Family resemblance as a relation occurs in Ludwig Wittgenstein’s treatment of language in Philosophical Investigations.
With the family resemblance explanation, Wittgenstein attacks conventional views on how words can have meaning. On the one hand, it attacks the traditional view that words acquire meaning from the thoughts of the person who utters them. On the other, it challenges Wittgenstein’s own concept from his earlier Tractatus Logico-Philosophicus, that words get their meaning by standing for objects in reality.
Instead, Wittgenstein says that some words do not have a single essence that encompasses their definition. He uses the example of the word ‘game’. Although we may think of the term as having a definite meaning, Wittgenstein points out counterexamples to this idea. No single thing is common to all uses of the word ‘game’. For instance, not all games are played for fun or as recreation; games like hockey and football are played professionally, and some casino games are played out of addiction. Not all games have scores or points, nor do they all have teams or any equipment that would define them as games and not some other activity.
Wittgenstein says that rather than each use of the word ‘game’ having a relationship to a common feature of reality or of the thoughts behind them, that is, to a single essence, the relationship between the uses of the word is more interesting. It is here that he brings up family resemblance.
Wittgenstein says that the way in which family members resemble each other is not through a specific trait but a variety of traits that are shared by some, but not all, members of a family.
To illustrate this point, consider a family of four siblings: Jane, John, Sally and Tim.
None of the features mentioned are common to all members of the family, but they all resemble each other in some way — there are family traits that show up in multiple members of the family.
For Wittgenstein, this is how ‘game’ and many other words have a consistent meaning. Common features of games, like recreation, scores, teams, rules, etc. are present in various games but not others, but the general overlapping mesh of these features is where the word gets its meaning.
Hence, the meaning of some words is a relation much like family resemblance.
Importantly, Wittgenstein does not say that the family resemblance relation is not always the way that words get their meaning. Instead, words can get their meaning by picking out objects in reality, as he claims in the Tractatus, but he asserts that philosophers must recognize the difference between the varied methods of assigning meaning to words.