Is Objectual Identity Really Dispensable?
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Kai Wehmeier’s Wittgensteinian Predicate Logic (W-logic) is a formulation of first-order logic under the exclusive interpretation of the quantifiers. W-logic has a distinguished relation constant for co-reference but no sign for objectual identity. Wehmeier denies that objectual identity exists on the grounds that it cannot be a genuine binary relation. Fortunately W-logic is equi-expressive with standard first-order logic with identity and it appears that objectual identity is dispensable across the broader logical enterprise. This paper challenges the latter claim as objectual identity seems to be needed in the exclusive interpretation of quantified modal logic, specifically, for implementing certain kinds of de re quantification.
Thanks to Kai Wehmeier for several very helpful email exchanges on earlier drafts of this paper. These discussions improved the paper in innumerable ways and his intellectual generosity is most appreciated. I am also sincerely grateful for the extensive comments, both technical and philosophical, provided by the anonymous referees.
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