The derivation
δαίμων is the soul-word with the most legible etymology and the most unsettling one. Beekes, Chantraine, and Frisk converge: δαίμων derives from the verb δαίομαι "to divide, distribute, allot" — the daimon is "the divider," the power that apportions (Beekes, EDG s.v. δαίμων, after Wilamowitz; Chantraine, DELG s.v. δαίμων, Et.: "tiré de δαίομαι… puissance qui attribue"). A god defined not by a name or a shape but by an act — the dealing-out of fate, the portion assigned.
The semantic parallel the dictionaries reach for is one of the most profound in Indo-European theology. Beekes sets δαίμων beside Old Persian baga-, Old Church Slavonic bogŭ "god" — words that also mean "the allotter," beside Avestan baga- "portion" and Sanskrit bhága- "portion, dispenser," from bhájati "to divide" (Beekes; Chantraine cites the same row). Twice, in two branches of the family, the word for god is built from the word for to apportion. To be divine, in this deep grammar, is to be the one who distributes lots. The same root δαι- gives Greek its words for the feast (δαίς) — the shared-out meal — and for the carver who divides it (δαιτρός). The god and the dinner are cut from one verb.
The dictionaries also preserve the folk-etymology the Greeks themselves made: a connection to δαήμων "knowing, skilled," as if a daimon were a knowing power — and Chantraine notes Plato plays on exactly this in the Cratylus (398b), and Archilochus may pun on δαίμων / δαήμων. False as derivation, it records how the Greeks heard the word. (Frisk's Nachträge adds a lone Iranian-loan speculation — Avestan daēman- "eye, glance" — marked, tellingly, with its own "(?)".)
Root
- *deh₂(i)- "to cut, divide" (Beekes, via δαίομαι; LIV s.v. *deh₂(i)- "teilen") — δαίμων as agent-noun, "the allotter." The same root yields δαίς "feast," δῆμος "district / people" (the divided land), δατέομαι "distribute." Theological parallel in *bhag- "apportion → god" (Iranian/Slavic/Indic).
In the corpus
193 occurrences across 15 works — present from the start (Iliad 27, Odyssey 33; earliest δαίμονας at Il. 1.222) and then steadily reinterpreted: Plotinus's Enneads (73) leads, with Plato (Cratylus 10, Republic 12), the Stoics, and Marcus Aurelius — for whom one's δαίμων becomes the indwelling guiding spirit, the precursor of "conscience." The word that began as an unnamed allotting power ends as the Platonic and Stoic inner daimon, and then — in Jewish and Christian Greek — as the demon. Unlike the heart-words ἦτορ and κραδίη that died with the epic, δαίμων kept being re-tooled for every later theology.
The word's world
The defining Homeric fact, all three dictionaries stress, is anonymity: δαίμων names "une puissance divine que l'on ne peut ou ne veut nommer" — a divine power one cannot or will not name (Chantraine). Where θεός is a god with a face and a cult, the δαίμων is the bare felt pressure of the divine in an event — and, Chantraine notes, "le δαίμων n'est pas l'objet d'un culte," it receives no worship. Dodds built his account of Homeric religion on exactly this: the daimon as the name for the moment when a person feels "not only itself but also something else" — the sudden impulse, the unaccountable swerve, attributed to a power from outside (The Greeks and the Irrational). It is the soul-word that faces outward — not a part of the self like θυμός or φρήν, but the divine share that falls to a self, the portion dealt to a life. Etymology and theology say the same thing here: your daimon is your allotment.
Authorities: Beekes, Etymological Dictionary of Greek (Brill 2010) s.v. δαίμων (scan pp. 344–345, #1538) and s.v. δαίομαι; Chantraine, Dictionnaire étymologique de la langue grecque s.v. δαίμων (scan pp. 260–261, #1785 + Et. at #1787); Frisk, Griechisches etymologisches Wörterbuch s.v. δαίμων (scan p. 372, #1402; Nachträge p. 2193, #6817). Interpretive sources retrieved from the Oracle library (Classical Philology & Ancient Thought): Dodds, The Greeks and the Irrational (1951); cf. Burkert, Greek Religion (1977); Kerényi, Hermes Guide of Souls (1944). Scholarly anchors named by the dictionaries: Wilamowitz, Der Glaube der Hellenen I.363; Nilsson, Geschichte der griechischen Religion I.216; LIV s.v. *deh₂(i)-. Corpus figures: Logoi corpus, live. Receipt: soul-word-journey-v0.