Zoom Talk: Volker Halbach (Oxford)
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Logical consequence is defined as truth preservation under all interpretations of the non-logical vocabulary. Interpretations are permitted to re-interpret all non-logical terms, while logical constants cannot be re-interpreted. Thus, the theory of logical consequence depends on the distinction between logical constants and other terms.
A term or operations is a logical constant if, and only it behaves in the same way on all objects, or so some logicians have claimed. Invariance criteria for logical constants are supposed to make this criterion precise. I will look at various incarnations of the criterion. I argue that existing accounts can be improved by not considering permutations of all domains, but rather permutations of the entire universe. I discuss whether second-order quantifiers, identity, and cardinality quantifiers are logical constants under the criterion.
While self-contained, this talk is connected with Professor's Halbach talk during The Philosophy of Metamathematical Results event that is going to take place on the 21 and 22 of January at the MCMP. You can find more information here.