Ideas from 'There Are No Abstract Objects' by Cian Dorr [2008], by Theme Structure

[found in 'Contemporary Debates in Metaphysics' (ed/tr Sider/Hawthorne/Zimmerman) [Blackwell 2008,978-1-4051-1229-1]].

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8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta

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Call 'nominalism' the denial of numbers, properties, relations and sets

8. Modes of Existence / E. Nominalism / 5. Class Nominalism

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Natural Class Nominalism says there are primitive classes of things resembling in one respect

10. Modality / A. Necessity / 11. Denial of Necessity

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Abstracta imply non-logical brute necessities, so only nominalists can deny such things