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    If V were a set, then something would be missing from V, ... — Carmelics
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    Home/Modality & Possibility
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    Supports→V is not a set

    If V were a set, then something would be missing from V, contradicting the fact that nothing is missing from V

    Modality & PossibilityTruth & Knowledge
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    Modality & PossibilityTruth & Knowledge

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    V is not a set

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    For every set B, something (namely R_B) is missing from BNothing can be missing from V (the universe of all sets)

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    For every set B, something (namely R_B) is missing from B86%Nothing can be missing from V (the universe of all sets)84%Set theory entails that if set A and set B have different members, the...81%V is not a set80%

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    SEP: russell-paradox
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    This same point can be made in yet another way, involving a relativized form of Russell’s argument. Let \(B\) be any set. By ZA, the set \(R_B = \{x \in B: x \not\in x\}\) exists, but it cannot be an element of \(B\). For if it is an element of \(B\), then we can ask whether or not it is an element of \(R_B\); and it is if and only if it is not. Thus something, namely \(R_B\), is “missing” from each set \(B\). So again, \(V\) is not a set, since nothing can be missing from \(V\). But notice the

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