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The Rule of Existential Generalisation and Explicit Substitution

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Rok publikování 2022
Druh Článek v odborném periodiku
Časopis / Zdroj Logic and logical philosophy
Fakulta / Pracoviště MU

Filozofická fakulta

Klíčová slova existential generalisation; quantifying in; explicit substitution; hyperintensional logic; natural deduction
Popis The present paper offers the rule of existential generalisation (EG) that is uniformly applicable within extensional, intensional and hyperintensional contexts. In contradistinction to Quine and his followers, quantification into various modal contexts and some belief attitudes is possible without obstacles. The hyperintensional logic deployed in this paper incorporates explicit substitution and so the rule (EG) is fully specified inside the logic. The logic is equipped with a natural deduction system within which (EG) is derived from its rules for the existential quantifier, substitution and functional application. This shows that (EG) is not primitive, as often assumed even in advanced writings on natural deduction. Arguments involving existential generalisation are shown to be valid if the sequents containing their premises and conclusions are derivable using the rule (EG). The invalidity of arguments seemingly employing (EG) is explained with recourse to the definition of substitution.
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