1. The definition (horos, horismos) was an important matter for Plato and for the Early Academy.
Concern with answering the question “What is so-and-so?” are at the center of the majority of Plato’s dialogues, some of which (most elaborately the Sophist) propound methods for finding definitions.
External sources (sometimes the satirical remarks of comedians) also reflect this Academic concern with definitions.
Aristotle himself traces the quest for definitions back to Socrates.
2. Definitions and Essences
For Aristotle, a definition is “an account which signifies what it is to be for something” (logos ho to ti ên einai sêmainei).
The phrase “what it is to be” and its variants are crucial:
– giving a definition is saying, of some existent thing, what it is, not simply specifying the meaning of a word (Aristotle does recognize definitions of the latter sort, but he has little interest in them).
The notion of “what it is to be” for a thing is so pervasive in Aristotle that it becomes formulaic:
– what a definition expresses is “the what-it-is-to-be” (to ti ên einai).
Roman translators, vexed by this odd Greek phrase, devised a word for it, essentia, from which our “essence” descends.
So, an Aristotelian definition is an account of the essence of something.
3. Species, Genus, and Differentia
Since a definition defines an essence, only what has an essence can be defined.
What has an essence, then?
That is one of the central questions of Aristotle’s metaphysics; once again, we must leave the details to another article.
In general, however, it is not individuals but rather species (eidos: the word is one of those Plato uses for “Form”) that have essences. […]
A species is defined by giving its genus (genos) and its differentia (diaphora):
– the genus is the kind under which the species falls, and the differentia tells what characterizes the species within that genus.
As an example, human might be defined as animal (the genus) having the capacity to reason (the differentia).
4. Essential Predication and the Predicables
Underlying Aristotle’s concept of a definition is the concept of essential predication (katêgoreisthai en tôi ti esti, predication in the what it is).
In any true affirmative predication, the predicate either does or does not “say what the subject is”, i.e., the predicate either is or is not an acceptable answer to the question “What is it?” asked of the subject.
Bucephalus is a horse, and a horse is an animal; so, “Bucephalus is a horse” and “Bucephalus is an animal” are essential predications.
However, “Bucephalus is brown”, though true, does not state what Bucephalus is but only says something about him.
Since a thing’s definition says what it is, definitions are essentially predicated.
However, not everything essentially predicated is a definition.
Since Bucephalus is a horse, and horses are a kind of mammal, and mammals are a kind of animal, “horse” “mammal” and “animal” are all essential predicates of Bucephalus.
Moreover, since what a horse is is a kind of mammal, “mammal” is an essential predicate of horse.
When predicate X is an essential predicate of Y but also of other things, then X is a genus (genos) of Y.
A definition of X must not only be essentially predicated of it but must also be predicated only of it:
– to use a term from Aristotle’s Topics, a definition and what it defines must “counterpredicate” (antikatêgoreisthai) with one another.
X counterpredicates with Y if X applies to what Y applies to and conversely.
Though X’s definition must counterpredicate with X, not everything that counterpredicates with X is its definition.
“Capable of laughing”, for example, counterpredicates with “human” but fails to be its definition.
Such a predicate (non-essential but counterpredicating) is a peculiar property or proprium (idion).
Finally, if X is predicated of Y but is neither essential nor counterpredicates, then X is an accident (sumbebêkos) of Y.
Aristotle sometimes treats genus, peculiar property, definition, and accident as including all possible predications (e.g. Topics I).
Later commentators listed these four and the differentia as the five predicables, and as such they were of great importance to late ancient and to medieval philosophy (e.g., Porphyry).