What Is a Definition? Fixing a Meaning and Choosing What It Excludes
By the BrainSnail editorial team. How these articles are written and checked, and how to tell us when one is wrong.
Defining a term looks like a preliminary to an argument and is frequently the argument itself, since a definition determines what falls inside a category and therefore what follows from being in it. Disputes that appear factual are regularly disputes about where a line is drawn.
The kinds
Definitions do several different jobs and confusing them causes trouble. A lexical definition reports how a word is actually used and can be correct or incorrect, since it is a claim about usage that a dictionary makes and that evidence can check. A stipulative definition announces how a term will be used in a particular discussion, cannot be wrong, and binds only that discussion. A precising definition takes a vague term and sharpens it for a purpose, which is what legal and technical definitions do and which always involves a choice about where to cut. An ostensive definition points at examples. A theoretical definition proposes an account embedded in a wider framework, so defining water as a particular chemical compound does more than record usage. And a persuasive definition packs an evaluation into an apparently descriptive statement, which is the move that makes definitional argument so frequently dishonest.
The classical requirements
The traditional standard for a definition is demanding and is met less often than expected:
- •It should state conditions that are jointly necessary and sufficient, so everything satisfying them is an instance and everything not satisfying them is not
- •It should not be circular, meaning it should not use the term or an obvious synonym
- •It should be neither too broad nor too narrow, which is tested by producing counterexamples in either direction
- •It should be clearer than the term defined, which rules out explaining an ordinary word with technical vocabulary
- •It should avoid negative formulation where a positive one is available, since saying what something is not rarely picks it out
- •It should avoid figurative language, which is expressive and imprecise
Arguing about words
A common response to a definitional dispute is to dismiss it as merely verbal, and the response is sometimes right and frequently lazy. It is right where two parties agree on every fact and simply use a word differently, in which case stipulating and moving on costs nothing. It is wrong where the word carries consequences, since a term embedded in law, in professional practice or in ordinary moral judgement brings obligations with it, and settling which cases fall under it settles those obligations. The test is straightforward, since if nothing changes once the parties adopt each other's usage the dispute was verbal, and if something changes it was not. Applying that test early saves considerable time, and it also identifies the cases where an apparently semantic disagreement is a substantive one wearing a disguise.
Why so many resist it
The classical project has a poor record for ordinary concepts and the failures are instructive rather than embarrassing. Attempts to define knowledge, art, game, life, person and cause have each generated large literatures without settled answers, with every proposal meeting a counterexample. Wittgenstein's response was that many concepts are held together by overlapping resemblances rather than by a shared essence, in the way that family members resemble each other without any single feature running through all of them, and that demanding a definition for such a concept misunderstands how it works. Prototype theory in psychology supports something similar empirically, since people judge some members of a category as better examples than others and respond faster to them, which a strict boundary would not predict. That does not make such concepts useless, since they function perfectly well without definitions, and it does mean that a demand for one before discussion can begin is frequently a way of preventing discussion.
Where the line has consequences
Precising definitions have to be written whenever a rule applies to a continuous reality, and the choice is substantive rather than technical. Legal definitions of employment determine who receives rights and protections, and the boundary between employee and contractor is fought over constantly because of what follows from it. Medical diagnostic thresholds define who has a condition, and moving one reclassifies millions overnight with consequences for treatment, insurance and identity. Statistical definitions of unemployment, poverty and homelessness determine what gets measured and therefore what gets addressed. Species definitions determine what is protected. In each case the argument is presented as a matter of getting the definition right and is actually a decision about who should be included, which is a question about consequences. The honest version of such an argument states the consequences and defends them, and the dishonest version presents a preferred outcome as a discovery about what a word means.
The takeaway
Reporting usage, stipulating a term for one discussion, sharpening a vague one and embedding a theory are different jobs, and a persuasive definition smuggles an evaluation into an apparently descriptive claim. The classical demand for necessary and sufficient conditions fails for most ordinary concepts, which hold together by overlapping resemblance. Where a line has consequences, arguing about the definition is arguing about who is included.