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From what I've collected, Quine seemed to have solved the problem of non-being by using Russell's theory of definite descriptions through the negation of the x having certain properties/descriptions. However, I hear Kripke rejected Russell's definite descriptions. How did Kripke solve the problem of non-being with his theory of reference?

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    I'll try to get around to providing an actual answer, but you might wanna check out Kripke's Reference and Existence. In particular, look at his treatment of names in fictional discourse. – Dennis Jun 19 '16 at 17:08

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