The Theological Direct Argument

The Theological Direct Argument is direct in that it purports to show that divine determinism is incompatible with human moral responsibility without running through intervening premises concerning human free will. Indeed, the argument makes no mention of free will at all. It rather argues that human moral responsibility is incompatible with divine determinism without getting into the weeds of why this is so.Footnote ⁷

To see how our Theological Direct Argument goes, first consider the original Direct Argument for incompatibilism about terrestrial or non-divine causal determinism and human moral responsibility. Informally, the argument goes like this:

For purposes of assessment, it helps to state the argument more formally.

To arrive at a more formal statement of the argument, first consider the following two rules of inference (where, ‘☐’ stands for broadly logical necessity; ‘→’ stands for material implication; and ‘NR p’ stands for ‘p and no mere human is now or ever has been even partly morally responsible for p’):

Rule A just says no mere human is even partly morally responsible for a necessary truth. Rule B says that if no mere human is even partly morally responsible for some fact, and no mere human is even partly morally responsible for the fact that this fact implies a further fact, then no mere human is even partly morally responsible for this further fact, either.

Keeping Rules A and B in mind, we get the following argument (where ‘p’ stands for any future fact whatever, ‘P’ labels a complete description of the world prior to the existence of any human person, and ‘L’ stands for a conjunction of the laws of nature; and, as before, where, ‘☐’ stands for broadly logical necessity; ‘→’ stands for material implication; and ‘NR p’ stands for ‘p and no mere human is now or ever has been even partly morally responsible for p’):

This is the Direct Argument. If this argument is sound, we can see, with Rules A and B in hand, that causal determinism is incompatible with human moral responsibility. We think the argument is sound; so, we conclude that causal determinism is incompatible with human moral responsibility.

This conclusion is important. It’s important because we think that the same logic found in the Direct Argument can be applied in the theological case we’re considering in this paper, that is, divine determinism. We therefore consider the Theological Direct Argument in what remains of this section.

We begin by couching ‘divine determinism’ in the way noted above from Heath White. Divine determinism is the view that ‘(1) the facts about God’s will entail every other contingent fact, and (2) the facts about God’s will are explanatorily prior to every other fact’. Now, here is the Theological Direct Argument informally put:

Notice that the Theological Direct Argument does not rely on premises about free will, control, and the like. Nor does the argument make explicit mention of our actions being causal consequences of events of the remote past or the divine decree. These are some of the ways that the Theological Direct Argument circumvents responses to theological versions of the Consequence Argument – or, minimally, reframes the discussion.Footnote ⁹

Put more formally, the Theological Direct Argument goes like this (where ‘GWA’ stands for ‘God’s willing activity’, i.e., that which God wills or decrees, ‘N’ stands for ‘all necessary truths’, and everything else is as before):

This version of the argument is clearly valid. Moreover, there isn’t even a single controversial premise. So, we conclude that the argument is sound and that divine determinism is incompatible with human moral responsibility.

The Theological Direct Argument doesn’t have a single controversial premise like the standard Direct Argument before it. Even so, one of the Argument’s inference rules, Rule B, is notoriously controversial, which emerged during discussions of the original or standard Direct Argument.Footnote ¹⁰ Numerous alleged counter-examples to that Rule exist in the literature. So, in the next section, we give a defence of Rule B. We argue that counter-examples to Rule B are impossible.

Rule B

Recall Rule B (where, as before, ‘☐’ stands for broadly logical necessity; ‘→’ stands for material implication; and ‘NR p’ stands for ‘p and no mere human is now or ever has been even partly morally responsible for p’):

Why should anyone agree that Rule B is a valid rule of inference? We later present a proof of Rule B by arguing that counter-examples to the rule are impossible, from which it follows that Rule B is valid. But the basic idea behind the Rule concerns the transfer of non-responsibility: if S isn’t responsible for p or for the fact that p implies q, S isn’t responsible for q either. Consider the following illustration of Rule B from van Inwagen:

Such illustrations of Rule B abound in the literature as standard ways of delineating classes of actions that plausibly rest outside of human moral responsibility. Many find Rule B incredibly intuitive. Even Michael McKenna, a leading defender of compatibilism, has in effect granted that, at first pass, ‘It is difficult to imagine how [Rule B] could be undermined’ (McKenna Reference McKenna2001, 48).

Despite its intuitive appeal, Rule B is not without its detractors. Indeed, the free will literature is rife with alleged counter-examples to the Rule. Here is one such (alleged) counter-example from John Martin Fischer and Mark Ravizza:

Notice how Erosion works. It is supposed to supply us with a substitution instance of Rule B that results in Rule B’s invalidity. If Erosion is right, then we get the following result when we plug in the relevant facts from Erosion into Rule B:

But, 17 is false. Betty is clearly at least partly morally responsible for the destruction of the enemy camp. If Erosion is right, then it follows that Rule B is an invalid rule of inference.

As we said, there are many such examples in the literature.Footnote ¹¹ Nevertheless, we argue in what follows that all alleged counter-examples are just that: alleged. In other words, we will argue that there are no successful counter-examples to Rule B. More strongly put, we will argue that counter-examples to Rule B are impossible.

Our argument begins by considering a corollary of truth. Following Trenton Merricks, we think that truth depends, in a very trivial way, on the way the world is.Footnote ¹² That is, it’s true, for example, that we write this paper at t because we write this paper when we do. It’s true that Rocky is a chocolate lab because Rocky is a chocolate lab. And so on. That truth depends on the way the world is in this trivial way is what Merricks calls the ‘truism about truth’ (Merricks Reference Merricks2009, 31). This truism is trivial in that it is intended to be neutral concerning questions and discussions about, for example, truth-makers and related metaphysical notions of grounding.Footnote ¹³

We agree with this truism about truth. Indeed, we think no-one should deny this truism. We also think that reflection on this truism about truth reveals something crucial about moral responsibility, viz., a principle about moral responsibility that renders counter-examples to Rule B impossible.

The ‘truism about truth’ is that truth depends, in a very trivial way, on how the world is. But, there is a corollary to this truism about truth, one of us introduces elsewhere.Footnote ¹⁴ Consider:

To see that TDM is true, consider a case wherein Jones murders Smith. In this case, it’s true that Jones murders Smith. We might ask, why is it true that Jones murders Smith? There are, perhaps, numerous ways we might try to answer this question. We might come up with motives that caused Jones to act as she did. We might try to explain the physical mechanics behind whatever was involved in or required for the murder of Smith. But, at its most basic level – the level of triviality – why it’s true that Jones murders Smith is because, obviously enough, Jones murders Smith.

Notice that Jones is morally responsible for the fact that Jones murders Smith simply because she murders Smith. That is, it’s being true that Jones murders Smith depends on Jones and what Jones does. Her being morally responsible for the fact that Jones murders Smith just illustrates this point. Or, put another way, Jones is morally responsible for the fact that Jones murders Smith because she is morally responsible for that which the truth of that Jones murders Smith depends on. This is just what TDM says.

Let’s reconsider Erosion in light of TDM. Along with Fischer and Ravizza, let’s agree that Betty is at least partly morally responsible for the destruction of the enemy camp. Even so, we deny that this leads to a counter-example to Rule B. For, we think that Betty’s responsibility for the destruction of the enemy camp implies her responsibility for the truth of the proposition found in 16, above.

To see how our argument for this conclusion goes, focus on the truth conditions of conditional propositions. By material implication, any proposition of the form p → q is equivalent to the proposition ∼ p v q. But, now notice that, in cases where p is true, ∼ p v q is true iff q is true. That is, the only reason that ∼ p v q is true is because q is true. So, it follows that in cases where p is true, any proposition of the form p → q is true iff q is true. That is, the only reason that p → q is true is because q is true.

Let’s apply these rules of logic to Erosion. We agree with Fischer and Ravizza that 15 is true (i.e., that no mere human is even partly morally responsible for the fact that the glacier is eroding). As we’ve said, we also agree that Betty is at least partly morally responsible for 17 (i.e., that 17 is false because someone, namely Betty, is at least partly responsible for an avalanche that crushes the enemy base). But, because of the rules of logic just discussed combined with TDM, we deny that 16 is true. No, we argue that because Betty is at least partly morally responsible for the destruction of the enemy base at T3, she is at least partly morally responsible for the truth of the conditional proposition found in 16 (i.e., if the glacier is eroding, then there is an avalanche that crushes the enemy base at T3). In other words, Betty is at least partly morally responsible for the truth of the conditional proposition in 16 in virtue of being at least partly morally responsible for the consequent of this conditional proposition. Thus, 16 is false. But, for Erosion to be a successful counter-example to Rule B, both 15 and 16 have to be true while 17 is false. Here we have shown that only 15 is true while both 16 and 17 are false. So, we conclude that Erosion fails as a counter-example to Rule B.

Importantly, this problem generalises to all alleged counter-examples to Rule B. For, all alleged counter-examples to this Rule have the same form. These cases stipulate that NR p is true; they stipulate that NR p → q is true; and they try to show that NR q is false. But, as we’ve just shown, if someone is responsible for q, then, in cases where p is true (which is every case that tries to be a substitution instance of Rule B), it’ll follow that someone is at least partly morally responsible for the fact that p → q.

Some divine determinists maintain that humans could be morally responsible for what God determines them to do. Call this position theological compatibilism. Theological compatibilists might initially be tempted to use TDM in response to our defence of Rule B.Footnote ¹⁶ According to the Theological Direct Argument, the following (allegedly) holds (where all is as before, but let ‘(S does A)’ take the place of ‘p’, where ‘S’ stands for ‘a mere human’ and ‘A’ stands for ‘some morally significant action’): NR (GWA & N), NR ((GWA & N) → (S does A)); therefore, NR (S does A). But theological compatibilists might look to TDM to deny this conclusion by denying the claim that NR ((GWA & N) → (S does A)). By the lights of TDM, if someone is responsible for the truth of (S does A), won’t it follow that the truth of ((GWA & N) → (S does A)) is true only because of the truth of (S does A)? If so, then theological compatibilists have nothing to fear from Rule B so long as it is plausible to maintain that S is morally responsible for A under the description of the relevant scenario.

This response on behalf of theological compatibilism is not as attractive as might initially appear. First, this response begs the question in favour of theological compatibilism. To see why this is so, notice the different uses of TDM in the different dialectical contexts. We have used TDM to counter an alleged counter-example to Rule B, where the interlocutors agree that it minimally seems that 15 and 16 are true but 17 is false. Most relevantly, compatiblists and incompatibilists, and defenders and deniers of Rule B, agree that 17 is false – someone is at least partly morally responsible for the avalanche’s crushing the enemy base at T3. We use the apparent falsity of 17, together with TDM, to argue that 16 is likewise false, first impressions notwithstanding. Hence, Erosion and alleged counter-examples to Rule B that take its form don’t realise their aim.

Yet the situation is much different in the proposed use of TDM by theological compatibilists. They seek to deny NR ((GWA & N) → (S does A)) by affirming the very claim under dispute: S is, or can be, morally responsible for some action that is determined by God. In the debate between theological compatibilists and incompatibilists, this affirmation by theological compatibilists is question-begging.

Consider the matter from another angle. Rule B is an intuitively plausible principle, which appeals to compatibilists and incompatibilists alike, that threatens to undermine theological compatibilism. This is at least partly why compatibilists – theological and otherwise – seek to provide counter-examples to this Rule. When TDM is then used to show that counter-examples to Rule B are impossible, the imagined response holds that TDM saves theological compatibilism, so long as it is agreed that persons can be responsible for actions that are determined (or entailed by God’s willing activity). No-one who is not already committed to theological compatibilism should grant this last clause, however.Footnote ¹⁷

A second problem for this theological compatibilist’s response concerns Rule A: from ☐p, we may infer NR p. NR ((GWA & N) → S does A) follows by Rule A from ☐((GWA & N) → S does A). Or stated in keeping with our Theological Direct Argument, above, NR (GWA → (N → p)) follows by Rule A from ☐(GWA → (N → p)). But Rule A is tremendously plausible.Footnote ¹⁸ We therefore hold that a theological compatibilist’s best defence against the Theological Direct Argument is to find a plausible way of objecting to Rule B.

So, consider another alleged counter-example to Rule B provided by Justin Capes.

Here’s how Double Dose is a proposed counter-example to Rule B. While it’s true, according to the details of the story, that

it’s also said to be true that

yet it is not true that

So, Capes concludes, Double Dose is a counter-example to Rule B.

Given what we’ve said so far in our argument for Rule B’s validity, we might attempt to respond to Double Dose by way of TDM. Given TDM, and what we’ve argued so far, if we agree with Capes that 20 is false (because Kathy is at least partly morally responsible for the fact that Earl dies before noon), it will follow that we think that 19 is false, too. That is, if what we argued above is correct, then Kathy is at least partly morally responsible for the fact that if Earl ingests the second substance at 11:54am, then Earl dies before noon. Why? Because Kathy is at least partly morally responsible for the fact that Earl dies before noon, and Earl’s dying before noon is why the conditional expressed in 19 is true.

On closer inspection, however, it’s unclear how 19 could be false. For, given the facts in Double Dose, it’s a necessary truth (assuming determinism) that Earl’s ingesting the second substance when he does implies that he dies before noon. We don’t pretend to know why any given necessary truth is true; but, here is something we can say with confidence: no necessary truth, qua necessary truth, is true because of what any mere human does. If a necessary truth were true because of what a human person does, it would follow that Rule A is invalid. But, as we previously stated, we are convinced that Rule A is valid. So, no necessary truth is true because of what a person does. It follows, then, that Earl’s dying when he does is not why the conditional expressed in 19 is true. So, it (apparently) also follows that 19 is true; that is, no human is even partly morally responsible for the fact that Earl ingests the second substance at 11:54am → Earl dies before noon. And, if 19 (along with 18) is true but 20 is false, then Double Dose is a counter-example to Rule B.

We aren’t persuaded that Double Dose serves as a genuine counter-example to Rule B, however. Indeed, in what follows, we will show why Double Dose is not a counter-example to Rule B, and our argument will drive home our conclusion that counter-examples to the Rule are impossible (and, thus, that Rule B is valid).

To begin to see how this part of our argument will go, notice that (according to classical logic) any conditional with a true consequent is true. Now, consider the details of Double Dose. It is stipulated that Earl ingests the second substance at 11:54am. But, now put the true proposition that Earl ingests the second substance at 11:54am in the consequent of any conditional and that conditional will be true. Here’s one:

Given Double Dose, 19* is true. And, given 19*, and the conditional expressed in 19 (i.e., Earl ingests the second substance at 11:54am → Earl dies before noon), it follows that

In other words, that Earl ingests the second substance at 11:54am is materially equivalent to that Earl dies before noon.

To put the point more clearly, from Double Dose we get (where ‘E’ stands for ‘Earl ingests the poison’; ‘K’ stands for ‘Kathy poisons Earl’s drink’; ‘L’ stands for a complete statement of the ‘laws of nature’; and ‘q’ stands for ‘Earl dies before noon’):

Now, let ‘p’ stand for ‘L&E’; so, it follows that, according to Double Dose, p → q.

Moreover, from Double Dose, we get the following (allegedly invalid) substitution instance of Rule B:

but, crucially,

That is, it is false, according to Double Dose, that no mere human is partly directly morally responsible for the fact that Earl dies before noon, and, so, Rule B is invalid.

Notice, though, that *, given the truth of E, trivially implies:

That is, * and ** are materially equivalent. Now, let ‘u’ stand for L&K such that u → q. With ** in hand, we can now generate a substitution instance of Rule B, the conjunction of which is materially equivalent to the propositions contained within 1*–3*, and one that, if 1*–3* successfully shows that Rule B is invalid, should also show that Rule B is invalid. Consider:

To see why the conjunction of propositions contained within 1**–3** is materially equivalent to the conjunction of propositions contained within 1*–3*, consider a different operator, the necessity operator (i.e., ‘☐’), and the following chain of reasoning:

Now, consider:

By way of explanation, suppose that ☐ p is true, and that it’s also true that ☐ (p ←→ u). It will follow from these assumptions that ☐ u. Now, suppose that NR p and NR (p ← → u) are true. If the NR operator functions anything like a unary sentential modal operator (on the model of the necessity operator ☐), then from premises 27–31 it follows that NR u, just as ☐ u follows from premises 21–25. We think it is at least plausible that the NR operator behaves something like a normal unary sentential modal operator – that is, one satisfying something like the K-distribution axiom (NR(p → u) → (NR p → NR u)). Under this assumption, it follows that if NR p, then NR u, where no mere human is even partly morally responsible for the fact that p and u are materially equivalent (as expressed in 28, above).Footnote ²¹

Return, then, to 1**–3**. Given TDM, NR (u → q) seems false (i.e., 2** seems false), if we grant that NR q is false (i.e., if we grant that 3** is true). Moreover, NR u (i.e., NR L&K) in 1** is at least plausibly false since Kathy is responsible for K, the fact that Kathy poisons Earl’s drink. But, the conjunction of propositions within 1**–3** and the conjunction of propositions within 1*–3* are logically equivalent; so, if one fails to be a substitution instance of Rule B that shows the Rule is invalid, then the other fails as well. We think that 1**–3** fails to show that Rule B is invalid; so, we conclude that 1*–3* fails to show that Rule B is invalid. So, we conclude that it’s at least plausible that Double Dose is not a counter-example to Rule B. Notice, also, that we’ve reached this conclusion without arguing that anyone is morally responsible for a necessary truth – hence, no violations of Rule A have occurred.

Our response to Double Dose generalises to all alleged counter-examples to Rule B. In every instance the details of the case can be interpreted as something like *; but, if that’s true, then they can be interpreted as something like ** since the conjunction of propositions contained within are logically equivalent. But, from any alleged counter-example to Rule B, we’ll get something like 1*–3*. And, if so, then, from any alleged counter-example to Rule B we can get something like 1**–3** since the conjunction of propositions within 1*–3* and the conjunction of propositions within 1**–3** are logically equivalent. Crucially, this means that both 1*–3* and 1**–3** will fail to show that Rule B is invalid. Since this is the form that any alleged counter-example to Rule B will have to take, it follows that counter-examples to Rule B necessarily fail.

In summary, here is our argument for the validity of Rule B. Either alleged counter-examples to Rule B will fail for TDM-related reasons plus how logical conditionals work (step one), or they will fail for additional reasons having to do with the rules of logic (step two). We think TDM is true. Moreover, we think that everyone should favour views that agree with the standard rules of logic. Our argument is that TDM combined with the standard rules of logic shows that counter-examples to Rule B are impossible. So, we conclude that Rule B is valid.

Since Rule B is valid and Rule A is (we think) beyond reproach, it follows that both of the Theological Direct Argument’s inference rules are valid. But, these are the only places to press on the Theological Direct Argument; so, we conclude that the Theological Direct Argument is sound.

Importantly, if the Theological Direct Argument is sound, then divine determinism is incompatible with human moral responsibility. We therefore conclude that divine determinism is incompatible with human moral responsibility.

Just in case Rule B is invalid

But maybe we shouldn’t affirm this conclusion too quickly. Maybe further inspection will reveal (impossibly, we believe) that Rule B is invalid; so, let’s agree, for the sake of argument, that Double Dose is a legitimate counter-example to Rule B. To avoid cases like Double Dose, Capes introduces an informal revision of Rule B as follows:

Put more formally (where NR_S p expresses the proposition that agent S is not even partly morally responsible for p, and C_p expresses a proposition describing all the antecedent conditions that led to its being the case that p), Capes gives us

Rule B* is obviously not susceptible to cases like Double Dose. For, as Capes puts it, ‘Kathy is at least partly morally responsible for the fact that Earl died before noon, to be sure, but she is also at least partly morally responsible for the fact that one of the events that led to its being the case that Earl died before noon, viz., her act of poisoning Earl at 11:49’ (Capes Reference Capes2016, 1490). And, importantly for our purposes, Rule B* works perfectly well with our Theological Direct Argument.

As an example, recall our argument against divine determinism:

Suitably revised, our argument will now go like this:

It should be noted that 2* rests upon a reformulated Rule A, also provided by Capes, which is called Rule A*.Footnote ²²

Rule A*: From ☐ p, we may infer NRs p

Rule A* is just an agent-relative version of Rule A. It says that if it’s broadly logically necessary that p, then we may infer that agent S is not even partly morally responsible for the fact that p. Rule A* is a necessary revision in light of Rule B*.

With that clarification in place, you can see how Rule B* works seamlessly within the Theological Direct Argument. And, as before, unless Rules A* and B* are invalid, the argument is sound. We think Rule A* is unassailable. Moreover, we think our argument for Rule B works at least as well for Rule B*; so, we conclude that counter-examples to Rule B* are impossible. So, we conclude that Rules A* and B* are valid. And, if so, our Theological Direct Argument against divine determinism is sound. So, we conclude that divine determinism is incompatible with human moral responsibility.