A critical examination of the philosophical defense of free logics

Abstract

In classical quantification theory, each singular term available in the formal language must denote some member of the quantificational domain. In this sense, standard systems of predicate logic do not allow for non-denoting singular terms of our ordinary discourse. In a non-standard family of logics called free logics, this classical requirement is dispensed with. This study is about these non-standard logics. It has a two-fold aim. Firstly, to provide a survey of free logics. To this end, I introduce definitions and characteristics of these systems, present axiomatic formulations of certain types of free logics, give a summary of different semantic approaches in free logics, and finally provide a brief historical information about their origins. Secondly, I discuss whether the adoption of free logics instead of classical logic is justified or not. To this end, I present and discuss six different kind of motivations behind the adoption of free systems. I ultimately conclude that none of the motivations provides us with enough reason to replace classical quantification theory with free logics. The study ends with a suggestion of a more successful argument in favor of free systems.