Abstract
Tarski and Mautner proposed to characterize the “logical” operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively “logical”, this lends support to the Tarski-Mautner proposal.
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Thanks to Shaughan Levine, Gila Sher, and the referee for their help.
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McGee, V. Logical operations. J Philos Logic 25, 567–580 (1996). https://doi.org/10.1007/BF00265253
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DOI: https://doi.org/10.1007/BF00265253