# Symmetry as a Criterion for Comprehension Motivating Quine’s ‘New Foundations’

@article{Holmes2008SymmetryAA, title={Symmetry as a Criterion for Comprehension Motivating Quine’s ‘New Foundations’}, author={M. Randall Holmes}, journal={Studia Logica}, year={2008}, volume={88}, pages={195-213} }

A common objection to Quine’s set theory “New Foundations” is that it is inadequately motivated because the restriction on comprehension which appears to avert paradox is a syntactical trick. We present a semantic criterion for determining whether a class is a set (a kind of symmetry) which motivates NF.

## 4 Citations

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- 2020

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If X is an infinite set with ∣X∣ = ∢X × X∣ then Symm(X) has no nontrivial normal subgroups of small index, and it is shown that every normal subgroup of Symm (X) (of small index) must contain every flexible permutation.

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A sequence of theories of sets and classes is presented, indexed by a natural number parameter k. The criterion for determining which classes are sets has to do with symmetry. The theories with k 2…

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