The proponent of divine command theory (DCT) claims that whatever God commands to any moral agent becomes a moral obligation.  Formulations of the commands are given symbolic form by David Efird as:[1]

(RIGHT)                     ∀ϕ☐(Rϕ ≣ Cgϕ)

(WRONG)                  ∀ϕ☐(Wϕ ≣ Cg~ϕ)

(PERMITTED 1)       ☐(~Eg ⊃ ∀ϕ~Wϕ)[2]

(PERMITTED 2)       [(∃ϕ☐Cgϕ ∙ ∃ϕ☐Cg~ϕ)] ∙ [(∃ϕ☐~Cgϕ ∙ ∃ϕ☐~Cg~ϕ)]

The arbitrariness objection claims that [for example] if God commanded moral agents to rape then the action of committing rape would be obligatory to all moral agents.[3]  The objector assumes an inference in the form of the argument stating that ∀ϕ☐(Rϕ ≣ Cgϕ) may also be applicable in the sense that ϕ could refer to rape (ρ).