Wittgenstein concludes his famous section in Philosophical Investigations on games (66) with these words: “we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail”. This he opposes to the idea that games have a single characteristic that defines them. He follows up this discussion by saying, “I can think of no better expression to characterize these similarities than ‘family resemblance’; for the various resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and criss-cross in the same way.—And I shall say: ‘games’ form a family.” (67) This is a rather casual introduction of the idea of family resemblance with very little elucidation offered, and Wittgenstein does not use the phrase again in the course of the Investigations; nevertheless, it has achieved canonical status in commentaries on Wittgenstein and analytical philosophy more broadly. I shall suggest that it is a misconceived idea best dropped. I don’t mean that Wittgenstein is wrong to claim that games are united only by various similarities and have no collective definition—though I believe that to be the case; I mean that, even accepting his view of the concept of a game, it is not helpful to compare the case to resemblances among family members. Games don’t have family resemblances in any significant sense.
Let me start with a crude point: football does not have the same nose or mouth or eyes or gait as rugby. Games are not people with various observable bodily traits, so they cannot be similar in the way family members can be. They are not even individuals but rule-governed activities. They can be similar or dissimilar, to be sure, but not in the way family members can be: there is resemblance but not family resemblance. So the concept of a family is here at best metaphorical: games do not literally form a family. There is no genetic linkage and family structure, no birth and child rearing, no brothers and sisters. It might be thought that there is still a specific type of similarity peculiar to family similarity that carries over to games (and perhaps to other things), but this is a confused idea: similarity is just similarity whether between family members or types of car or animals or works of art. Different objects are involved in these cases, but there is no relation of “family-similarity” that differs intrinsically from other types of similarity. Objects are similar or dissimilar in certain respects, depending on the type of object they are, but there is no notion of family-similarity that singles this case out; it is not that family similarity is a special kind of similarity of some peculiarly profound or subtle kind. Wittgenstein could have inverted his explanation and claimed that family similarity is like game similarity: just as games overlap and criss-cross, so family members overlap and criss-cross. The two involve similarities, but it isn’t that family similarity is somehow unique and that games happen to mimic it. In the only way that family resemblance is unique it fails to generalize to games, viz. that it involves having the same nose or mouth or eyes, etc.
Second, the kind of resemblance between people that Wittgenstein is referring to is not confined to families. In fact, it is neither necessary nor sufficient for family membership since some members of a family can be quite unlike other members (perhaps because of some genetic accident) and people outside a family can strongly resemble people in the family (people can have unrelated lookalikes). People can look alike in all sorts of ways whether they are members of the same family or not (and does Wittgenstein intend extended families as well as nuclear families—how extended?). They can have a sort of physical resemblance that is not the result of family membership in the narrow sense. For example, Finns have a characteristic appearance that distinguishes them from other national groups; and racial groups also exhibit physical similarities. So Wittgenstein’s point about family resemblance holds also for larger social groupings; it has nothing specifically to do with families. He could therefore have compared games to nationalities or ethnic groups. Come to think of it, he could have cited animal groups—families or breeds or species. The class consisting of all mammals exhibits various kinds of similarity and dissimilarity, with no observable feature shared by all: there is phenotypic similarity as well as dissimilarity. Again, families are not germane; they are just one instance of human and animal resemblance (think how different mice are from giraffes). In all these cases we have the same logical pattern: a can be similar to b in respect R1 and b can be similar to c in respect R2, but a might not be similar to c in any respect. I can be similar to my brother in respect of nose and mouth, and he may be similar to our father in respect of eyes and chin, but I may share no features with our father. The same is true for many social groups; this is not a point about families as such. Indeed, the same pattern occurs quite generally: musical instruments, say, exhibit various similarities and differences with no common thread—that is, no observable trait shared by all (taut strings, a mouthpiece, a particular type of sound). Selecting family similarity seems random and arbitrary; a great many types of similarity would have done just as well. And the case of families is misleading in at least one important respect: families are natural biological groupings, united by genetics and inheritance, whereas games are united in no such ways. An obvious reply to Wittgenstein is that games are quite unlike families in that families have another principle of unity apart from overt appearance, namely genetic overlap and connection. His point about games (whether right or wrong) is that games have no unity apart from overt similarities, but that is precisely not the case with biological families. Family resemblance is thus a poor choice to illustrate his claim about games. In fact, trait similarities within families are the result of underlying facts that create family unity: they rest upon a shared genetic endowment. No such thing is true of games, and Wittgenstein would certainly reject any analogous claim for games.
What is true is that games can resemble each other in multiple ways, as well as differ in multiple ways: not all games have the same form. They can also vary widely in the kinds of rules they adopt. They don’t all involve a ball or running or keeping score. That is fine as far as it goes, but the analogy with family resemblance is unhelpful and misleading. That is just one instance of resemblance among many (the kind that involves individual humans and their physical appearance), but there is nothing unique about it, nothing that allows it to shed light on games that other cases can’t shed. The case of musical instruments, say, would have done just as well, and better in some ways. All instruments are played, as all games are played, and there are purposes that unite the members of each class; it is just that the physical make-up and form of the objects deployed are very various (compare drums and violin). Wittgenstein says he “can think of nothing better” to characterize the case of games than the expression “family resemblance”, but it seems that there are many better analogies and that this one is quite unapt. To use Wittgenstein’s own concept of a language game, the language game of talking about games is quite unlike the language game of talking about families: we never remark, upon first encountering the game of rugby, “Oh, you look just like football”, as if we have noticed a striking visual feature common to both. Nor do we offer comments like, “Football and rugby look like they belong to the same family, but curling looks like it belongs to a different family altogether”. We don’t think about game resemblance as if it is comparable to physiognomic resemblance between people; how games look is not the main point of judgments of resemblance and difference between them.
 I accept that Bernard Suits satisfactorily defines the concept of a game in The Grasshopper (1978), but I am not discussing that question here. I am merely considering the question of whether similarities among games are aptly characterized by the phrase “family resemblance”—whether or not these are all there is to the concept of a game.
 Wittgenstein also claims that different kinds of number are linked by family resemblance (67); the points made in this paper apply a fortiori to that suggestion. Numbers, being abstract, don’t even have perceptible characteristics, and their similarities and differences are really nothing like those between family members. At this point the phrase “family resemblance” has lost any real content beyond simply “similar in some way”. That is an extraordinarily weak relation, logically speaking.