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Journal of Philosophical Logic

, Volume 37, Issue 6, pp 575–591 | Cite as

Symmetric Propositions and Logical Quantifiers

  • R. Gregory TaylorEmail author
Article

Abstract

Symmetric propositions over domain \(\mathfrak{D}\) and signature \(\Sigma = \langle R^{n_1}_1, \ldots, R^{n_p}_p \rangle\) are characterized following Zermelo, and a correlation of such propositions with logical type-\(\langle \vec{n} \rangle\) quantifiers over \(\mathfrak{D}\) is described. Boolean algebras of symmetric propositions over \(\mathfrak{D}\) and Σ are shown to be isomorphic to algebras of logical type-\(\langle \vec{n} \rangle\) quantifiers over \(\mathfrak{D}\). This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those invariant under domain permutations.

Key words

generalized quantifier logical notion symmetric proposition 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceManhattan CollegeRiverdaleUSA

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