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.
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.
Before continuing with the objector’s case against DCT and its proponent’s response, God must be assigned an understood ontological value. There will be an assumption of the Anselmian notion of God, a being that which nothing greater can be conceived, or a maximally great being. For anything that is morally good, it must be founded in a maximally great being, which would apply deontological status.
God’s attributes are necessarily so, he maintains such attributes in all possible worlds. These attributes would be anything, which is of the greatest. To make a minimalistic case for a perfect ontology of God, Occam’s razor will be used as a referent for the greatest intuition. All things being equal, more knowledge is greater than less knowledge. Intuitively, this seems to be true, at least in the actual world. This would also include all moral goodness.
The task of the DCT proponent is to substantiate the validity of the claim that God maintains all attributes in all possible worlds. To pose the task in the form of a question: is there a possible world in which God commands rape to be morally obligatory?
If the DCT proponent is to defend his position he must demonstrate the necessary falsehood of the counterfactual: If God did command rape then there would be a moral obligation to rape. There will be an assumption of ethical realism since ethical anti-realism is argued for and against in completely different arguments. The ethical realist objector [to DCT] claims that it is possible for God to command rape in some possible world, or in an impossible world close to the actual world, making it obligatory for all moral agents, whereas rape is still morally bad in that same world, thus, making DCT arbitrary and is defeated.
The nonstandard semantics objection to the arbitrariness of DCT suggests that there is an impossible world, however close to the actual world, in which God commands rape or the torture of innocent children. Approaching the objection from an explanandum-driven consideration, would a contingent command be an adequate objection? Consider the following contingencies of a command:
(CONTCOM) ∀ϕ[(◊~Cgϕ) ∙ (◊Cgϕ)]
(CONTCOMʹ) ∀ϕ[(◊~Cg~ϕ) ∙ (◊Cg~ϕ)]
The objector assumes that ϕ can be any command and could thus look like:
(CONTCOM″) ∀ϕ[(◊~Cgϕ ∙ ◊~Cg~ϕ) ∙ (◊Cgϕ ∙ ◊Cg~ϕ)]
(CONTCOM‴) ∀ρ[(◊~Cgρ ∙ ◊~Cg~ρ) ∙ (◊Cgρ ∙ ◊Cg~ρ)]
Conceding the use of impossible world semantics, the command ρ is counteressential to God. God cannot arbitrarily concoct the commands if it is counteressentially false. Thus, CONTCOM is contingently true depending on whether or not ϕ can be predicated to God as being essentially true. The first conjunct merely suggests the silence of God whereas the second conjunct is contingent on its essential relationship to God. ϕ could mean any action of love, which would be a true contingent command of CONTCOM whereas it would be false CONTCOMʹ because to not-love is counteressential to God. The same is conversely true with rape (ρ). CONTCOMʹ is a true command if ~ρ is essentially true to God; thus, a prohibition.
Referring back to Efird’s model of the commands:
(RIGHT) ∀ϕ☐(Rϕ ≣ Cgϕ)
(WRONG) ∀ϕ☐(Wϕ ≣ Cg~ϕ)
As long as ϕ is essential to God’s goodness then RIGHT is a command that makes ϕ necessarily obligatory. If ϕ is counteressential to God’s goodness (i.e. rape, ρ), then ϕ is necessarily prohibited and equivalent to WRONG. The contingency of DCT is only applicable to whether or not God chooses to reveal such commands or remains silent. The objection also tries to divide the ontological and epistemic relationship to moral goodness. These essential truths are necessary truths, which retain ontological foundation within God.
Another way of handling the objection would be explanans-driven considerations. This will assume that morality and God are both necessary under the Anselmian concept of God. The question then is, must morality ontologically depend of God? If this were the case it would seem like it would not. These two necessary truths can obtain independent of each other in as long as they are both necessary. The same would be true if God were contingent since morality is still necessary; thus, relinquishing a foundation for morality because of its independent necessary existence. For the proposition, “If God doesn’t exists, then moral facts obtain” (~Eg ⊃ Om) the consequent is necessarily true, by supposition, which, according to the standard semantic of counterfactuals, has the same effect as a necessarily false antecedent, namely, that the conditional is trivially true. However, consider the proposition “If an Anselmian God does not exist, then moral facts obtain” (~Ea ⊃ Om). If the use of standard semantics apply, and the consequent is necessarily true, then to render ~Ea as true would be highly problematic. The Anselmian notion of God bases all reality in his existence. To affirm ~Ea, or simply put, to affirm the nonexistence of all reality, and to consequently affirm that moral facts obtain would be metaphysically incoherent or even a contradiction. Metaphysically, and logically, the only things that cannot obtain are contradictions. Thus, ~Ea ⊃ Om is nontrivially false. For the atheist to suggest
(EQUIV) ~◊G ∙ (G ⊃ R)
as a retort to dismiss the claim again would be equivocation and misunderstanding the metaphysical and ontological connection between an Anselmian God and necessary truths (like that of moral truths). In this instance, the God in the first conjunct is the Anselmian God whereas the god in the second conjunct is a less-than-Anselmian God. When the equivocation is explicated it would render
(EQUIVEX) ~◊G ∙ (g ⊃ R)
The second conjunct may certainly be conceded whereas G ⊃ R cannot obtain, it would be a nonsensical world.
If DCT is to prove true, the God manifesting the commands must be an Anselmian God. In Louise Antony’s example, “If DCT is correct, then the following counterfactual is true: If God had commanded us to torture innocent children (τ), then it would have been morally right to do so.” Antony is assuming the counterfactual, in the subjunctive mood, is a feasible circumstance for God to find himself in. Thus, Cgτ ⊃ Mτ, the antecedent is necessarily false. If something were necessarily false it would be nonsensical to derive any meaningful counterfactuals since it is counteressential to an Anselmian God.
Concerning the notion of permission in DCT, recall (PERMITTED 1), would suggest moral nihilism, since Karamazov’s Thesis is a notion of permission by denying any deontic ethics be founded in anything or anyone. PERMITTED 2 would hold true in the Anselmian model as well because in the absence of any command there are no obligations to fulfill (both to carry out and by prohibition). No moral agent can be obligated to do anything in the absence of a command since there is no moral duty to adhere to since the command is what predicates moral obligations.
A statement like “God is good” may be taken as a synthetic statement expressing a proposition that is metaphysically necessary both in the sense that the proposition is true in all possible worlds and in the sense that goodness is an essential property of God. To separate the essential properties of God from the necessary truths derived from these essential properties would render an incoherent proposition.
Nonstandard semantics renders an impossible and incoherent proposition if applied to an Anselmian God because it attempts to separate the metaphysical and ontological truth-values between an Anselmian God and moral truths. To suggest that there is a possible world, or the closest impossible world, where an Anselmian God commands rape is a non-sequitor because it is counteressential to an Anselmian God, such a state of affairs cannot obtain.
God’s moral nature is expressed in relation to humanity in the form of commands and deontic ethics. Far from being arbitrary, these commands flow necessarily from his moral nature. On this foundation it can be affirmed that the objective goodness and rightness of love, generosity, self-sacrifice and equality, and condemn as objectively evil and wrong selfishness, hatred, abuse, discrimination and oppression.
 ‘ϕ’ ranges over action types, such as going to fight at the front, and ‘∼ϕ’ stands for ‘refraining from ϕ’, ‘R’ stands for the predicate ‘__ is morally right’, ‘W’ stands for the predicate ‘__ is morally wrong’, ‘C’ stands for the relation ‘__ commands __’, where the first term of the relation stands for an agent and the second term stands for an action type, ‘g’ is a singular term standing for God, and ‘x forbids ϕ’ is true just in case ‘x commands ∼ϕ’. David Efird, “Divine Command Theory and The Semantics of Quantified Modal Logic,” in New Waves in Philosophy of Religion, Erik Wielenberg and Yujin Nagasawa, eds. (United Kingdom: Palgrave MacMillan, 2009). See http://www.york.ac.uk/depts/phil/about/staff/efird/dct_qml.pdf (November 22, 2010).
 This is a negative claim for permission, Karamazov’s Theorem: Necessarily, the non-existence of God implies that for every action, the action is not a wrong action. This, of course, has no deontological value, but it would a true counterfactual to the actual deontological claims of the DCT proponent.
 As advocated by Walter Sinnott-Armstrong in “Why Traditional Theism Cannot Provide an Adequate Foundation for Morality,” in Is Goodness without God Good Enough? (Lanham, MD: Rowman & Crutchfield, 2009), 106.
 The objector would need to deny necessity as the quantifier and merely suggest that the command is possible.
 This needs to be understood as a mere explication of what the proponent of DCT is assuming.
 I am not suggesting an Occamist understanding of God, rather I’m using this an as illustration to explicate how one may discern between the values of particular attributes.
 I’m assuming that there is an intuitive sense that there are some objective values and duties. To avoid situational ethics, which would introduce more ethical theories, I will simply refer to Occam’s razor as: greater moral goodness is greater than less moral goodness.
 At this point, given the formulation for the contingency of a command, CONTCOM and CONTCOMʹ could appear to be indistinguishable. Let’s use ϕ to represent love and ρ to represent rape. To translate CONTOM using love, it would read: For all actions of love, it is possible for God not to command love and it is possible for God to command love. The first conjunct is certainly possible render the existence of God and God remains silent and issues no such commands. CONTCOMʹ, still using love, would read: For all actions of love, it is possible for God not to command not-love and it is possible for God to command not-love. The model of contingency that the objector would purport would be CONTCOM″ since it renders a conjunct of the negations between CONTCOM and CONTCOMʹ. CONTCOM″ thus purports that whatever ϕ may represent, it is inessential to God, hence the arbitrariness. CONTCOM‴ is an example of what this would look like if rape were command. There would both be possible and impossible worlds in which the contingency of the command, arbitrarily contrived, is commanded.
 For more see David Baggett and Jerry L. Walls, Good God.
 Let ‘G’ represent “God commands rape,” and ‘R’ represent “Rape is morally acceptable.” As given in Baggett and Walls, Good God.
 Let ‘g’ represent “less-than-Anselmian God.” Ibid.
 Louise Antony, “Atheism as Perfect Piety,” Goodness Without God, 71.
 M = Morally obligated to. Assuming an Anselmian God in the proposition.
 I want to explicate what I mean by this point. There are possible worlds in which God is silent and does not give a command. For example, in a world that has only one person, that person cannot be given a command to abstain from rape since rape must involve at least one other person. Every command is predicated to the moral attributes of God (by biblical witness to be holy). So God’s silence concerning some commands are categorically specific and in this world containing this one person, had such circumstances taken place that would warrant the command to be given (and introduction of a second person), the command would be given (though the concept of rape is morally reprehensible in all possible worlds).
 William Lane Craig, J.P. Moreland, Philosophical Foundations for a Christian Worldview (Downers Grove, IL: InterVarsity, 2003), 531.
 Ibid., 491.