Existence, Ontological Neutrality and The Square of Opposition: An
Abstract Model-Theoretic Approach
As a theory of what is true regardless of how the world is, logic is
often thought to be ontologically neutral. From the standpoint of
predicate logic, traditional logic falls short of that standard, as it
introduces tacit existential assumptions in the Aristotelian Square of
Opposition. Predicate logic fares better, but, as it turns out, it is
not entirely ontologically neutral either. We investigate
Aristotelian and non-Aristotelian Squares of Opposition within the
framework of Abstract Model Theory, through which the logical
transformations of the Square of Opposition due to existential
assumptions are made apparent.
Alkis Plithas and Asteris Gkantzounis
Last modified: Tue Apr 29 2025