Some clearer reactions: Gauker on the validity of universal instantiation
Keywords:universal instantiation (UI), existential generalization (EG), many-sorted languages, typed languages, logical orthodoxy, ordinary intuitions, contexts
It is part of the logical orthodoxy that quantifiers are interdefinable and that the rules of Universal Instantiation (UI) and Existential Generalization (EG) hold or fail together. Christopher Gauker has presented some cases which seemingly undermine the validity of UI but nonetheless leave EG untouched, and has developed a very sophisticated theory to explain why this is so. In the process, he has rejected several attempts to explain the asymmetry, especially those aiming at saving the logical orthodoxy by showing what is wrong with the counterexamples to UI. In this paper I argue that some of those proposals are better grounded than Gauker thinks and that ultimately they should be preferred over his since they satisfactorily explain the apparent counterexamples.
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