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  1. Can mereological sums serve as the semantic values of plurals?David Nicolas - 2007
    Abstract: Friends of plural logic—like Oliver & Smiley (2001), Rayo (2002), Yi (2005), and McKay (2006)—have argued that a semantics of plurals based on mereological sums would be too weak, and they have adduced several examples in favor of their claim. However, they have not considered various possible counter-arguments. So how convincing are their own arguments? We show that several of them are easily answered, while some others are more problematic. Overall, the case against mereological singularism—the idea that mereological sums (...)
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  • 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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  • (1 other version)Aggregate theory versus set theory.Hartley Slater - 2003 - Erkenntnis 59 (2):189 - 202.
    Maddy's (1990) arguments against Aggregate Theory were undermined by the shift in her position in 1997. The present paper considers Aggregate Theory in the light of this, and the recent search for `New Axioms for Mathematics'. If Set Theory is the part-whole theory of singletons, then identifying singletons with their single members collapses Set Theory into Aggregate Theory. But if singletons are not identical to their single members, then they are not extensional objects and so are not a basis for (...)
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  • Negatives, numbers, and necessity some worries about Armstrong's version of truthmaking.Peter Simons - 2005 - Australasian Journal of Philosophy 83 (2):253 – 261.
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  • Literalism and the applicability of arithmetic.L. Luce - 1991 - British Journal for the Philosophy of Science 42 (4):469-489.
    Philosophers have recently expressed interest in accounting for the usefulness of mathematics to science. However, it is certainly not a new concern. Putnam and Quine have each worked out an argument for the existence of mathematical objects from the indispensability of mathematics to science. Were Quine or Putnam to disregard the applicability of mathematics to science, he would not have had as strong a case for platonism. But I think there must be ways of parsing mathematical sentences which account for (...)
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