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:
(RIGHT) ∀ϕ☐(Rϕ ≣ Cgϕ)
(WRONG) ∀ϕ☐(Wϕ ≣ Cg~ϕ)
(PERMITTED 1) ☐(~Eg ⊃ ∀ϕ~Wϕ) 
(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. 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). What would make the command arbitrary is the truth of the counterfactual: If God did command rape then there would be a moral obligation to rape. If this counterfactual were true then it would serve as a defeater for DCT. The objection is not a defeater for the existence of God; it is a defeater for the DCT’s model of deontological ethics.