The phrase "a real definition" is correct and usable in written English.
It can be used when discussing the precise meaning of a term or concept, often in contrast to vague or informal definitions.
Example: "In academic writing, it is important to provide a real definition of key terms to ensure clarity and understanding."
Alternatives: "an accurate definition" or "a true definition".
The method involves a process of question and answer designed to elicit a "real definition".
By a real definition Plato means a set of necessary and sufficient conditions that exactly determine the entities to which a given concept applies.
A verbal definition does indeed state what a word means; but a real definition states what an object is, and the thought of a straight line is the thought of an object, not of words.
Under the former conception, we are aiming at a nominal definition; under the latter, at a real definition.
A real definition is somehow supposed to reveal the essential metaphysical structure of what it defines; nominal definitions do not do that.
So a "real" definition for the attribute would have to express things extrinsic to the attribute, its subject and that which brings it to actuality in the subject.
He aims to establish agreement about the kind to which they ascribe the name (Sophist 218b c), and he wants to find a real definition a definition that applies to all and only members of the kind, and one that explains why any instance is an instance of that kind: the inquirers seek the essence of the target kind, the property or collection of properties that make the kind what it is.
Indeed, he insists that nothing of interest follows for a demonstration from the real definition of a subject giving its genus and difference.
Whether the search for an answer to the Socratic question "What is virtue?" is a search for real definition or one for nominal definition depends upon one's conception of this particular philosophical activity.
For example, the real definition of a circle is that it is a set of points in a plane equidistant from a given point.
(Aquinas has a similar view concerning the first principles of a demonstration of the highest sort. With acquaintance with the real definition of a substantial nature, one can simply see, intellectually, what its immediate powers are).
