The mis-typed designator objection

In response to Mullins's argument, Joseph Schmid has raised the following objection to the formulation of (M2):

Before responding to Schmid's objection, a point of clarification is in order. Schmid misdirects his ire against (M2). Given that we understand the conditional in (M1) as strict entailment – as Schmid (Reference Schmid2022, 7) concedes – (M2) merely follows by one application of the K-axiom.Footnote ⁷ We can perhaps see the point more prominently if we reformulate the premises as follows:

1. (M1*) Necessarily [if God intentionally acts to actualize this world, then this world obtains].Footnote ⁸

2. (M2*) If necessarily [God intentionally acts to actualize this world], then necessarily [this world obtains].

(M1*) expresses Mullins's point in the standard formalization for strict entailment. Moreover, (M2*) follows by dint of deduction from the first. Our clarification creates some tension in Schmid's analysis. Schmid was willing to accept (M1) while rejecting (M2) (Schmid Reference Schmid2022, 10). As we have seen, however, the two are logically bound together. Thus, Schmid cannot reject (M2) without likewise rejecting (M1). Despite the mischaracterization of the problem, further analysis will reveal that one can redirect Schmid's critique to the appropriate target without loss of force.

The nature of Schmid's critique centres on the appropriate classification of the designator ‘God's intentional act to actualize this world’. All designators serve to pick out objects within the world. For instance, the designator ‘the president of the United States’ picks out Joe Biden while ‘Alvin Plantinga’ picks out Alvin Plantinga. Following Kripke, we can distinguish between two types of designators within a modal context (see Kripke Reference Kripke1980). Rigid designators pick out the same object in every world. The primary example of these sorts of designators is proper names. Thus, ‘Alvin Plantinga’ not only picks out Alvin Plantinga in our world but every other world as well.Footnote ⁹ Non-rigid designators, by contrast, pick out different objects within different possible worlds. ‘The president of the United States’ is a designator of this type. The description picks out Joe Biden in the actual world. However, in alternative versions of reality, a different candidate won the 2020 election. Hence, the designator would pick out that individual in those worlds instead.

Returning to the conversation at hand, Schmid rightly notes that the validity of Mullins's argument hinges on taking ‘God's intentional act to actualize this world’ as a rigid designator. We can perhaps see this point more clearly by reformulating the inference from (M3–M5) to (M6) in Mullins's argument as follows – letting α serve as a name for the actual world:

1. (A) Necessarily [God exists].

2. (B) God is identical to God's intentional act to actualize α.

3. (C) Therefore, necessarily [God's intentional act to actualize α exists].

Given the principle of the necessity of identity, (C) follows from (A) and (B) provided one takes ‘God's intentional act to actualize α’ as a rigid designator.Footnote ¹⁰ Schmid, however, straightforwardly rejects this claim. Indeed, he charges Mullins and company with question-begging to construe the designator in this way. Without that assumption, however, one cannot reach the key conclusions given in (M6) and (M7). As a result, even if one grants (M2), the antecedent of the conditional is never deduced; ipso facto, the consequent is never concluded.

To drive his point home, Schmid develops a parody of Mullins's argument that runs as follows (Schmid Reference Schmid2022, 10–11):

1. (P1) <The infallibly omnipotent creator of this world exists> necessarily entails <this world exists>.

2. (P2) If the infallibly omnipotent creator of this world exists of absolute necessity, then this world exists of absolute necessity.

3. (P3) God exists of absolute necessity.

4. (P4) If God is identical to x, then x exists of absolute necessity (P3).

5. (P5) God is identical to the infallibly omnipotent creator of the world.

6. (P6) The infallibly omnipotent creator of this world exists of absolute necessity (P4, P5).

7. (P7) This world exists of absolute necessity (P2, P6).

One might wonder if the same concern regarding designators applies to Schmid's parody as well. Indeed it does, but that is precisely the point. Schmid's parody is likewise invalid for the same reason that ‘the infallibly omnipotent creator of this world’ is a non-rigid designator. Structurally, then, Schmid's parody argument mirrors his reading of Mullins's original. Moreover, Schmid maintains that the premises of his parody are central affirmations not only for classical theists but for ‘any view on which God exists necessarily and is the infallibly omnipotent creator of this world’ (Schmid Reference Schmid2022, 11). Schmid then backs the advocate of Mullins's modal collapse into a corner. Unless they can show where Schmid's parody diverges from the original, the success of the latter formulation leads to the success of the former formulation.

Immutability re-collapse

What are we to make of Schmid's argument? As we've seen Schmid's key move lies in taking ‘God's intentional act to actualize this world’ as a non-rigid designator. Already, one can object to Schmid's objection on that score (Mullins and Byrd Reference Mullins and Byrd2022, 34). However, for the sake of argument, we shall grant Schmid the point. A new question now emerges. What manner of non-rigid designator is the term in question supposed to be? The most obvious candidate is a definitive description. We can understand a definitive description as a characterization that adheres to only one object in a world. Consider again, for example, the designator ‘The president of the United States’. Since the United States only ever has a single president, the description only ever characterizes one object. Yet, depending on the context of utterance, which object the description picks out differs.

Following the canonical analysis of definitive descriptions given by Bertrand Russell (1905) we can render ‘God's intentional act to actualize this world’ a bit more rigorously as follows – again letting α stand for the actual world:

1. (1) For some x, x is God's intentional act to actualize α and for all y, if y is God's intentional act to actualize α, then x = y.Footnote ¹¹

So formulated, the error in reasoning presented in (A)–(C) becomes apparent. Consider the result of substituting ‘God's intentional act to actualize this world’ with (1):

1. (A*) Necessarily [God exists].

2. (B*) For some x, x is God's intentional act to actualize α and for all y, if y is God's intentional act to actualize α, then x = y and God = x.

At most, one can infer from (A*) and (B*) that

1. (C*) For some x, x is God's intentional act to actualize α and for all y, if y is God's intentional act to actualize α, then x = y and necessarily [x exists].

Unfortunately, (C*) falls short of what Mullins needs for the modal collapse argument. The proposition affirms that x exists necessarily but not that x has the property of being ‘God's intentional act to actualize α’ in every world at which it exists. Applying these same manoeuvres to Schmid's parody leads to like results.

While our reformulation of the argument lays bare the invalidity of Mullins's original formulation – assuming one accepts Schmid's reading of the designator – it simultaneously opens the door for a new route to modal collapse by way of divine immutability. Proponents of classical theism embrace not only a strong version of DDS but strong versions of divine immutability as well.Footnote ¹² According to the latter, God is not subject to change with respect to any of his intrinsic properties. Put another way, God lacks any internal potentiality.Footnote ¹³ We could make a first attempt at formulating this strong doctrine of divine immutability (DDI) as follows:

The above formulation, while accurate, suffers from incompletion. So formulated, we are limited to considerations of only monadic predications such as ‘God is omnipotent’ or ‘God is omnipresent’. We may, however, wish to consider intrinsic predicates of a polyadic nature such as ‘God believes that p’ or ‘God desires that q’. To accommodate the latter, we can revise our definition as follows:

With Strong DDI* in view, we can return to Mullins's argument with renewed perspective. Consider again the claim made in (B*):

1. (B*) For some x, x is God's intentional act to actualize α and for all y, if y is God's intentional act to actualize α, then x = y and God = x.

While this premise proved ill-suited to Mullins's original plans, we can infer from (B*) the following:

1. (2) God is God's intentional act to actualize α.Footnote ¹⁵

Next, we can tie (2) to Strong DDI* via the following instance of the principle:

1. (3) If God is God's intentional act to actualize α and God's being God's intentional act to actualize α is intrinsic to God, then necessarily [God is God's intentional act to actualize α].Footnote ¹⁶

(2) affirms one of the two conjuncts in (3)'s antecedent. As such, to reach the conclusion that God is necessarily his intentional act to actualize α, we need only establish that God is intrinsically so characterized.

Here our definition of ‘intrinsic’ becomes crucial. Schmid endorses the definition given by David Lewis according to which ‘we distinguish intrinsic properties, which things have in virtue of the way they themselves are, from extrinsic properties, which they have in virtue of their relations or lack of relations to other things’ (Schmid Reference Schmid2022, 61; Schmid draws this quote from Lewis Reference Lewis1986, 61).Footnote ¹⁷ Perhaps as a merely preferential matter, we shall by contrast adopt the definition given in Koons and Pickavance (Reference Koons and Pickavance2017, 20):

Applying this definition to the question at hand, we can now ask whether God's being an intentional act to actualize α is in any way grounded by or dependent upon something that is neither God nor a part of God. We may give at least two arguments for the conclusion that it is not.

First, God's act of creating α is independent of anything within α. Indeed, all creative acts stand apart from that which is created by virtue of the fact that the former brings into existence the latter. By extension, God's being this act cannot depend upon anything that is neither God nor a part of God since all such objects are brought into existence by the act itself. Per our operative definition of intrinsicality, therefore, God's being such an act must be intrinsic to him.

Second, God's act of creating α is identical to other intrinsic properties. Consider again Mullins's claims in (M5) and (M6):

1. (M5) All of God's intentional actions are identical to each other such that there is only one divine act.

2. (M6) God's one divine act is identical to God's existence.

According to (M5), all of God's intentional acts – including the intentional act to actualize α – are identical to his one divine act. (M6) then adds that God's one divine act is identical to God's very existence. Since identity relations are transitive, we can conclude that God's intentional act to actualize α is identical with God's very existence. The latter, moreover, is indisputably not grounded in anything that is neither God nor a part of God by virtue of his aseity. Thus, God's existence is intrinsic. By extension, anything identical to God's existence must likewise be intrinsic, which includes – per Mullins – God's intentional act to actualize α. Hence, the predication is intrinsic (see Mullins Reference Mullins, Arcadi and Turner2021, 95).Footnote ¹⁸

Finally, given that God both is ‘God's intentional act to actualize α’ and is so intrinsically, we have met both the conditions specified in the antecedent of (3). Therefore, we can conclude:

1. (4) Necessarily [God is God's intentional act to actualize α].

We can now combine this conclusion with a revised version of Mullins's claim to the infallibility of omnipotence:

1. (M1**) Necessarily [if God is God's intentional act to actualize α, then α obtains].

From (M1**) we can deduce:

1. (M2**) If necessarily [God is God's intentional act to actualize α], then necessarily [α obtains].

Lastly from (4) and (M2**) we conclude that

1. (5) Necessarily [α obtains].

The conclusion given in (5) mirrors that of Mullins's original argument presented in (M9).

In summary, by taking ‘God's intentional act to actualize this world’ as a non-rigid designator, Schmid successfully defuses Mullins's modal collapse argument from DDS. In doing so, however, Schmid opens the door for a re-collapse by way of DDI. If the designator in question is non-rigid, then it must be a definitive description. Taken as a definitive description together with Strong DDI* and plausible auxiliary assumptions, however, leads to the same conclusion as Mullins's original argument. Since the classical theist is equally committed to strong DDI as they are to strong DDS, I conclude that the modal collapse survives Schmid's attempt at disarmament.

The re-collapse manoeuvre, moreover, marks a point of disanalogy between Mullins's argument and Schmid's parody. Unlike the classical theist, non-classical theists can freely reject Strong DDI*. As such, even if one grants that Mullins's argument is structurally identical to Schmid's parody, the re-collapse applies only to the former not the latter formulation.

Failure of the ought implies can principle

The ought implies can principle (OIC) famously traces to the work of Immanuel Kant. Kant articulates the principle at numerous places throughout his corpus. For instance, in Critique of Pure Reason he writes:

The last line captures the core of the principle. An action, according to Kant, is obligatory provided one has the ability to perform it. Intuition weighs heavily in favour of this principle. If a father promises to attend his son's baseball game, we naturally think he has a moral obligation to be there. If, however, on route to the game, the father's car is hit by another driver rendering him unable to reach his destination, the moral obligation no longer adheres. Any number of examples – both mundane and severe – could be given along these lines. All of them, however, point not only to the accuracy of Kant's principle but its ubiquity as well. What makes Kant's principle so compelling is how pervasive the use of it is within our everyday, pedestrian ethical reasoning.

Before turning to consider the ramifications of a modal collapse on Kant's principle, we first need to clarify its nature. Alex King has helpfully noted that OIC admits to a wide range of interpretations (King Reference King2019, 3). Building off King's point, we can conceive of the various options as differing analyses of the following schema:

The sundry formulations of the principle arise through alternative understandings of each element within OIC. For instance, one must determine: (i) what objects ‘S’ and ‘A’ range over; (ii) the meaning of the ‘ought’ and ‘can’ operators; (iii) the nature of the conditional (‘only if’); (iv) whether or not to temporally index the principle.

Since our concern at present rests with moral matters, we shall understand the ‘ought’ as normative in nature. Likewise, we shall adopt the standard readings of ‘S’ and ‘A’ as ranging over individual moral agents (as opposed to collections of agents) and actions respectively (King Reference King2019, 14–15). Since the material conditional and strict entailment are equivalent in a modal collapse scenario, we shall adopt the former as our understanding of ‘only if’ (King Reference King2019, 7). In addition, for simplicity's sake, we shall avoid including the temporal indexical; however, one could amend the scheme with this added element without changing the results discussed below.

We come, lastly, to OIC's most turbulent element: ‘can’. As King observes, this component of the scheme has received the most attention from exegetes and admits to the widest range of interpretations (King Reference King2019, 9–10). In navigating these waters, we begin by noting that most readings of ‘can’ construe the operator as a species of restricted possibility. Generally speaking, metaphysicians understand metaphysical possibility as the broadest kind of potentiality.Footnote ²⁰ More restricted versions – causal, nomological, etc. – are subsets of metaphysical possibility that meet some further restriction such as adhering to the actual laws of nature.

To understand why defenders of OIC opt for narrower notions of possibility, we need to first recognize the function of OIC within ethical discourse. The principle primarily serves as an obligation defeater. Thus, most uses of the principle argue from ‘S cannot A’ to ‘S does not have an obligation to A’ rather than from ‘S has an obligation to A’ to ‘S can A’. As such, the problem with the metaphysical reading of ‘can’ lies not in its falsity but its triviality. Virtually every conceivable action is metaphysically possible. Consequently, on this reading virtually no obligation has a defeater via OIC.

To illustrate the problem, consider again the case of our father attempting to attend his son's game. We can ask, in what sense the stranded father was ‘unable’ to attend the game. A natural reading takes the possibility in question as causal (see Gensler Reference Gensler1996, 46). The father was ‘unable’ to attend because he lacked any available causal means of arriving at his destination. Metaphysical possibilities, by contrast, abound. The father could have instantaneously teleported to his destination or opened a wormhole to the baseball field. In short, defenders of OIC aim to deploy the principle in exactly these sorts of scenarios to serve as a defeater for the standing obligation. Unfortunately, the metaphysical reading of the modal operator fails to accomplish this feat for many of the paradigm examples.

Before leaving our discussion of OIC's modal element, we have one last observation to make. Though the metaphysical reading proved too broad, failure at this level entails failure at every level. As noted above, every other version of possibility exists as a subset of the metaphysical. Hence, if a scenario lacks metaphysical possibility, it lacks every other species of possibility (causal, nomological, etc.) as well. In what follows, therefore, we shall opt for the metaphysical reading of ‘can’ in order to demonstrate the severity of a modal collapse on OIC. For demonstration that the problems infect the broad reading trickle down to the more plausible readings as well see for example Bassford (Reference Bassford2022).

Taken together, our interpretative decisions yield the following version of OIC:

Here ‘S’ ranges over individual agents and ‘A’ over individual actions. Likewise, we shall take the conditional (‘only if’) as material. Finally, the ‘ought’ operator is understood as normative, and the modal operator is taken as metaphysical in scope. Interpreting OIC-(M) in terms of the standard possible world semantics, the principle states that if it is obligatory that an agent perform a particular action, then a possible world exists in which the agent does that action.

The difficulties a modal collapse poses to OIC-(M) are perhaps most clearly seen in the case of moral failure. Whereas we are inclined to recuse the stranded father from his duty to attend his son's game, the same does not hold for everyone. The world is replete with instances of moral failure for which the perpetrators are wholly liable.

Consider, for example, a dark tale between two individuals: Sam and Sarah. Suppose that Sam and Sarah work for the same corporation and are both up for a promotion at the company. One day, a fire breaks out in their office. Sarah manages to make it through the escape door just before Sam, who is the last person on the floor. As Sarah passes through the exit, the door closes behind her, locking from the outside. Sam arrives at the closed door and begins to beg Sarah to open it. In a fit of wicked ambition, Sarah pretends not to hear Sam's pleas, thereby sealing Sam's fate and ensuring she gets the promotion.

Unquestionably, Sarah had a moral obligation to open the door for Sam in this scenario. Sadly, combining OIC-(M) with a modal collapse will not abide these results. Take the following instance of the principle:

1. (6) It is obligatory for Sarah to open the door for Sam only if it is (metaphysically) possible for Sarah to open the door for Sam.

As noted above, we can understand the consequent of this conditional as requiring that a possible world exists in which Sarah opens the door for Sam. In a modal collapse, however, reality contains only one world and that world is actual. Hence, since by hypothesis Sarah does not open the door for Sam in the actual world, Sarah does not open the door for Sam in any world. Since Sarah did not actually open the door for Sam, she could not possibly have opened the door for him either. Applying these results to (6) we arrive via modus tollens at the following conclusion:

1. (7) It is not obligatory for Sarah to open the door for Sam.

By definition (7) entails:

1. (8) It is permissible for Sarah not to open the door for Sam.Footnote ²¹

But (8) is surely wrong. In the envisioned scenario, Sarah's actions were indisputably evil. Nevertheless, attempting to apply OIC-(M) within a modal collapse runs directly counter to this intuition.

Indeed, we can generalize these results to any unmet obligation. Since possibility and actuality are synonymous in a modal collapse scenario, OIC-(M) is equivalent to:

OIC-(M)* states that a necessary condition of S's obligation to A is that S actually does A. Put another way, no unmet obligations exist. We can never say, therefore, that people ought to have acted differently than they did. Whatever actions people perform in the world are, at a minimum, permissible (as (8) demonstrates).

Given the untenable nature of these results, a modal collapse demands that we abandon OIC-(M). A fortiori, we must abandon Gensler's more plausible causal version as well. Hence, if we are forced for one reason or another to embrace a modal collapse, we are left with the unwelcome result of having to abandon the ought implies can principle as well.

Failure of SDL

We reach similar results when we consider the impact of a modal collapse upon the standard semantics for deontic logic (SDL). Deontic logic is a species of modal logics applied to moral reasoning. Scope prohibits a full description of the system. For present purposes, then, we will focus on just two aspects. First, deontic logic replaces the necessity operator of alethic modal logic with an obligation operator. To understand the second aspect, we must first introduce the notion of an accessibility relation.

Within possible world semantics, we say that a proposition p is possible at a world w just in case at some world w* accessible to w, p is true. Likewise, a proposition is necessary at w just in case at every world w* accessible to w, p is true. By varying which worlds are accessible to which, we can generate different modal systems.

When discussing notions of metaphysical necessity and possibility in a formal context, metaphysicians typically require that the accessibility relation is at least reflexive (i.e. w is accessible to itself). Adding this requirement validates the following inference:

1. (9) Given necessarily p, p follows.

Clearly, the argument goes, if something is metaphysically necessary it must also be true. While assured for the metaphysical, (9) proves anathema for the moral. Consider the result of replacing the necessity operator with the obligation operator:

1. (10) Given it is obligatory that p, p follows.

The above theorem takes us back to the problem of no unrealized obligations. According to (10), if anything is obligatory, then it is actual. Hence, one can never claim that a moral duty went unmet.

Given the problems with (10), logicians have insisted that the accessibility relation for SDL be serial rather than reflexive. A serial relation requires that for any world w, at least one other world, w*, exists which is accessible to w. Since we have no guarantee that w* is w, (10) is not validated. Instead, we get the more promising inference schema:

1. (11) Given it is obligatory that p, it is permissible that p.

Much more could be said about the nature of deontic logics and SDL. This overview, however, will suffice for present purposes.Footnote ²²

Returning to our discussion of the consequences of modal collapse, we can ask what impact such a collapse has on SDL. To simulate the scenario, we shall require that all the models within SDL be one-world models. If one takes a strict reading of the serial relation, this has the effect of turning a serial relation into a reflexive relation. Recall that a serial relation holds that for any world w, a world w* exists accessible to w. But suppose there is only one world. What follows then? In that case w must be accessible to itself, for no other world is available to satisfy the requirements of the serial relation. Yet if w is accessible to itself, that by definition makes the accessibility relation reflexive. Moreover, as we noted a moment ago, a reflexive accessibility relation validates the inference from obligation to actuality – see (10) above.Footnote ²³

The above result holds provided we take a strict reading of the serial relation. Technically speaking, the serial relation requires only that a given world has access to some other world. Informally, however, the relation is often understood as irreflexive as well. The irreflexive condition adds the additional restraint that the world in question is not accessible to itself.Footnote ²⁴ Rather, the serial relation grants a world access to the morally correct version of itself. We might ask, then, what the impact of a modal collapse is on SDL provided we understand the accessibility relation as both serial and irreflexive. In his masterful textbook on modal logic, James Garson helpfully notes the results of the envisioned scenario:

Garson here envisions a scenario in which the world of evaluation – which we may take as the actual world in this case – has no accessibility to another world (including itself). Under these conditions, we are left with the startling conclusion that a contradiction is morally obligatory – symbolized by Garson as ‘O⊥’.

The application of modal collapse to SDL, therefore, drives us once again into the unwelcomed embrace of moral absurdity. Regardless of whether one takes the strict or informal reading of the serial relation, we are left with unacceptable moral conclusions. If the former, we must conclude that the world contains no unmet moral obligations. However things ought to be, is how they are. If the latter, we must say that the obtaining of a contradiction is a standing moral obligation. Hence, if we are forced for one reason or another to embrace a modal collapse, we are left with the unwelcome result of having to abandon SDL and with it the standard semantics for reasoning about moral matters in a formal context as well.Footnote ²⁵

Katherine Rogers's theistic multiverse proposal

Before leaving our discussion of the moral collapse problem, we ought to pause to consider the import of a recent proposal developed by Katherine Rogers. Rogers suggests that the classical theist could embrace a version of the theistic multiverse to mitigate the impact of a modal collapse (Rogers Reference Rogers2020a, Reference Rogers2020b).Footnote ²⁶ The starting point for the theistic multiverse proposal lies in the assumption that possible worlds and universes do not stand in a one-to-one correspondence. Rather, a possible world can contain a multiplicity of universes. Applying this concept to the modal collapse scenario, the suggestion becomes that the singular possible world contains within itself a host of actual universes. While Rogers rejects the notion that such a multiverse would ground modal claims about individuals, she suggests that it might serve to ground modal claims regarding certain kinds:

Despite the ingenuity of Rogers's proposal, her suggestion does nothing to mitigate either of the moral collapse issues discussed above. With respect to the ought implies can principle, the principle makes a necessary condition of obligation not the potentiality of a kind but of an individual. Take for instance Sarah's diabolical plot to gain the promotion over Sam. As we saw, on a modal collapse, OCI-M entails that Sarah had no obligation to open the door for Sam because no possible world exists in which she performs that action. Merely saying that humans have the potential to open doors does nothing to mitigate this fact. What matters is not generic potentiality regarding a kind, but the specific potentiality of an individual with respect to a specific action. Indeed, if one could argue from the potentiality of a kind to the obligation of an individual, then our stranded father would bear the full weight of responsibility for missing his son's game, since presumably other people were able to attend. With respect to SDL, the situation is completely unchanged. On Rogers's proposal, modal space still contains only one possible world. That world merely contains an unspecified number of universes. Hence, the semantics would still entail that no unmet moral obligations exist within the multiverse (or that a contradiction is a moral obligation within the multiverse if one takes Garson's approach). Therefore, while Rogers's proposal may succeed in defusing other deleterious impacts of a modal collapse, it does nothing to mitigate the spiral into moral collapse.