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A note on Gabriel Uzquiano’s “Varieties of indefinite extensibility”. (English) Zbl 1396.03004
Summary: G. Uzquiano [Notre Dame J. Formal Logic 56, No. 1, 147–166 (2015; Zbl 1372.03015)] has offered an account of indefinite extensibility for sets in the context of a modal logic. The modal operators are interpreted in terms of linguistic extensibility. After reviewing the proposal, I argue that the view should be understood as a version of in rebus structuralism about set theory. As such it is subject to the usual problems for in rebus structuralism. In particular, there is no good extra set-theoretic reason to assent to an ontology of sufficient cardinality to make true the theorems of ZFC.
03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
03E30 Axiomatics of classical set theory and its fragments
Zbl 1372.03015
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