Abstract

Eliminativists say that the idea of extending rigidity beyond singular terms must be abandoned, especially because they claim that Kripkean “identifications” involving natural kind terms can be shown to be necessary if true by the standard theory of reference fixing, using at most singular term rigidity. First I note that this claim is false for Cats are animals and analogous identifications involving ordinary natural kind terms of different types. Then I recall that the view of rigidity as necessary application provides a modal-logical derivation of the necessity of those identifications, and is thus supported by this set of facts. I also consider, on behalf of the eliminativist, a rigidity-free derivation of that necessity, using the apparatus of higher-order metaphysics. I note that this derivation does not better motivate eliminativism, in part because its conceptual apparatus is not clearly more fundamental or less controversial than the apparatus of rigidity as necessary application.