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Øystein Linnebo (2018) offers an account of mathematical objects that promises to bypass some of the features that can make standard Platonism seem unpalatable. Although Linnebo’s mathematical objects are abstract and indeed exist of necessity, their existence is lightweight: they make little by way of demands on the world. As such the costs of realism about mathematical objects are, in Linnebo’s account, much lower than is standardly assumed. Worries about how we can know about mathematical objects, or indeed refer to them, given what Linnebo calls their ‘shallow nature’, fall away. Why then persist, as the mathematical fictionalist does, with nominalist scruples about accepting the existence of abstract mathematical objects, if the existence of objects turns out to be so metaphysically undemanding?

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To Be (Thin) or Not to Be? Are Thin Objects Fictional Objects, or Are Fictional Objects Thin?

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  • 发表日期：

    2025年

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  • Mary Leng

摘要

Øystein Linnebo (2018) offers an account of mathematical objects that promises to bypass some of the features that can make standard Platonism seem unpalatable. Although Linnebo’s mathematical objects are abstract and indeed exist of necessity, their existence is lightweight: they make little by way of demands on the world. As such the costs of realism about mathematical objects are, in Linnebo’s account, much lower than is standardly assumed. Worries about how we can know about mathematical objects, or indeed refer to them, given what Linnebo calls their ‘shallow nature’, fall away. Why then persist, as the mathematical fictionalist does, with nominalist scruples about accepting the existence of abstract mathematical objects, if the existence of objects turns out to be so metaphysically undemanding?