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The later Wittgenstein would explain to someone what a "game" is by

    { 1 } - describing different games -- and then perhaps adding, "These and similar things are called 'games'."
    { 2 } - giving a strict definition of a game -- for example, as being something that is competative, involves luck and skill, and is done mainly for amusement.

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1 is correct!

The later Wittgenstein would explain to someone what a "game" is by

This is the best that we can do, since "game" admits of no strict definition.

Our notion of "game" has vague boundaries, but that's generally all right. If we need to make the boundaries more precise in a given context, we can do that.

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2 is wrong. Please try again.

The later Wittgenstein would explain to someone what a "game" is by

    { 1 } - describing different games -- and then perhaps adding, "These and similar things are called 'games'."
    { 2 } - giving a strict definition of a game -- for example, as being something that is competative, involves luck and skill, and is done mainly for amusement.

Some games lack one or another of these characteristics. For example, solitary isn't competitive, dice is all luck, chess is all skill, and professional sports are sometimes done mainly for money. So we can't define "game" in strict terms -- but only in terms of looser "family resemblances" that tend to characterize games.

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