First Philosophy: The Boundary Condition: A Geometric Derivation of Reality from the Logic of Distinction

This paper establishes a geometric foundation for first philosophy by demonstrating that the fundamental structure of reality can be derived from the logic of distinction alone. I prove that for any entity to exist as a distinct, bounded thing, there must be interstitial space separating it from other bounded entities. This interstitial space cannot itself be bounded without infinite regress, establishing the Indeterminate Ground as a geometric necessity—not a metaphysical postulate. From this Boundary Condition, I derive the necessity of plurality, the primacy of becoming over being, the limits of knowledge, and the origins of semantic meaning and ethical value. The result is a self-contained, axiom-free framework that resolves the infinite regress problem, dissolves the fact-value gap, and provides a navigational basis for epistemology and ethics—all without appeal to substance, consciousness, or empirical assumption. This work reorients first philosophy from the search for a "first thing" to the study of the conditions for thinghood itself.