Philosophers have spent much time and energy trying to determine what “exists”. The study of this question is called ontology. The problem comes when they try to apply the property of “existence” to abstractions, like numbers. Does the number three exist?
I have decided to avoid this problem by confining the term “existence” to physical things. Thus, axiom 1: physical stuff exists.
Within the current framework it is easy to describe what exists. Something exists if it is a mechanism for at least one task. It’s that simple.