Asymmetry Misplaced: Meta-Logical Constraints on the Reverse Modal Ontological Argument

In a recent article published in Noûs — “Symmetry lost: A modal ontological argument for atheism?” — the authors propose a substantive asymmetry between the classical Modal Ontological Argument (MOA) and its reverse formulation. In this paper, I argue that the alleged asymmetry is neither semantic nor genuinely modal in character, but instead arises from a meta-logical interpretation of the possibility operator. Adopting, for analytical purposes, an arithmetic interpretation of modal possibility as the consistency of a theory extension (◇φ := Con(T + φ)), I show that the affirmation of possibility takes the form of a negative statement (the absence of a proof of contradiction), whereas its proper negation has existential form (the existence of a proof of contradiction). This corresponds to the distinction between Π- and Σ-type sentences in the classical arithmetization of proof theory. I then demonstrate that this asymmetry is structural and persists under iterated consistency extensions, including transfinite progressions. Gödel’s Second Incompleteness Theorem precludes the existence of a level at which the consistency of a given extension becomes internally settled. Consequently, the difference between affirming and denying possibility does not disappear at stronger theoretical levels. The proposed “loss of symmetry” therefore does not concern the structure of modal logic itself, but rather stems from the arithmetic representation of consistency and its associated meta-logical limitations. The dispute is not resolved at the level of S4/S5, but at the level of the interpretation of modal operators. The analysis is purely meta-logical and carries no ontological commitments; it suggests, however, that what is interpreted as ontological asymmetry may result from a shift between object-level and meta-level considerations. The asymmetry identified here is not an artifact of analytical convention, but a structural invariant of any interpretation that equates modal possibility with the consistency of theory extension—independently of the specific formal system or level of reflective progression employed. The argument is conditional and rests on the arithmetic interpretation of modal possibility.