illogical (adj.)

word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."

In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.

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.