Socratic Definition (the "What Is X?" Question)

The demand, made canonical in the Euthyphro, for a definition by essence: not examples of X but "that form itself (eidos) by which all X-things are X," a single account usable "as a model" (paradeigma) to sort any case (6d–e). This ti esti ("what is it?") question is the target the elenchus tests answers against and the demand the Forms will later be posited to satisfy. Its distinctive — and contestable — corollary is the priority of definition: one must know what X is before knowing anything else about X (whether virtue is teachable waits on what virtue is).

Key Points

One form over many, as a standard. Socrates "did not bid you tell me one or two of the many pious actions but that form itself that makes all pious actions pious" — to be used "as a model" (Euthyphro 6d–e). The Meno makes the same demand with the swarm-of-bees image: many bees, "all the same … in being bees," so one form of virtue over its many kinds (72a–c).
The naive miss: interlocutors answer with a true instance ("the pious is what I am doing now," Euthyphro 5d–e; the Meno's catalogue of virtues, 71e–72a) and think they have answered. The elenchus wants the eidos by which instances are sorted, not a sample of them. The Hippias Major is the cleanest case: asked what the fine is, Hippias answers "a fine girl is a fine thing," and when pressed on the difference between "what is a fine thing" and "what is the fine" replies, "There's no difference" (287e) — the form/instance gap stated outright.
The "same in all cases" requirement: a definition must capture what is common to courage at sea, in illness, in politics, against desire — modeled on swiftness ("the same power in all," Laches 191e–192b).
Essence vs. property (ousia vs. pathos): even a feature that all and only X-things have can fail — god-belovedness attaches to pious things but is "an affect or quality" of the pious, "not … what the pious is" (Euthyphro 11a–b). Extensional coextension ≠ essence.
The priority of definition: "isn't it necessary for us to start out knowing what virtue is?" before asking how it is acquired (Laches 190b; Meno 71b) — the premise critics later call the "Socratic fallacy."
The dubia and spuria push the form three ways. The Minos reaches a positive τί-ἐστι on its headline question — law = "the discovery of reality" (315a) — where the genuine definitional dialogues stall (see claims#plato-minos-supplies-the-laws-missing-definition-of-law, candidate); the Clitophon sharpens "what is justice?" into "what is justice's peculiar product (ergon)?" (409a–b); and the spuria imitate the "what is X?" search as a schematic, inert genre (On Justice, On Virtue, Sisyphus) — definition detached from live dialectic (see claims#plato-spuria-academy-reception-stratum, candidate).

What the Concept Does

Fixes the elenchus's target — gives refutation a standard of success (a single, non-circular, essence-giving account), without which "testing a definition" would be aimless.
Makes ethics answerable to a standard of correctness — virtues become things there is a fact of the matter about, not honorific labels for approved behavior.
Generates the motive for the Forms — the stable, self-standing "X-itself" the ti esti demand keeps reaching for but the elenchus keeps failing to pin down.

What It Rejects

Definition by enumeration / example — the "many fine things" answer (Euthyphro 14a), the list of virtues "for a man, for a woman, for a child" (Meno 71e).
Relativized or merely extensional accounts — a property coextensive with X that does not say what makes X be X.

Stakes

The ti esti demand is the seed of the theory of Forms — but it predates the metaphysics, and conflating the two is a standing anachronism. In the Euthyphro and Meno the sought eidos is a single common feature / model (a "Meno-level" universal), with no separation (auto kath' hauto), no recollection, no two-world ontology. Euthyphro 6d–e and the Meno's swarm thus serve the wiki as pre-Forms anchors for "the X-itself," and the theory-of-forms page should credit them as such without reading the Republic/Phaedo apparatus back into them.

Problem-Space

The concept carries the priority-of-definition problem (the "Socratic fallacy"): must one know what X is in order to know anything about X? If yes, inquiry is paralyzed wherever no definition is in hand (which, given the aporetic dialogues, is everywhere); if no, the elenchus's refusal to grant the interlocutor's confident examples looks unmotivated. The Meno feels this directly: it demands "what is virtue?" first, then concedes virtue may be had by true opinion without the account.

Connections

is the condition of intelligibility of elenchus — the "what is X?" demand is the standard the elenchus tests answers against; refutation aims at this unmet target.
contrasts with theory-of-forms — the Socratic eidos is a single common feature / paradeigma, not yet the separated transcendent Form; the demand precedes the metaphysics (the genealogical guard-rail).
is the condition of intelligibility of aporia — the felt impasse just is the experience of the ti esti demand going unmet across successive refutations.
applies … to … the virtues socratic-intellectualism — pressed on piety, courage, temperance, the demand drives each toward "knowledge of good and evil," feeding the unity-of-virtue thesis.
is reached positively by the Minos — a dubium that, unusually, lands a positive τί-ἐστι of law (315a) where the genuine definitional dialogues fail.
is imitated as a genre by the spuria — the "what is X?" search frozen into schematic, doxographic exercises (Definitions, On Justice, On Virtue).

Open Questions

Is the priority of definition a genuine commitment or a dialectical device? The Meno both asserts it (71b) and undercuts it (true opinion suffices for action, 97a–c).
Where exactly does the eidos-as-model become the separated Form? The corpus offers no clean line; the Euthyphro/Meno sit before it, the Phaedo/Republic after.

Sources

plato-euthyphro — the locus classicus: the eidos-as-paradeigma demand (6d–e); essence vs. property (11a–b).
plato-meno — the swarm-of-bees universal (72a–c); the priority of "what is virtue?" (71b).
plato-laches — the "same in all cases" requirement, modeled on swiftness (191e–192b).
plato-charmides — the ti esti of temperance pursued on the craft-analogy, without Forms machinery.
plato-hippias-major — the form/instance demand at its starkest ("not what is a fine thing, but what is the fine," 287e) and the priority of definition as the dialogue's frame (304d–e); the search for "the fine itself" refuted through seven candidates.
plato-minos — a positive τί-ἐστι of law (313a, 315a), unusual among definitional dialogues (a dubium).
plato-clitophon — the τί-ἐστι sharpened into the demand for justice's peculiar product/ergon (409a–b) (a dubium).
plato-spuria — the "what is X?" form imitated as an inert genre (On Justice, On Virtue, Sisyphus). Spurious.