What numbers could be (and, hence, necessarily are)

Philosophia Mathematica 4 (3):238-255 (1996)
Abstract
This essay explores the commitments of modal structuralism. The precise nature of the modal-structuralist analysis obscures an unclarity of its import. As usually presented, modal structuralism is a form of anti-platonism. I defend an interpretation of modal structuralism that, far from being a form of anti-platonism, is itself a platonist analysis: The metaphysically significant distinction between (i) primitive modality and (ii) the natural numbers (objectually understood) is genuine, but the arithmetic facts just are facts about possible progressions. If correct, modal structuralism is best understood not as an alternative to, but as a species of, platonism.
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