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Small sets

Philosophical Studies 63 (1):119 - 123 (1991)

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  1. David Armstrong on the Metaphysics of Mathematics.Thomas Donaldson - 2020 - Dialectica 74 (4):113-136.
    This paper has two components. The first, longer component (sec. 1-6) is a critical exposition of Armstrong’s views about the metaphysics of mathematics, as they are presented in Truth and Truthmakers and Sketch for a Systematic Metaphysics. In particular, I discuss Armstrong’s views about the nature of the cardinal numbers, and his account of how modal truths are made true. In the second component of the paper (sec. 7), which is shorter and more tentative, I sketch an alternative account of (...)
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  • Cantorian set theory.Alex Oliver & Timothy Smiley - 2018 - Bulletin of Symbolic Logic 24 (4):393-451.
    Almost all set theorists pay at least lip service to Cantor’s definition of a set as a collection of many things into one whole; but empty and singleton sets do not fit with it. Adapting Dana Scott’s axiomatization of the cumulative theory of types, we present a ‘Cantorian’ system which excludes these anomalous sets. We investigate the consequences of their omission, examining their claim to a place on grounds of convenience, and asking whether their absence is an obstacle to the (...)
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