Wittgenstein's Family Resemblance

Good to continue from Rand’s measurement-omission account. Rand’s theory retained the classical ambition: members of a concept share a distinguishing characteristic, while their particular measurements vary. Wittgenstein’s challenge is more disruptive. For some ordinary concepts, he argues, there may be no single characteristic shared by every member in the first place.

This lesson reconstructs that challenge carefully. The central example is game, but the issue is much broader: whether a concept must have an essence expressible as necessary and sufficient conditions, or whether overlapping connections can sometimes do the classificatory work.

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The target: the classical demand for an essence

The classical picture treats a concept as delimiting a class through a definition. Its members have something in common that non-members lack. In logical form, the aspiration is:

$$\mathrm{Game}(x)\leftrightarrow C_1(x)\wedge C_2(x)\wedge \cdots \wedge C_n(x)$$

The conditions on the right should jointly be:

• necessary: every game has each relevant condition;
• sufficient: anything with all of them is a game.

Aristotle’s genus-and-differentia definitions are one influential version of this model. Rand’s measurement omission differs in its account of abstraction, but it likewise assumes that units grouped under a concept possess the same distinguishing characteristic(s), differing only in degree or measure.

Wittgenstein asks us to question a tacit inference:

If we correctly use one word for many cases, must there be one common property that explains the use?

His answer is: not necessarily. The request for a definition may be appropriate for some concepts, but it is a mistake to assume in advance that every meaningful general word has a hidden essence waiting to be extracted.

The relevant passages are §§65–67 of Philosophical Investigations. Read them first, since they are exceptionally compact and contain the whole argumentative shape. I couldn't locate that online, but I found some references here in case you don't have a copy:

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“Look and see”: the case of games

Wittgenstein does not begin by proposing a rival definition of game. He begins with an instruction: look at the variety of cases already called games.

Consider chess, poker, football, solitaire, tag, a child’s pat-a-cake game, and the Olympic Games. Various features appear across these activities:

Feature	Present in some games	Absent or doubtful in others
Competition	football, chess, poker	solitary or cooperative games
Winning and losing	tournament chess, football	pat-a-cake and some forms of play
Luck	poker, roulette	chess
Skill	chess, football	pure games of chance
Physical exertion	football, tag	card and board games
Amusement	many recreational games	professional or compulsory contexts

The point is not that this table settles every case. One can always try a more sophisticated definition. Wittgenstein’s challenge is that the usual candidates repeatedly fail to be necessary across the full heterogeneous range.

The mistake, on his view, is to treat this pattern of failure as evidence merely that philosophers have not yet been clever enough. Perhaps the failure is systematic because the concept game does not have the required structure.

A useful reconstruction runs as follows:

1. The classical theory claims that every genuine concept has a common essence, articulable through necessary and sufficient conditions.
2. Examination of many activities called “games” reveals no obvious feature shared by all of them.
3. Instead, particular games resemble particular other games in different respects: chess resembles poker in rules and winning; poker resembles roulette in gambling and chance; football resembles chess in competition and skill; tag resembles football in physical activity.
4. These similarities overlap and criss-cross, but no one feature need run through the entire collection.
5. Therefore, at least some concepts may be held together by a network of relations rather than by a shared essence. The universal classical claim is undermined.

Notice the force and the limit of the conclusion. Wittgenstein does not establish that no concept can be defined by necessary and sufficient conditions. Triangle, even number, and perhaps bachelor are plausible candidates for concepts with tighter definitions. His examples instead challenge the universal demand that every concept must fit that mold.

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Family resemblance is a network, not a concealed common core

The expression family resemblance identifies the alternative structure. Relatives may share eye colour, a gait, a nose, a temperament, or a particular voice. But there need not be a single feature found in every individual. One sibling may resemble a parent in facial structure, another in mannerisms, and cousins may look alike while differing markedly from a grandparent.

The metaphor is meant to foreground overlap without total intersection.

The image is useful because it blocks two tempting but mistaken interpretations.

First, family resemblance does not mean that members share nothing at all. There are real similarities and affinities. The claim is only that they need not share one and the same property across the whole extension.

Second, it does not mean that the category is an arbitrary heap. The items are interconnected in a structured way. Wittgenstein’s metaphor of a thread makes this especially clear: a thread’s strength does not depend on one fibre extending from end to end. It comes from many fibres overlapping over different stretches.

In the same way, a family-resemblance concept may have a connected structure even when no feature is universal. Think of the category as a graph: cases are linked by salient shared features, although a feature connecting one pair may be absent from another pair.

A short discussion by John Searle and Bryan Magee provides a helpful orientation to this move from essence to use, before we sharpen its implications.

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What Wittgenstein is—and is not—claiming

It is easy to overstate the argument in three ways.

1. He is not merely pointing to vagueness

A vague concept has borderline cases: perhaps it is unclear exactly when a collection of grains becomes a heap. But it may still have one governing feature.

A family-resemblance concept raises a different structural possibility: even among uncontroversial members, there may be no common feature. The issue is not merely that the boundary is fuzzy. It is that there may be no essence at the centre from which a boundary could be derived.

This distinction matters for the question driving the course. “Fuzzy” can mean at least two things:

• uncertain or graded application around a criterion;
• absence of a single criterion because membership rests on heterogeneous relations.

Wittgenstein’s argument concerns primarily the second.

2. He is not offering “resemblance to something” as a clean replacement definition

An immediate objection is: everything resembles everything else in some respect. A chess set and a lettuce leaf are both physical objects; chess and financial trading both involve strategy; roulette and weather both involve uncertainty. If any resemblance suffices, then any activity can count as a game.

That objection is sound against a crude version of family resemblance. Wittgenstein cannot mean:

$$x\text{ is a game if }x\text{ resembles any game in any respect}$$

Rather, resemblance must be relevant within an established practice of use. People learn to use “game” through examples, corrections, comparisons, and shared activities. The category has paradigmatic cases and patterns of extension, even if it lacks an essence.

This leaves a substantive explanatory question: what makes some similarities relevant and others irrelevant? Later, Rosch’s cognitive work will offer one empirical route to that question. Wittgenstein’s own emphasis is more on the role of shared human practices and linguistic use.

3. A disjunctive definition does not restore the classical ambition

One might write an enormous disjunction:

$$\mathrm{Game}(x)\leftrightarrow (\text{chess-like}(x))\vee (\text{football-like}(x))\vee (\text{poker-like}(x))\vee \cdots$$

Formally, such a statement could always be made true if it simply enumerates every accepted case. But it would not supply what the classical theorist sought: a non-circular, explanatory account of why these cases belong together and how new cases should be classified.

This is Wittgenstein’s response to the thought that “there must be something common after all: the disjunction of all common properties.” Of course all games share the property being one of the things we call games. But that is a verbal restatement of the classification, not the discovery of an underlying essence.

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The pressure on Rand’s measurement omission

The disagreement with Rand can now be stated precisely.

For Rand, concept formation requires units possessing the same distinguishing characteristic, whose measurements can be omitted. The relevant structure is variation along shared dimensions: some height, any height in the appropriate range; some hue, any hue in a relevant range.

For Wittgenstein’s game case, the proposed problem is prior to measurement. It is not that every game has a shared property whose values vary widely. It is that chess, tag, poker, and solitary play may be connected through different properties altogether.

So, if game genuinely is a family-resemblance concept, measurement omission cannot explain it in the straightforward Randian way. There is no single distinguishing characteristic for which the particular measurements are being omitted.

But this is a conditional result, not a blanket refutation of Rand:

• Where a category tracks a stable shared structure, measurement omission may be an illuminating account.
• Where a category is held together by multiple overlapping relations, the search for that shared structure may be misguided.

The next task is therefore not to declare a winner prematurely. It is to identify what deeper metaphysical picture motivates each side: whether concepts primarily discover objective common natures, or whether many concepts depend on patterns of human use and convention.

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Conclusion

Wittgenstein’s family-resemblance argument attacks the assumption that meaningful concepts must always have classical definitions.

The key points are:

• The classical model seeks conditions shared by all and only members of a concept.
• Wittgenstein’s game example asks us to inspect actual uses rather than assume such a common feature exists.
• Games appear linked by overlapping similarities—competition, rules, luck, skill, amusement, physical activity—without one feature spanning every case.
• A family-resemblance category is neither essence-based nor arbitrary: it is a structured web of salient, local connections.
• The argument challenges the claim that all concepts have essences; it does not deny that some concepts may have precise necessary-and-sufficient-condition definitions.
• This poses a direct challenge to applying Rand’s measurement omission universally, because some concepts may lack a single shared characteristic whose measurements could be omitted.

Next, we will make explicit the deeper disagreement: whether family resemblance is best understood as a feature of our conventions and practices, while classical accounts track objective common natures.