"foolish, stupid," 1530s, from Latin fatuus "foolish, insipid, silly;" which is of uncertain origin. Buck suggests originally "stricken" in the head. But de Vaan says from Proto-Italic *fatowo- "of speech," from PIE root *bha- (2) "to speak, tell, say."
[I]f we connect the fact that Fatuus is said to be an alternative name for Faunus, and that he predicted the future, and that this god is attested on an Etruscan mirror as Fatuvs in a clear oracular function (Weiss 2007b), we may venture a derivation from for 'to say' (Untermann 2000). The name of the god would then have come to be used pejoratively as 'silly'. [de Vaan]
Related: Fatuously; fatuousness.
1640s, from French fatuité (14c.), from Latin fatuitatem (nominative fatuitas) "foolishness, folly," from fatuus "foolish, insipid" (see fatuous).
1530s, "turn (something) to foolishness, frustrate by making foolish," from Latin infatuatus, past participle of infatuare "make a fool of," from in- "in" (from PIE root *en "in") + fatuus "foolish" (see fatuous). Specific sense of "inspire (in someone) a foolish passion beyond control of reason" is from 1620s. Related: Infatuated; infatuating.
An infatuated person is so possessed by a misleading idea or passion that his thoughts and conduct are controlled by it and turned into folly. [Century Dictionary]
*bhā-; Proto-Indo-European root meaning "to speak, tell, say."
It forms all or part of: abandon; affable; anthem; antiphon; aphasia; aphonia; aphonic; apophasis; apophatic; ban (n.1) "proclamation or edict;" ban (v.); banal; bandit; banish; banlieue; banns (n.); bifarious; blame; blaspheme; blasphemy; boon (n.); cacophony; confess; contraband; defame; dysphemism; euphemism; euphony; fable; fabulous; fado; fairy; fame; famous; fandango; fatal; fate; fateful; fatuous; fay; gramophone; heterophemy; homophone; ineffable; infamous; infamy; infant; infantile; infantry; mauvais; megaphone; microphone; monophonic; nefandous; nefarious; phatic; -phone; phone (n.2) "elementary sound of a spoken language;" phoneme; phonetic; phonic; phonics; phono-; pheme; -phemia; Polyphemus; polyphony; preface; profess; profession; professional; professor; prophecy; prophet; prophetic; quadraphonic; symphony; telephone; xylophone.
It is the hypothetical source of/evidence for its existence is provided by: Greek pheme "speech, voice, utterance, a speaking, talk," phōnē "voice, sound" of a human or animal, also "tone, voice, pronunciation, speech," phanai "to speak;" Sanskrit bhanati "speaks;" Latin fari "to say," fabula "narrative, account, tale, story," fama "talk, rumor, report; reputation, public opinion; renown, reputation;" Armenian ban, bay "word, term;" Old Church Slavonic bajati "to talk, tell;" Old English boian "to boast," ben "prayer, request;" Old Irish bann "law."