Abstract

This paper defends a minimal principle of absolute non-vacuity: (AntiNull / IPN) □¬EmptyA, where EmptyA expresses absolute nothingness: no concrete or abstract entities, no modal or logical structures, no domains, interpretations, worlds, states, or facts of any kind exist. From AntiNull one immediately obtains a very weak but non-trivial form of necessary existence: (NECEX) □∃x(x = x) in standard first-order modal logic with non-empty domains, and (NECEX*) □∃x E!(x) in free logic with an existence predicate. The central claim is that AntiNull is not a mere semantic stipulation about model domains, but a substantive metaphysical thesis, supported by a metasemantic theorem and several independent arguments, and compatible with a wide range of ontological positions (moderate platonism, proxy actualism, necessitism). Technically, the core result is a non-satisfiability theorem for absolute emptiness (NEAC: Nonsatisfiability / Non-Applicability of Emptiness Claim). Once we spell out the minimal semantic structure required to interpret a quantified modal language and implement an absolute reading of EmptyA, the formula EmptyA itself is unsatisfiable at any index of any admissible Kripke model; a fortiori, ◇EmptyA is unsatisfiable as well. I then generalize to a schema gNEAC that covers at least four families of modal semantics: first-order Kripke semantics, neighborhood semantics with an existential possibility operator, modal truthmaker semantics, and topological semantics for S4. Under a weak one-way Adequacy Bridge (AB) from metaphysical possibility to semantic realizability, NEAC yields AntiNull and hence NECEX/NECEX*. Four further lines of argument—minimal truthmaking for fundamental modal truths, a comparative cost analysis of theories of possible worlds, a transcendental reading of NEAC, and a dilemma about abstracta and noneism—converge on the same conclusion. The paper thus uses formally regimented modal semantics to settle a central metaphysical question concerning the possibility of absolute nothingness.