L

Labour

Labour is, in the first place, a process in which both man and nature participate, and in which man of his own accord starts, regulates, and controls the material reactions between himself and nature. (Marx, Capital, Vol. 1, p. 177.) By acting on external nature, man changes both nature and himself. In changing nature he achieves his conscious purpose, adapts natural objects to his requirements. The labour process includes three things: (1) man's purposeful activity, or labour proper; (2) the object of labour; (3) the instruments of production with which man acts on this object.

Labour is the primary condition of human existence. Labour supplies man with the necessary means of subsistence and, moreover, it created man himself. It was thanks to labour that man raised himself out of the animal world. One of the essential distinctions between man and the animal is that the animal makes use of ready products of nature, whereas man makes nature serve his purposes thanks to his labour, changes it and subordinates it to his needs.

In different socio-economic formations labour appears in different forms which indicate the level of the development of the social relations at the given epoch. In the primitive-communal system labour is common, collective by its nature, and ownership of the means of production and its fruits is also common. Under this system there is no exploitation of the labour of others. In all the subsequent antagonistic socio-economic formations man's labour is subjected to exploitation: the slave's labour in slave society, the serf's labour under feudalism, and the worker's under capitalism. Only the socialist revolution releases the worker from exploitation. Under socialism and especially under communism labour has genuine purpose—to serve not only as the source of existence, but also as the source of creative inspiration and enjoyment (see Communist Labour; Antithesis of Mental and Physical Labour; Socialism and Communism).

Labriola, Antonio (1843–1904)

First Italian Marxist; writer, and philosopher.

Labriola became a Marxist after having rejected bourgeois democratism and the idealism of Hegel. Labriola asserted that with the advent of historical materialism communism had ceased to be a "doubtful hypothesis" and could now be regarded as the inevitable "final result and outcome of the class struggle of our times". Labriola regarded the publication of the Manifesto of the Communist Party as a revolution in the social sciences. Referring to the derived character of the superstructure, Labriola nevertheless refuted economic materialism, and held that only in the final count the economic element is instrumental in determining the trend of thinking in art, religion, and the various fields of human knowledge.

He criticised the theories of Nietzsche, E. Hartmann, Croce, and Neo-Kantianism. His evaluation of colonialism was erroneous in certain respects. His best work, Saggi intorno alla concezione materialistica della storia (1895–98; 1925—posthumous edition), greatly influenced the thinking of Gramsci and Togliatti.

Lafargue, Paul (1842–1911)

French socialist, active in the international working-class movement, disciple of Marx and Engels.

His main work was in philosophy and political economy, the history of religion and morals, literature and language. Lenin said that Lafargue was one of the most gifted propagators of the ideas of Marxism. Having become a member of the First International in 1866, Lafargue freed himself of Proudhonist and positivist views. He took an active part in the affairs of the Paris Commune; later associated with Jules Guesde; both of them became leaders of the French Workers' Party. Lafargue fought anarchism and the opportunist theory of capitalism "growing peacefully" into socialism, and criticised the reformist and nationalist mistakes committed by Guesde.

In his major philosophical work Le determinisme economique de Karl Marx (1909) Lafargue stressed the objective nature of the laws of history and revealed the interconnection between economics and the superstructure of society. He opposed revisionist attempts to "synthesise" Marxism with the doctrine of Kant and reconcile materialism with idealism. He also opposed Social-Darwinism and other unscientific theories. His book Problems of Cognition (1910) was a profound and witty repudiation of agnosticism. Lafargue's anti-religious pamphlets Pius IX in Heaven, The Myth of Adam and Eve, and La religion du capital exposed religion as a defender of capitalism. His reminiscences of Marx, giving a picture of the great fighter and thinker, are of considerable interest.

Lafargue's works, despite a number of defects (oversimplification of certain problems, underestimation of the active part played by the superstructure, failure to fully comprehend the specific features of the imperialist stage of capitalism, etc.) played an important part in the struggle against reactionary ideology.

Lamarck, Jean Baptiste (1744–1829)

French naturalist.

In his Philosophie Zoologique (1809) he expounded the first comprehensive theory of the evolutionary development of the living world. Having summed up the results achieved by natural science in his day, Lamarck advanced the proposition that changes in the environment cause organisms to acquire new qualities, which are transmitted by heredity. He thus attacked the metaphysical theory of the permanence of species and also the Cuvier catastrophe theory. According to Lamarck, the animate arises from the inanimate with the aid of special material "fluids". At first the simplest forms are evolved and from these more complex forms gradually develop.

Lamarck held, however, that matter is incapable of self-propulsion and that the development of both the animate and the inanimate is guided by a "divine innate purpose". The teleological side of Lamarck's doctrine was taken up by the Neo-Lamarckists, who maintained that the mind plays a predominant part in the process of evolution. Lamarck's idea of the role of environment and heredity in evolution was used by Darwin in his theory of evolution.

La Mettrie, Julien Offroy de (1709–1751)

French materialist philosopher and doctor.

His chief works were L'homme machine (1747) and Le Systeme d'Epicure (1750). He was victimised by both the clergy and the secular authorities. La Mettrie's teaching is based on the physics of Descartes and the sensualism of Locke. La Mettrie recognised an internally active material substance possessing extension and sensation. The forms of matter were the organic, vegetable and animal kingdoms (man being included in the animal kingdom), between which, according to La Mettrie, there were no qualitative differences.

La Mettrie denied the universality of thought, the ability to think being common only to man and arising as the result of a complex organisation of matter. La Mettrie understood the ability to think as the comparison and combination of conceptions arising on the basis of sensation and memory. A representative of the school of mechanistic materialism, La Mettrie gradually moved nearer to the theory of evolution. He held that the enlightenment and the actions of outstanding individuals are the main causes of historical development and advocated enlightened absolutism. His atheism was limited and he was in favour of preserving religion for the common people.

Langevin, Paul (1872–1946)

French physicist, active in public life, Communist, advocate of dialectical materialism, professor of Paris University, member of the Paris Academy of Sciences, and foreign member of the Academy of Sciences of the USSR.

Author of several major researches on the ionisation of gases, the theory of para- and dia-magnetism, etc., Langevin gave a scientific interpretation of the transformations propounded by Lorentz, of the defect of mass, of the wave-corpuscular dualism, of the statistical laws appertaining to microphenomena and other matters. He also criticised positivist theories, indeterminism, and subjectivist interpretations of the uncertainty principle. Towards the end of his life he became acquainted with Marxism-Leninism and valued it as being of great importance to natural science. According to Langevin, dialectical materialism makes it possible to widen and enrich the experimental method itself.

Language

Sign-system of any physical nature, fulfilling the cognitive and communicative functions in the process of human activity.

Language can be both natural and artificial. Natural language is the language of everyday life, serving as a form of thought expression and as a means of communication among men. Artificial language is a language created by men for some exclusive needs (the language of mathematical symbols, the language of physical theories, the different systems of signalling, etc.). Language is a social phenomenon. It arises in the course of development of social production, of which it is an indispensable aspect—a means of co-ordinating human activity. Physiologically, language acts as a second signal system, which Pavlov called a specific addition to the human psyche.

Language is a form of existence of thought and a form of its expression. At the same time it plays an important role in the formation of consciousness. Consciousness does not and cannot exist outside of language. The language sign, conventional in relation to what it designates by virtue of its physical nature, is nevertheless socially conditioned by the content of consciousness, which in language is the linguistic content (the lexical and grammatical meaning of the language sign). Language is a means of fixing and preserving the accumulated knowledge and passing it on from generation to generation. Only language makes possible the existence of abstract thought. The presence of language is a necessary condition for the thought's generalising activity (see Generalisation). "Every word (speech) generalises" (Lenin).

And yet language and thought are not identical. After it has arisen, language becomes relatively independent, obeying specific laws differing from those of thought. For this reason there is no identity between concept and word, judgement and sentence. Language, moreover, is a definite system, which has an inner "structure" outside which the nature and the meaning of a language sign cannot be understood. In connection with the growing role of theoretical studies in recent decades, more interest is shown in the study of the laws of artificial, formal languages, of their logical syntax and logical semantics. Contemporary neo-positivism absolutises the role and significance of these studies and tries, incorrectly, to reduce the problems involved in philosophical studies to a logical analysis of language.

Lassalle, Ferdinand (1825–1864)

Opportunist figure in the German working-class movement, who supported Bismarck.

Born into a rich merchant family, he took part in the revolution of 1848. As one of the organisers of the All-German Workers' Union, he repudiated the class struggle and compromised with the Prussian reactionaries. His philosophy was idealist and eclectic. He interpreted Hegel scholastically and used his philosophy to justify his own conciliatory political line. In sociology Lassalle held Malthusian views (see Malthusianism) and was one of the authors of the anti-scientific and reactionary "iron law of wages", according to which any struggle on the part of the workers for wage increases was considered futile. He regarded the state as an organisation standing above classes.

Lassalle's views were criticised by Marx in his Criticism of the Gotha Programme and by Lenin in the Philosophical Notebooks. Their estimation of Lassalle's work as an agitator, however, was favourable.

Lavrov, Pyotr Lavrovich (1823–1900)

Theoretician of Narodism, creator of the Russian "subjectivist school" in sociology, and writer.

Son of a landowner. Participated in the work of such illegal revolutionary organisations as Zemlya i Volya (Land and Freedom) and Narodnaya Volya (People's Will). Member of the First International. While in London, became acquainted with Marx and Engels. Wrote and spoke on problems of philosophy, sociology, ethics, history of public opinion, and art. Lavrov's chief interest lay in the ways of the revolution in Russia. Admitting the validity of the theory of socialist revolution for the developed capitalist countries of Europe, Lavrov was sceptical about its applicability to the conditions prevailing in Russia.

His sociopolitical doctrine (influenced by Herzen) rested on two interdependent concepts: (1) the socialist nature of the Russian peasant community, and (2) the special role of the intelligentsia in the Russian liberation movement. These concepts determined Lavrov's whole philosophico-historical conception. Referring to the characteristic features of history "as a process", Lavrov distinguished the concept of culture and the concept of civilisation. Culture is of community origin and is reflected in a people's psychology and the characteristic features of its daily life and social relations. The degree of receptivity to reasoning rather than the nature of thinking is the criterion of culture. According to Lavrov, the culture of society is environment given by history for thinking.

Civilisation is a conscious developing principle; it is manifested in a progressive replacement of cultural forms. "The critically thinking individuals" are the vehicles of civilisation. The measure of the critical enlightenment of human consciousness (primarily moral consciousness) is the criterion of progress. Social development implies the growth of the individual's consciousness and of the solidarity between individuals. Philosophically, Lavrov was eclectic, combining materialism and idealism. Influenced by positivism and agnosticism, he gravitated to subjective idealism.

Main works: Istoricheskiye pisma (Historical Letters), 1869; Tsel i znacheniye klassifikatsii nauk (The Purpose and Importance of the Classification of Sciences), 1886; Zadachi positivisma i ikh resheniye (Tasks of Positivism and Their Solution), 1886; Vazhneishiye momenty v istorii mysli (Essential Moments in the History of Thought), 1899.

Law

1. Philosophical Definition

An inner essential connection of phenomena which determines their necessary, natural development. Law expresses a definite order of causal, necessary and stable connections between phenomena or properties of material objects, of recurring essential relations, in which the change of some phenomena causes a definite change in others. The concept of law is close to the concept of essence, which constitutes the sum total of inner connections and processes determining the major features and tendencies in the development of objects. Knowledge of a law presupposes transition from appearance to essence (see Essence and Appearance) and always proceeds through abstract thinking, abstraction from many purely individual and non-essential features of phenomena.

There are three main groups of laws: (1) specific or particular; (2) general, for large groups of phenomena; (3) universal. The first group expresses relations between specific phenomena, or particular properties of matter. The second group is displayed in a wide range of conditions and characterises relations between general properties of large aggregates of objects and phenomena (for example, in physics, laws of the conservation of mass or the electric charge and in biology, law of natural selection, etc.). The third group represents the main dialectical laws of the world which express the relations between universal properties or trends of development of matter. They act as the universal principles of all being, as the common elements which are manifested in many laws of the first and second group. But the distinctions between these laws are relative and mobile.

The operation of general laws is manifested in particular, specific laws and the general laws are cognised through the generalisation of concrete phenomena, including specific laws. Another distinction between laws is that some operate differentially in time, in such a way that the ensuing consequences are fulfilled in each, sufficiently small, span of time, while others operate integrally, i.e., their consequences are fulfilled not at each given moment, but only over a sufficiently big span of time or when the system changes as a whole. Such are statistical laws. Operation of law depends on the existence of the corresponding conditions. The creation of the latter helps to turn the consequences of law from possibility into reality.

In society, application of laws presupposes the activity of people who are capable of creating or destroying—consciously or unconsciously—the conditions for the operation of laws. People, however, do not create laws, they only restrict or extend the scope of their operation according to their needs and interests. As for laws as such, they exist objectively, independent of the consciousness of people, as an expression of the relations between properties of bodies or different tendencies of development.

2. Legal Definition

The will of the ruling class as embodied in its own specific system of jurisprudence and determined by the material conditions and interests of that class. Law is drawn up as a system of rules and standards of behaviour, established or sanctioned by the state power. The specific feature of legal rules is that their fulfilment is forcibly ensured by the state power. Being part of the superstructure, law is determined by the given society's dominant relations of production, which it sanctions together with the social relations based on them.

The historical type of law corresponds to the appropriate socio-economic formation. The common feature of the slave-owning, feudal and bourgeois law is the consolidation of the master and subordinate relations, the relations of exploitation, based on private property. A qualitatively new legal system is found in socialist law, which legally embodies production relations as characterised by friendly collaboration and mutual aid and which, based on socialist ownership, provides a firm foundation for the building of communism. Socialist law is the will of the people given the statutory force; for the first time in history it establishes and really guarantees truly democratic liberties. It differs from bourgeois law in that it provides the working people with genuine rights guaranteed by all the means at the disposal of the state.

Laws, Statistical and Dynamic

Forms of regular causal connection between phenomena.

Dynamic laws are a form of causal connection in which a given condition of a system determines unequivocally all its subsequent conditions, knowledge of the initial conditions allowing an accurate prediction of the further development of the system. Dynamic laws operate in all autonomous systems which are but insignificantly dependent on outside influences and consist of a relatively small number of elements. For example, they determine the character of the motion of planets in the solar system.

Statistical laws are a form of causal connection in which a given state of a system determines all its subsequent conditions not unequivocally but with a definite degree of probability, which is the objective measure of the possible realisation of the tendencies of change implanted in the system in the past. Statistical laws operate in all non-autonomous systems consisting of a large number of elements dependent on continuously changing external conditions.

Strictly speaking, every law is statistical, since matter is inexhaustible and every system consists of a countless number of elements. Besides, every system is not closed and interacts with the surrounding medium. This is why every dynamic law is statistical with a probability of realisation approaching 1, because external influences and many intrinsic connections in the system do not exert any substantial influence on it. Statistical laws cannot in principle be reduced to dynamic laws, due to (1) the inexhaustibility of matter and the systems being not closed, (2) the impossibility of realising many of the tendencies of development, and (3) the emergence in the process of development of possibilities and tendencies of qualitatively new states. This is why every complex process of development is governed by statistical laws, whereas dynamic laws are no more than an approximate expression of separate stages of this process.

Leap

A stage in the radical changes in a thing or phenomenon, the moment or period when the old quality is changed into the new as a result of quantitative changes.

In comparison with the preceding, evolutionary stage of development, the leap represents more or less apparent, relatively quick changes. The destruction of an old and the coming into being of a new quality, as also every possible qualitative change, can be accomplished only by a leap. But the leap may take exceptionally diverse forms, depending on the character of a phenomenon and on the conditions in which it develops. Essentially, every phenomenon assumes a new quality in a way of its own. But all these developments can be divided into two relatively definite types: sudden and gradual leaps.

The former take place in such a manner that the old quality is fully changed at once (e.g., the change-over of certain elementary particles into others; in social life, the October Revolution in Russia was an example of such a sudden and tempestuous leap). The latter takes place in such a way that the existing thing or phenomenon changes by parts, by individual elements, until, as a result of gradual mutation, it is transformed as whole.

In social life, the first type of leap is characteristic of antagonistic formations, in which the dominant class is an obstacle to the historically urgent transition from the old to a new system. Such a transition (for instance, from capitalism to socialism) can be accomplished only by a political revolution. The second type of leap is typical of non-antagonistic systems, in which all the basic social forces are interested in society's progressive development. This is what Marx had in mind when he foretold that in a classless society social evolution would cease to be a political revolution.

The Programme of the Communist Party of the Soviet Union proceeds from the fact that gradual qualitative change is a law of communist construction. The creation of the material and technical basis of communism, the obliteration of class and other distinctions, the withering away of the state, the education of the new man, are all decisive revolutionary turns in the development of socialist society, which do not take place at once and all of a sudden, but gradually and continuously. Communism grows out of socialism, is its direct continuation. It would be incorrect and erroneous to think that communism will appear all of a sudden. The transition from socialism to communism takes place continuously. Nevertheless the gradual transition from socialism to communism must not be considered as a kind of slow motion. On the contrary, it is a period in which all aspects of social life develop rapidly. Besides, such a form of development does not preclude quick, sudden leaps in some fields, for instance, in technology and science.

Lebedev, Pyotr Nikolayevich (1866–1912)

Russian scientist, founder of the first Russian school of physicists.

He conducted important researches in various fields of physics such as acoustics, electricity, and optics. His greatest achievement, which brought him world renown, was the discovery and measurement of the pressure of light on solid bodies and gases, which furthered the development of the electromagnetic theory of light. He showed that light is one of the forms of existence of matter. Lebedev's researches helped to reveal the falseness of energism and Machism.

Left Hegelians

See Young Hegelians.

Legal Marxism

The reflection of Marxism to be found in bourgeois literature, the liberal-bourgeois distortion of the actual doctrine. It arose in the 1890s, when Narodism had been ideologically routed by Lenin, Plekhanov, and other Marxists and Marxism was becoming widespread in Russia. Certain bourgeois intellectuals became temporary "fellow travellers" of the working-class movement. Their writings were published in legal newspapers and journals, that is, publications appearing with the sanction of the government, and they thus became known as "legal Marxists". They opposed the Narodniks in the name of Marxism. Lenin, however, said that for the "legal Marxists" the break with Narodism meant going over from petty-bourgeois or peasant socialism not to proletarian socialism but to bourgeois liberalism. Struve, M. Tugan-Baranovsky, and Berdyayev were prominent representatives of Legal Marxism. They attempted to adapt the workers' movement to the interests of the bourgeoisie, lavished praises on the capitalist system, and instead of calling for revolutionary struggle advocated learning from capitalism. Legal Marxism repudiated the principal Marxist tenets: the doctrine of proletarian revolution and the dictatorship of the proletariat.

Lenin conducted an irreconcilable struggle against Legal Marxism, though in order to hasten the downfall of Narodism he allowed a temporary agreement with the "legal Marxists". In his book The Economic Content of Narodism and the Criticism of It in Mr. Struve's Book (1894-95), Lenin showed the anti-Marxist essence of Legal Marxism and made a profound criticism of bourgeois objectivism, to which he counterposed the Party spirit of revolutionary Marxism. In philosophy the "legal Marxists" usually adopted the Kantian positions (see Vekhism).

Leibniz, Gottfried Wilhelm (1646–1716)

German philosopher, an objective idealist. The first president of the Berlin Academy of Sciences. From 1676 till his death in 1716, he was librarian at Hanover. Combining a profound knowledge of both mathematics (he was one of the inventors of the differential calculus) and physics (he anticipated the law of the preservation of energy), he was also a geologist, biologist, and historian.

The philosophy of Leibniz should be regarded as an attempt to achieve a synthesis between the ideas of mechanistic materialism (see Descartes and Hobbes) and the Aristotelian scholastic doctrine of active substantial forms. In explaining reality he strove to unite the mechanistic principle with the theory of monads, which he propounded in his Monadologie (1714). The monads, according to Leibniz, are the indivisible, spiritual substances, of which the whole Universe is composed. Infinite in number, all monads are percipient and self-active.

Leibniz was one of the founders of German idealist dialectics. As Lenin observed, Leibniz "through theology arrived at the principle of inseparable connection of matter and motion" (Vol. 38, p. 379). In explaining motion, however, Leibniz came up against a contradiction. The monads, in his view, cannot have any causal relation with each other and yet they form a harmonious developing and moving world, which is regulated by a "pre-established harmony" depending on the supreme monad (the absolute, God). The concept of pre-established harmony formed the most reactionary part of Leibniz's philosophy, as expounded in his Theodicee (1710).

Leibniz's theory of knowledge—idealist rationalism—is aimed against the sensualism and empiricism of Locke. To Locke's postulate "There is nothing in the mind which has not been in the senses", Leibniz added: "Except the intellect itself". Not sharing Locke's view that the mind is but a blank sheet (tabula rasa) and renouncing sensory experience as the source of the universality and necessity of knowledge, Leibniz contends that only reason can provide this source, and that the soul has from time immemorial possessed the principles of the various concepts and postulates, which are only awakened by external objects (Nouveaux Essais sur l'entendement humain, 1704, published in 1765). In effect, Leibniz modified the Cartesian doctrine on innate ideas, which he described as residing in the mind like the veins of rock in a slab of marble.

Leibniz held that the criteria of truth are clarity and absence of contradiction. Thus to test the truths of reason it was enough to apply the logic of Aristotle (the laws of identity, contradiction, and the excluded middle); while the law of sufficient reason was needed to test "truths of fact". Leibniz is considered (by Bertrand Russell and others) to have been the founder of mathematical logic. His view of the world expressed the ideology of the compromise between the German bourgeoisie and feudalism.

Lemma

From Greek "proposition". In mathematics, a theorem proved for the sake of its use in proving another theorem; in logic, a conditional conclusion (premiss of a syllogism). Depending on the number of consequences involved in the larger premiss (according to the members of disjunctive propositions in the smaller), Lemma becomes a dilemma, trilemma or multilemma. The most common form of Lemma is the dilemma, implying the need to choose between two alternatives.

Lenin, Vladimir Ilyich (1870–1924)

Continuator of Marx and Engels, leader of the Russian and international proletariat, founder of the Communist Party of the Soviet Union and the Soviet state. Born in Simbirsk (now Ulyanovsk). After finishing the gymnasium (secondary school) in 1887, he entered the law faculty of Kazan University, but was arrested for his activities in the student movement, banished from the city and placed under police surveillance in the village of Kokushkino. In 1891, he graduated as an external student at St. Petersburg University. In Kazan (1888-89) and Samara (1889-93) Lenin studied Marxism and became a Marxist, organising the first Marxist circle in Samara.

Arriving in St. Petersburg in 1893, he became leader of the St. Petersburg Marxists and was active in propagating Marxist teaching among the workers. In 1894, he wrote his first major work What the "Friends of the People" Are and How They Fight the Social-Democrats, in which he demolished the false theory and tactics of Narodism and showed the working class of Russia the true path of struggle. In 1895, he united the Marxist groups of St. Petersburg in the League of Struggle for the Emancipation of the Working Class. Soon afterwards Lenin was arrested and imprisoned, then exiled to Siberia.

Early in 1900, he emigrated. Abroad he founded Iskra (The Spark), the first Marxist newspaper to be widely circulated in Russia, which played an enormous part in forming a Marxist party of a new type and in working out its first programme, and in the struggle against reformists and opportunists. The Second Congress of the RSDLP in 1903 saw the inauguration of the Bolshevik Party, which under Lenin's leadership guided the proletariat and the toiling peasantry in the struggle to overthrow the tsarist autocracy and replace it by a socialist system. The milestones in this struggle were the bourgeois-democratic revolution of 1905, the February bourgeois-democratic revolution of 1917, and the October Socialist Revolution in 1917.

The great service Lenin rendered was that he developed Marxist teaching creatively, with reference to the new historical conditions, and gave it concrete form on the basis of the practical experience of the Russian revolutions and the international revolutionary movement after the death of Marx and Engels. In Imperialism, the Highest Stage of Capitalism (1916) Lenin continued the analysis of the capitalist mode of production which Marx had made in Capital and discovered the laws governing the economic and political development of capitalism in the era of imperialism. The creative spirit of Leninism was expressed in his theory of the socialist revolution. He proved that under conditions of the uneven development of capitalism in the imperialist stage socialism could be victorious in one or several countries to start with, but not in all countries simultaneously. He evolved the doctrine of the party of the proletariat as the leading and organising force without which there could be no dictatorship of the proletariat or building of communist society.

Lenin became head of the first proletarian state, which was able to survive the struggle against internal and foreign enemies and to launch the peaceful building of socialism. Developing the ideas of Marx and Engels, Lenin drew up a concrete programme of socialist construction in the USSR, which became a working guide for the Party and the whole Soviet people. Lenin's name is associated with the development of all aspects of Marxism, including its philosophy. From the outset he paid great attention to the further development of dialectical and historical materialism. Marxist philosophy was his means of solving every problem that confronted the working class and its Party in the new age, and he enriched that philosophy with many new ideas.

In 1908, he wrote his fundamental philosophical work Materialism and Empirio-Criticism, in which he gave a profound analysis of the latest achievements of natural science in the light of dialectical materialism and developed the basic principles of Marxist philosophy, particularly its theory of knowledge. In Machism Lenin perceived the trend in contemporary philosophy that attempts by new methods to undermine the influence of materialism and to defend idealism by concentrating on epistemology and logic. His criticism of Machism has lost none of its significance today and teaches Marxists how to fight reactionary philosophy. With an urgency unprecedented in this field Lenin posed the question of partisanship in philosophy and demanded that Marxists fight consistently against any and every type of idealism or metaphysics.

He worked particularly hard to develop and perfect materialist dialectics, which he called the "soul of Marxism", its "fundamental theoretical basis". He showed the versatility of dialectics as a theory of development and substantiated the extremely important and fruitful postulate on the unity of dialectics, logic, and the theory of knowledge. Pointing to Marx's Capital as a model of such unity, Lenin put forward a host of valuable ideas on this subject (see Philosophical Notebooks), which may be regarded as a programme of further work on dialectics. His works covering the most diverse fields of economics, politics, strategy, and tactics provide unsurpassed models of the application of dialectics to real life.

In his article "On the Significance of Militant Materialism" (1922) Lenin outlined important tasks that must be undertaken for the further development of Marxist philosophy, including the struggle against the religious view of the world. These directions retain their importance today. Lenin considered the materialist understanding of history the greatest achievement of Marxist philosophy. He regarded the theory of historical materialism as a scientific basis for getting to know the laws of social development and for revolutionary struggle for the socialist transformation of society. His creative study of the economic, political, and spiritual development of society in the new age developed all aspects of Marxist sociology.

Of particular importance is his investigation of the problems of the classes and the class struggle, the state and revolution (see The State and Revolution), the role of the masses in the epoch of socialist revolution and the building of communist society, on the relationship between the masses, the Party and the leaders, his ideas concerning the new forms taken by the economic laws of social development during socialist construction, on the relationship between economics and politics, on culture and the cultural revolution, and on socialist morals and the principles of socialist art.

Lenin also had valuable ideas in the field of Marxist historico-philosophical science and gave us penetratingly accurate assessments of many philosophers of the past (the philosophers of the ancient world, the French materialists, Kant, Hegel, and others). He valued the work of the Russian revolutionary-democratic thinkers (Belinsky, Herzen, Chernyshevsky), and what he had to say about them and the processes of the development of the revolutionary movement and social thought in Russia, form a theoretical basis for the scientific history of Russian materialist philosophy.

Leninism, as the continuation and development of Marxism, Marxism-Leninism as a single and indissoluble entity, has become in our day the watchword of progressive people all over the world who are fighting for peace, democracy, and socialism.

Lesevich, Vladimir Viktorovich (1837–1905)

Russian positivist philosopher. Lenin called him the first and most outstanding Russian empirio-criticist (Vol. 14, p. 56). Till 1877, he was a supporter of Comte (see his Ocherk o razvitii idei progressa [Essay on the Development of the Idea of Progress], 1868). He then moved to the position of the neo-critical German school (Carl Goring, Alois Riehl, Richard Avenarius, Joseph Petzoldt, etc.), which he considered the highest stage of positivism. According to Lesevich, this school supplemented Comte's philosophy with a fully elaborated theory of knowledge constructed on the basis of "pure experience". Denying that philosophy could be a world outlook, Lesevich declared that its task was merely to "unite" concepts produced by the specialised sciences. He explained the life of society from an idealist standpoint (see Subjective Method in Sociology).

Main works: Opyt kriticheskogo issledovaniya osnovonachal pozitivnoi filosofii (Critical Investigation of the Basic Principles of Positivist Philosophy), 1876; Pisma o nauchnoi filosofii (Letters on Scientific Philosophy), 1878, and Chto takoye nauchnaya filosofiya? (What Is Scientific Philosophy?), 1890.

Lessing, Gotthold Ephraim (1729–1781)

German Enlightener and philosopher, publicist, playwright, critic, and art theorist. He was an active opponent of feudal policy and ideology and worked for the free and democratic development of the German people and their culture. In his philosophical work Erziehung des Menschengeschlechts (1780) Lessing envisaged a future society free of all coercion, in which religion would give place entirely to enlightened reason. In his philosophical play Nathan der Weise Lessing proclaims not only the idea of religious toleration but also the right of free thought, asserting the equality of nations and appealing for friendship among them.

Lessing expressed the contradictions in the German movement for enlightenment and his world outlook remained idealistic, though it contained some materialist features as well. In his Laokoon (1766) and Hamburgische Dramaturgie (1767-69), which constitute a landmark in the development of world aesthetic thought, Lessing upholds the principles of realism in poetry, drama, and acting and demolishes the classicist theory and practice of the nobility. Lessing limited the sphere of the fine arts to the beautiful. He strove to define the objective laws of composition in various types and genres of art, but could not see the historical character of these laws. Always opposed to dull moralising, Lessing attached enormous importance to the moral and educative function of art, particularly in the theatre. His writing for the theatre heralded the emergence of German classical literature, and his aesthetic views exercised a beneficial effect on its development.

Leucippus (c. 500–440 B.C.)

A contemporary of Democritus, with whom he founded the system known as atomistics. Owing to the almost complete lack of texts and of information concerning the man himself, it was at one time suggested that Leucippus was a literary myth (Erwin Rohde and Paul Tannery). Further data in the papyri discovered at Herculaneum exploded this assumption.

Leucippus contributed three new concepts to science: (1) absolute vacuum; (2) atoms moving in this absolute vacuum; and (3) the concept of mechanical necessity. On the basis of the one text that has been preserved it may be stated that Leucippus was the first to establish both the law of causality and the law of sufficient reason. "Nothing arises without cause, but everything arises on some grounds and by force of necessity."

Levy-Bruhl, Lucien (1857–1939)

French sociologist and ethnologist; professor at the Sorbonne from 1899. His sociological views were formed under the influence of Durkheim. While studying primitive peoples, Levy-Bruhl arrived at the conclusion that various social types had their corresponding patterns of thought. The thinking of the primitive man differed from the logical thinking of modern man in that it ignored the law of contradiction and made no distinction between the natural and the supernatural. Levy-Bruhl maintained that primitive man sees only the connection between first cause and final effect while failing to perceive the intervening relationships. This process he described as the operation of the law of participation.

Some of Levy-Bruhl's conclusions and the extensive ethnographical material he collected are of considerable interest. His basic postulate on the qualitative difference between primitive thinking and the thinking of the cultured man does not, however, stand up to scientific criticism. His main works are Les fonctions mentales dans les societes inferieures (1910) and La mentalite primitive (1922).

Li

The basic concept of Chinese philosophy signifying law, the order of things, form, and so on. The idealists interpreted it as the spiritual, immaterial principle in contrast to the material principle, ch'i. In Confucianism, another conception of Li was to be found, signifying the code of conduct of various social groups.

Life

A form of the motion of matter, the highest of the physical and chemical forms. Its specific features are expressed in Engels' famous definition: "Life is the mode of existence of protein bodies, the essential element of which consists in continual metabolic interchange with the natural environment outside them." (Dialectics of Nature, p. 396.) "Protein body" or "protoplasm" is nowadays understood to mean the system of a series of substances specific to Life such as proteins, nucleic acids, phosphoric compounds, etc.

Life exists in the form of separate living organisms, each of which arises from its own kind, passes through a cycle of individual development, reproduces its own kind, and dies. Organisms, by entering into relations with inanimate nature and with one another create systems of more complex orders and, ultimately, the unified system of life on earth, which has developed from the simplest forms to that of man. An essential feature of all living bodies is metabolism, the destruction and rebuilding of organic structures, dissimilation and assimilation.

The correct philosophical interpretation of the laws of Life, including those which science has not yet discovered, plays an important part in determining the methods to be followed in investigating them. The vitalists (see Vitalism) attribute the specific features of Life (organisation, purposefulness, regulation, etc.) to the influence of a non-material life force, which is supposed to control "inert" matter. The mechanists regard Life merely as a more complicated system of physico-chemical processes and deny its specific features. From the point of view of dialectical materialism, physical and chemical laws play a subordinate part in Life. Besides these, Life has its own specific biological laws.

The study of Life involves a number of general theoretical, philosophical problems such as the relation of the part to the whole, form to content, the correlation of preformation and directed complication, the problem of the specific nature of biological determination, and the principles of self-constructing systems, the problems of evolution, etc.

Lilburne, John (1614–1657)

Ideologist and leader of the petty-bourgeois democratic wing of the English revolution (the Levellers) in the middle of the 17th century. He was the son of a country gentleman. As a pamphleteer and orator he fought for the fulfilment of the bourgeois revolution in the political and social spheres. With his supporters Walwyn, Overton, and others, he pressed for bourgeois-democratic reforms and was the first to formulate the fundamentals of bourgeois-radical political doctrine, which he strove to put into practice by revolutionary means. He advocated popular sovereignty (on the basis of the theory of natural law), universal franchise and referenda, republican government, the separation of legislation, administration, and judiciary, etc., and also peasant ownership of the land.

Linnaeus, Carolus (1707–1778)

Swedish naturalist, professor at Uppsala University. The historical service rendered by Linnaeus was his classification of the vegetable and animal world. He took as the basic unit for his classification the species. His system was artificial because it was based on the similarity of a small number of arbitrarily selected outward characteristics. His outlook was metaphysical. He denied the mutability of species and held that their number remained unchanged from the day of their "creation".

Lobachevsky, Nikolai Ivanovich (1792–1856)

Russian mathematician who pioneered a new geometry known as the geometry of Lobachevsky. He graduated at the University of Kazan in 1811 and at the age of 23 became a professor. For 19 years he was Rector of Kazan University. His basic works are O nachalakh geometrii (Principles of Geometry), 1829, and Noviye nachala geometrii s polnoi teoriyei parallelnykh (New Principles of Geometry with a Complete Theory of Parallels), 1835–38.

Lobachevsky's geometry was based on the idea of the close dependence of geometrical relations on the actual nature of material bodies. His discovery consisted, first, in proving the independence of the fifth postulate of Euclidean geometry (see Euclid) from its other postulates and, secondly, in constructing a new geometry free of logical contradictions, whose fifth postulate states: through a point lying outside a straight line not one but at least two parallel lines may be drawn. Lobachevsky sought to prove the postulate on parallels by recourse to reality itself, to the nature of things.

Developing modern geometry, Lobachevsky showed that denial of the dependence between segments and angles in Euclidean geometry does not fully describe the qualities of space, and suggested that in reality there must be such a dependence. This is seen, for example, in the fact that there is a connection between the lateral dimensions of a triangle and its angles. For this reason, according to Lobachevsky, the sum of the angles of a triangle is actually less than two right angles. Lobachevsky assumed that new geometrical relations could be discovered either through astronomical research or in the field of microphenomena. The geometrical relations commonly used, however, are those existing within the limits of earthly dimensions for which Euclidean geometry remains valid.

Lobachevsky's geometry was a convincing argument against Kant's a priori theory. Philosophically, Lobachevsky was a materialist and considered our conceptions of the world the result of the impact of reality on the human consciousness. After Lobachevsky's discovery of the new geometry it was no longer possible to treat Euclidean geometry as proof of the apriority of spatial forms. Criticizing the a priori theory, Lobachevsky contended that knowledge is acquired through sense perception, and that innate concepts do not exist. By discovering and defending new ideas that revolutionized geometry Lobachevsky rendered a great service to philosophy.

Locke, John (1632–1704)

English materialist philosopher. The works of Locke belong to the age of the Restoration. He joined the struggle of classes and parties as a philosopher, economist, and political writer. In his major work Essay Concerning Human Understanding (1690) he developed the theory of knowledge of materialist empiricism, which had been complicated by the nominalism of Hobbes and the rationalism of Descartes.

Rejecting the Cartesian doctrine of innate ideas, Locke declared experience to be the sole source of all ideas. Ideas come into being either through the influence of external objects on the sense-organs (ideas of sensation) or through attention being directed on the condition and activity of the soul (the idea of reflection). The latter alternative was a concession to idealism. Through the ideas of sensation we apprehend in things either primary or secondary qualities (see Primary and Secondary Qualities). Ideas acquired through experience are only the material of knowledge, not knowledge itself. To become knowledge the material of ideas must undergo the process of reasoning, which differs both from sensation and from reflection and is a matter of comparing, combining, and abstracting. Through this activity simple ideas are transformed into complex ones.

Following Hobbes, Locke considers that universal knowledge depends entirely on language. Having defined knowledge as apprehension of the correspondence (or non-correspondence) between two ideas, Locke considers all speculative knowledge, i.e., perception of the correspondence of ideas by means of the reason, as valid. On the other hand, experimental knowledge is only probable, for here perception of the correspondence of ideas is achieved by reference to the facts of experience. Our faith in the existence of external objects rests on the senses. Locke places this type of knowledge ("sensitive knowledge") above simple probability but below the validity of speculative knowledge. Though convinced of certain limitations in our ability to know material and particularly spiritual substances, Locke should not be considered an agnostic. According to Locke, our task is to know not everything but only what matters as far as our conduct and practical life are concerned, and for the attainment of such knowledge our abilities are ample.

In his doctrine on state power and law Locke develops the idea of transition from the natural to the civil condition and various forms of government. The purpose of the state, according to Locke, is to preserve freedom and property acquired through labour. Government cannot, therefore, be arbitrary. He divides it into (1) legislative, (2) executive, and (3) federative. Locke's doctrine of the state was an attempt to adapt theory to the political form of government that was adopted in England as a result of the bourgeois revolution of 1688 and the compromise between the bourgeoisie and the section of the aristocracy that had become bourgeois.

His philosophy has had a great influence on many generations of thinkers. The idea that people themselves should change the existing social system if it does not provide the individual with proper opportunities for education and development was of great importance in justifying the bourgeois revolution. One of the trends in French materialism takes its origin from Locke. His distinction between primary and secondary qualities was used by Berkeley, the idealist, and Hume, the agnostic.

Logic, Combinatory

A branch in mathematical logic analyzing concepts which, within the framework of classical mathematical logic, are accepted without further study. Among them are the concepts: variable, function, rule of substitution, etc. In classical mathematical logic rules of two kinds are used. The first are formulated simply and are applied without any restrictions. Such, for instance, is the rule of modus ponens. It is formulated as follows: "Given A and A → B to infer B." This rule is accessible for a one-act automatic performance. Other rules (for example, the rule of substitution) are very intricately formulated and presuppose a number of restrictions and reservations (without which they cannot be applied purely formally).

One of the purposes of Combinatory Logic is to construct a formal system having no rules like the rule of substitution. The beginning of Combinatory Logic was laid by the Soviet mathematician M. I. Sheinfinkel (his main results were published in 1924). Independent of him, A. Church also constructed a lambda conversion calculus closely linked with Combinatory Logic. Important results were also obtained by the American logician H. Curry. Problems of Combinatory Logic are studied by J. B. Rosser, W. Craig, R. Feys, and others.

Logic, Constructive

A trend in mathematical logic. Constructive Logic derives from the intuitionist school, though it is not connected with philosophical intuitionism. It was first propounded in the works of L. Brouwer, H. Weyl, and A. Heyting. The central concept of Constructive Logic is the impermissibility of extending to infinite numbers the principles valid for finite numbers (see Numbers, Theory of), such as the principle that the whole is greater than its parts, the law of the excluded middle, etc.

Traditional logic and Constructive Logic differ in their views of the concept of infinity: the former considers it as actual, completed, whereas the latter sees it as potential, becoming (see Infinity, Real and Potential). Characteristic of Constructive Logic is the inductive construction of objects. The principles of Constructive Logic are used in attempts to revise the principal results of modern mathematical logic and mathematics. Such Soviet scientists as A. N. Kolmogorov, A. A. Markov, and P. S. Novikov, have made notable contributions to the development of Constructive Logic.

Logic, Dialectical

The logical teaching of dialectical materialism, science of the laws and forms of the mental reflection of the development and change of the objective world, and of the laws governing the cognition of truth. Scientifically, Dialectical Logic arose as part of Marxist philosophy. However, elements of it were already in evidence in antique philosophy, particularly the doctrines of Heraclitus, Plato, Aristotle, and others.

For historical reasons, formal logic reigned for a long time as the sole teaching on the laws and forms of thought. Approximately in the 17th century the requirements of developing natural science and philosophy revealed its insufficiencies and the need for a truer teaching on the general principles and methods of thought and cognition (see Francis Bacon, Descartes, Leibniz, and others). This tendency emerged most clearly in classical German philosophy. Kant, for instance, distinguished between general and transcendental logic, the latter differing from the former, i.e., formal logic, in that it examined the development of knowledge and did not abstract itself, as the former, from the content. Special credit in the development of Dialectical Logic goes to Hegel, who produced the earliest comprehensive system which was, however, permeated with his idealistic outlook.

The Marxist teaching on logic absorbed all the valuable elements of the preceding development, molding the vast experience of human knowledge into a harmonious science of cognition. Dialectical Logic does not reject formal logic, but demonstrates its limits as a necessary though inexhaustive form of logical thinking. Dialectical Logic combines the teaching on being with the teaching on its reflection in the mind. It is a substantive logic. Inasmuch as the world is in constant motion and development, the forms of thought, and the concepts and categories, too, should be based on the principle of development, for otherwise they cannot be ideal forms of objective content.

The cardinal task of Dialectical Logic is, therefore, to investigate how best to express in human concepts motion, development, the internal contradictions of phenomena, their qualitative change, and the passage of one into another; it is to investigate the dialectical essence of the logical categories, their mobility and flexibility, "reaching to the identity of opposites" (Lenin, Vol. 38, p. 110). The reason why dialectics is a logical teaching is that it investigates the logical, cognitive functions of general laws and categories of development. With this is linked also the other basic task of Dialectical Logic, examination of the process of coming into being and the development of cognition itself. Dialectical Logic is based on the history of cognition. It is a generalized history of human thought and of the historical practice of society.

From the standpoint of Dialectical Logic, the laws of cognition are laws governing the development of thought from the external to the internal, from appearance to essence, from less profound to more profound essence, from the immediate to the mediate, from the abstract to the concrete, and from relative truth to absolute truth. Every proposition of Dialectical Logic is, like all science, permeated with this historicity.

Dialectical Logic overcomes the division of analysis and synthesis, induction and deduction, and empirical and theoretical into independent forms of cognition typical of the preceding theories of knowledge. These, like all other forms of cognition, are examined by Dialectical Logic in the highest synthesis, as interpenetrating opposites. The method of ascent from abstract to concrete (see the Abstract and the Concrete) is prominent as the general logical principle of Dialectical Logic, completely embodying the unity of the historical and the logical. Dialectical Logic is a system of logical categories which synthesize the fruits of man's cognitive and practical activity. This system, in which categories are arranged in their order of subordination and co-subordination, has not yet been studied exhaustively enough, but the approach based on the principles of unity of the logical and the historical, and of the development of knowledge from appearance to essence, from the simple to the complex, and so on, appears to be the most probable and fruitful.

Lenin, who contributed very greatly to the development of Dialectical Logic, laid a strong accent on this aspect of the matter. In contemporary science a big part is played by formalized logical systems and formal substantive logical theories which study the various aspects and tasks of thought. Dialectical Logic is the general logical basis of human cognition, the general logical theory which can and must be employed to explain all the particular and concrete logical theories, their significance and role.

Logic, Formal

A science which studies acts of thinking (see Concepts, Propositions, Inferences, and Proof) as regards their logical structure or form, i.e., by abstraction of the concrete content of thoughts and singling out only the general means by which the parts of that content are linked. The main task of Formal Logic is to formulate laws and principles whose observance is a requisite for achieving valid results in obtaining knowledge by deduction.

The foundation of Formal Logic was provided by the works of Aristotle, who elaborated syllogistic. Contributions to its development were made by the early stoics and the scholastics in the Middle Ages—Duns Scotus, William of Occam, Albert von Sachsen, Raymond Lulle, and others. The departure from the long-standing tradition of studying problems of deductive logic was connected with the study of induction and attempts to formulate rules of inductive inferences (Francis Bacon, and later John St. Mill). But a turning point took place only in the second half of the 19th century, when the mathematical (symbolic) logic received its modern form.

Logic, Inductive

That part of traditional logic concerned with logical processes of conclusions from the particular to the general (see Induction). Traditional inductivists saw the task of Inductive Logic in analyzing the process of obtaining general theoretical knowledge from the single, empirical. There were also other concepts of the subject-matter of Inductive Logic, limiting its tasks to analyzing logical criteria for verifying universal laws. William Whewell, a 19th century British logician, was the first to formulate such an understanding of Inductive Logic. The hypothetical deductive method was considered as the means of such verification.

This concept is now shared by neo-positivist logicians and many other specialists in Inductive Logic. It stems from the inadequacy of the inductive method for obtaining theoretical propositions, which require the singling out of new thought-content and the formation of new scientific abstractions. The shortcoming of this concept is its unjustified renunciation of logical study of the processes for obtaining scientific knowledge in general, i.e., their analysis as socially necessary processes independent of individual consciousness and determined by the objective content of the cognitive processes.

Modern Inductive Logic widens the sphere of its application and examines not only conclusions from the particular to the general, but all logical relationships in general when the truth-value of the knowledge we want to verify cannot be reliably established on the basis of the knowledge whose truth-value is known to us, when we can only determine whether it is confirmed by further knowledge, and if so, to what extent. Therefore, one of the central concepts of modern Inductive Logic is the degree of confirmation which is usually interpreted as the probability of the hypothesis with available empirical knowledge. Modern Inductive Logic thereby utilizes methods of calculating probabilities and the logic of probability.

Logic, Many-Valued

A formal logical system whose propositions in interpretation assume more than two meanings (in the case of only two meanings—"true" or "false"—we have classical two-valued logic), but in the general case we have any finite or infinite multitude of meanings. The first such systems—the tri-valued logic of propositions and the n-valued logic of propositions—were built by J. Lukasiewicz in 1920 and E. Post in 1921. Today there is a series of different systems of Many-Valued Logic and a general theory of such systems.

Among the works on the general theory of Many-Valued Logic the most important are those by J. B. Rosser and A. R. Turquett, and also the investigations by S. V. Yablonsky, dealing with functional constructions in n-valued logic. These systems of Many-Valued Logic have been elaborated with a view to solving concrete problems of scientific research, both general logical ones and specifically scientific ones. For instance, the tri-valued and four-valued logic of propositions elaborated by Lukasiewicz were constructed with a view to creating a modal logic, while the tri-valued calculus by D. A. Bocvar was aimed at solving the paradoxes of classical mathematical logic.

Other most important applications of Many-Valued Logic include the attempts to study it in order to explain quantum mechanics (works by G. Birkhoff, J. Neumann, H. Reichenbach) and also the attempts in the sphere of technology and the theory of relay-schemes (works by V. I. Shestakov, G. Moisil, T. D. Maistrova).

Logic, Mathematical

Mathematical Logic (or symbolic logic) appeared as a result of the application of mathematical methods in the realm of formal logic, of the use of a special language of symbols and formulas. Mathematical Logic investigates logical thinking (reasoning and proof) as reflected in the systems of formal logic or calculi. Thus Mathematical Logic has for its subject-matter logic and for its method mathematics; it contains far-reaching generalizations.

Typical of the present stage of formal logic is the development of the ideas and methods of traditional formal logic. Contemporary Mathematical Logic includes a whole series of logical calculi, and is the theory of such calculi, their premises, properties, and applications. Besides its study of the formal structure of logical calculi (see Logical Syntax) Mathematical Logic also examines the relations between calculi and those substantive fields which serve as interpretations and models. This task reflects the problems of logical semantics. Logical syntax and semantics belong to metalogic, the theory of the means of describing the premises and properties of logical calculi.

The discovery of the formal investigation of logic is attributed to Aristotle (see Syllogistic). The Megarian school of stoics (3rd century B.C.) already knew some of the initial concepts of Mathematical Logic, whereas the idea of logical calculi was first formulated by Leibniz. As an independent branch of science Mathematical Logic established itself only in the mid-19th century, thanks to the works of Boole, who founded the algebra of logic. Later Ernst Schroder summed up and systematized the results of such development in his Algebra der Logik (1890–95).

Another trend in Mathematical Logic appeared at the end of the 19th century, arising from the need of mathematics to provide a foundation for its concepts and methods of proof. The sources of this trend are to be found in the works of Frege. The main contribution to its development was made by Russell and Whitehead (Principia Mathematica, 1910–13), and Hilbert. Two fundamental logical systems—the classical propositional calculus and functional calculus—were elaborated at the time.

Today Mathematical Logic investigates the various types of logical calculi and takes interest in semantical problems and metalogic in general, as well as in the problems of special scientific and technical application of logic. Alongside the studies by classical logic, constructive logic was created in order to substantiate mathematics. An analysis of the foundations of logic promoted the research into combinatory logic. The theory of many-valued logic was also created. Attempts to solve the problem of formalizing logical thinking led to the formation of the calculations of strict and material implication. The foundations of modal logic were laid as well.

At the same time Mathematical Logic exerted great influence upon contemporary mathematics itself. The essential sections of contemporary mathematics sprang up from Mathematical Logic, e.g., the theories of algorithms and recursive functions. Mathematical Logic is applied in electrical engineering (the study of relay-contacts and electronic systems), in computers (programming), in cybernetics (theory of automatic devices), in neurophysiology (simulation of the neuronic nets), and linguistics (in structural linguistics and semiotic). Such close interlacing of logical problems with the solution of special scientific problems and use of logic in concrete scientific studies were unknown to formal logic.

Logic, Modal

A logical system which formulates such relations as "necessity", "reality", "possibility", "chance", and their negations (see Modality). The first attempt to construct Modal Logic was undertaken by Aristotle (see Syllogistic), who formulated a number of important definitions and principles. The development of mathematical logic gave a new stimulus to the elaboration of Modal Logic.

The result was the construction of a number of Modal Logic systems, the best known of which are: the tri-valued and four-valued systems of Lukasiewicz, the axiomatic systems of strict implication of C. Lewis, and the systems of relative modality of G. H. Wright. In the systems of Lukasiewicz and Lewis the modalities are absolute, i.e., they are assigned to one proposition independently of any others. In Wright's systems the modalities are relative, i.e., they are assigned to one of the propositions under certain conditions, which are expressed in other propositions. At the same time there is not yet any satisfactory general theory of Modal Logic, although the demand for its elaboration is obviously felt in some branches of knowledge (e.g., mathematics, linguistics).

Logic of Relations

Department of mathematical logic dealing with relations.

Logical and Factual Truth

Logical concepts dating from Leibniz, who distinguished between necessary truth, or "truths of reason", and incidental truths, or "truths of fact". The truth of the former is derived from the laws of logic, the truth of the latter, from correspondence with the actual state of affairs. Leibniz, who regarded the laws of logic as absolute, held that "truths of reason" are true in all possible worlds (i.e., worlds that are not contradictory to logic), whereas truths of fact are true only in some worlds (including the world we live in).

A similar distinction was made by Hume and Kant (see Synthetic and Analytic). Modern logic maintains this distinction without regarding it as absolute. Thus, the Carnap-Kemeny logical semantics considers statements to be logically true that are true in all admissible interpretations (see Interpretation and Model) of the given formalized language, while statements that are true in a particular interpretation but not in all admissible interpretations are only factually true.

Logical Atomism

A conception formulated by Russell in Our Knowledge of the External World (1914), The Philosophy of Logical Atomism (1918), and other works, and by Wittgenstein in Tractatus Logico-Philosophicus. According to Logical Atomism, the whole world is a totality of atomic facts.

The philosophy of logical atomism, as Russell himself has admitted, is an extreme pluralism, because it asserts the existence of a multiplicity of individual things and denies them any unity or integrity. To some extent Logical Atomism was a reaction to the absolute idealism of F. Bradley, who held that only the absolute, the whole was real and that individual things were merely apparent.

In Wittgenstein's Tractatus, Logical Atomism forms a kind of ontological argument for a definite logico-epistemological conception which regards all knowledge as a totality of "atomic" propositions connected by logical operations and infers the structure of the world by analogy with the logical pattern of knowledge. Logical Atomism absolutizes the discrete and the individual. The unsoundness of the theory was ultimately acknowledged even by its advocates.

Logical Empiricism

A trend in contemporary idealist philosophy stemming directly from the logical positivism of the late twenties and early thirties and forming one of the varieties of analytical philosophy. The main exponents of Logical Empiricism are Carnap, Reichenbach, Feigl, Hempel, Bergman, and Frank.

Logical Empiricism preserves the basic ideas of logical positivism—reduction of philosophy to the logical analysis of language (now not only syntactical, as in the early thirties, but also semantic—see Logical Semantics) and the proposition that it is impossible to provide theoretical proof of the existence of objective reality, etc.; but it has been slightly modified in comparison with the earlier logical positivism. The logical empiricists have repudiated the extreme subjectivism of the Vienna circle. As an "empirical language of science" they offer a so-called physical-object language expressing sensually perceptible physical phenomena instead of a language of the personal experience of the subject. This does not mean, however, the adoption of materialist positions, since for Logical Empiricism the acceptance of a physical-object language does not involve recognition of the theoretical assertion of the objective existence of the world of things.

Logical Empiricism also rejects the principle advanced during the period of the Vienna circle that scientific knowledge may be reduced to what is empirically given. In scientific concepts, however, Logical Empiricism sees only "purposive" forms of organizing the data obtained by the senses, not the reflection of objective reality. Recognition of the fact that besides the data scientific knowledge has its own specific content is essentially at variance with the basic epistemological ideas of the Vienna circle, i.e., the principle of verification, etc., to which Logical Empiricism seeks to remain loyal. This gives rise to internal contradictions and eclecticism in its epistemological doctrine.

As a philosophical trend Logical Empiricism is undergoing a profound internal crisis, as is shown by its abandonment of the widely proclaimed programmes characteristic of the early logical positivism, by its acceptance of watered-down versions, and by its gravitating away from the broad philosophical problems to specifically logical and specifically methodological researches in which representatives of Logical Empiricism have performed good service.

Logical Fallacies

Mistakes caused by an incorrect step in the process of reasoning. Logical Fallacies are of various kinds. They may arise through an erroneous interpretation of a proposition or through its incorrect use as a premise (e.g., a proposition which is true under certain circumstances is taken to be unconditionally true); or through violation of the rules of logic in the process of reasoning (e.g., the quaternio terminorum or four-term fallacy in syllogisms, when the premises appear to be connected by a common term, the middle term, which is in fact ambiguous); or through drawing a conclusion from a proposition that cannot, in fact, be drawn (e.g., ignoratio elenchi, etc.).

Logical Fallacies may be divided into the unintentional (paralogisms) and the deliberate (sophisms).

Logical Forms

Ways of constructing, expressing, and connecting ideas (and partial ideas) in the process of cognition, irrespective of their concrete meaning. These forms have taken shape in the course of man's socio-historical development and have a universally human character; they are forms of the reflection of reality in thought and themselves reflect the most general features of reality (e.g., the fact that every object has certain qualities, exists in certain relations to other objects, that objects form classes, that certain phenomena cause other phenomena, etc.).

Logical Forms, such as concepts, judgements, inferences, proofs and definitions, are studied in formal logic. In cognition, the use of one or another Logical Form is determined by the character of the content reflected in thought. In language, Logical Forms are expressed by the grammatical structure of the expressions involved and also by the use of particular words ("all", "no", "certain", "or", "if ... then", "only", etc.), which indicate a corresponding logical structure of thought.

In mathematical logic, Logical Forms are expressed by constructing logical calculi whose formulas correspond to expressions in the natural language; the structure formulas and the rules for operating them in a calculus reproduce Logical Forms, so that these calculi act as special logical, or formalized languages (see Formalization, Logical Syntax). In dialectical logic, Logical Forms are studied from the point of view of how the changing and developing reality and the development of cognition itself are reflected in thought.

Logical Positivism

A variety of neo-positivism. Originating in the 1920s with the Vienna circle, its leading figures were R. Carnap and Otto Neurath, who were closely associated with the Berlin Society for Scientific Philosophy (H. Reichenbach, C. G. Hempel, and others). By the early thirties it had become widespread as the ideological basis of the neo-positivist "scientific philosophy". Since the late thirties the stronghold of Logical Positivism has been in the USA, where it is found in a considerably modified form as compared with the days of the Vienna Circle and is known as logical empiricism.

Logical Positivism takes its succession from Machism and the generally subjective-idealist tradition originating from Berkeley and Hume. Logical positivists, however, repudiate the old and discredited psychological and biological approach to knowledge that was adopted by positivism and try to combine subjective-idealist empiricism with a method of logical analysis. According to Logical Positivism, a genuinely scientific philosophy is possible only through the logical analysis of science.

The function of this logical analysis is, first, to get rid of "metaphysics" (i.e., philosophy, in the traditional sense), and on the other hand, to investigate the logical structure of scientific knowledge in order to determine the "protocol-statement", or the empirically verifiable meaning of scientific concepts and assertions. The ultimate aim of this investigation was held to be the reorganization of scientific knowledge within a system known as "the unity of science", which would describe the "protocol-statement" and eliminate the distinctions between the separate sciences—physics, biology, psychology, sociology, etc.—both as regards the concept and the method of their formation.

Logic and mathematics are regarded as "formal sciences", not as knowledge of the world, but as a collection of "analytical" assertions which formulate the agreed rules of formal transformation. In the early thirties, Logical Positivism attempted to free itself of some of the more unpleasant consequences of the principle of the "protocol-statement". It accepted the concept of physicalism, but this did not change the subjective nature of the philosophy. The enforced repudiation of consistent subjective-idealist sensationalism brought the logical positivists to equally untenable conventional concepts (Neurath and Carnap's coherence theory).

The subjective-idealist essence of Logical Positivism disposes of its claim to be a "philosophy of science". Nevertheless, some representatives of Logical Positivism (Carnap, Reichenbach, and others) have achieved valuable results in the field of logical research.

Logical Positivism in Ethics

A neo-positivist interpretation of morality. Widespread since the twenties in the United States, Britain, Austria, Scandinavia, and Latin America. There are a number of schools of Logical Positivism in ethics (emotivism, the Oxford school, etc.).

The neo-positivists ignore the fact that morality is a social relationship and a special form of social consciousness; they regard it merely as a "moral language". Ethics is replaced by a purely logical analysis of moral judgements and "terms". The "metaethics" of the neo-positivists is an abstract and scholastic theory divorced from life and may be treated as a department of logic rather than a theory of morality.

Instead of an objective investigation of the categories of ethics the neo-positivists seek to elucidate how and in what sense moral judgements and such terms as "good" and "evil" and "duty" are used. The neo-positivists approach morality from the standpoint of the natural sciences and frequently draw the wrong conclusions. For example, assuming that good and evil are not characteristics of any phenomena that can be perceived by the sense-organs or determined by experiment, they infer that these concepts have, therefore, no meaning at all and are merely "pseudo-concepts".

The neo-positivists fail to realize that good and evil are not natural but social characteristics of actions, and that these characteristics are determined by the social import of the latter. They cannot, therefore, be seen or "touched", and can be determined only by rational means. In general, logical positivism has a destructive influence on ethics (see Neo-Positivism).

Logical Semantics

The department of logic that studies the meaning of linguistic expressions, or more precisely, a department of metalogic which studies interpretations (see Interpretation and Model) or logical calculations (see Formalized Language).

The basic concepts of Logical Semantics can be divided into two groups: (1) concepts included in what is called the theory of the designation, their application to the expressions of the given language depending to a great extent on choice of interpretation (concepts of truth, designation, decidability, name, extension, synthetic truth, etc.); (2) concepts belonging to what is known as the theory of meaning (see Denotation and Sense) synonymy, analytical truth, etc., are determined in relation to all the possible interpretations of the given language.

Semantic analysis must be used when considering formalized languages from the standpoint of metatheory because many essential facts (e.g., those regarding the completeness and non-contradiction of the language) cannot be established within the framework of a purely syntactical examination (see Logical Syntax). As Tarski has shown, the description of the semantic properties of a language within the framework of the language itself leads to semantic antinomies of the "liar" type. The semantic properties of any language must, therefore, be analyzed in the logically richer metalanguage (see Metalanguage and Object Language).

The problems of Logical Semantics were pioneered by Frege, significant contributions in this field being made by the Lvov-Warsaw school of Polish logicians, and by R. Carnap, W. Quine, A. Church, and J. Kemeny. Investigation of the semantic properties of the language of science and the natural languages is increasingly applied in connection with the development of mathematical linguistics, machine translation, and the automatic processing of information, etc.

Logical Symbols

Modern formal logic makes extensive use of a language of symbols to achieve a precise and simple interpretation of the object and to enable the investigator to apply the formal mathematical method. The symbols used for constructing, according to definite rules, the formulas of a system in formal logic are of three basic types: (1) those denoting the elementary logical objects of the system; (2) those denoting logical connections or operations; (3) auxiliary symbols, e.g., brackets and stops.

Several systems of symbolic notation are accepted in modern logic, as a result of which different symbols may represent the same logical concepts. The meanings of the most important of these symbols are given below:

1. A, B, C ... X, Y, Z ... (also used with indices) denote variable propositions.

a, b, c ... x, y, z ... (also used with indices) denote variable objects.

P(.), R(.,.), S(.,.,.) (also used with indices) denote variable predicates.

1. ¬, \~, → —symbols of negation (read as "not")

∨, + —symbols of disjunction (read as "or")

·, ∧ —symbols of conjunction (read as "and")

⊃, → —symbols of implication (read as "if ... then")

≡, ↔ —symbols of equivalence (read as "if and only if ... then")

∃, E —symbols of the existential quantifier

∀, (x) —symbols of the universal quantifier

Logical Syntax

1. Set of rules governing the construction and transformation of the expressions of a calculus.

2. Branch of metalogic concerned with studying the structure and properties of uninterpreted calculi. The main problems arising from the syntactical examination of logical calculi are the problems of non-contradiction, completeness (see Non-Contradiction and also Axiomatic Theory, Completeness of), independence (see Axiomatic System, Independence of), decision (see Decision Problem), and provability. The problem of provability is to find the algorithm which provides the proof for any demonstrable. Logical Syntax thus includes the theory of proof.

The concept of Logical Syntax was introduced by Wittgenstein in 1919, although the problems of Logical Syntax had been considered by many representatives of mathematical logic by the end of the 19th century (Frege, Russell, Hilbert, Gödel, Church, Kleene, and others). Carnap gave a systematic exposition of the problems and concepts of Logical Syntax in The Logical Syntax of Language (1934), which shows the fertility of the syntactical investigation of the languages that formalize the various branches of the natural sciences (see Formalized Language).

Logicism

The thesis that mathematics is reducible to logic. Although this idea was originally advanced by Leibniz, it was only at the end of the last century that Frege attempted to put it into practice. Frege set himself the aim of (1) defining the basic concepts of mathematics in terms of pure logic, and (2) proving its principles while restricting himself entirely to the principles of logic and employing only logical proofs.

Further work in this direction (Russell and Whitehead, 1910-13, Ramsey, 1926, Quine, 1940) failed to produce the desired results, due to the fundamentally incorrect methodological assumption of Logicism that mathematics is independent of the real world and the objects of its investigation. The development of mathematical logic has, on the contrary, led to the conclusion, as in Gödel's theorem, that even the comparatively elementary departments of mathematics cannot be reduced to logic.

Logistic

Originally applied to the art of arithmetical calculation. Leibniz occasionally spoke of mathematical logic as "logistica". The use of Logistic as a synonym for symbolic or mathematical logic was accepted at the Geneva International Congress of Philosophy of 1904, where it was proposed by Itelson, Lalande, and Couturat (see Logicism).

Logistic Method

In modern mathematics and logic, a method of building formalised systems and calculations. In logical syntax, the term "syntactical system" is used. Such systems are built on a purely formal basis without reference to the meaning of the expressions involved.

The construction of a logistic system requires: (1) a list of primitive symbols of the system; (2) a determination of what kind of sequence of primitive symbols forms the correctly constructed formulas of the system, the first two requirements being regarded as rules of formation; (3) a determination of what correctly constructed formulas can be classed as axioms; (4) a determination of the rules of inference (or rules of conversion) by which a correctly constructed formula is immediately inferred from the set of formulas taken as premisses.

A finite sequence consisting of one or more correctly constructed formulas is regarded as a proof if each formula in the sequence is either an axiom (primitive formula) or can be immediately inferred according to the rules of inference from the preceding formulas of the sequence. The correctly constructed formulas for which proofs exist are called theorems of the system.

Sometimes the Logistic Method includes interpretation as well as construction of a formal system (see Logical Semantics). This purely formal construction of a system does not, of course, imply complete disregard for content, particularly the class of logical laws employed, which must always be taken into account when constructing a calculus.

Logos

Greek term meaning discourse or reason, whose original meaning in philosophy was universal law, the basis of the world. Heraclitus speaks of Logos in this sense when he says that everything proceeds according to Logos, which is eternal, universal, and essential. The idealists (Hegel, Windelband, Trubetskoi, etc.) wrongly regarded the Logos of Heraclitus as universal reason.

Among the stoics the term Logos denotes the law of the physical and spiritual worlds insofar as they merge in a pantheistic unity (see Pantheism). Philo of the Alexandrian school (1st century A.D.) developed the doctrine of the Logos as the totality of platonic ideas and also as a creative force acting as mediator between God and the created world. We find a similar interpretation of Logos in Neo-Platonism, among the gnostics, and later in Christian literature and scholasticism (see Erigena, for example). Hegel in his philosophy described Logos as an absolute concept.

An attempt was made by representatives of religious idealist philosophy in Russia (Trubetskoi, V. Ern, 1881-1915, and others) to revive the idea of a divine Logos. In oriental philosophy concepts analogous to Logos are tao and, in a certain sense, dharma. The term Logos is not used in Marxist literature.

Lokayata

A materialist doctrine in ancient India. The earliest information on Lokayata is to be found in the Buddhist canonical texts known as the Vedas and in the Sanskrit epics. Traditionally, the origin of the Lokayata is supposed to have been connected with the mythical sage Brihaspati. Certain atheistic attacks on the Vedas are attributed to the legendary Charvaka, and in a number of ancient texts this materialism is known as the Charvaka.

The teaching of Lokayata on the nature of being is founded on the idea that everything in the Universe consists of four elements—earth, fire, water, and air (in some texts the fifth element of ether is added). Every element has its particular type of atoms, which are immutable, indestructible, and have existed from the beginning of time. The properties of an object depend on the types of atoms it consists of and in what proportion they are combined. The consciousness and sense-organs are also the result of a certain combination of atoms; after the death of a living being this combination disintegrates into elements which join up with the atoms of the corresponding type existing in inanimate nature. Some texts contain a notion of evolution, treating certain elements as originating from others with earth as primordial.

The epistemology of Lokayata is sensory, the sole valid source of knowledge being sense perception. The sense-organs can apprehend objects to the extent that they themselves are composed of the same elements ("like is known by like"). Lokayata completely denies the validity of any indirect knowledge. Inference and conclusion are considered as false instruments of cognition, as is evidence offered by the Vedas. Lokayata denies the existence of God, the soul, karma, and the transmigration of souls. The predominant feature of the ethics of Lokayata is hedonism.

Lokayata evidently exercised a certain influence on ancient Indian methods of government. Not a single text written by the followers of Lokayata has come down to us in modern times. Lokayata is most fully expounded in the philosophical treatises and compendiums (darsana) written by the idealist opponents of Lokayata, who upheld the Vedas between the 9th and 16th centuries.

Lomonosov, Mikhail Vasilyevich (1711–1765)

Russian encyclopaedist, founder of materialist philosophy in Russia. Son of a peasant. As the best pupil of the Slavonic-Greco-Latin Academy in Moscow, which he entered in 1731, he was sent to the St. Petersburg Academy of Sciences in 1736, then abroad, to Marburg University. In 1741, Lomonosov returned to Russia.

A thinker of immense versatility, Lomonosov made a great contribution to the development of physics and chemistry. He also did much for Russian philology, history, and poetry. The materialist tradition of Russian philosophy stems from Lomonosov. As a materialist, he contested the various speculative views that dominated science in his day. In opposition to idealist theories he insisted on the natural origin of natural bodies.

In his treatise O sloyakh zemnykh (On the Strata of the Earth), 1763, he anticipated the theory of the evolution of the vegetable and animal worlds, stressing the need to study the causes of change in nature. Basing his explanation of natural phenomena on the transformation of matter, which, he held, consisted of minute particles or "elements" (atoms) united in "corpuscles" (molecules), Lomonosov always regarded matter as being in motion. He expressed this idea in his law of the conservation of matter and motion, which he formulated in a letter to Eiler of July 5, 1748 (see Conservation of Energy, Law of).

Lomonosov firmly opposed the unscientific views dominating natural science in the 18th century. In Razmyshleniya o prichine teploty i kholoda (Reflections on the Cause of Heat and Cold), 1749, he rejects the concept of heat as being caused by a special type of heat-giving material (the thermogen) and shows that the cause of heat processes is to be found in the movement of particles of matter. This leads him to the assumption that the variety of natural phenomena is due to the various forms of the motion of matter. The basic properties of matter, according to Lomonosov, are: extension, power of inertia, shape, imperviousness, and mechanical motion.

Lomonosov considered a "first push" to be one of the causes of the development of nature; in this respect, too, he was following the interpretation given by mechanistic materialism. In epistemology Lomonosov was a materialist. Considering the effect of the external world on the sense-organs to be the source of knowledge, he opposed the theory of innate ideas, and the doctrine of secondary qualities (see Primary and Secondary Qualities). Though he attached great importance to experience as a source of knowledge, Lomonosov postulated that only the combination of empirical methods and theoretical generalisations could reveal the truth.

Lomonosov was the founder of physical chemistry. He was the first to provide evidence of the existence of an atmosphere surrounding the planet Venus, and introduced quantitative analysis as a systematic method of research in chemistry. He also played a great part in the geological and geographical study of Russia and in setting up the mining and porcelain industries. As the founder of Moscow University (1755), Lomonosov was responsible for the emergence of the eminent Russian scientists and scholars who carried forward the development of the natural sciences and materialist philosophy in Russia.

In the field of social studies Lomonosov advocated enlightenment and moral improvement as the sole means of improving the life of society and pointed to the ignorance of the priests as one of the causes of the widespread ignorance of the people. In his struggle against the clergy he adopted rationalist positions, with a tendency towards deism. His poetry and historical writing have a strong patriotic vein. In his Drevnyaya rossiiskaya istoriya (History of Ancient Russia), published in 1766, he proved the falsity of the theory, held by some historians, that the Russians were descended from the Scandinavian peoples.

Lorentz, Hendrik Antoon (1853–1928)

Dutch mathematical physicist, professor at Leyden University. Lorentz pioneered electronic theory, evolved the hypothesis of ether at rest and anticipated the theory of relativity. His ideas constituted a tremendous step forward in the development of the electromagnetic theory and led directly to the modern physics of the 20th century.

He was the first to show the invariance of the laws of electromagnetic phenomena, their independence of various systems of measurement moving with uniform velocity and rectilinearly. His transformations connecting spatial co-ordinates and time in moving systems, being a generalisation of the transformations of Galileo, have become a permanent fact in the mathematical apparatus of the theory of relativity. Lorentz held materialist views and opposed the denial of causality and other idealist conclusions concerning quantum mechanics and the theory of relativity.

Lossky, Nikolai Onufriyevich (1870–1965)

Russian idealist philosopher; professor at the Russian Orthodox Seminary in New York, once a professor at St. Petersburg University. Emigrated in 1922. In co-operation with another Russian philosopher, S. L. Frank (1877-1950) he attempted to create a system of "integral" intuitionism. This system is an eclectical combination of the ideas of Plato and Bergson, of the immanentists, and the mysticism of Solovyov.

Lossky holds that philosophy should evolve a theory of the world as a single whole. He attempts to build this "theory" on the basis of religious experience and a doctrine of God as a kind of supratemporal substantial agent. Epistemologically, Lossky is close to immanence philosophy. Objects are to be apprehended by means of intellectual or mystical intuition. Though he distinguishes between the content of knowledge and the act of knowing, Lossky never emerges from the framework of subjective idealism.

His History of Russian Philosophy (1951), besides being a complete distortion of the history of materialism, aims many false charges at Soviet Government. His works include: Obosnovaniye intuitivizma (The Intuitive Bases of Knowledge), 1906; Mir kak organicheskoye tseloye (The World as an Organic Whole), 1917; Dostoyevsky i yego khristianskoye mirovozzreniye (Dostoyevsky and his Christian Outlook), 1945.

Lotze, Rudolf Hermann (1817–1881)

German philosopher, professor at Gottingen University. Lotze's philosophy is a compromise between materialism and idealism, in which the latter predominates. His knowledge of the natural sciences, including medicine, is combined with idealism in the vein of Leibniz. His best known work was Mikrokosmus (1856-64). Lotze's ideas paved the way for the "phenomenology" of Husserl. His Logik influenced Karinsky.

Lucretius, Carus (c. 99–55 B.C.)

Roman poet and materialist philosopher, continued the work of Epicurus, author of De Rerum Natura. Lucretius set out to reveal the path to happiness for the individual thrust into the vortex of social conflict and disaster and haunted by fear of the gods, death, and punishment after death. Release from fear was to be had through acceptance of the philosophy of Epicurus regarding the nature of things, man, and society.

The soul, Lucretius maintains, is mortal, for it is merely a temporary combination of particles and, when the body dies, it disintegrates into atoms. Realisation of the mortality of the soul eliminates not only belief in the after-life but also in punishment after death. It releases man from his fear of hell. The fear of death is similarly dismissed. While we are alive there is no death, when death comes we no longer exist. Lastly, even fear of the gods disappears as soon as we realise that the gods live not in this world but in the empty spaces between worlds; living a life of bliss in these regions, they can have no influence on the life of man.

Lucretius gave a vivid materialist picture and interpretation of the world and the nature of man, the development of material culture and technology. He was a great Enlightener of the Roman world and his poem had an immense influence on the development of the materialist philosophy of the Renaissance.

"Ludwig Feuerbach and the End of Classical German Philosophy"

A philosophical work by Engels (1886), which played a prominent role in the substantiation and development of dialectical and historical materialism. The author appended to it Marx's "Theses on Feuerbach". Engels begins with an analysis of the essence of Hegel's philosophy and the contradictions inherent therein and shows that Marxist dialectics and Hegelian dialectics are opposites.

Engels gives a classical definition of the fundamental question of philosophy, its two aspects, and criticises agnosticism (above all that of Hume and Kant), showing that practice is the most decisive refutation of it. Giving a scientific definition of materialism and idealism, Engels analyses the views of the 17th-18th century English and French materialists and of Feuerbach, and proves that the old mechanical, metaphysical materialism is limited and that its understanding of social phenomena is idealistic.

Engels underscores the significance of Feuerbach's criticism of idealism, but at the same time criticises his attempt to create a new religion and his idealistic views on ethics. Having established the fundamental difference between dialectical materialism and all previous philosophies, Engels, in the latter part of his work, expounds in a concise form the materialist conception of history.

Developing the theory of historical materialism, he emphasises the idea that the superstructure is relatively independent. This was of great importance for the critique of economic materialism, which sprang up at the time. Engels' analysis of the causes, content, and significance of the radical revolution wrought in philosophy by Marxism and his popular exposition of the essence of dialectical and historical materialism make this work (which Lenin placed on the same level as The Manifesto of the Communist Party) an indispensable manual for the study of the origin and history of the basic ideas of Marxist philosophy.

Lukasiewicz, Jan (1878–1956)

Polish logician, professor at Lvov and Warsaw universities, and towards the end of his life at the Royal Irish Academy. In his philosophical views Lukasiewicz aligns positivist tendencies with Catholic ideas. He is one of the most eminent representatives of the Lvov-Warsaw school of logic.

Lunacharsky, Anatoly Vasilyevich (1875–1933)

Soviet statesman and public figure, writer on the theory of art, and journalist. Joined the working class movement in the 1890s, became a Bolshevik in 1903. In the years of reaction following the defeat of the Russian revolution of 1905-07 he turned away from Bolshevism and professed Machism and god-building (Sotsialism i religiya [Socialism and Religion], Part 1, 1908; Part 2, 1911). In 1917, he was readmitted to the Bolshevik Party, and from 1917 to 1929 was People's Commissar for Education. In 1930, he was elected to the Academy of Sciences.

Lunacharsky's early works Osnovy pozitivnoi estetiki (Fundamentals of Positivist Aesthetics), 1904, etc., showed the influence of positivism (Spencer, Avenarius, Bogdanov). But in his best pre-revolutionary writings, Dialog ob iskusstve (Dialogue on Art), 1905; Zadachi s.-d. khudozhestvennogo tvorchestva (Tasks of Social-Democracy in the Arts), 1907; Pisma o proletarskoi literature (Letters on Proletarian Literature), 1914, he criticises decadence and attempts to elaborate from a proletarian standpoint such problems as partisanship in art, the influence of the revolution on the development of culture, the significance of art in the class struggle of the proletariat, the connection between the artist's world outlook and his art, etc.

After the revolution, as a large-scale organiser of socialist culture, Lunacharsky displayed his talent to the full in the theory of art. Adopting the standpoint of dialectical materialism, he contributed to the history of literature (his writings on the Russian and Soviet classics, on the revolutionary democrats, on West European writers, and so on), to aesthetics, e.g., Kultura na Zapade i u nas (Culture in the West and in Our Country), 1928; Klassovaya borba v iskusstve (The Class Struggle in Art), 1929; Lenin i literaturovedeniye (Lenin and Literary Studies), 1932, and to theatrical and musical criticism.

He paid particular attention to the elucidation of problems that were of great importance to the theory of art and creative work: Lenin's ideological legacy, scientific aesthetics, the Party's guidance of the arts, the task of Marxist criticism, socialist realism, the connection between proletarian art and the classical heritage, and the struggle against bourgeois modernism and vulgar sociologism in the study of art. He also wrote a number of dramatic works.

Luther, Martin (1483–1546)

Eminent leader of the Reformation and founder of Protestantism. He influenced all spheres of spiritual life of Germany in the 16th-17th centuries. His translation of the Bible played an important role in the formation of the German language. Luther was a supporter of moderate burgher reformation. He denied that the church and the clergy were mediators between man and God. He affirmed that the "salvation" of man does not depend upon the performance of "good deeds", mysteries, and rituals, but upon man's sincere belief.

According to him, religious truth is based not on the "sacred tradition" (decrees of oecumenical councils, papal judgements, etc.), but on the Gospel itself. These demands reflected the conflict between the early bourgeois world outlook, on the one hand, and the feudal ideology and the church, on the other. At the same time Luther opposed the doctrines which expressed the material interests of the German burghers, criticised the theory of natural law, the ideas of early bourgeois humanism, and the principles of free trade. Luther stood on the side of the ruling classes during the Great Peasant War (1525). "Luther," Marx wrote, "has conquered slavery based on belief in God only by substituting for it slavery based on conviction". (Marx and Engels, Works, Russ. ed., Vol. 1, p. 422.)

Lvov-Warsaw School

Group of Polish logicians and philosophers (J. Lukasiewicz, T. Kotarbiriski, K. Ajdukiewicz, S. Lesniewski, L. Chwistek, Tarski, and others), who worked in the inter-war period mainly in Warsaw, Lvov, and Cracow. Its founder was K. Twardowski. Philosophically, the school was representative of widely varying trends (from the materialism of Kotarbiriski to the Neo-Thomism of Salamuja and Bocherinski).

Characteristic of the majority of its representatives were: (a) rejection of irrationalism, concrete enumeration through mathematical logic of the basic ideas and principles of traditional rationalism; (b) stress on precise research into the logic of scientific reasoning; (c) interest in logical semantics. Representatives of the school made a considerable contribution to the development of mathematical logic, the fundamentals of mathematics, the methodology of the deductive sciences and the history of logic and logical semantics.

J. Lukasiewicz, M. Wajsberg, and J. Slupecki, pioneered many-valued and modal logic, and Chwistek, Lesniewski, Sobocinski, Lukasiewicz, Tarski, and others investigated the fundamental concepts of metalogic. The logicians of this school also dealt with the problems of the logic of relations, axiomatisation, the set theory, the name theory, etc. The philosophers and logicians of People's Poland base much of their work on the progressive ideas of the Lvov-Warsaw School.

Lyceum

The name applied to the sacred garden adjoining the temple of Apollo near Athens and to the gymnasium erected there in the 5th century B.C. It was there in 335 B.C. that Aristotle founded his school of philosophy, which was to exist for nearly eight centuries. After Aristotle the Lyceum was taken over by his pupil Theophrastus. The most outstanding representatives of the school were Eudemus of Rhodes, Dicaearchus, and Strato. By the 1st century B.C., however, the Lyceum had ceased to be a creative centre of philosophy and was merely publishing and commenting on the works of Aristotle. With the collapse of the slave-owning system the Lyceum also ceased to exist.

Lyell, Charles (1797–1895)

British geologist and naturalist. In his Principles of Geology (3 vols., 1830-33) he opposed Cuvier's catastrophe theory. Lyell attributed geological changes to the slow transformation of the Earth under the influence of constantly operating causes (atmospheric precipitation, earthquakes, etc.). Though essentially a materialistic theory, it had the defect of reducing the whole development of the Earth to changes of only one kind. On the other hand, it had a damaging effect on the teleological view of the absolute immutability of nature and paved the way for the collapse of the metaphysical way of thinking. In later life Lyell acknowledged Darwin's theory of evolution, which he had rejected in earlier editions of his Principles.