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

Neil Barton
University of Konstanz
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.
Keywords set theory  continuum hypothesis  foundations of mathematics  multiverse
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