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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.
MSC:
03A05 Philosophical and critical aspects of logic and foundations
00A30 Philosophy of mathematics
03E30 Axiomatics of classical set theory and its fragments
Citations:
Zbl 1372.03015
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References:
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