The Burali-Forti paradox

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Abstract
In the system presented by Quine in his book Mathematical logic, one can derive the Burali-Forti Paradox. It is the purpose of this paper to present the details of this derivation. For the derivation, only familiarity with Quine's book is assumed.The present derivation is based on the derivations given by Hobson and by Whitehead and Russell.In both these sources, the primary interest is the theory of ordinals, and the Burali-Forti Paradox is of interest only as something to be avoided. In the present paper the primary interest is the Burali-Forti Paradox, so that much of the theory of ordinals is absent from this paper and only those details remain which are relevant to the derivation of the paradox.

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