Etymology
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Pythagorean (adj.)

1540s, from Latin Pythagoreus "of or pertaining to Pythagoras" of Samos, Greek philosopher (6c. B.C.E.) said to have travelled to Egypt and Babylon, whose teachings included transmigration of the soul and vegetarianism (these are some of the commonest early allusions in English).

Also in reference to a school he supposedly founded in Crotona in Italy. As a noun, "a follower of Pythagoras," by 1540s. The Pythagorean theorem is the 47th of the first book of Euclid: The area of the square whose side is the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides.

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Orphic (adj.)

"of or related to Orpheus or the doctrines attributed to him," 1670s, from Latinized form of Greek orphikos "pertaining to Orpheus," the legendary master musician of ancient Thrace, son of Eagrus and Calliope, husband of Eurydice, who had the power of charming all living things and inanimate objects with his lyre. His name is of unknown origin. In later times he was accounted a philosopher and adept in secret knowledge, and various mystic doctrines were associated with his name, whence Orphic mysteries, etc. (late 17c.). The earlier adjective was Orphean (1590s). Related: Orphism.

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neopaganism (n.)

also neo-paganism, "a revival or reproduction of paganism," 1858; see neo- "new" + paganism. Related: Neopagan (1854 as an adjective, 1855 as a noun).

[The 'positive' philosopher of the present day] offers in the stead of Christianity a specious phase of neo-paganism, by which the nineteenth century after Christ may be assimilated to the golden age of Mencius and Confucius; or, in other words, may consummate its intellectual freedom, and attain the highest pinnacle of human progress, by reverting to a state of childhood and of moral imbecility. [Introduction to Charles Hardwick, "Christ and Other Masters," Cambridge, 18758]
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Confucius 

1724, a Latinization of Chinese K'ung Fu-tzu "K'ung the philosopher (or Master)" (c. 551 B.C.E.-c. 479 B.C.E.), who sought to remedy the degeneracy and oppression of his time by the spread of virtue and learning. The name first appears in the West in a Latin publication of Chinese works (Paris, 1687).

His ethico-political philosophy is based on proper observance of the relationships of human life (parent/child, husband/wife, prince/subject, etc.). The term Confucianism (1836) sometimes is extended to ancient Chinese speculative philosophy generally. Related: Confucian (adj.), 1759.

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epicure (n.)

late 14c., "follower of Epicurus," a Latinized form of Greek Epicouros (341-270 B.C.E.), Athenian philosopher who taught that pleasure is the highest good and identified virtue as the greatest pleasure; the first lesson recalled, the second forgotten, and the name used pejoratively for "one who gives himself up to sensual pleasure" (1560s), especially "glutton, sybarite" (1774). Epicurus's school was opposed by the stoics, who first gave his name a reproachful sense. Non-pejorative meaning "one who cultivates refined taste in food and drink" is from 1580s.

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polytheism (n.)

"belief in more gods than one," 1610s, from French polythéisme (16c.), formed from Greek polytheia "polytheism," polytheos "of or belonging to many gods," from polys "many" (from PIE root *pele- (1) "to fill") + theos "god" (from PIE root *dhes-, forming words for religious concepts).

The various modes of worship, which prevailed in the Roman world, were all considered by the people, as equally true; by the philosopher, as equally false; and by the magistrate, as equally useful. And thus toleration produced not only mutual indulgence, but even religious concord. [Gibbon]
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stoic (n.)
late 14c., "philosopher of the school founded by Zeno," from Latin stoicus, from Greek stoikos "pertaining to a member of or the teachings of the school founded by Zeno (c. 334-c. 262 B.C.E.), characterized by austere ethical doctrines," literally "pertaining to a portico," from stoa "porch," specifically Stoa Poikile "the Painted Porch," the great hall in Athens (decorated with frescoes depicting the Battle of Marathon) where Zeno taught (see stoa). Meaning "person who represses feelings or endures patiently" first recorded 1570s. The adjective is recorded from 1590s in the "repressing feelings" sense, c. 1600 in the philosophical sense. Compare stoical.
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sophomore (n.)
Origin and meaning of sophomore

1680s, "student in the second year of university study," literally "arguer," altered from sophumer (1650s), from sophume, an archaic variant form of sophism, ultimately from Greek sophistēs "a master of one's craft; a wise or prudent man, one clever in matters of daily life."

The modern form probably is by folk etymology derivation from Greek sophos "wise" + mōros "foolish, dull" (see moron).

The original reference of the "arguer" name might be to the dialectic exercises that formed a large part of education in the middle years. At Oxford and Cambridge, a sophister (from sophist with spurious -er as in philosopher) was a second- or third-year student (what Americans would call a "junior" might be a senior sophister).

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automatic (adj.)

"self-acting, moving or acting on its own," 1812 (automatical is from 1580s; automatous from 1640s), from Greek automatos of persons "acting of one's own will;" of things "self-moving, self-acting," used of the gates of Olympus and the tripods of Hephaestus (also "without apparent cause, by accident"), from autos "self" (see auto-) + matos "thinking, animated," *men- (1) "to think."

Of involuntary animal or human actions, from 1748, first used in this sense by English physician and philosopher David Hartley. Meaning "done by self-acting machinery" is by 1850. In reference to a type of firearm, from 1877; specifically of machinery that imitates human-directed action from 1940.

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nihilism (n.)

1817, "the doctrine of negation" (in reference to religion or morals), from German Nihilismus, from Latin nihil "nothing at all" (see nil), coined by German philosopher Friedrich Heinrich Jacobi (1743-1819). In philosophy, an extreme form of skepticism (1836). The political sense, "rejection of fundamental social and political structures," was first used c. 1824 by German journalist Joseph von Görres (1776-1848). Turgenev used the Russian form of the word (nigilizm) in "Fathers and Children" (1862) and claimed to have invented it. With a capital N-, it refers to the Russian revolutionary anarchism of the period 1860-1917, supposedly so called because "nothing" that then existed found favor in their eyes.

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