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A Paradox about Sets of Properties

Synthese 199 (5-6):12777-12793 (2021)

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  1. Some Highs and Lows of Hylomorphism: On a Paradox about Property Abstraction.Teresa Robertson Ishii & Nathan Salmón - 2020 - Philosophical Studies 177 (6):1549-1563.
    We defend hylomorphism against Maegan Fairchild’s purported proof of its inconsistency. We provide a deduction of a contradiction from SH+, which is the combination of “simple hylomorphism” and an innocuous premise. We show that the deduction, reminiscent of Russell’s Paradox, is proof-theoretically valid in classical higher-order logic and invokes an impredicatively defined property. We provide a proof that SH+ is nevertheless consistent in a free higher-order logic. It is shown that the unrestricted comprehension principle of property abstraction on which the (...)
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  • Singular Concepts.Nathan Salmón - 2024 - Synthese 204 (20).
    Toward a theory of n-tuples of individuals and concepts as surrogates for Russellian singular propositions and singular concepts. Alonzo Church proposed a powerful and elegant theory of sequences of functions and their arguments as singular-concept surrogates. Church’s account accords with his Alternative (0), the strictest of his three competing criteria for strict synonymy. The currently popular objection to strict criteria like (0) on the basis of the Russell-Myhill paradox is misguided. Russell-Myhill is not a problem specifically for Alternative (0). Rather (...)
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