Meaning "illogical, absurd" is attested from 1640s. Related: Irrationally. The mathematical sense "inexpressible in ordinary numbers" is from late 14c. in English, from use of the Latin word as a translation of Greek alogon in Euclid.
word-forming element meaning "excessive or irrational fear, horror, or aversion," from Latin -phobia and directly from Greek -phobia "panic fear of," from phobos "fear" (see phobia). In widespread popular use with native words from c. 1800. In psychology, "an abnormal or irrational fear." Related: -phobic.
Meaning "irrational, maniacal, lacking or deprived of mental sense" is from 1520s; meaning "lacking or deprived of moral sense, unfeeling" is from 1550s. Insensate means "not capable of feeling sensation," often "inanimate;" insensible means "lacking the power to feel with the senses," hence, often, "unconscious;" insensitive means "having little or no reaction to what is perceived by one's senses," often "tactless." Related: Insensately; insensateness.