|Universal instantiation, logic: on the condition that all objects x have the property F, one can conclude that a particular object, which can be designated, has the property F. See also universal generalization, existential generalization.|
|Geach, Peter T.
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|Universal Instantiation||I 142f
UI / Geach: universal Instantiantiation: from (x) Fx to Fw. - IE: instantial existentiation: from Fw to (Ex) Fx - EI: existenial instantiation: from (Ex) Fx to Fw. - IU: Instantial universalization of Fw to (x) Fx, ((s), if any w is F, then everything is F?). - Geach: a proof with IU may be replaced by one which only uses EI. - IU and UI are valid also in not non-Shakespearean contexts. - (N-Shakesp: a rose would smell even if it were not be called a rose.
Logic Matters Oxford 1972