Metaphysical symmetry and the modal ontological argument

Abstract Fritz, Lo, and Schmid argue that the symmetry problem for the modal ontological argument dissolves in modal logics weaker than S5, where (P1) white medium square left parenthesis g right arrow white medium square g right parenthesis $\square\left( g\rightarrow \square{g} \right)$ ◻ ( g → ◻ g ) , (P2) backslash unicodex 2 upper B 26 g $\unicode{x2B26}{g}$ ⬦ , and (P2*) backslash unicodex 2 upper B 26 not sign g $\unicode{x2B26}\neg g$ ⬦ ¬ g are jointly consistent. We grant their formal results but deny their dialectical conclusion. The symmetry problem is not dissolved but relocated. Their atheist advantage in S4 depends on privileging (P1) over its mirror, (P1*) white medium square left parenthesis not sign g right arrow white medium square not sign g right parenthesis $\square\left( \neg g\rightarrow \square\neg g \right)$ ◻ ( ¬ g → ◻ ¬ g ) . We argue that the principal metaphysical frameworks relevant to (P1) – including dispositional modality, actualist constraints together with divine simplicity, the inexplicability of God’s contingent existence, and theistic grounding – provide no stable advantage for (P1) over (P1*). Depending on their details, these frameworks support both principles, support neither, or generate an asymmetry that does not favour (P1). The symmetry therefore reappears at the level of the necessity claims, and the reverse argument gains no decisive advantage over the original.