Definitions

A definition is a statement that identifies the nature of the units subsumed under a concept. Objectivism holds that a definition is a proposition about reality rather than a convention about words, and that it is therefore true or false — a position that puts it against most of modern philosophy of language and is the ground of its rejection of the analytic-synthetic dichotomy.

“A definition is a statement that identifies the nature of the units subsumed under a concept.”
~ Ayn Rand, "Definitions", Introduction to Objectivist Epistemology

What a definition has to do

A concept subsumes an unlimited number of characteristics of its units — every one they have, known and not yet discovered. No statement could list them. So a definition selects, and the whole question is whether the selection is a choice or a discovery.

The traditional form is genus and differentia, and Objectivism keeps it because it matches how concepts are formed:

The genus is the wider category the units belong to. It is the conceptual common denominator against which they were distinguished in the first place.
The differentia is what distinguishes them within it — a specified range of measurements along that shared dimension.

"Man is a rational animal" names the genus (animal) and the differentia (rationality). The structure is not a stylistic convention inherited from Aristotle; it is a report of the two-step process by which the concept was formed. See Concept formation.

The rule of fundamentality

Which differentia? Many characteristics distinguish men from other animals: language, tool use, laughter, cooking, the capacity for religion. All are true and all are distinguishing.

Objectivism holds that one of them is not on the same footing. The essential characteristic is the one that explains the greatest number of the others — and rationality explains language, tools, cooking and the rest, while none of them explains rationality. That relation of dependence is a fact about human beings, discovered rather than stipulated, which is what makes the choice of differentia objective. See Fundamental and Rule of Fundamentality.

This is also why a definition is not a summary of a concept's meaning. The concept means the units, with everything they are. The definition identifies what makes them that kind of thing.

Contextual, and absolute within the context

A child who has just formed "man" cannot define it as a rational animal, because he does not yet have those concepts. He will define it by what he can observe — a thing that walks upright and talks. That definition is not a mistake; it is correct within the knowledge he has, and it distinguishes men from everything else he has met.

“Definitions are not changelessly absolute, but they are contextually absolute.”
~ Ayn Rand, "Definitions", Introduction to Objectivist Epistemology

The key claim is that later definitions expand earlier ones rather than contradicting them, if both were formed properly. The referents never change: "man" picked out the same beings before and after anyone knew about rationality, language or DNA. What changes is how much of what those beings are has been integrated. See Context and Certainty.

A definition is revised when new knowledge reveals a deeper dependency, not when someone finds the old wording inconvenient.

Rules a definition must meet

It must be essential, not incidental. "Featherless biped" distinguishes men correctly and explains nothing.
It must not be circular. Defining a concept by a term that presupposes it establishes nothing.
It must not be exclusively negative. Saying what a thing is not fails to identify it, since an unlimited number of things are also not that.
It must be neither too broad nor too narrow. It must include every unit and exclude everything else.
It must be reducible. The terms used must themselves trace down the hierarchy to perceptual concretes, or the definition is a floating abstraction with a formal shape.

A supposed concept that cannot be defined under these rules is generally an invalid concept or a package deal — the defect being in the grouping, not in anyone's phrasing. See Rand's Razor.

Why it matters that definitions are true or false

If definitions were conventions, then propositions that follow from them would be true "by definition" and would say nothing about the world, while everything substantive would be a separate class of factual claim. That division is the analytic-synthetic dichotomy, and Objectivism's rejection of it rests directly on this page's argument: since a concept subsumes all the characteristics of its referents rather than only those named in the definition, there is no set of truths that follow from meaning alone.

The practical form of the same error is the retreat to "it's just semantics" when a definition is challenged. On the Objectivist account a disputed definition is a disputed claim about what the things in question are, and it is settled by evidence like any other. See Truth and Objectivity.

Common misunderstandings

That a definition is a description. A description conveys as much as possible about a thing. A definition identifies the one characteristic on which the rest depend, and is short for that reason rather than for brevity's sake.
That the dictionary settles it. A dictionary records usage, which is evidence about what concept a word names. It has no authority over whether that concept is validly formed or correctly defined.
That contextual definitions make knowledge unstable. Contextual means established within a known body of evidence, with a known scope. It is the opposite of provisional. See Certainty.
That changing a definition changes the facts. Redefining "man" does not alter any human being. This is what makes definition by stipulation a form of evasion when used to win an argument.
That a concept without a formal definition is meaningless. Axiomatic concepts — existence, identity, consciousness — cannot be defined in genus-and-differentia terms, because there is no wider category to place them in. They are defined ostensively, by pointing. See Axioms.

Discussion

References

Rand, Ayn. "Definitions" and "Axiomatic Concepts", Introduction to Objectivist Epistemology. The Objectivist, 1967.
Peikoff, Leonard. "The Analytic-Synthetic Dichotomy", appendix to Introduction to Objectivist Epistemology.
Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 4.

External links

Definitions at the Ayn Rand Lexicon

Epistemology Topics
Senses \| Consciousness \| Volition \| Concepts: Unit, Concept-Formation
Objectivity \| Knowledge: Context, Hierarchy \| Reason: Certainty, Truth, the Arbitrary \| Emotions