Indeterminacy and `The' Universe of Sets: Multiversism, Potentialism, and Pluralism

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In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.
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Archival date: 2020-04-10
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