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Hofweber’s Nominalist Naturalism

In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo (eds.), Objects, Structures, and Logics. Cham (Switzerland): Springer. pp. 31-62 (2022)

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  1. Restricted nominalism about number and its problems.Stewart Shapiro, Richard Samuels & Eric Snyder - 2024 - Synthese 203 (5):1-23.
    Hofweber (Ontology and the ambitions of metaphysics, Oxford University Press, 2016) argues for a thesis he calls “internalism” with respect to natural number discourse: no expressions purporting to refer to natural numbers in fact refer, and no apparent quantification over natural numbers actually involves quantification over natural numbers as objects. He argues that while internalism leaves open the question of whether other kinds of abstracta exist, it precludes the existence of natural numbers, thus establishing what he calls “restricted nominalism” about (...)
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  • Resolving Frege’s Other Puzzle.Eric Snyder, Richard Samuels & Stewart Shapiro - 2022 - Philosophica Mathematica 30 (1):59-87.
    Number words seemingly function both as adjectives attributing cardinality properties to collections, as in Frege’s ‘Jupiter has four moons’, and as names referring to numbers, as in Frege’s ‘The number of Jupiter’s moons is four’. This leads to what Thomas Hofweber calls Frege’s Other Puzzle: How can number words function as modifiers and as singular terms if neither adjectives nor names can serve multiple semantic functions? Whereas most philosophers deny that one of these uses is genuine, we instead argue that (...)
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