Definitions and Their Limits

Scenario

Suppose you are asked to give a precise definition of the word "game," one exact enough to settle, for any activity, whether it counts. A reasonable first attempt: a game is an activity in which two or more sides compete against each other under rules, aiming to win. This covers chess, tennis, poker, football. It looks like it also excludes whatever you would not call a game.

Test it against a case already inside the word by ordinary use: solitaire, the card game played alone. Solitaire has no second side, no opponent, nothing to compete against. By the definition above it fails to qualify, yet no English speaker hesitates to call it a game, and it is shelved as one in card sets and rulebooks everywhere. The definition was not careless. It was built from the clearest central cases, chess and tennis, and it still lets a real member of the category through its exclusion.

Try to patch it. Weaken "compete against each other" to "governed by rules and undertaken for enjoyment," and a new problem opens immediately: professional chess played for a salary, or a military exercise called a "war game" and run for training rather than enjoyment, are now hard to place, while the patch has quietly introduced two new terms, "rules" and "enjoyment," that need their own definitions before it does any work. Each repair buys coverage of one case at the price of a new case it does not fit. That pattern, not this or that failed wording, is what this entry is about.

Definition

The classical model

The classical model of definition, running from Aristotle through the standard logic textbook, holds that to define a term is to state conditions that are individually necessary and jointly sufficient for something to fall under it: features every instance must have (necessary), which together guarantee membership (sufficient). A triangle is a closed plane figure with exactly three straight sides; nothing lacking any of those three features is a triangle, and nothing having all three fails to be one. The attempted game definition above was reaching for exactly this form: features (two sides, competition, rules, aiming to win) meant to be jointly sufficient. The solitaire case showed that at least one of those features, competition between sides, is not actually necessary, and no repair tried above restores both necessity and sufficiency at once.

Family resemblance

Wittgenstein's response, in the Philosophical Investigations (1953), gives up the search for a single shared feature. Surveying board games, card games, ball games, and children's games such as ring-a-ring-a-roses, he finds no trait common to all of them: competition is missing from solitaire, winning and losing are absent from some ball games played purely for movement, skill is absent from games of pure chance, and enjoyment is absent from games run as drills. What he finds instead is a web of overlapping and crisscrossing similarities, the way members of one family resemble each other in build, features, and temperament without any single trait running through every member. He calls this family resemblance: a concept can hold together through a chain of partial overlaps between neighboring cases, chess overlapping with card games in one respect and card games overlapping with children's games in another, even when no property runs through the whole chain. Games form such a family. The word groups real similarities; it is a working concept, only one without a single defining core.

The competing view: epistemicism

Not every philosopher accepts that boundaries like this are genuinely absent, though the rival view targets a related but distinct phenomenon that is worth separating cleanly. Timothy Williamson's epistemicism (Vagueness, 1994) is a theory of vagueness, the trouble with terms like "heap" or "bald" that have clear cases at each end and a fog of borderline ones between. Williamson holds that such a term does have an exact cutoff, a fact about precisely where "heap" gives way to "non-heap," and that the difficulty is only that speakers cannot know where the cutoff falls, because ordinary use does not track the boundary finely enough to reveal it, the way a lens can have a real point of sharpest focus finer than any eye can locate by looking. Family resemblance and vagueness are not the same problem: "game" is Wittgenstein's case of a concept with no single shared feature, while "heap" is the standard case of a concept with a shared dimension but no visible cutoff. A concept can raise one, the other, or both, and an epistemicist who extends the hidden-boundary claim onto a family-resemblance concept like "game" is making the further bet that even it has a sharp line standing behind the overlaps. That extension remains contested rather than settled.

Common mistakes

The most common mistake is treating the failure of one definition as evidence the concept is empty or arbitrary. Solitaire breaking the competition-based definition of game does not show that "game" means nothing; it shows that the classical model, necessary and sufficient conditions, was the wrong tool for this particular concept. A second mistake is treating any borderline case as fatal to a definition. A workable classical definition can survive a handful of debatable edges (is a staring contest a game?) without collapsing, because a definition earns its keep by sorting the clear cases correctly and handling the unclear ones honestly, not by eliminating unclear cases altogether. A third mistake is confusing a stipulation with a discovery: a tournament rulebook can stipulate, for its own purposes, that a game is any activity scored under its official rules. That is a decision about how the word will be used in one setting, not a finding about what the word already meant beforehand, and treating the stipulation as if it had uncovered the concept's real boundary begs the question against family resemblance rather than answering it.

Family resemblance is also not the fate of every concept, and assuming it is would be its own mistake. Some concepts carry a clean set of necessary and sufficient conditions with no known borderline case at all. A prime number is a whole number greater than one divisible only by one and itself; every whole number either meets that description or does not, with no fringe of disputed cases the way "game" has. A triangle is a closed plane figure with exactly three straight sides, and the same holds. Concepts of this kind are typically stipulated into existence with their boundary built in from the start, which is why they escape the vagueness that affects a concept like "game," assembled by centuries of ordinary use rather than fixed by a single founding definition. The pattern in this entry applies to concepts that grew that way. It is not a claim about concepts in general.

Test yourself

Take a common word you use with confidence: art, sport, or fair. Write one candidate definition in the classical form, a set of features you take to be necessary and, together, sufficient. Then find a real case, not a hypothetical one, that your definition mishandles: something it excludes that plainly belongs, or something it admits that plainly does not. Decide which of two things the case shows: that your definition needs a specific repair (name the repair, and check whether the repair introduces a new failing case of its own), or that the term more likely works by family resemblance, in which case name two or three of the overlapping features doing the work instead of a shared core. A completed attempt has three things on the page: the definition, the real case that breaks it, and a stated verdict, with a reason, on which of those two outcomes the break shows.