While at the VT Debate on the existence of God one of the atheists’, in passing, briefly mentioned the Euthyphro dilemma. Does God command something because it’s good or is it good because God commands it? The first horn makes goodness apart from God and the second makes goodness arbitrary. This came up in the Q&A as well. What if God commanded you to strap a bomb to your chest and blow other people up or rape others? As an advocate of divine command theory the response to this question is a bit more nuanced then any prima facie answer. (Also, see my moral argument I presented at this debate).
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)]
*∀= for all…, ☐=necessarily, ◊=possibly. For instance, RIGHT is read as for all actions, ϕ, ϕ is right if and only if God commands ϕ.