1660s, "pertaining to or resembling fire," from Latin igneus "of fire, fiery; on fire; burning hot," figuratively "ardent, vehement," from ignis "fire, a fire," extended to "brightness, splendor, glow;" figuratively "rage, fury, passion," from PIE root *egni- "fire" (source also of Sanskrit agnih "fire, sacrificial fire," Old Church Slavonic ogni, Lithuanian ugnis "fire"). Geological meaning "produced by volcanic forces" is from 1791, originally in distinction from aqueous. Earlier in the sense "fiery" were ignean (1630s), ignic (1610s).
"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.
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Harper, D. (n.d.). Etymology of ignis fatuus. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/ignis fatuus