Quantification and Existence in Natural and Formal Languages

Abstract

Quantification and existence have an intimate yet complicated relationship, which has bearing on important issues for philosophers, linguists, and logicians alike. This paper focuses on the interface between philosophical logic and linguistics regarding the ‘particular’ quantifier as it is used in natural and formal languages. In classical logic, the ‘particular’ quantifier is symbolized as ∃ and has now more widely come to be known as the ‘existential’ quantifier. True to its name, ∃ has been interpreted as the logical notation for existence, drawing the connection between quantification and existence. I challenge this interpretation through a formal study of the semantics of quantification in natural and formal languages, to deny the connection. I put forward a linguistically motivated view of how the semantics of existence works and how it interacts with quantificational expressions, to show that quantification should have nothing to do with existence. I argue that the ontological loading of the quantifier is smuggled in through the restriction of domains of quantification, without which it is clear to see that ∃ is not existential in any way. Once we remove domain restrictions, domains of quantification can include non-existent things, and quantification and existence can be separated once and for all.