Etymology
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logic (n.)

mid-14c., logike, "branch of philosophy that treats of forms of thinking; the science of distinction of true from false reasoning," from Old French logique (13c.), from Latin (ars) logica "logic," from Greek (he) logike (techne) "(the) reasoning (art)," from fem. of logikos "pertaining to speaking or reasoning" (also "of or pertaining to speech"), from logos "reason, idea, word" (see Logos). Formerly also logick. Sometimes formerly plural, as in ethics, but this is not usual. Meaning "logical argumentation" is from c. 1600. Contemptuous logic-chopper "sophist, person who uses subtle distinctions in argument" is from 1846.

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formal (adj.)
late 14c., "pertaining to form or arrangement;" also, in philosophy and theology, "pertaining to the form or essence of a thing," from Old French formal, formel "formal, constituent" (13c.) and directly from Latin formalis, from forma "a form, figure, shape" (see form (n.)). From early 15c. as "in due or proper form, according to recognized form," As a noun, c. 1600 (plural) "things that are formal;" as a short way to say formal dance, recorded by 1906 among U.S. college students.
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formalism (n.)
1840, "strict adherence to prescribed forms," from formal + -ism. Used over the years in philosophy, theology, literature, and art in various senses suggesting detachment of form from content, or spirituality, or meaning; or belief in the sufficiency of formal logic. Related: Formalist.
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informal (adj.)
mid-15c., "lacking form; not in accordance with the rules of formal logic," from in- (1) "not, opposite of" + formal (adj.). Meaning "irregular, unofficial, not according to rule or custom" is from c. 1600. Sense of "done without ceremony" is from 1828. Related: Informally.
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physicological (adj.)

"pertaining to logic as illustrated by physics," 1704, from physicologic "logic illustrated by physics," from physico- + logic. Related: Physicologic; physicologically.

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dialectic (n.)

1580s, earlier dialatik (late 14c.), "critical examination of the truth of an opinion, formal reason and logic applied to rhetoric and refutation," from Old French dialectique (12c.) and directly from Latin dialectica, from Greek dialektike (techne) "(art of) philosophical discussion or discourse," fem. of dialektikos "of conversation, discourse," from dialektos "discourse, conversation" (see dialect).

Originally synonymous with logic; in modern philosophy refined by Kant ("the theory of false argumentation leading to contradictions and fallacies), then by Hegel, who made it mean "process of resolving or merging contradictions in character to attain higher truths." Used generally in 20c. Marxism for "evolution by means of contradictions." Related: Dialectics.

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logician (n.)
"person skilled in logic," late 14c., from Old French logicien (13c.), from logique (see logic). The Greek word was logistes.
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metalogical (n.)

"beyond the sphere of logic, transcending logic," by 1865; see meta- in the third sense of "transcending, overarching, dealing with the most fundamental matters of" + logical. Related: Metalogic (n.), by 1842; metalogical.

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logical (adj.)
early 15c., "based on reason, according to the principles of logic," from logic + -al (1). Meaning "pertaining to logic" is c. 1500. Attested from 1860 as "following as a reasonable consequence." Related: Logically. Logical positivism, in reference to the ideas of the Vienna Circle of philosophers, is from 1931.
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formalize (v.)
1590s, "give an appearance of being to," from formal + -ize. Meaning reduce to form" is from 1640s; sense of "render formal" is from 1855. Related: Formalized; formalizing.
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