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The Logic of Infinity

In Mathematics and Science: Last Essays. Dover Publications. pp. 45--64 (1963)

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  1. No Easy Road to Impredicative Definabilism.Øystein Linnebo & Sam Roberts - 2024 - Philosophia Mathematica 32 (1):21-33.
    Bob Hale has defended a new conception of properties that is broadly Fregean in two key respects. First, like Frege, Hale insists that every property can be defined by an open formula. Second, like Frege, but unlike later definabilists, Hale seeks to justify full impredicative property comprehension. The most innovative part of his defense, we think, is a “definability constraint” that can serve as an implicit definition of the domain of properties. We make this constraint formally precise and prove that (...)
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  • In defense of Countabilism.David Builes & Jessica M. Wilson - 2022 - Philosophical Studies 179 (7):2199-2236.
    Inspired by Cantor's Theorem (CT), orthodoxy takes infinities to come in different sizes. The orthodox view has had enormous influence in mathematics, philosophy, and science. We will defend the contrary view---Countablism---according to which, necessarily, every infinite collection (set or plurality) is countable. We first argue that the potentialist or modal strategy for treating Russell's Paradox, first proposed by Parsons (2000) and developed by Linnebo (2010, 2013) and Linnebo and Shapiro (2019), should also be applied to CT, in a way that (...)
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  • On the dimensionality of surfaces, solids, and spaces.Ernest W. Adams - 1986 - Erkenntnis 24 (2):137 - 201.
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