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Any two sets have different conditions for membership, so if object O is in set S because it's blue or green, then being blue or green cannot be the reason why any other object is in any other set. If so, how can there exist a set of green objects?

### Suppose S is the set of all

Suppose S is the set of all things that are blue or green. Then my mug is in S because it's green and therefore satisfies "x is blue or x is green," and my pen is in the set S because it's blue and therefore satisfies "x is blue or x is green." Now it's true: satisfying "x is blue or x is green" picks out only one set: the set of all things that satisfy "x is blue or x is green." But the condition "x is green" is a different condition, and so is "x is blue."
However: when you say "being blue or green cannot be the reason why any other object is in any other set," there's an ambiguity. That could be read as "being blue cannot be the reason why an object is in any other set and being green cannot be the reason why an object is in any other set." In that case, however, it's false. Being green, and hence satisfying "x is green" puts my mug in the set G of all green things, and in the set S of all things that are either green or blue—that satisfy "x is green or x is blue." These two sets are not the...

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