the weighted mean reduces to the simple arithmetic mean.)
    5. In statistics, given a population (i.e., an aggregate of observed or observable quantities) and a variable x having the population as its range, we have:
      1. The mean value of x is the weighted mean of the values of x, with the probability (frequency ratio) of each value taken as its weight. In the case of a finite population this is the same as the simple arithmetic mean of the population, provided that, in calculating the arithmetic mean, each value of x is counted as many times over as it occurs in the set of observations constituting the population.
      2. In like manner, the mean value of a function f(x) of x is the weighted mean of the values of f(x), where the probability of each value of x is taken as the weight of the corresponding value of f(x).
      3. The mode of the population is the most probable (most frequent) value of x, provided there is one such.
      4. The median of the population is so chosen that the probability that x be less than the median (or the probability that x be greater than the median) is ½ (or as near ½ as possible). In the case of a finite population, if the values of x are arranged in order of magnitude -- repeating any one value of x as many times over as it occurs in the set of observations constituting the population -- then the middle term of this series, or the arithmetic mean of the two middle terms, is the median. -- A.C.
  3. In cosmology, the fundamental means (arithmetic, geometric, and harmonic) were used by the Greeks in describing or actualizing the process of becoming in nature. The Pythagoreans and the Platonists in particular made considerable use of these means (see the Philebus and the Timaeus more especially). These ratios are among the basic elements used by Plato in his doctrine of the mixtures. With the appearance of the qualitative physics of Aristotle, the means lost their cosmological importance and were thereafter used chiefly in mathematics. The modern mathematical theories of the universe make use of the whole range of means analyzed by the calculus of probability, the theory of errors, the calculus of variations, and the statistical methods.
  4. In ethics, the 'Doctrine of the Mean' is the moral theory of moderation, the development of the virtues, the determination of the wise course in action, the practice of temperance and prudence, the choice of the middle way between extreme or conflicting decisions. It has been developed principally by the Chinese, the Indians and the Greeks; it was used with caution by the Christian moralists on account of their rigorous application of the moral law.
    1. In Chinese philosophy, the Doctrine of the Mean or of the Middle Way (the Chung Yung, literally 'Equilibrium and Harmony') involves the absence of immoderate pleasure, anger, sorrow or joy, and a conscious state in which those feelings have been stirred and act in their proper degree. This doctrine has been developed by Tzu Shu (V. C. B.C.), a grandson of Confucius who had already described the virtues of the 'superior man' according to his aphorism "Perfect is the virtue which is according to the mean". In matters of action, the superior man stands erect in the middle and strives to follow a course which does not incline on either side.
    2. In Buddhist philosophy, the System of the Middle Way or Madhyamaka is ascribed more particularly to Nagarjuna (II c. A.D.). The Buddha had given his revelation as a mean or middle way, because he repudiated the two extremes of an exaggerated ascetlsm and of an easy secular life. This principle is also applied to knowledge and action in general, with the purpose of striking a happy medium between contradictory judgments and motives. The final objective is the realization of the nirvana or the complete absence of desire by the gradual destruction of feelings and thoughts. But while orthodox Buddhism teaches the unreality of the individual (who is merely a mass of causes and effects following one another in unbroken succession), the Madhyamaka denies also the existence of these causes and effects in themselves. For this system, "Everything is void", with the legitimate conclusion that "Absolute truth is silence". Thus the perfect mean is realized.
    3. In Greek Ethics, the doctrine of the Right (Mean has been developed by Plato (Philebus) and Aristotle (Nic. Ethics II. 6-8) principally, on the Pythagorean analogy between the sound mind, the healthy body and the tuned string, which has inspired most of the Greek Moralists. Though it is known as the "Aristotelian Principle of the Mean", it is essentially a Platonic doctrine which is preformed in the Republic and the Statesman and expounded in the Philebus, where we are told that all good things in life belong to the class of the mixed (26 D). This doctrine states that in the application of intelligence to any kind of activity, the supreme wisdom is to know just where to stop, and to stop just there and nowhere else. Hence, the "right-mean" does not concern the quantitative measurement of magnitudes, but simply the qualitative comparison of values with respect to a standard which is the appropriate (prepon), the seasonable (kairos), the morally necessary (deon), or generally the moderate (metrion). The difference between these two kinds of metretics (metretike) is that the former is extrinsic and relative, while the latter is intrinsic and absolute. This explains the Platonic division of the sciences into two classes: those involving reference to relative quantities (mathematical or natural), and those requiring absolute values (ethics and aesthetics). The Aristotelian analysis of the "right mean" considers moral goodness as a fixed and habitual proportion in our appetitions and tempers, which can be reached by training them until they exhibit just the balance required by the right rule. This process of becoming good develops certain habits of virtues consisting in reasonable moderation where both excess and defect are avoided: the virtue of temperance (sophrosyne) is a typical example. In this sense, virtue occupies a middle position between extremes, and is said to be a mean; but it is not a static notion, as it leads to the development of a stable being, when man learns not to over-reach himself. This qualitative conception of the mean involves an adaptation of the agent, his conduct and his environment, similar to the harmony displayed in a work of art. Hence the aesthetic aspect of virtue, which is often overstressed by ancient and neo-pagan writers, at the expense of morality proper.
    4. The ethical idea of the mean, stripped of the qualifications added to it by its Christian interpreters, has influenced many positivistic systems of ethics, and especially pragmatism and behaviourism (e.g., A. Huxley's rule of Balanced Excesses). It is maintained that it is also involved in the dialectical systems, such as Hegelianism, where it would have an application in the whole dialectical process as such: thus, it would correspond to the synthetic phase which blends together the thesis and the antithesis by the meeting of the opposites.
    -- T.G.

Mean, Doctrine of the: In Aristotle's ethics, the doctrine that each of the moral virtues is an intermediate state between extremes of excess and defect. -- O.R.M.
Meaning: A highly ambiguous term, with at least four pivotal senses, involving
  1. intention or purpose,
  2. designation or reference,
  3. definition or translation,
  4. causal antecedents or consequences.
Each of these provides overlapping families of cases generated by some or all of the following types of systematic ambiguity: --
  1. Arising from a contrast between the standpoints of speaker and interpreter.
  2. arising from contrast between the meaning of specific utterances (tokens) and that of the general (type) symbol.
  3. arising from attention to one rather than another use of language (e.g., to the expressive rather than the evocative or referential uses).

Some of these ambiguities are normally eliminated by attention to the context in which the term 'meaning' occurs. Adequate definition, would, accordingly, involve a detailed analysis of the types of context which are most common. The following is a preliminary outline.

  1. "What does X {some event, not necessarily linguistic) mean?" =
    1. "Of what is X an index?"
    2. "Of what is X a sign?"
  2. "What does S (a speaker) mean by X (an utterance)?" =
    1. "What are S's interests, intentions, purposes in uttering X?"
    2. "To whom (what) is he referring?"
    3. "What effect does he wish to produce in the hearer?"
    4. "What other utterance could he have used to express the same interest, make the same reference, or produce the same effect?"
  3. "What does X (an utterance of a speaker) mean to an interpreter?" =
    1. "What does I take S to have meant by X (in any of the senses listed under B)?"
  4. "What does X (a type symbol) mean in language L?"
    1. "What symbols (in L) can be substituted for X (in specified contexts) without appreciable loss of expressive, evocative or referential function?"
    2. In a translation from L into another language M, either of X or of a more complex symbol containing X as part, what portion of the end-product corresponds to X?"
In addition to the above, relatively nontechnical senses, many writers use the word in divergent special ways based upon and implying favored theories about meaning.

See also: Index, Sign, Types of Language.

Reference: Ogden and Richards, Meaning of Meaning, Chs. 8 and 9. -- M.B.

Meaning, Kinds of: In semiotic (q. v.) several kinds of meaning, i.e. of the function of an expression in language and the content it conveys, are distinguished.
  1. An expression (sentence) has cognitive (or theoretical, assertive) meaning, if it asserts something and hence is either true or false. In this case, it is called a cognitive sentence or (cognitive, genuine) statement; it has usually the form of a declarative sentence. If an expression (a sentence) has cognitive meaning, its truth-value (q. v.) depends in general upon both
    1. the (cognitive, semantical) meaning of the terms occurring, and
    2. some facts referred to by the sentence.
  2. If it does depend on both (a) and (b), the sentence has factual (synthetic, material) meaning and is called a factual (synthetic, material) sentence.
  3. If, however, the truth-value depends upon (a) alone, the sentence has a (merely) logical meaning (or formal meaning, see Formal 1). In this case, if it is true, it is called logically true or analytic (q. v.); if it is false, it is called logically false or contradictory.
  4. An expression has an expressive meaning (or function) in so far as it expresses something of the state of the speaker; this kind of meaning may for instance contain pictorial, emotive, and volitional components (e.g. lyrical poetry, exclamations, commands). An expression may or may not have, in addition to its expressive meaning, a cognitive meaning; if not, it is said to have a merely expressive meaning.
  5. If an expression has a merely expressive meaning but is mistaken as being a cognitive statement, it is sometimes called a pseudo-statement. According to logical positivism (see Scientific Empiricism, IC) many sentences in metaphysics are pseudo-statements (compare Anti-metaphysics, 2).
-- R.C.
Measurement: (Lat. metiri, to measure) The process of ascribing a numerical value to an object or quality either on the basis of the number of times some given unit quantity is contained in it, or on the basis of its position in a series of greater and lesser quantities of like kind. See Intensive, Extensive Quantity. -- A.C.B.
Mechanism: (Gr. mechane, machine) Theory that all phenomena are totally explicable on mechanical principles. The view that all phenomena is the result of matter in motion and can be explained by its law. Theory of total explanation by efficient, as opposed to final, cause (q.v.). Doctrine that nature, like a machine, is a whole whose single function is served automatically by its parts. In cosmology, first advanced by Leucippus and Democritus (460 B.C.-370 B.C.) as the view that nature is explicable on the basis of atoms in motion and the void. Held by Galileo (1564-1641) and others in the seventeenth century as the rnechanical philosophy. For Descartes (1596-1650), the essence of matter is extension, and all physical phenomena are explicable by mechanical laws. For Kant (1724-1804), the necessity in time of all occurrence in accordance with causality as a law of nature. In biology, theory that organisms are totally explicable on mechanical principles. Opposite of: vitalism (q.v.). In psychology, applied to associational psychology, and in psychoanalysis to the unconscious direction of a mental process. In general, the view that nature consists merely of material in motion, and that it operates automatically. Opposite of: all forms of super-naturalism. See also Materialism, Atomism. -- J.K.F.
Mechanics: The science of motion, affording theoretical description by means of specification of position of particles bound by relations to other particles, usually having no extension but possessing mass. This involves space and time and frames of reference (in a relative fashion). Particles are assumed to traverse continuous paths. Auxiliary kinematical concepts are displacement, velocity, acceleration. The dynamical concept of forces (F's) acting independently of one another is coupled with mass (M) in a defining law, as F = Ma, where a = acceleration. Explicit reference to causation is avoided and is held to be unnecessary. Classical mechanics is restricted to the use of central forces (along the lines joining particles and a function of the length of those lines). This with a knowledge of boundary conditions leads to complete mechanistic determinism. The entire system of mechanics may also be developed by starting with other cortcepts such as energy and a stationary principle (usually that of "least action") in either an integral or differential form. -- W.M.M.
Mediation: (Lat. mediatio) The act or condition in which an intermediary is supplied between heterogeneous terms.

(a) In philosophy: Mediation is necessary in systems in which two forms of reality are held to be so different that immediate interaction is impossible; this is the case in later Neo-PIatonism, and particularly in the Cartesiam'sm of Malebranche, Geulincx and Spinoza, where mind and matter cannot directly interact; God supplies the principle of mediation in these latter systems.

(b) In theology: Mediation is an important aspect of the doctrine and practice of many religions; particularly in Judaism and Christianity because of the Transcendency of God and the imperfection of men. Mediation is an important function of Christ; as the God-Man, He is eminently fitted to form the connecting link between God and creatures; His Incarnation is considered as supplying the means (i.e. media) of salvation to man. -- V.J.B.

Meinong, Alexius: (1853-1921) Was originally a disciple of Brentano, who however emphatically rejected many of Meinong's later contentions. He claimed to have discovered a new a priori science, the "theory of objects" (to be distinguished from metaphysics which is an empirical science concerning reality, but was never worked out by Meinong). Anything "intended" by thought is an "object". Objects may either "exist" (such as physical objects) or "subsist" (such as facts which Meinong unfortunately termed "objectives", or mathematical entities), they may either be possible or impossible and they may belong either to a lower or to a higher level (such as "relations" and "complexions", "founded" on their simple terms or elements). In the "theory of objects," the existence of objects is abstracted from (or as Husserl later said it may be "bracketed") and their essence alone has to be considered. Objects are apprehended either by self-evident judgments or by "assumptions", that is, by "imaginary judgments". In the field of emotions there is an analogous division since there are also "imaginary" emotions (such as those of the spectator in a tragedy). Much of Meinong's work was of a psychological rather than of a metaphysical or epistemological character. -- H.G.

Main works:

Psychol.-ethische Untersuch. z. Werttheorie, 1894;
Ueber Annahmen, 1907;
Ueber d. Stellung d. Gegenstandstheorie im Syst. d. Wissensch., 1907;
Ueber Möglichkeit u. Wahrscheinlichkeit, 1915.
Cf. Gesammelte Abh. 3 vols., 1914.
Meliorism: (Lat. melior, better) View that the world is neither completely evil nor completely good, but that the relative amounts of good and evil are changeable, that good is capable of increase. Human effort to improve the world can be effective in making the world better and probably the trend of biological and social evolution tends in that direction. Opposed to Optimism and Pessimism. The term was coined by George Eliot. -- A.J.B.
Melissus: (c. 450 B.C.) Of Samos. He advanced a positive proof of the Eleatic doctrine of being as one and eternal, motionless and without change. The senses deceive us. He wrote in the Ionic dialect. -- L.E.D.
Memory: (Lat. memoria) Non-inferential knowledge of past perceptual objects (perceptual memory) or of past emotions, feelings and states of consciousness of the remembering subject (introspective memory). See Introspection. Memory is psychologically analyzable into three functions:
  1. revival or reproduction of the memory image,
  2. recognition of the image as belonging to the past of the remembering subject, and
  3. temporal localization of the remembered object by reference to a psychological or physical time-scheme.
-- L.W.
Mencius: (Meng Tzu, Meng K'o, 371-289 B.C.) A native of Tsao (in present Shantung), studied under pupils of Tzu Ssu, grandson of Confucius, became the greatest Confucian in Chinese history. He vigorously attacked the "pervasive teachings" of Yang Chu and Mo Tzu. Like Confucius, he travelled for many years, to many states, trying to persuade kings and princes to practice benevolent government instead of government by force, but failed. He retired to teach and write. (Meng Tzu, Eng. tr. by James Legge: i.) -- W.T.C.
Mendelsohn, Moses: (1729-1786) A German Jewish popular philosopher, holding an admired position in German literature. He was the first to advocate the social emancipation of the Jews, to plead in Germany for the separation of the Church and the State and for freedom of belief and conscience. He is philosrohically best known for his adduced proofs of the immortality of the soul and of the existence of a personal God. Schriften z. Philos., Aesthetik u. Apologetik (ed. Brasch, 1880). -- H.H.
Mental: (Lat. mens, mind) Pertaining to the mind either in its functional aspect (perceiving, imagining, remembering, feeling, willing, etc.) or in its contential aspects (sense data, images and other contents existing "in" the mind). See Mind. -- L.W.
Mental Chemistry: Psychological procedure, analogous to chemical analysis and synthesis, consisting in the attempted explanation of mental states as the products of the combination and fusion of psychic elements. See Associationism. -- L.W.
Mentalism: Metaphysical theory of the exclusive reality of individual minds and their subjective states. The term is applied to the individualistic idealism of Berkeley and Leibniz rather than to the absolutistic Idealism of Hegel and his followers. -- L.W.
Mental tests: Measurement of independent variables in a person to specific situations controlled by the medium of the instrument, expressing measurable differences in individuals. Chief form: intelligence test. -- J.E.B.
Mesmerism: A term formed from the name of F. Mesmer (1734-1815) to designate hypnotic phenomena (see Hypnotism) but now little used. -- L.W.
Metalanguage: A language used to make assertions about another language; any language whose symbols refer to the properties of the symbols of another language. (Formed by analogy with "metamathematics", the study of formalized mathematical systems.) -- M.B.
Metalogical: That which belongs to the basis of logic. Metalogical truths are the laws of thought, the formal conditions of thinking inherent in reason. (Schopenhauer.) -- H.H.

The same word is now commonly used in quite a different sense, as a synonym of syntactical. See syntax, logical. -- A.C.

Metamathematics: See Proof theory, and Syntax, logical.
  1. Rhetorical figure transposing a term from its original concept to another and similar one.
  2. In its origin, all language was metaphoric; so was poetry.
Metaphor is a short fable (Vico). -- L.V.
Metaphysical deduction: An examination of the logical functions of thought that there are certain a priori forms of synthesis which belong to the very constitution, the bare, purely formal machinery of the understanding. -- H.H.
Metaphysical essence: (in Scholasticism) The complexus of notes which are in a thing, as it is conceived by us -- i.e. the principle and primary notes by which that thing is sufficiently understood and distinguished from other things. -- H.G.
Metaphysical ethics: Any view according to which ethics is a branch of metaphysics, ethical principles being derived from metaphysical principles and ethical notions being defined in terms of metaphysical notions. -- W.K.F.
Metaphysics: (Gr. meta ta Physika) Arbitrary title given by Andronicus of Rhodes, circa 70 B.C. to a certain collection of Aristotelean writings.

Traditionally given by the oracular phrase: "The science of being as such." To be distinguished from the study of being under some particular aspect; hence opposed to such sciences as are concerned with ens mobile, ens quantum, etc. The term, "science", is here used in its classic sense of "knowledge by causes", where "knowledge" is contrasted with "opinion" and the term cause has the full signification of the Greek aitia. The "causes" which are the objects of metaphysical cognition are said to be "first" in the natural order (first principles), as being founded in no higher or more complete generalizations available to the human intellect by means of its own natural powers.

Secondary and derivative meanings: (a) Anything concerned with the supra-physical. Thus "metaphysical healing", "metaphysical poetry", etc. (b) Any scheme of explanation which transcends the inadequacies or inaccuracies of ordinary thought. -- W.S.W.

Metempsychosis: (Gr. meta, over + empsychoun, to animate) The doctrine that the same soul can successively reside in more than one body, human or animal. See Immortality. The doctrine was part of the Pythagorean teaching incorporated in mythical form in the Platonic philosophy (see Phaedrus, 249; Rep. X, 614). The term metempsychosis was not used before the Christian era. -- L.W.
Method: (Gr. methodos, method)
  1. Any procedure employed to attain a certain end.
  2. Any knowing techniques employed in the process of acquiring knowledge of a given subject-matter.
  3. The science which formulates the rules of any procedure.
-- A.C.B.
Methodic Doubt: The suspension of judgment in regard to possible truths until they have been demonstrated to be either true or false; in Cartesianism the criterion is the clearness and distinctness of ideas. -- V.J.B.
Method of simple enumeration: Inductive process by which the initial probability of a generalization is increased by more instances exactly the same as those previously observed. -- A.C.B.
Method of trial and error: Method of solving a problem, or of accomplishing an end, by putting the hypotheses or means to direct test in actuality rather than by considering them imaginatively in terms of foreseen consequences; opposed to reflection. -- A.C.B.
Methodology: The systematic analysis and organization of the rational and experimental principles and processes which must guide a scientific inquiry, or which constitute the structure of the special sciences more particularly. Methodology, which is also called scientific method, and more seldom methodeutic, refers not only to the whole of a constituted science, but also to individual problems or groups of problems within a science. As such it is usually considered as a branch of logic; in fact, it is the application of the principles and processes of logic to the special objects of the various sciences; while science in general is accounted for by the combination of deduction and induction as such. Thus, methodology is a generic term exemplified in the specific method of each science. Hence its full significance can be understood only by analyzing the structure of the special sciences. In determining that structure, one must consider
  1. the proper object of the special science,
  2. the manner in which it develops,
  3. the type of statements or generalizations it involves,
  4. its philosophical foundations or assumptions, and
  5. its relation with the other sciences, and eventually its applications.
The last two points mentioned are particularly important: methods of education, for example, will vary considerably according to their inspiration and aim. Because of the differences between the objects of the various sciences, they reveal the following principal methodological patterns, which are not necessarily exclusive of one another, and which are used sometimes in partial combination. It may be added that their choice and combination depend also in a large degree on psychological motives. In the last resort, methodology results from the adjustment of our mental powers to the love and pursuit of truth.

  1. There are various rational methods used by the speculative sciences, including theology which adds certain qualifications to their use. More especially, philosophy has inspired the following procedures:
    1. The Soctattc method of analysis by questioning and dividing until the essences are reached;
    2. the synthetic method developed by Plato, Aristotle and the Medieval thinkers, which involves a demonstrative exposition of the causal relation between thought and being;
    3. the ascetic method of intellectual and moral purification leading to an illumination of the mind, as proposed by Plotinus, Augustine and the mystics;
    4. the psychological method of inquiry into the origin of ideas, which was used by Descartes and his followers, and also by the British empiricists;
    5. the critical or transcendental method, as used by Kant, and involving an analysis of the conditions and limits of knowledge;
    6. the dialectical method proceeding by thesis, antithesis and synthesis, which is promoted by Hegelianlsm and Dialectical Materialism;
    7. the intuitive method, as used by Bergson, which involves the immediate perception of reality, by a blending of consciousness with the process of change;
    8. the reflexive method of metaphysical introspection aiming at the development of the immanent realities and values leading man to God;
    9. the eclectic method (historical-critical) of purposive and effective selection as proposed by Cicero, Suarez and Cousin; and
    10. the positivistic method of Comte, Spencer and the logical empiricists, which attempts to apply to philosophy the strict procedures of the positive sciences.
  2. The axiomatic or hypothetico-deductive method as used by the theoretical and especially the mathematical sciences. It involves such problems as the selection, independence and simplification of primitive terms and axioms, the formalization of definitions and proofs, the consistency and completeness of the constructed theory, and the final interpretation.
  3. The nomological or inductive method as used by the experimental sciences, aims at the discovery of regularities between phenomena and their relevant laws. It involves the critical and careful application of the various steps of induction: observation and analytical classification; selection of similarities; hypothesis of cause or law; verification by the experimental canons; deduction, demonstration and explanation; systematic organization of results; statement of laws and construction of the relevant theory.
  4. The descriptive method as used by the natural and social sciences, involves observational, classificatory and statistical procedures (see art. on statistics) and their interpretation.
  5. The historical method as used by the sciences dealing with the past, involves the collation, selection, classification and interpretation of archeological facts and exhibits, records, documents, archives, reports and testimonies.
  6. The psychological method, as used by all the sciences dealing with human behaviour and development. It involves not only introspective analysis, but also experimental procedures, such as those referring to the relations between stimuli and sensations, to the accuracy of perceptions (specific measurements of intensity), to gradation (least noticeable differences), to error methods (average error in right and wrong cases), and to physiological and educational processes.
-- T.G.
Miao: (a) Mystery of existence, which is unfathomable. (Lao Tzu.) (b) Subtlety, such as the subtle presence of the Omnipotent Creative Power (shen) in the myriad things. -- W.T.C.
Middle Term: (Gr. mesos horos) That one of the three terms in a syllogism which appears in both premisses; so called by Aristotle because in the first, or perfect, figure of the syllogism it is commonly intermediate in extension between the Major Term and the Minor Term. See Aristotelianism; Major Term; Minor Term. See Logic, formal, § 5. -- G.R.M.
Mill, James: (1773-1836) Father of John Stuart Mill and close associate of Jeremy Bentham as a member of the Utilitarian School of Philosophy. His chief original contributions were in the field of psychology where he advanced an associational view and he is likewise remembered for his History of India. See Utilitarianism.

Main work: Analysis of the Phenomena of the Human Mind, 1829. -- L.E.D.

Mill, John Stuart: (1806-1873) The son of James Mill, was much influenced by his father and Jeremy Bentham. Principal philosophical works: Logic, 1843; Liberty, 1859; Utilitarianism, 1861. In logic and epistemology he was a thorough empiricist, holding that all inference is basically induction on the basis of the principle of the uniformity of nature from one particular event to another or a group of others. Syllogistic reasoning, he holds always involves a petitio, the conclusion being included in the premises, with knowledge of those in turn resting on empirical inductions. Mill defines the cause of an event as the sum total of its necessary conditions positive and negative.

In ethics his Utilitarianism has been very influential in popularizing universalistic hedonism, albeit with certain confusions (see Hedonism). His essay on Liberty is authoritative as concerns liberty of thought and discussion, stimulating as concerns liberty of action in general. -- C.A.B.

Mill's methods: Inductive methods formulated by John Stuart Mill for the discovery of causal relations between phenomena.
  1. Method of Agreement: If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon.
  2. Method of Difference: If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance in common save one, that one occurring in the former; the circumstance in which alone the two instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.
  3. Joint Method of Agreement and Difference: If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstances the circumstance in which alone the two sets of instances differ, is the effect, or the cause, or an indispensable part of the cause, of the phenomenon.
  4. Method of Concomitant Variations: Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation.
  5. Method of Residues: Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents.
See Mill's System of Logic, bk. Ill, ch. VIII. -- A.C.B.
Mimamsi: Short for Purva-Mimamsa, one of the six major systems of Indian philosophy (q. v.), founded by Jaimini, rationalizing Vedic ritual and upholding the authority of the Vedas by a philosophy of the word (see vac). In metaphysics it professes belief in the reality of the phenomenal, a plurality of eternal souls, but is indifferent to a concept of God though assenting to the superhuman and eternal nature of the Vedas. There is also an elaborate epistemology supporting Vedic truths, an ethics which makes observance of Vedic ritual and practice a condition of a good and blissful life. -- KS.L.
Mimpathy: (Ger. Nachfühlen) The suffering of another must already be given in some form before it is possible for anyone to become a fellow sufferer. Pity and sympathy as experienced are always subsequent to the already apprehended and understood experience of another person who is pitied. One may share another's feeling about a matter, and yet have no sympathy for that one. The historian, novelist, dramatic artist must possess in high degree the gift of "after-experiencing" or mimpathizing, but they do not in the least need to have sympathy with their objects and persons. See Sympathy. -- H.H.
Mind: (Lat. mens) Mind is used in two principal senses: (a) The individual mind is the self or subject which perceives, remembers, imagines,feels, conceives, reasons, wills, etc. and which is functionally related to an individual bodily organism. (b) Mind, generically considered, is a metaphysical substance which pervades all individual minds and which is contrasted with matter or material substance. -- L.W.
Mind-body relation: Relation obtaining between the individual mind and its body. Theories of the mind-body relation are monistic or dualistic according as they identify or separate the mind and the body. Monistic theories include:
  1. the theory of mind as bodily function, advanced by Aristotle and adhered to by thinkers as divergent as Hobbes, Hegel, and the Behaviorists,
  2. the theory of body as mental appearance held by Berkeley, Leibniz, Schopenhauer and certain other idealists,
  3. the two-aspect theory of Spinoza and of recent neutral monism which considers mind and body as manifestations of a third reality which is neither mental nor bodily.
The principal dualistic theories are:
  1. two sided interacti'onism of Descartes, Locke, James and others. See Interactionism.
  2. psycho-physical parallelism. See Parallelism, Psycho-physical.
  3. Epephenomenalism. See Epephenomenalism.
-- L.W.
Mind-Dust Theory: Theory that individual minds result from the combination of particles of mind which have always existed in association with material atoms. The rival theory is emergent evolution which assumes that mind is a novel emergent in the process of biological evolution. -- L.W.
Mind-Stuff Theory: Theory that individual minds are constituted of psychic particles analogous to physical atoms. Differs from mind-dust theory in its emphasis on the constitution rather than the genesis of mind. See Mind-Dust Theory. -- L.W.
Ming: Name, or "that which designates a thing." This includes "designations of things and their qualities," "those referring to fame and disrepute," and "such descriptive appellations as 'intelligence' and 'stupidity' and 'love' and 'hate.' " "Names are made in order to denote actualities so as to make evident the honorable and the humble and to distinguish similarities and differences." For Rectification of Names, see Cheng ming. -- W.T.C.
Ming: Fate; Destiny; the Decree of Heaven. The Confucians and Neo-Confucians are unanimous in saying that the fate and the nature (hsing) of man and things are two aspects of the same thing. Fate is what Heaven imparts; and the nature is what man and things received from Heaven. For example, "whether a piece of wood is crooked or straight is due to its nature. But that it should be crooked or straight is due to its fate." This being the case, understanding fate (as in Confucius), establishing fate (as in Mencius, 371-289 B.C.), and the fulfillment of fate (as in Neo-Confucianism) all mean the realization of the nature of man and things in accordance with the principle or Reason (li) of existence. "That which Heaven decrees is true, one, and homogeneous . . . Fate in its true meaning proceeds from Reason; its variations (i.e., inequalities like intelligence and stupidity) proceed from the material element, the vital force (ch'i) . . . 'He who understands what fate is, will not stand beneath a precipitous wall.' If a man, saying 'It is decreed,' goes and stands beneath a precipitous wall and the wall falls and crushes him, it cannot be attributed solely to fate. In human affairs when a man has done his utmost he may talk of fate." The fate of Heaven is the same as the Moral Law (tao) of Heaven. The "fulfillment of fate" consists of "the investigation of the Reason of things to the utmost (ch'iung li)" and "exhausting one's nature to the utmost (chin hsing)" -- the three are one and the same." In short, fate is "nothing other than being one's true self (ch'eng)." -- W.T.C.
Ming chia: Sophists or Dialecticians, also called hsing-ming chia, including Teng Hsi Tzu (545-501 B.C.?), Hui Shih (390-305 B.C.?), and Kung-sun Lung (between 400 and 250 B.C.), at first insisted on the correspondence between name and reality. The school later became a school of pure sophistry which Chuang Tzu and the Neo-Mohists strongly attacked. See Chien pai. -- W.T.C
Ming (dynasty) philosophy: See Li hsueh and Chinese philosophy.
Ming te: (a) Illustrious virtue; perfect virtue. (Early Confucianism.) (b) Man's clear character; the virtuous nature which man derives from Heaven. (Neo-Confucianism.) -- W.T.C.
Minor Arts: Empirically distinguished from sculpture and painting. .They are: jewelry, miniature, textiles, pottery, etc. -- L.V.
Minor premiss: See figure (syllogistic).
Minor Term: (Gr. elatton horos) That one of the three terms in a syllogism that appears as subject of the conclusion; so called by Aristotle because it is commonly the term of least extension. See Aristotelianism; Major Term; Middle Term; Logic, formal, § 5. -- C.R.M.
Mishnah: (Heb., repetition) Older part of the Talmud (q.v.) containing traditions from the close of the Old Testament till the end of the second century A.D. when it was compiled (in several revisions) by R. Judah Hanasi (the prince, known also as Rabbi (my master) and Rabbenu Nakkadosh (our saintly master) who sedarim (orders), 63 massektot (tractates) and died between 193-215 A.D. It is divided in 6 524 perakim (chapters).

Here is a very brief summary of the Mishnah according to its sedarim:

Seder I, zeraim (seeds), 11 tractates: liturgy, tithes, inhibited mixtures of plants, animals and textiles, sabbatical year, produce offerings, first fruits.

Seder II, Moed (feast), 12 tractates: observance of sabbath, feasts and fasts.

Seder III, Nashim (women) -- 7 tractates: laws of marriage, divorce, forced marriage, adultery, asceticism.

Seder IV, Nezikin (damages), 10 tractates -- laws of damages, injuries, property, buying, selling, lending, hiring, renting, heredity, court proceedings, fines and punishment, cities of refuge, oaths. Special tractates on ethics (Abot) and idolatry and testimonials of special decisions.

Seder V, Kodashim (holy things), 11 tractates: sacrifices, slaughter of animals, ritual dietetics, first born animals, vows, excommunication, sacrilege, temple architecture and rituals.

Seder VI, Toharot (purifications) -- 12 tractates: lay and levitical purity and impurity.

Oldest complete manuscript of the Mishna, of the XIIIth century, is preserved in the Library of Parma, Italy.

First complete printed edition of the Mishnah appeared in Naples, 1492.

An excellent one-volume English translation of the entire Mishnah, with introduction and copious notes was made by Herbert Danbv, D.D. (Oxford, 1933). -- H.L.G.

Mishnah, authorities of: The authorities cited in the Mishnah as rings in "golden chain" of the Jewish masorah (tradition) are:
  1. Sopherim (scribes) known also as Anshe Keneseth Hagedolah (men of the great synod), beginning with Ezra of the Bible and terminating with Simeon the Just.
  2. Five Zugoth (duumviri) the last pair being the noted Hillel and Shamai. The former was according to E. Renan's hypothesis, a teacher of Jesus,
  3. Tannaim (repeaters) -- They numbered 277 and are divided into 5 generations. In the first generation were men who still held office in the temple of Jerusalem and witnessed its destruction (70 A.D.).

The second generation counts the celebrated Nasi Rabban Gamaliel II and R. Eliezer ben Hyrcanus, excommunicated for opposing the rule of the majority, R. Ishmael who was held hostage in Rome, and R. Akiba, supporter of Bar Koheba who suffered a martyr's death by the Romans, Elisha b, Abuiah, the heretic.

The third generation consisted of the disciples of R. Ishmael and R. Akiba: R. Meir, Simeon b. Johal to whom the authorship of the Zohar is ascribed.

R. Juda Hanasi, compiler of the Mishnah and possibly friend of Marcus Aurelius (161-180), belonged to the fourth generation, while R. Hiyya, author of the Tosephta, belonged to the fifth and last generation. -- H.L.G.

Mishnah, extra canonical: R. Juda Hanasi included in his Mishnah (now the Mishnah par excellence) selected materials from the older Mishnah-collections, particularly from that of R. Akiba (d. 135 A.D.) and his disciple, R. Meir. In fact, it is assumed that any anonymous statement in the Mishnah is R. Meir's (setam mathnithin R. Meir).

The vast traditions not included in the official Mishnah are known as Baraitha (extraneous). These Baraithas were ultimately collected in separate works.

Misology: (Gr. miseo: to hate; logia: proposition) A contempt for logic. -- V.F.
Misoneism: A term derived from the Greek, miso, I hate, and neos, new, employed by Lombroso (1836-1909) to express a morbid hatred of the new, or the dread of a new situation. -- J.J.R.
Mneme: (Gr. Mneme, memory) Term proposed by Semon (Die Mneme, 1904; Die mnemeschen Empfindungen, 1909) and adopted by B. Russell (Analysis of Mind) to designate the conservation in a living organism of the effects of earlier stimulation. Ordinary memory is interpreted as an instance of mnemic conservation. -- L.W.
Mnemic Causation: (Gr. mneme, memory) Type of causation of which memory is an instance, in which a present phenomenon (e.g. a present memory) is explained not only by its immediate antecedents but by a remote event in time (e.g. an earlier experience). See Mneme. -- L.W.
Mnemonics: (Gr. mnemonikos, pertaining to memory) An arbitrary framework or device for assisting the memory, e.g. the mnemonic verses summarizing the logically valid moods and figures of the syllogism. See J. M. Baldwin, Dictionary of Philosophy and Psychology, II, pp. 87-9. -- L.W.
Mo: Sometimes spelled Moh. (a) Mo Tzu. (b) Mohism. See Mo chia. (c) Followers of Mo Tzu. See Mo che. -- W.T.C.
Mo che: Neo-Mohists, followers of Mo Tzu in the third century B.C., probably organized as a religious or fraternal order, who continued the utilitarian humanism of Mo Tzu wrote the Mo Ching (Mohist Canons) which now form part of Mo Tzu; developed the seven methods of argumentation, namely, the methods of possibility, hypothesis, imitation, comparison, parallel, analogy, and induction; discovered the "method of agreement," which includes "identity, generic relationship, co-existence, and partial resemblance," the "method of difference," which includes "duality, absence of generic relationship, separateness, and dissimilarity," and the "joint method of differences and similarities;" refuted the Sophists (pien che) theory of distinction of quality and substance; and became the outstanding logical school in Chinese philosophy. -- W.T.C.
Mo chia: The School of Mo Tzu (Moh Tzu, Mo Ti, between 500 and 396 B.C.) and his followers. This utilitarian and scientific minded philosopher, whose doctrines are embodied in Mo Tzu, advocated:
  1. "benefit" (li), or the promotion of general welfare and removal of evil, through the increase of population and of benevolence and righteousness toward this practical objective, the elimination of war, and the suppression of wasteful musical events and elaborate funerals;
  2. "universal love" (chien ai), or treating others, their families, and their countries as one's own, to the end that the greatest amount of benefit will be realized;
  3. agreement with the superiors (shang t'ung);
  4. a method of reasoning which involves a foundation, a survey, and application (san piao);
  5. the belief in Heaven and the spirits both as a religious sanction of governmental measures and as an effective way of promotion of peace and welfare.
For the development of his teachings by his followers, see Mo che. -- W.T.C.
Modalism: (Lat. modus, mode) A theological doctrine, of the second and third centuries A.D., affirming the unity of substance and personality in God. The Son and the Holy Ghost are but "modes" of God the Father. Also known as Monarchism; adherents of this position were Patripassians or Sabellians. -- V.J.B.
Modality: (Kant. Ger. Modalität) Concerning the mode -- actuality, possibility or necessity -- in which anything exists. Kant treated these as a priori categories or necessary conditions of experience, though in his formulation they are little more than definitions. See Kantianism. -- O.F.K.

Modality is the name given to certain classifications of propositions which are either supplementary to the classification into true and false or intended to provided categories additional to truth and falsehood -- namely to classifications of propositions as possible, problematical, and the like. See Strict implication, and Propostitional calculus, Many-valued.

Or, as in traditional logic, modality may refer to a classification of propositions according to the kind of assertion which is contained rather than have the character of a truth-value. From this point of view propositions are classed as assertoric. (In which something is asserted as true), problematic (in which something is asserted as possible), and apodeictic (in which something is asserted as necessary). -- A.C.

Mode: (Lat. modus, measure, standard, manner)

(a) In Augustinism: a measure imprinted upon human minds by God, enabling man to know what is good and true.

(b) In mediaeval Aristotelianism: a determination of being-in-general to some limited condition; also, in Non-Thomism, an entitative component of a composite being, as "union" is called a mode combining matter and form in a thing (Olivi and Suarez).

(c) In Spinoza: "that which exists in, and is conceived through, something other than itself." These modes are determinations of the infinite Attributes of Divine Substance; of the attribute, Thought, the two chief modes are intellect and will; of the attribute, Extension, the chief modes are motion and rest. These modes are nothing apart from God's Substance; they are infinite from one point of view (natura naturans) and finite from another (natura naturata).

(d) In Locke: the simple mode of an idea is the manner of thinking in which one idea is taken several times over, e.g. a dozen; mixed modes of ideas are those types of ideation in which various non-similar simple ideas are combined by the mind so as to produce a complex idea which does not represent a substance: e.g. obligation, drunkenness.

(e) In statistics: see Mean. -- V.J.B.

Moderate Realism: See Realism.
Modus tollens: See Logic, formal, § 2.
Moha: (Skr.) Distraction, perplexity, delusion, beclouding of the mind rendering it unfit to perceive the truth, generally explained as attachment to the phenomenal; in Buddhism, ignorance, as a source of vice. -- K.F.L.
Mohammedanism: The commonly applied term in the Occident to the religion founded by Mohammed. It sought to restore the indigenous monotheism of Arabia, Abraham's uncorrupted religion. Its essential dogma is the belief in the absolute unity of Allah. Its chief commandments are: profession of faith, ritual prayer, the payment of the alms tax, fasting and the pilgrimage. It has no real clerical caste, no church organization, no liturgy, and rejects monasticism. Its ascetic attitude is expressed in warnings against woman, in prohibition of nudity and of construction of splendid buildings except the house of worship; condemns economic speculation; praises manual labor and poverty; prohibits music, wine and pork, and the portrayal of living beings. -- H.H.
Mohism: See Mo chia and Chinese philosophy.
Moksa: (Skr.) Liberation, salvation from the effects of karma (q.v.) and resulting samsara (q.v.). Theoretically, good karma as little as evil karma can bring about liberation from the state of existence looked upon pessimistically. Thus, Indian philosophy early found a solution in knowledge (vidyd, jnana) which, disclosing the essential oneness of all in the metaphysical world-ground, declares the phenomenal world as maya (q.v.). Liberation is then equivalent to identification of oneself with the ultimate reality, eternal, changeless, blissful, or in a state of complete indifference either with or without loss of consciousness, but at any rate beyond good and evil, pleasure and pain. Divine grace is also recognized by some religious systems as effecting moksa. No generalization is possible regarding the many theories of moksa, its nature, or the mode of attaining it. See Nirvana, Samadhi, Prasada. -- K.F.L.
Molecule: A complex of atoms, which may be of the same kind or different. Thus there may be molecules of elements and molecules which are compounds. So far no single molecule has been synthesized larger than the wave length of light so that it could be rendered visible. Molecular aggregates, however, exist, which may be looked upon in a sense as giant molecules visible under the microscope. -- W.M.M.
Monad: (Gr. Monas, a unit)
  1. In Greek usage, originally the number one. Later, any individual or metaphysical unit.
  2. Bruno named his metaphysical units monads to distinguish them from the Democritean atoms. The monads, centers of the world life, are both psychic and spatial individuals.
  3. Leibniz (borrowing the term possibly from Augustine, Bruno or Protestant scholastics) identified the monads with the metaphysical individuals or souls, conceived as unextended, active, indivisible, naturally indestructible, teleological substances ideally related in a system of pre-established harmony.
  4. By extension of Leibnizian usage, a soul, self, metaphysical unit, when conceived as possessing an autonomous life, and irrespective of the nature of its relations to beings beyond it.
-- W.L.
Monadology: (also Monadism) The doctrine of monads, the theory that the universe is a composite of elementary units. A monad may also be a metaphysical unit. The notion of monad can be found in Pythagoras, Ecphantus, Aristotle, Euclid, Augustine, et al. Plato refers to his ideas as monads. Nicolaus Cusanus regards individual things as units which mirror the world. Giordano Bruno seems to have been the first to have used the term in its modern connotation. God is called monas monadum; each monad, combining matter and form, is both corporeal and spiritual, a microcosm of the whole. But the real founder of monadology is Leibniz. To him, the monads are the real atoms of nature, the elements of things. The monad is a simple substance, completely different from a material atom. It has neither extension, nor shape, nor divisibility. Nor is it perishable. Monads begin to exist or cease to exist by a decree of God. They are distinguished from one another in character, they "have no windows" through which anything can enter in or go out, that is, the substance of the monad must be conceived as force, as that which contains in itself the principle of its changes. The universe is the aggregate, the ideal bond of the monads, constituting a harmonious unity, pre-established by God who is the highest in the hierarchy of monads. This bond of all things to each, enables every simple substance to have relations which express all the others, every monad being a perpetual living mirror of the universe. The simple substance or monad, therefore, contains a plurality of modifications and relations even though it has no parts but is unity. The highest monad, God, appears to be hoth the creator and the unified totality and harmony of self-active and self-subsistent monnds. -- J.M.
Monadology, The New: Expression used by Renouvier for his type of personalism. -- R.T.F.
Monergism: The view that the human will contributes nothing to its regeneration but that this is the work of one factor, the Divine. -- V.F.
Monism: (Gr. mones, single)

(a) Metaphysical: The view that there is but one fundamental Reality; first used by Wolff. (A Universe.) Sometimes spoken of as Singularism. The classical ancient protagonist of an extreme monism is Parmenides of Elea; a modern exponent is Spinoza. Christian Science is an example of a popular contemporary religion built on an extreme monistic theory of reality. Most metaphysical monists hold to a modified or soft monistic theory (e.g. the metaphysics of Royce).

(b) Epistemological: The view that the real object and the idea of it (perception or conception) are one in the knowledge relation. (e.g. the school known as New Realism; extreme mystics.) -- V.F.

Monism, neutral: The doctrine that regards neither mind nor matter as ultimates. -- H.H.
Mono-personalism: A term ascribed by Kohnstamm to Stern's doctrine of an impersonal-God. -- R.T.F.
Monosyllogism: See Polysyllogism.
Montague, William Pepperell: (1873-) Professor of Philosophy at Columbia University. He was among the early leaders of the neo-realist group. He developed views interpreting consciousness, variation and heredity In mechanical terms. He has characterized his view as animistic materialism. Among his best known works are: The Ways of Knowing or the Methods of Philosophy, Belief Unbound, A Promethean Religion for the Modern World and his most recent, Knowledge, Nature and Value - A Philosophy of Knowledge, Nature and Value. See Neo-Realism. -- L.E.D.
Montaigne, Michel De: (1533-1592) French novelist whose renowned Essays are famous for his tolerant study of himself and through himself of mankind as a whole. He doubts the possibility of certain knowledge and recommends a return to nature and revelation. He was a keen observer of the frailties of human nature and has left among the essays crowned masterpieces of insight and delight. -- L.E.D.
Montanism: A Christian movement dated about the middle of the second century centering about the teachings of the prophet Montanus and two women, Prisca and Maximilla. They distinguished between mortal and venial sins, practiced ascetic ideals and believed themselves to possess the pure type of Christian living on the authority of a special revelation from the Holy Spirit. The movement faded out about the 4th century. Tertullian, famous Latin churchman, was for a time a member. -- V.F.
Montesquieu, Charles De Secondat: (1689-1755) French historian and writer in the field of politics. His Lettres persanes, thinly disguise trenchant criticism of the decadence of French society through the letters of two Persian visitors. His masterpiece, L'Esprit des Lois, gives a political and social philosophy in pointing the relation between the laws and the constitution of government. He finds a relation between all laws in the laws of laws, the necessary relations derived from the nature of things. In his analysis of the English constitution, he stressed the separation of powers in a manner that has had lasting influence though based on historical inaccuracy. -- L.E.D.
Monumentality: Artistic character suggesting the sense of grandeur, even though small in size. -- L.V.
Moods of the syllogism: See figure (syllogistic), and logic, formal, § 5.
Moore, George Edward: (1873-) One of the leading English realists. Professor of Mental Philosophy and Logic at Cambridge. Editor of "Mind." He has been a vigorous opponent of the idealistic tradition in metaphysics, epistemology and in ethics. His best known works are: Principia Ethica, and Philosophical Studies. Belief in external things having the properties they are normally experienced to have. Founder of neo-realistic theory of epistemological monism. See Neo-Realism. -- L.E.D.
Moral Argument for God: Basing the belief upon the fact of man's moral nature which compels him to make moral assertions about the world and destiny. The argument assumes many forms. Kant held, e.g., that the moral consciousness of man is a priori and compels him willy nilly to assert three great affirmatives; his freedom, immortality, and the existence and high character of God. -- V.F.
Moral Judgment:

(a) good or bad judgment in moral matters,

(b) any ethical judgment, especially judgments of good and bad, right, wrong, and duty (see ethics). For Kant a moral judgment or imperative is one which enjoins a categorical imperative as contrasted with the hypothetical imperatives of skill and prudence. -- W.K.F.

Moral Law: (in Kant's ethics) That formula which expresses the necessity of an action done from duty in terms of one's own reflection. -- P.A.S.
Moral Optimism: See Religious meliorism.
Moral Order: The phrase may refer to the order or harmony which is often said to be an essential part of the good or virtuous life, but it is generally used in such expressions as "the moral order" or "belief in the existence of a moral order," which refer either (a) to a conceived transcendental order of what ought to be, an intelligible moral universe or realm of values or ends, an a priori system of objective ethical truth -- which somehow underlies this natural or existential order as Its basis or overarches it as its pattern and law-giver, or (b) to a belief that there is a moral direction in the affairs of the world. -- W.K.F.
Moral Philosophy: See Ethics.
Morals: The term is sometimes used as equivalent to "ethics." More frequently it is used to designate the codes, conduct, and customs of individuals or of groups, as when one speaks of the morals of a person or of a people. Here it is equivalent to the Greek word ethos and the Latin mores. -- W.K.F.
Moral Sense School, The: The phrase refers primarily to a few British moralists of the late 17th and early 18th centuries, notably Shaftesbury and Hutcheson, who held the organ of ethical insight to be, not reason, but a special "moral sense," akin to feeling in nature. -- W.K.F.
Moral Virtues: (Gr. aretai ethikai) In Aristotle's philosophy those virtues, or excellences, which consist in the habitual control of conduct by rational principle; as distinct from the intellectual virtues, whose end is the knowledge of principles. See Artstotelianism; Dianoetic Virtues. -- G.R.M.
More, Paul Elmer: An American literary critic and philosopher (1864-1937), who after teaching at Bryn Mawr and other colleges, edited The Nation for several years before retiring to lecture at Princeton University and write The Greek Tradition, a series of books in which he argues for orthodox Christianity on the basis of the Platonic dualism of mind-body, matter-spirit, God-man. In The Sceptical Approach to Religion he gave his final position, as ethical theism grounded on man's sense of the good and consciousness of purpose, and validated by the Incarnation of God in Christ. -- W.N.P.
More, Thomas: (1478-1535) Lord chancellor of England. One of the leading humanists along with his friends Colet and Erasmus. He was beheaded for his refusal to recognize the king as the head of the church. In his classic, Utopia, he has left a vision of an Ideal state in which war and all glories connected with it were abhorrent. The prince and all magistrates were elected. Nothing is private. All work and all enjoyment are shared. There is no oppression, neither industrial nor religious. The work gives no philosophical analysis of the nature of the state, but merely an exposition of what the author conceived to be and what we have since come to call utopian. -- L.E.D.
Mores: (Lat. mos, usage) Customs, Folkways, Conventions, Traditions. -- A.J.B.
Motion: (Lat. moveo, move) Difference in space. Change of place. Erected into a universal principle by Heraclitus. Denied as a possibility by Parmenides and Zeno. Subdivided by Aristotle into alteration or change in shape, and augmentation or diminution or change in size. In realism: exclusively a property of actuality. -- J.K.F.
Motion: (in Scholasticism) The passing of a subject from potency to act. -- H.G.
Motivation: Designation of the totality of motives operative in any given act of volition or of the mechanism of the operation of such motives. See Motive. -- L.W.
Motive: (Lat. motus, from movere, to move) An animal drive or desire which consciously or unconsciously operates as a determinant of an act of volition. -- L.W.
Mo Tzu: (Mo Ti, between 500 and 396 B.C.) Founder of Mohism (Mo chia), studied Confucianism, later repudiated it, especially its doctrines of Fate and elaborate rituals. As a high officer in the state of Sung (in present Honan, most probably his native state) he "skillfully carried out military defense and practiced economy." He vigorously defended religious beliefs and practices, became the chief promoter, if not the only founder, of religion in ancient China. His pupils became an organized religious group, or possibly a society of people who had been punished with branding and had become slaves, which is what the word mo in one sense meant. Mo Tzu (Eng. tr. by Y. P. Mei: The Ethical and Political Works of Motse) contains his teachings recorded by his followers. -- W.T.C.
Mou: The method of parallel in argumentation. See Pien. -- W.T.C.
Mukti: (Skr.) Liberation. Same as moksa (q.v,). -- K.F.L.
Multiple Inherence, Theory of: The view that qualities, secondary qualities in particular can inhere in a triadic or multiple relationship. (Broad.) -- H.H.
Multiplicative axiom: See choice, axiom of.
Multiplicity: The doctrine of the plurality of beings, or the manifoldness of the real, denied by the Eleatics, who contended that the multiplicity of things was but an illusion of the senses, was defended by Aristotle who maintained that the term, being, is only a common predicate of many things which become out of that which is relatively not-being by making the transition from the potential to the actual. -- J.J.R.
Mundus intelligibilis: (Lat.) The world of intelligible realities; Plato's realm of Ideas, or St. Augustine's rationes aeternae in the Divine Mind. Each species of things is represented here by one, perfect exemplar, the pattern for the many, imperfect copies in the world of sense. See Mundus sensibilis. -- V.J.B.
Mundus sensibilis: (Lat.) The world of things perceived by the human senses. In Platonism, Neo-Platonism, Augustinism, and some Renaissance thought (Ficino) this realm of sensible objects was regarded as an imitation of the superior world of Intelligible realities. See Mundus intelligibilis. -- V.J.B.
Muni: (Skr.) A philosopher, sage, especially one who has taken upon himself observance of silence. -- K.F.L.
Münsterberg, Hugo: (1863-1916) German-born philosopher and psychologist, for many years professor of psychology at Harvard University. One of the advance guard of present axiological development, he is affiliated with the ideological criticism stemming from Fichte. Agrees that pure reason is endowed with a priori principles which enable it to achieve objective super-individual affirmations which transcend and which can neither be confirmed nor denied by psychological investigation. Main works: Der Ursprung d. Sittlichkeit, 1889; Beiträge z. Experim. Psychol., 1889-92; Psychol. u. Lehre, 1906; Philos. der Werte, 1908 (Eng. tr. The External Values); Grundzüge d. Psychotechnik, 1914. -- H.H.
Mutazilite: (Ar. seceders) Member of a Shiite sect of Islam dating from the 8th century, which stood for free will and against divine predestination.
Mysticism: Mysticism in its simplest and most essential meaning is a type of religion which puts the emphasis on immediate awareness of relation with God, direct and intimate consciousness of Divine Presence. It is religion in its most acute, intense and living stage. The word owes its origin to the Mystery Religions. The initiate who had the "secret" was called a mystes. Early Christians used the word "Contemplation" for mystical experience. The word "mystical" first came into use in the Western World in the writings ascribed to "Dionysius the Areopagite", which appeared at the end of the fifth century.

"Dionysius" used the word to express a type of "Theology" rather than an experience. For him and for many interpreters since his day, Mysticism stands for a religious theory or system, which conceives of God as absolutely transcendent, beyond reason, thought, intellect and all approaches of mind. The way up is a via negativa. It is Agnostia, "unknowing knowing". This type of Mysticism, which emerged from the Neo-Platonic stream of thought might be defined as Belief in the possibility of Union with the Divine by means of ecstatic contemplation.

The word, furthermore, has been loosely used for esoteric, gnostic, theosophical types of "knowledge", not capable of verification. It has been used, too, for the whole area of psychic phenomena and occult happenings, borderland phenomena. The result of this confusion has been that in scientific laboratories the word mysticism often connotes spurious knowledge, occult lore or abnormal phenomena. The Germans use the word Mysticismus for this dubious type of knowledge and Mystik for the loftier types of experience.

It is not historically sound to find the essentia of Mysticism in ecstasy, or in a via negativa, or in some kind of esoteric knowledge, or in mysterious "communications". The essentia of Mysticism is the experience of direct communion with God.

Henri Delacroix, Etude d'Histoire et de Psychologie du Mysticisme (Paris, 1908); Baron Friedrich von Hügel, The Mystical Element of Religion (London, 1908); Evelyn Underhill, Mysticism. (London, 1911); William James, Varieties of Religious Experience (New York, 1902); Rufus M. Jones, Studies in Mystical Religion (London, 1909). -- R.M.J.

Myth: (Gr. mythes, legend) The truth, symbolically, or affectively, presented. Originally, the legends of the Gods concerning cosmogonical or cosmological questions. Later, a fiction presented as historically true but lacking factual basis; a popular and traditional falsehood. A presentation of cosmology, employing the affective method of symbolic representation in order to escape from the limitations of literal meaning. -- J.K.F.