Higher-order free logic and the Prior-Kaplan paradox

Canadian Journal of Philosophy 46 (4-5):493-541 (2016)
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The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior’s and Kaplan’s derivations at face value.
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.Williamson, Timothy
Modal Logic as Metaphysics.Williamson, Timothy

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Some Results on the Limits of Thought.Bacon, Andrew & Uzquiano, Gabriel

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