Monday, December 31, 2012

The Unsatisfied Paradox

In this month's issue of The Reasoner (page 185), Peter Eldridge-Smith gave the following informal description of his Unsatisfied paradox:
My favourite predicate just happens to be 'does not satisfy my favourite predicate'. Crete satisfies 'does not satisfy my favourite predicate' iff Crete does not satisfy my favourite predicate. Therefore, Crete satisfies my favourite predicate iff Crete does not satisfy my favourite predicate.
And not just Crete, there is no thing that satisfies Peter's favourite predicate, and no thing that fails to satisfy it without it also not being the case that it fails to satisfy it. Nevertheless, Peter's favourite predicate could be as true as not of Crete, or anything else. Predicates can do that, e.g. 'is blue' is as true as not of an object that is as blue as not, and some predicates apply equally to all things, e.g. 'is a thing' is true of all things.

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