No Outside

Abstract

This paper derives the uniqueness of existence from two axioms: the universal negation of externality (A1) and the affirmation that at least one object exists (A2). Externality is defined as the presence, in either of two objects, of a part not contained in the other. Under this definition, A1 eliminates every residual difference between any two objects. De Morgan’s law converts the universal negation of externality into mutual inclusion; the axiom of extensionality then yields identity. A2 secures existence, and the derived identity excludes plurality. Exactly one existent remains, denoted W. The conclusion follows necessarily within the stated axiomatic framework: There is only one thing that exists: W.