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