Wittgenstein's notion of family resemblance shows that concepts can legitimately extend across domains through overlapping, non-transitive similarities rather than shared proof-critical features.

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Non-transitive(describing how similarities work in family resemblance): A logical property where if A is related to B, and B is related to C, it doesn't automatically mean A is related to C; for example, 'is a friend of' is non-transitive because your friend's friend isn't necessarily your friend.
Proof-critical features(contrasted with how family resemblance actually operates): Essential or defining characteristics that you'd need to point to prove something belongs in a category—like 'has four legs' for chairs; the idea here is that family resemblance works WITHOUT needing such strict defining features.
Wittgenstein: Ludwig Wittgenstein was an Austrian-British philosopher who fundamentally changed how people think about language and meaning in the 20th century. He argued that many philosophical problems arise from misunderstanding how words actually work in everyday life, rather than from deep metaphysical mysteries. His ideas influenced not just philosophy but also mathematics, logic, and even how people approach psychology and artificial intelligence today.
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