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**Leibniz, Gottfried W.**(1646-1716)German mathematician and philosopher who invented the integral calculus independently of Newton and developed an intricate pluralistic philosophy, according to which individual substances are dimensionless mathematical points (monads) functioning in a pre-established harmony with each other.

For a discussion of his life and works, see

*Leibniz*.

**Lenin, Vladimir Ilyich**(1870-1924)Russian revolutionary who led the October Revolution of 1917 and became head of state. His State and Revolution (1917) discusses the practical application of

*Marx*'s principles to the success of the Bolshevik revolution. On Lenin's view, the dictatorship of the proletariat is a temporary expedient that will inevitably lead to the creation of a truly socialist government. In his Materialism and Empiro-Criticism (1909) and the Philosophical Notebooks (1929), Lenin sought to purge Marxism of any tendency toward subjective idealism by encouraging critical study of*Hegel*.Recommended Reading: Vladimir Lenin, Essential Works of Lenin: 'What Is to Be Done?' and Other Writings, ed. by Henry M. Christman (Dover, 1987); Robert Service, Lenin: A Biography (Harvard, 2000); Louis Althusser, Lenin and Philosophy and Other Essays (Monthly Review, 2001); Georg Lukacs, Lenin: A Study in the Unity of His Thought (Verso, 1998); and Kevin Anderson, Lenin, Hegel, and Western Marxism: A Critical Study (Illinois, 1995).

Also see The Marxist Internet Archive,

*EB*, and .

**Lessing, Gotthold Ephraim**(1729-1781)German philosopher, critic, and playwright who vigorously opposed dogmatism in any form and supported the ideals of the Enlightenment. In Die Erziehung des Menschengeschlechts (The Education of the Human Race) (1780) he argued that both revealed religion and philosophical rationality represent stages of historical development rather than expressions of eternal truth. Popular plays such as Minna von Barheim, along with Lessing's aesthetic writings, including the Laokoon (1766), helped to revive German interest in Shakespeare and Spinoza.

Recommended Reading: Gotthold Ephraim Lessing, Nathan the Wise, Minna Von Barnhelm, and Other Plays and Writings, ed. by Peter Demetz (Continuum, 1991).

Also see

*EB*, and Gutenberg-DE.

**Leucippus**(c. 450 BCE)Presocratic philosopher and atomist who opposed the Eleatics and argued that everything that happens is strictly determined by rational laws. His views were more fully developed and expressed by Democritus and

*Epicurus*.Recommended Reading: George Sarton, Ancient Science Through the Golden Age of Greece (Dover, 1993) and C. C. W. Taylor, The Atomists: Leucippus and Democritus (Toronto, 1999).

Also see SEP, IEP, John Burnet, WSB,

*EB*, MMT, and ELC.

**Lewis, Clarence Irving**(1883-1964)American philosopher and logician. Lewis's Symbolic Logic (1932) contributed significantly to the development and refinement of modern modal logic. His empiricist epistemology, employing significant elements of pragmatism, is developed in Mind and the World-Order (1929). An Analysis of Knowledge and Valuation (1946) defends a naturalistic account of human morality.

Recommended Reading: E. Paul Colella, C.I. Lewis and the Social Theory of Conceptualistic Pragmatism: The Individual and the Good Social Order (Edwin Mellen, 1992) and The Philosophy of C. I. Lewis, ed. by Paul A. Schilpp (Open Court, 1981).

**lexical definition**A faithful report of the way in which a term is used within a particular language-community.

*lex talionis*Latin phrase meaning, "law of retaliation." Hence, a strictly retributive notion of punishment, according to which anyone who causes injury to another should suffer exactly the same injury in return.

Recommended Reading: Hugo Adam Bedau, Retribution and the Theory of Punishment (Rowman & Littlefield, 1981) and Charles K. B. Barton, Getting Even (Open Court, 1999).

**liar, paradox of the**The sentence

*"I am now lying"*would seem to be true (because I am lying) only in those cases when it is false (since what I say is the case) and false (because I am not lying) when it is true (since what I say is not the case). Less personally, the statement*"This sentence is not true"*generates a similar perplexity. These are particular instances of the self-referential semantic paradoxes that have troubled logicians since Epimenides, the Cretan who is supposed to have said, "All Cretans are liars."Recommended Reading: Paradox of the Liar, ed. by Robert L. Martin (Ridgeview, 1979); Recent Essays on Truth and the Liar Paradox, ed. by Robert L. Martin (Oxford, 1997); Vann McGee, Truth, Vagueness, and Paradox: An Essay on the Logic of Truth (Hackett, 1990); Robert C. Koons, Paradoxes of Belief and Strategic Rationality (Cambridge, 1992); and Benson Mates, Skeptical Essays (Chicago, 1981).

Also see SEP, IEP,

*EB*, and Peter Suber.

*libertas*Latin word for freedom.

Recommended Reading: Chaim Wirszubski, Libertas As a Political Idea at Rome During Late Republic and Early Principate (Cambridge, 1950).

Also see SEP.

**Lobachevsky, Nikolai Ivanovich**(1792-1856)Russian mathematician who developed a non-Euclidean geometry, denying the truth of Euclid's parallel postulate by supposing that there may be two or more such lines passing through a given point.

Recommended Reading: H. S. Coxeter, Non-Euclidean Geometry (Math. Assn. of Amer., 1998); Marvin Jay Greenberg, Euclidean and Non-Euclidean Geometries: Development and History (Freeman, 1995); Non-Euclidean Geometry, ed. by Roberto Bonola and H. S. Carslaw (Dover, 1954); and Morris Kline, Mathematical Thought from Ancient to Modern Times (Oxford, 1990).

Also see Dan Bucsescu, SEP, MMT, WSB,

*EB*, and .

**Locke, John**(1632-1704)British philosopher who outlined the central tenets of empiricism in philosophy and in political theory argued that civil authorities rule only with the consent of those who are governed.

For a discussion of his life and works, see

*Locke*.

**locutionary act**The simple speech act of generating sounds that are linked together by grammatical conventions so as to say something meaningful. Among speakers of English, for example, "

*It is raining*" performs the locutionary act of saying that it is raining, as "*Grablistrod zetagflx dapu*" would not.Recommended Reading: J. L. Austin, How to Do Things With Words, ed. by Marina Sbisa and J. O. Urmson (Harvard, 1975) and John R. Searle, Speech Acts (Cambridge, 1970).

**logic**Branch of philosophy concerned with the distinction between correct and incorrect reasoning. It commonly comprises both deductive and inductive arguments.

Recommended Reading: Graham Priest, Logic: A Very Short Introduction (Oxford, 2000); Irving M. Copi and Carl Cohen, Introduction to Logic (Prentice Hall, 2001); Graeme Forbes, Modern Logic: A Text in Elementary Symbolic Logic (Oxford, 1994); Douglas N. Walton, Informal Logic: A Handbook for Critical Argumentation (Cambridge, 1989); and John Bacon, Michael Detlefsen, and David McCarty, Logic from A to Z (Routledge, 1999).

Also see

on logic and its history, and*EB***SEP**on classical, infinitary, informal, intuitionistic, many-valued, paraconsistent, relevance, substructural, and temporal logic, logic and games, and logical constructions.

**logic, modal**Study of reasoning about what

**must**or**might**be the case, as well as what merely happens to be the case. The formalization of modal logic for the propositional calculus introduces special operators designating necessity and possibility (*L*and*M*). "It is necessary that*p*" (*Lp*) is interpreted to mean that*p*must be true in all possible worlds, and "It is possible that*p*" (*Mp*) that*p*is true in at least one possible world. On these interpretations,*Lp*`≡`*~M~p*is tautologous.Recommended Reading: Brian F. Chellas, Modal Logic: An Introduction (Cambridge, 1980); G. E. Hughes and M. J. Cresswell, A New Introduction to Modal Logic (Routledge, 1996); Alvin Plantinga, Essays in the Metaphysics of Modality, ed. by Matthew Davidson (Oxford, 2003); and Rudolf Carnap, Meaning and Necessity: A Study in Semantics and Modal Logic (Chicago, 1989).

Also see

**SEP**on modal logic and medieval theories of modality, and*EB*, Michael Huemer.

**logical form**The structure of a proposition or an argument from which all content has been removed. Tautology and validity are features that hold only in virtue of logical form.

Recommended Reading: William G. Lycan, Logical Form in Natural Language (MIT, 1969); Peter Long, Logic, Form, and Grammar (Routledge, 2001); and Robert May, Logical Form (MIT, 1985).

Also see SEP.

**logical positivism**Twentieth-century philosophical movement that used a strict principle of verifiability to reject as meaningless the non-empirical statements of metaphysics, theology, and ethics. Under the influence of

*Hume*,*Russell*, and the early*Wittgenstein*, the logical positivists regarded as meaningful only statements reporting empirical observations, taken together with the tautologies of logic and mathematics. Prominent logical positivists included members of the Vienna Circle and Ayer.Recommended Reading: A. J. Ayer, Logical Positivism (Free Press, 1966); Michael Friedman, Reconsidering Logical Positivism (Cambridge, 1999); and Science and Philosophy in the Twentieth Century: Basic Works of Logical Empiricism, ed. by Sahotra Sarkar (Garland, 1996) — Vol. 1: The Emergence of Logical Empiricism: From 1900 to the Vienna Circle, Vol. 2: Logical Empiricism at Its Peak: Schlick, Carnap, and Neurath, Vol. 3: Logic, Probability, and Epistemology: The Power of Semantics, Vol. 4: Logical Empiricism and the Special Sciences: Reichenbach, Feigl, and Nagel, Vol. 5: Decline and Obsolescence of Logical Empiricism: Carnap vs. Quine and the Critics, and Vol. 6: The Legacy of the Vienna Circle: Modern Appraisals.

Also see SEP, IEP,

*EB*, and ISM.

**logicization of arithmetic**The program—conceived by Dedekind, Peano, Frege, and Hilbert, but completed by

*Russell*and Whitehead in Principia Mathematica (1913)—of showing that arithmetical knowledge can be demonstrated upon the basis of purely logical axioms and definitions. The project was effectively demolished by Gödel's proof that some true formal propositions must nevertheless remain undecidable within the system.Recommended Reading: J. R. Lucas, Conceptual Roots of Mathematics (Routledge, 1999); Howard Whitley Eves, Foundations and Fundamental Concepts of Mathematics (Dover, 1997); Ivor Grattan-Guinness, The Search for Mathematical Roots, 1870-1940 (Princeton, 2001); and From Frege to Godel 1879-1931: A Source Book in Mathematical Logic, ed. by Jean Van Heijenoort (iUniverse, 1999).

Also see SEP.

**λογος / μυθος**[logos / mythos]*Plato*'s Greek distinction between two ways of explaining what happens: either by providing an explicit rational account (**λογος**), which combines with belief to form accurate knowledge {Gk. επιστημη [epistêmê]} of the essence of things; or merely by telling a story with figurative significance (**μυθος**). The Stoics elevated λογος into an active principle that generates the specific "seminal reasons" {Gk. λογοι σπερματικοι [logoi spermatikoi]} from which individual things flow. Philo Judaeus fully personified this notion as the divine agent responsible for creation of the world.Recommended Reading: F. E. Peters, Greek Philosophical Terms: A Historical Lexicon (NYU, 1967).

Also see Stephen Daniel,

*EB*, and PP.

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