A Groundwork for A Logic of Objects

David Winters, The University of Western Ontario

Abstract

The history of philosophy is rich with theories about objects; theories of object kinds, their nature, the status of their existence, etc. In recent years philosophical logicians have attempted to formalize some of these theories, yielding many fruitful results. My thesis intends to add to this tradition in philosophical logic by developing a second-order logical system that may serve as a groundwork for a multitude of theories of objects (e.g. concrete and abstract objects, impossible objects, fictional objects, and others). Through the addition of what we may call sortal quantifiers (i.e. quantifiers that bind individual variables ranging over objects of three unique sorts), a groundwork for a logic that captures concrete and non-concrete objects will be developed. We then extend this groundwork by the addition of a single new operator and the modal operators of a Priorian temporal logic. From this extension, our formal system can represent and define concrete, abstract, fictional, and impossible objects as well as formally axiomatize informal theories of them.