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    A contemporary Millian must take set theory to be about o... — Carmelics
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    Challenges→A contemporary Millian account of mathematics is untenable

    A contemporary Millian must take set theory to be about ordinary physical objects

    Philosophy of LanguageTruth & Knowledge
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    A contemporary Millian account of mathematics is untenableNo account of piles or bunches of physical stuff can accommodate infinitely many...Set theory cannot be about ordinary physical objects because it entails infinite...

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    Let us move on now to immanent-realist, or physicalist, views of mathematics, and let us concentrate first on views like Mill's (1843, book II, chapters 5 and 6), i.e., views that maintain that sentences about numbers are really just general claims about bunches of ordinary objects. On this view, the sentence ‘2 + 1 = 3’, for instance, isn't really about specific objects (the numbers 1, 2, and 3). Rather, it says that whenever we add one object to a pile of two objects, we will get a pile of thr

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