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Maximality and ontology: how axiom content varies across philosophical frameworks
2017
Synthese
Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in
doi:10.1007/s11229-017-1336-9
pmid:32214510
pmcid:PMC7061924
fatcat:3zousqdz7bcw5b37hnoqx5ibbq