Quantifiers in ontology

Abstract

This paper is a reaction to G. Küng's and J. T. Canty's ‘Substitutional Quantification and Leśniewskian quantifiers'Theoria 36 (1970), 165–182. I reject their arguments that quantifiers in Ontology cannot be referentially interpreted but I grant that there is what can be called objectual — referential interpretation of quantifiers and that because of the unrestricted quantification in Ontology the quantifiers in Ontology should not be given a so-called objectual-referential interpretation. I explain why I am in agreement with Küng and Canty's recommendation that Ontology's quantifiers not be substitutionally interpreted even if Leśniewski intended them to be so interpreted. A notion of an interpretation which is referential but yet which does not interpret ∃ as an assertor of existence of objects in a domain is developed. It is then shown that a first order version of Ontology is satisfied by those special kind of referential interpretations which read ∃ as ‘Something’ as epposed to ‘Something existing’.