Open AccessThe Rule of Existential Generalisation and Explicit Substitution
Author(s) -
Jiří Raclavský
Publication year - 2021
Publication title -
logic and logical philosophy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.416
H-Index - 10
eISSN - 2300-9802
pISSN - 1425-3305
DOI - 10.12775/llp.2021.011
Subject(s) - substitution (logic) , generalization , existentialism , quine , quantifier (linguistics) , mathematics , modal , computer science , mathematical economics , calculus (dental) , epistemology , philosophy , artificial intelligence , programming language , medicine , chemistry , dentistry , polymer chemistry
The present paper offers the rule of existential generalization (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.