On Definitions of Existence

In this paper, I propose several definitions of existence. I begin with a foundational “first definition” and then introduce further definitions based on denotation, morphisms, and terminal objects. The first definition characterizes existence as that \bf which is named and spoken of, while allowing for the possibility that existence is not exhausted by what is actually spoken\rm. The subsequent definitions are presented as systematic refinements of this initial idea. I also provide a preliminary discussion of these definitions and indicate directions for future work.