32 Peter M. Sullivan

Define ‘het’ as a predicate that truly applies to itself if and only if it does not truly apply to itself and which also truly applies to any predicate that does not truly apply to its own name. We know that the attempted definition of ‘hes’ is a failure, and so a fortiori is that of ‘het’. Similarly, there is no Qussell class which contains itself as a member if and only if it does not contain itself as a member, so a fortiori there is no Russell Class which contains itself as a member if and only if it does not contain itself as a member and which also contains all and only non-self-membered classes (such as the class of dogs). The second conjunct in both the definition of ‘het’ and of the Russell class cannot revive a definition doomed to failure. Likewise, the ‘definition’ of n as ‘n > 1 iff n < 1’ fails, and the attempted definition of m as ‘m > 1 iff m < 1 and m is prime’ is hopeless too; its final clause buys it no respectability.
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