On Divine Simplicity, Hyperintensionality and Collapse Arguments

The Byzantine complexities of a simple God

The Debate as it Currently Stands

The roots of the modal collapse argument against divine simplicity are quite old: in fact, it has its origins (within analytic philosophy, at least) in William Rowe’s argument against the principle of sufficient reason (PSR). Taken as such, it is an argument against the existence of any necessary being which is the explanans of the contingency of the world. Indeed, the original proponent of the argument for God’s existence based on the PSR was the 17th century philosopher Gottfried Wilhelm Leibniz, who did subscribe to modal collapse. One might attempt to address this problem by appealing to the libertarianly free choices of the necessary being in question, viz., God. But introducing the doctrine of divine simplicity (henceforth, DDS) into the mix would surely complicate this or even lead to incoherence: for if God and his act of willing are really identical, and God is necessarily existent, then just as God exists in all possible worlds, his act of willing also exists in all possible worlds, and therefore the effects of God’s act of willing must also exist in all possible worlds, ergo the actual world, which is the effect of God’s will, is necessarily actual. A lot of ink has flown onto a lot of paper ever since the argument was proposed in this, its original form (as far as I know) by W.L. Craig and J. P. Moreland, and therefore I shall here look into the positions of the principal proponents of both sides of the debate as it currently stands.

It would first do to look at a defender of DDS. Christopher Tomaszewski in his 2022 paper Collapsing the Modal Collapse Argument: On an Invalid Argument Against Divine Simplicity argues that although God and God’s act of creation are really identical, the term “God’s act of creation does not rigidly designate God:

While God’s act is indeed intrinsic (and therefore identical) to Him, “God’s act of creation” designates that act, not how it is in itself, but by way of its contingent effects. That is, whether “God’s act of creation” designates God’s act depends on the existence of a creation which is contingent, and so the designation is not rigid. And since the designation is not rigid, the identity statement is not necessary, as it must be in order to validate the argument from modal collapse.

Against this, John William Waldrop in his response to Tomaszewski Modal Collapse and Modal Fallacies: No Easy Defense of Simplicity points out that Tomaszewski’s counter begs a very pertinent question against the opponent of DDS: that God’s act can be creative in world W₁ but not in world W₂ and yet remains the same act is what is in question here. Why think this is possible? If the divine will intends to create in W₁ but not in W₂, then God’s act in W₁ is distinct from God’s act in W₂. Waldrop posits what he calls the “essentialist” thesis that

(E) Necessarily, something is a divine creative act only if it is essentially the unique divine creative act.

Waldrop argues that Tomaszewski’s position is essentially the denial of (E), and is no less controversial that the commitment of the opponent of DDS to (E). It is to say that it is contingent whether or not God’s act is an act of creation, and of this he points out that

This is a substantive claim. Have we any reason to accept it? Neither the defender nor the opponent of DDS has any requirement per se to accept this claim. In fact, this claim is nothing short of a flat denial of what we have above called (E), the crucial premise in the enthymeme argument. While this is not in itself illicit, it should be clear that at this point Tomaszewski has tried to evade the modal collapse argument by invoking auxiliary metaphysical theses no less contentious than those required to make modal collapse arguments successful in the first place.

In other words, whether a modal collapse follows from divine simplicity turns on whether (E) is true.

The other important critique of DDS comes from Joseph Schmid. In his 2022 paper The fruitful death of modal collapse arguments, Schmid contends that DDS is compatible with the contingency of the actual world: all the classical theist has to do is posit that the relation between God and the created order is one of indeterministic causation. And yet, the defender of DDS is not out of the woods, for two other problems beset him: intentional and providential collapse, which he articulates in further detail in a subsequent paper. Both arguments can be said to have the following structure in common:

(1) If DDS is true, God is invariant and necessary, and is identical to his acts. (by definition)

(2) God’s act C is intentional and exercises providential control over all contingent entities (also affirmed by both classical and nonclassical theists)

(3) For any x, x is created iff x is contingent. (premise of classical theism under DDS)

(4) For all x, where x is some contingent entity, if C exercises both an intentional and providential control, then C specifies what x are actualized.

(5) For all x where x is a contingent entity, C specifies which x is actualized. (from 2 and 4).

(6) For any x, x is a contingent entity iff x is extrinsic to C.

(7) For any x, x is a contingent entity iff C is causally prior to x

(8) For all x where x is a contingent entity, C specifies which x is actualized and is causally prior x (from 5, 7)

(9) For any contingent entity x, if C specifies x as actualized, then C satisfies the predicate “specifies x as actualized” either intrinsically through some feature y of C, or extrinsically through some z which is related to C.

(10) It is not the case that C satisfies the predicated “specifies x as actualized” extrinsically through some z which is related to C.

(11) Therefore C satisfies the predicate “specifies x as actualized” through some y which is intrinsic to C. (from 9, 10)

(12) If C is specified to some x, then x obtains.

(13) For any x, where x is a contingent entity, x obtains in some worlds and not others.

(12) If C is intentional and exercises providential control, it satisfies the predicate “specifies x as actualized” for any x where x is a contingent entity, in virtue of some y which is intrinsic to C. (from 4, 11)

(13) C is specified to x in some worlds but not others. (from 12, 13)

(14) C satisfies the predicate “specifies x as actualized” in some world but not others. (from 13)

(15) C has an intrinsic feature y in some worlds but not others. (from 12, 14)

(16) For any p, where p is intrinsic to some divine feature d, p is identical to d. (definition od DDS)

(17) y is identical to C. (from 11, 16).

(18) God exists in all worlds. (by definition)

(19) Therefore y exists in all worlds. (from 1, 17, 18)

(15) and (19) form a contradiction, and the only solution to this is to either deny DDS, or deny that God’s act is intentional and exercises providential control, and thus only an indeterministic relation exists between God’s act and his effects (Schmid’s “Biconditional Solution”).

The last important critique of the standard DDS position comes from the Islāmic Neoplatonic position as elucidated by Khalil Andani in his 2022 paper Divine Simplicity and the Myth of Modal Collapse: An Islamic Neoplatonic Response. Andani distinguishes between a mere modal necessity (which he concedes) versus an ontological necessity, which he denies to all created things. God necessarily creates the actual world, as it is the best of all possible worlds, however the world and all its denizens are dependent upon God and are thus only extrinsically necessary, as opposed to God, who alone is intrinsically necessary. Furthermore, God necessarily creates, for unlike Schmid, Andani does not think non-classical theisms can overcome the luck objection to libertarianism, and therefore any actual contingency thus entails that there is no sufficient explanation, for a sufficient explanation must be contrastive.

Identity: An Excursus

It will be appreciated by the careful reader that the entire debate hinges on a few crucial concepts, one of which is the identity of God and his attributes which is so central to classical theism. It might be tempting for those unfamiliar with the broader Scholastic metaphysics underlying classical theism to think of this as Leibnizean identity (as in this paper for example), but this would be grossly mistaken, as it papers over the numerous distinctions drawn by Scholastics not just between the divine attributes themselves, but also between the kinds of identity and distinction. The Dominican friar and Thomist philosopher Fr. Reginald Garrigou-Lagrange in Volume II of his book God: His Existence and His Nature, Chapter III ‘Reconciliation of the Divine Antinomies’ distinguishes between divine attributes which are identical in the strong, Leibnizean sense, such as God’s existence and simplicity or infinity or immutability; versus attributes which are really identical to the divine essence but virtually distinct from the same, either (a) in virtue of the relations they have to creatures, or (b) in themselves. As to the former the examples given are between the divine essence considered as the act of intellection versus the same act as freely knowing creatures, or between the divine will in itself (which is identical to the divine essence) and the will as freely loving creatures. As to the latter, the example given is that of intellection and volition in God, which are virtually distinct even apart from any relation to creatures. In other words: the real identity of some x and y, where x and y are divine attributes as DDS proponents traditionally use the term is not Leibnizean identity as in indiscernibility, rather, it is the lack of metaphysical composition, i.e., x and y do not stand to one another or to some z in any part-whole relation, which is to say that for any x and y, x does not delimit or negate y or exclude y from its intension.

In other words, a virtual or conceptual distinction is “in the intrinsic eminence of the thing whereby, being the same in itself, it offers, through a simple containment of perfections, the intellect a foundation for distinguishing one of these perfections from another”, as stated by the classical theist philosopher Austin Woodbury. These distinctions might be (a) minor, where the one concept is contained in the other, such as when one concept is actually but implicitly contained in another, more explicit one, such between triangularity and trilaterality — each is implicitly contained in the other and explicit in itself; or (b) major, where one concept adds something objective to another concept without the former being implicitly contained in the latter, such as between man and animal — the concept of man contains in it the concept of animal, and is thus virtually distinct from it. Thus, Socrates’ humanity is virtually distinct from his animality, but the latter is included in the intension of the former and they are thus one «thing»; they are really identical (Image 1). Thus, if some x and y are really identical but virtually distinct, then x is included in the intension of y but not vice versa, or x and y both have the same intension but are hyperintensionally distinct. It is here that we can see the glimmerings of a solution to the objections to classical theism raised by its critics.

Image 1 (courtesy: Matthew Minerd)

Hyperintensionality and Reasons

Consider the Islāmic Neoplatonic model, in which God necessarily creates out of the perfection of his will. The divine will creates this world, the actual world, which is the best of all conceivable worlds, and the divine will actualizes this world out of all conceivable worlds because it is the best. In other words, that this world is the best of all conceivable worlds is the reason for its actualization. And given necessitarianism, given this fact R about the world’s perfection, the world’s obtaining O follows.

Suppose for any x and y, if x is the divine reason for y, i.e., x stands in the relation 𝜃 to y. And to say that x is the reason for y is to say that the intentional state t(x), which is the thought of x motivates y or moves one to bring about y, and thus on the necessitarian picture Islamic Neoplatonism presents to us, tx entails y.

(1) x𝜃y → (t(x) → y))

On Islamic Neoplatonism,

(2) R𝜃O

Therefore from (1) and (2) and substituting for x and y, we have

(3) t(R) → O

Now although the actual world is the most perfect of all conceivable worlds, it is also imperfect. As a multiplicity of finite, material entities which are all only extrinsically necessary, it falls far short of the perfection which is possessed by God alone. In addition, this world also contains much chaos, suffering and destruction. And given necessitarianism, all of these are entailed by the existence of the actual world, and they in turn entail the existence of the actual world. The actual world is both a glass partially full and partially empty as it were, and each entails the other. Let the aggregate of imperfections in the world be F. Therefore clearly,

(4) R ↔ F

In addition, given the real identity of all the divine attributes, given R, God considers R as a reason to create and thereby decides to create, and since a reason is the explanation for a rational agent’s intentional act, given (3), it follows that F explains God’s act O. But this is contrary to God’s perfection of will — the imperfections themselves cannot be God’s reason to create, since he intends by creation the manifestation of his perfection. In other words, if God’s reasons necessitate his actions, i.e., that some reason P which is the explanans of some Q also entails Q, then the Islāmic Neoplatonist would have to conclude that the imperfections of the actual world are the reason why God creates. For, unlike a finite rational agent, God’s thinking does not consist of numerically distinct mental states. Thus, if God were to conceive of the perfections of the actual world R and conclude “I ought to actualize R” (as it were), given his perfect and singular act of intellection without actual distinctions, God grasps both R and F, and therefore R motivating God’s act of O-ing entails that F also motivates the same act. Thus if R stands in the relation 𝜃 to O, then given the real, numerical identity of God’s thought of R as well as his thought of F, it also follows from (4) that

(5) t(R) = t(F)

And from this it follows that

(6) t(F)𝜃O

But surely this is not true, as God’s perfect will and goodness entail that he does not create for the sake of actualizing imperfections and chaos and destruction. Therefore reasons-based explanation must be hyperintensional when it comes to intentional acts, and if so, then the reason R cannot necessitate the action O. In other words, (1) is false.

In other words, the Islamic Neoplatonist must draw a distinction between what is known and what is intended, for the imperfections of the world are known to God even prior to creation, yet they are not the reason why he creates the world, and thus the same thing stands in two distinct relations to God, which entails at least a minor virtual distinction in God. In other words, R and F are hyperintensionally distinct, for although they’re cointensional, God can have R as a reason without willing F as a reason. But this means that the distinctions between and even within the objects of God’s will are more fine-grained than modal space (and indeed, this is true of intentional acts in general). But this means that although the divine intentions are numerically identical to one another (inasmuch as they are cointensional), they are nonetheless hyperintensionally distinct inasmuch as the same divine thought can stand in distinct relations to a divine action. Thus the identity that obtains between them is not the Leibnizean one of indiscernibility. Therefore the divine intention is both one in re and virtually many, in a way redolent of the thought of one of the greatest of the Church Fathers.

A Maximian Solution

S. Maximos the Confessor (AD 580-662) was one of the most prolific and innovative of the Fathers of the Church, and in his writings, the Christian Platonism of the early Church reaches its apogee. The Logos, the Second Person of the Blessed Trinity contains in himself all the logoi, the various divine exemplars of all things, both particulars and universals. Indeed, Maximos thought of even universals as created, with the logoi playing the role of the uncreated universals of earlier Platonic thought (and thus one might understand the created universals to be immanent universals, whereas the logoi correspond to Plato’s transcendent universals). These logoi are the Ideas, which God eternally conceives in himself as various ways in which his goodness can be diffused. And yet, as Andrew Louth points out in his essay St Maximos’ Doctrine of the Logoi of Creation (published in Selected Essays, Volume I: Studies in Patristics, 2023), the logoi are identical to the Logos. And yet they are somewhat distinct from Plato’s universals too — they are not only exemplars and ideas, they are also divine wills. And yet, as Torstein Tollefsen points out in his book The Christocentric Cosmology of St Maximus the Confessor, it would be a mistake to think of these as necessarily creative wills:

… God, according to Maximus, in His essence transcends relation. This implies that the eternal activity of God is independent of any relations to creatures. However, one aspect of this internal activity is God’s knowledge of creatures. This knowledge or wisdom is eternal, and I believe it correct to say that it is God’s contemplation of Himself as diffusive of good. According to Maximus, it is proper for the Good to diffuse or distribute itself in creative activity. This, actually, is something God wills. The principles of this diffusion or distribution (διαστολή) are the logoi of beings, these logoi being identical with God’s eternal knowledge of creatures. In Ambiguum 7 St Maximus says that creatures are known in their logoi, but that this only represents a possiblity for their being created in actual fact.

Further, the logoi themselves are nested in one another, thus the logos of man for instance is nested in the ultimate logos of Being. They are all “aspects of a unitary divine purpose”.

Putting it all together, we see a solution shaping up: each kind of created thing has a logos corresponding to it, and this logos is an aspect of the divine will-and-intellect. Each logos can be stated to have two further aspects as logoi nested within it, (a) that of the creature as good inasmuch as it’s a diffusion of the divine goodness, a “portion of God” (as Maximos put it) and thus desirable, and (b) that of the creature as less than perfectly good, as only imperfectly and finitely good and is thus not desirable. Each of these logoi are aspects of the one logos of the creature, and they mutually entail one another, and are thus both really identical (as cointensional) and hyperintensionally distinct. Thus each logos is an active potential or δυνάμις for the corresponding creature, and like all rational potentials, have contrary determinations (see Metaphysics IX Chapter 2). The divine will sees evaluates and relates to every possible creature as both desirable and not-desirable, and as such is indeterminate with respect to the creature. And because there is only a hyperintensional i.e., virtual distinction between the creature-qua-desirable and the creature-qua-not-desirable, for the divine will to express these virtually distinct logoi in different worlds does not constitute a real variation across those worlds. Thus, given the hyperintensional nature of the logoi and thus of the divine will, Waldrop’s thesis that the divine creative act is essentially one cannot be sustained. The divine will thus acts indeterministically, in that it acts differently across different worlds without there being any cause for why. This is not a denial of the PSR, pace Andani — the PSR quantifies over really distinct entities or states, and since these states are only hyperintensionally distinct, for the divine will to be thus variant across possible worlds is not to be possessed of really distinct modes across those worlds, and therefore there needs to be no further explanation of why the divine intention was in this rather than some other state. To quote Christopher Tomaszewski, whose 2022 paper How the Absolutely Simple Creator Escapes a Modal Collapse spurred my own thoughts on the subject:

One might wonder or object here: how can God’s intellectual activity, or the Divine ideas which figure in His creative act, differ from possible world to possible world without any difference in how God really is across possible worlds? This is simply a fundamental truth about the intentional order: it is considerably and necessarily more fine-grained than the real order. Consider, for example, a triangle: one and the same real thing, without any real difference, can be conceptualized either as triangular or as trilateral. Or consider the number 2: one and the same real thing, without any real difference, can be conceptualized either as the first prime or as half of 4. These concepts are obviously distinct in the intentional order. But they also obviously necessarily represent one and the same real thing. And such examples abound. So one cannot insist against the defender of the DDS that there is a one-to-one correspondence between the real order and the intentional order, and therefore there can be no decisive objection here against logical discernibility in God across possible worlds without real discernibility in God across those same possible worlds.

… How, then, does God’s intellectual activity differ from possible world to possible world without any real difference in Him? Simply in virtue of being intellectual activity. No further explanation is necessary, and its possibility, at least to me, is doubtful at best.

Intentionality, Intrinsicality and Indeterminism

Given all this, it can be seen that far from entailing an intentional collapse, indeterminism in this sense is necessary for intentional free choices. In fact, this is true even for created rational agents, in whom at least one act of will must be identical to the will itself, but its most easily shown with respect to God’s volition.

At the outset we go in with certain assumptions:

(1) God's essence is uncaused

(2) Whatever exists other than God's essence is caused by him

(3) Whatever God causes is caused intentionally

(4) What God causes, he causes freely.

(1) Is theological bedrock. Denying (2) or (3) leads to providential collapse. Denying (4) leads to necessitarianism/moral collapse.

Now assuming that God causes the created order freely, intentionally and solely (from 2, 3 and 4), it follows that if his acts are really distinct from him, that they are contingent. If they are contingent, they're caused. If they're caused by God, they're caused intentionally and freely. So let's assume that if God causes world W to be actualized, he does so through the intentional, free and contingent act V1. But given the contingency of V1, it requires another cause, which must also be an act of God, and also intentional and free and contingent. Let's call it V2. But since V2 is also contingent it requires a further act of God V3. We here come up with an infinite regress, and the only solution to this, as with all infinite regresses is to deny that God's act of willing is another entity additional to God's essence: it is what is called a "basic action" which doesn't require any more fundamental action to actualize it. But if so, then we must deny a real distinction between God and his act of willing.

It is also worth pointing out that a key premise of all the collapse arguments is that since on classical theism God and his act of willing are identical, and God remains unchanged across all possible worlds, therefore his act of willing is also identical across all possible worlds, therefore the same effects are actualized across all possible worlds. In other words, the modal collapse arguments are implicitly or explicitly beholden to the principle that for an agent to do otherwise, they must be otherwise. We'll call this the strong difference principle or S.

Consider what happens if S is true. If true, then for God to will otherwise than he actually has, he must be otherwise than he actually is. But since this is a contingent state of affairs, there must be an explanation for why God differs from world 1 in world 2, and this explanation can exist only in God. But if S is truly the case, then libertarian freedom is not possible, because it requires that the agent as undetermined as to whether to choose A or B choosing A in world 1 and B in world 2 without anything else inside or outside the agent determining what they choose. In other words, the same cause must be able to give rise to different effects in different worlds. But since the modal collapse arguments deny this due to their commitment to the strong difference principle, they cannot avail themselves of this. Therefore they're stuck with either the fact of God causing deterministically, thereby leading to modal collapse or him causing indeterministically yet not being the source of that indeterminsm, leading to providential collapse.

As can be seen from this, both libertarian freedom and the very nature of volition require that least some acts of willing are basic actions which are not really distinct from the divine essence.

The same can be extended to intentional collapse: given the contingency of divine intentions themselves, for God, or any rational agent for that matter to form them (assuming they are really distinct from them), they must be intentionally brought about, for if an intention is not brought about intentionally, then we have an intentional collapse anyway, just one step further down the road. Therefore the process by which the intention is brought about must itself be intentional, and yet it must also not be specified towards this or that intention if that intention is to be brought about contingently. And this can only be the case if the indeterminism is at the level of the volition itself, which in God is the divine essence itself. However, both the logoi — those of the creature-as-existent and the creature-as-non-existent — exist in God only virtually and are virtually distinct from one another. Furthermore, it does not follow from the fact that God’s creative act is causally prior, it cannot be specified to this or that end in virtue of something extrinsic. For, each logos is a relation of the divine will to some state of affairs which is extrinsic to God, and is thus each logos, inasmuch as it’s a disposition to something other than God, is a constituted by a relation to a creature, something which is other than God, and is thus extrinsic. That the creature does not exist “yet” does not affect the extrinsicality: it is a primitive fact about intentionality that it can be about non-existent objects. The relation that thus obtains between God’s will and the as-yet nonexistent object is thus not a real relation, to use Aquinas’ terminology. It is only a conceptual one, and it doesn’t obtain in virtue of some intrinsic actuality that is added to the divine essence, given that it is an unity that obtains between God’s will and a non-existent entity. Thus, given that the notion of the creature as contained in its logos which is an aspect of the Divine intellect-and-will is indeterminate with respect to both existence and non-existence, given its abstract nature (and is thus only virtuaslly distinct from God, and both “poles” of this logos, the creature-as-desirable and the creature-as-not-desirable are only hyperintensionally distinct from each other, for God to intend either of the two possibilities does not involve a real modification of the divine essence, and the variation across possible worlds between these two “poles” only hyperintensionally distinct from one another is not a real variation. We can thus deny that whatever feature of God’s creative act specifies what is created is an intrinsic actuality that is really distinct from God, or really distinct from an intentional act of God in another possible world. That it is an intrinsic actuality which is really distinct from God’s essence is what is required to entail the falsity of DDS, and that hasn’t been established.

Conclusion

The doctrine of divine simplicity as affirmed in the broadly conciliar Christian philosophical-theological tradition, far from denying all distinctions in God, denies only real distinctions within the divine essence, and «real» is a term of art. It admits of several kinds of virtual distinctions, one of them being between God and the objects of his will, and between those objects themselves. Since the objects differ from God only virtually, he does not stand in real relations to them, and since they differ from each other only virtually, the relational differences that obtain across possible worlds are not real differences in God either. Given the virtual nature of these entities, classical theism is not susceptible to modal, intentional or providential collapse.