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.
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Taylor, R.G. Symmetric Propositions and Logical Quantifiers. J Philos Logic 37, 575–591 (2008). https://doi.org/10.1007/s10992-008-9081-7
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DOI: https://doi.org/10.1007/s10992-008-9081-7