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αρχη [archê]

Greek term for beginning or ultimate principle. The Milesian philosophers looked for a single material stuff of which the entire universe is composed, while Empedocles identified no fewer than four elements whose mixture makes up ordinary things. For both Plato and Aristotle, however, the αρχη most worth seeking would be an originating power from which the material order flows and upon which theoretical knowledge of its nature might be grounded logically.

Recommended Reading: F. E. Peters, Greek Philosophical Terms: A Historical Lexicon (NYU, 1967).

Also see PP.

Archimedes (287-212 BCE)

Sicilian geometrician who calculated an accurate value for π, demonstrated the relationship between the volume of spheres and cylinders, discovered methods for determining the center of gravity of plane figures, and provided a foundation for the science of hydrostatics. Archimedes also invented many ingenious machines, including a pump for raising water, effective levers and compound pulleys, and a mechanical planetarium. He died defending Syracuse against a Roman seige during the second Punic war.

Recommended Reading: E. J. Dijksterhuis, Archimedes (Princeton, 1987).

Also see Chris Rorres, EB, WSB, and MMT.

Arendt, Hannah (1906-1975)

German-American political philosopher. Although she had studied with Jaspers and Heidegger in Heidelberg, Arendt fled Germany in 1933 and, from her new home in the United States, wrote powerfully about the anti-Semitism of the Nazi regime, describing its emergence as an instance of "the eerie banality of evil" in Eichmann in Jerusalem: A Report on the Banality of Evil (1963). Arendt's The Origins of Modern Totalitarianism (1951) decried the concentration of political power engendered by imperialism of every sort. In The Human Condition (1958), On Revolution (1963), and The Life of the Mind (1978), however, she expressed a profound skepticism about the prospect that philosophical thought could significantly influence the individual actions that determine the political structure of human culture.

Recommended Reading: The Portable Hannah Arendt, ed. by Peter Baehr (Penguin, 2000); Hannah Arendt / Karl Jaspers Correspondence 1926-1969, ed. by Lotte Kohler and Hans Saner (Harcourt Brace, 1993); Maurizio d'Entreves, The Political Philosophy of Hannah Arendt (Routledge, 1993); Margaret Canovan, Hannah Arendt: A Reinterpretation of Her Political Thought (Cambridge, 1994); Feminist Interpretations of Hannah Arendt, ed. by Bonnie Honig (Penn. State, 1995); and Dana Richard Villa, Arendt and Heidegger (Princeton, 1995).

Also see The Hannah Arendt Papers at The Library of Congress, SEP, EB, ELC, Hideyuki Hirakawa, and Bethania Assy.

Αρης [Ares]

Greek god of destruction, slaughter, and war, later called Mars by the Romans. Hence, for poets and philosophers, a symbol of strife and discord generally.

Also see EB and PP.

αρετη [aretê]

Greek word for unique excellence or skill of any sort; hence, especially, moral virtue. Socrates supposed that αρητη can be identified with knowledge of the good, but Plato distinguished four distinct virtues as crucial components of the perfect state or person. Aristotle maintained that moral αρετη is invariably found as the mean between vicious extremes.

Recommended Reading: F. E. Peters, Greek Philosophical Terms: A Historical Lexicon (NYU, 1967).

Also see PP.


A collection of two or more propositions, all but one of which are the premises supposed to provide inferential support—either deductive or inductive—for the truth of the remaining one, the conclusion. The structure of arguments is the principal subject of logic.

Recommended Reading: Stephen Toulmin, Uses of Argument (Cambridge, 1958) and Douglas Walton, Argument Structure: A Pragmatic Theory (Toronto, 1996).

Also see EB.

argument form

The general logical structure of an argument, considered apart from any of its specific content. In categorical logic, an argument form is any one of the 256 distinct varieties of categorical syllogism. In the propositional calculus, an argument form is a set of two or more statement forms such that the substitution of an actual statement for each of its statement variables would result in an argument.

argumentum . . .

. . . ad baculum: see appeal to force.

. . . ad hominem: see ad hominem argument.

. . . ad ignoratiam: see appeal to ignorance.

. . . ad misericordiam: see appeal to pity.

. . . ad populum: see appeal to emotion.

. . . ad verecundiam: see appeal to authority.

Aristippus (435-356 B.C.E.)

North African philosopher. Originally a student of Socrates, Aristippus (and his eponymous grandson) established the Cyrenaic school of philosophy, according to which sensual pleasure in the present moment, tempered only by moderation, is the genuine good for human life.

Also see IEP, EB, and CE.


Rule by "the best," usually a privileged class with special responsibilities for the public welfare. Plato, for example, defended as ideal a system of government in which carefully educated individuals were permitted to make wise decisions on behalf of the society as a whole.

Recommended Reading: Plato, The Republic, tr. by G. M. Grube (Hackett, 1992); Nickolas Pappas, Routledge Guidebook to Plato and the Republic (Routledge, 2003);

Also see EB.

Aristotelian logic

Traditional categorical logic, as developed originally in the Organon of Aristotle.

Also see Kelly L. Ross and George Boger.


A tradition, dating from the medieval period, concerned with promoting and defending significant portions of the philosophy of Aristotle.

Also see , EB, and ISM.

Aristotle (384-322 BCE)

Greek philosopher who developed an observational and logical method for investigating the natural world.

For a discussion of his life and works, see Aristotle.


The study of natural numbers. Although familiar to schoolchildren everywhere, arithmetical truths are often supposed to be problematic in their epistemological origins. Peano and Frege showed that all of arithmetic could be axiomatized, but Kurt Gödel demonstrated that such systems are invariably incomplete.

Recommended Reading: Gottlob Frege, The Basic Laws of Arithmetic (1903); J. R. Lucas, Conceptual Roots of Mathematics (Routledge, 1999); From Frege to Godel 1879-1931: A Source Book in Mathematical Logic, ed. by Jean Van Heijenoort (iUniverse, 1999).

Also see EB.

Armstrong, David M. (1926- )

Australian philosopher. In Perception and the Physical World (1961) and A Materialist Theory of Mind (1968) Armstrong strictly defends the identity of mental events with states of the brain. Armstrong also argues for the objective reality of qualities and relations in Universals and Scientific Realism (1978) and Universals (1989).

Recommended Reading: D. M. Armstrong, A World of States of Affairs (Cambridge, 1997) and Ontology, Causality, and Mind: Essays in Honor of D. M. Armstrong, ed. by John Bacon, Keith Campbell, and Lloyd Reinhardt (Cambridge, 1993).

Arnauld, Antoine (1612-1694)

French theologian and philosopher. Influential as co-author (with Pierre Nicole} of La logique, ou l'art de penser (The "Port-Royal" Logic) (1662), Arnauld was active in the seventeenth-century French philosophical community that also included Mersenne and Pascal. Arnauld wrote the fourth set of Objections that were published along with Descartes's Meditations (1641), criticized the occasionalist philosophical system and theological views of Malebranche in Traité de vraies et fausses idées (On True and False Ideas) (1683), and engaged in a lengthy correspondence with Leibniz.

Recommended Reading: Steven Nadler, Arnauld and the Cartesian Philosophy of Ideas (Princeton, 1989).

Also see CE, SEP, EB, ELC, and MMT.

Arrow, Kenneth Joseph (1921- )

American economist and social theorist. In Social Choice and Individual Values (1951) Arrow introduced the general impossibility theorem, which shows that the rationally collective preference of a group cannot always be derived from the transitive preferences of its individual members. (This point is often illustrated with instances of the voting paradox.) Arrow won the Nobel Prize in Economic Sciences in 1972.

Recommended Reading: Kenneth Joseph Arrow, The Limits of Organization (Norton, 1974) and Markets, Information, and Uncertainty: Essays in Economic Theory in Honor of Kenneth J. Arrow, ed. by Graciela Chichilnisky (Cambridge, 1999).

Also see EB.

artificial intelligence

Scientific research aimed at building machines capable of performing a variety of functions as well as (or better than) human agents do. Although early efforts focused on symbolic manipulation and linguistic representation, most now use the notion of parallel distributed processing for the construction of a quasi-neural network that recognize and associate patterns. Hopes (or fears) of the success of this discipline often give rise to philosophical questions about whether purely physical systems can adequately support consciousness, perception, and mind.

Recommended Reading: The Simulation of Human Intelligence, ed. by Donald Broadbent (Blackwell, 1993); Jack Copeland, Artificial Intelligence: A Philosophical Introduction (Blackwell, 1993); Understanding Artificial Intelligence, ed. by Scientific American (Time-Warner, 2002); Craig DeLancey, Passionate Engines: What Emotions Reveal about Mind and Artificial Intelligence (Oxford, 2002); Renée Elio, Common Sense, Reasoning, and Rationality (Oxford, 2002); Sam Williams, Arguing A.I.: The Battle for Twenty-First-Century Science (Random House, 2002); Craig DeLancey, Passionate Engines: What Emotions Reveal about Mind and Artificial Intelligence (Oxford, 2002); Daniel C. Dennett, Brainchildren: Essays on Designing Minds, 1984-1996 (Bradford, 1998); and Semantic Information Processing, ed. by Marvin L. Minsky (MIT, 1969).

Also see Ned Block, IEP, EB, John Sullins, SEP on Automated Reasoning and Logic and Artificial Intelligence, and DPM.


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Last modified 21 November 2011.
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