Prominent Christian philosopher and apologist William Lane Craig recently (2016) published a book God over All: Divine Aseity and the Challenge of Platonism (Oxford) focused on divine aseity, i.e., the idea that God exists a se, from Himself alone. Aseity is a standard commitment of monotheism. It means that nothing is more fundamental than God and nothing is co-fundamental alongside God. God, therefore, is the sole fundamental being. Everything else depends on God in some way, whether as a derivative facet of God’s own being or as a something created by God. Divine aseity is closely tied to the doctrine of creation ex nihilo, the view that in the beginning there was God and God alone and that everything that is not-God is therefore a fiat creation of God’s.
One longstanding challenge for the doctrine of divine aseity is the thought that there may be other things in reality that are co-fundamental alongside God. This view is often called Platonism in reference to Plato’s proposal in the Timaeus that God is a “Demiurge” who fashions the physical world out of independently existing unformed matter and with reference to independently existing Forms. This theory denies divine aseity because it posits two types of realities—unformed matter and transcendent Forms—that exist independently of God. It also denies creation ex nihilo because it says the world we inhabit was fashioned out of preexisting stuff and thus not created ex nihilo, i.e., from nothing.
Today Plato’s Demiurge theory proper has few adherents, though process theism remains a relatively popular variation on it, mainly in theologically liberal academic circles. But what Craig means by the “challenge of Platonism” is neither the Demiurge theory nor process theism but modern mathematical Platonism. This is the view that numbers, concepts, propositions, and various other “abstract” objects exist necessarily and on their own, independently of God. (I put “abstract” in scare quotes because this is a tricky term, as I discuss below.) There are important philosophical arguments that purport to establish mathematical Platonism for reasons independent of theism. Of course, the mere fact that such arguments purport to establish Platonism independently of theism does not entail that anything actually exists independently of God, but they do at least amplify the worry that maybe there are things that exist independently of God, a fact which, if true, would entail the falsity of divine aseity.
To push back against this worry the theist has to do one or both of two things: (a) reconcile the existence of mathematical objects and other abstractions with divine aseity by showing how they can exist necessarily without being independent of God, or (b) show that arguments for mathematical Platonism are flawed and so we need not posit “abstract” objects at all. Craig ultimately endorses approach (b), but Christians and most other monotheists have traditionally preferred (a). The main strategy historically for developing (a) is called theistic conceptualism. It’s the view that numbers, concepts, propositions, and other abstractions exist most fundamentally as divine ideas, i.e., as mental objects in God’s mind.
In this blog post I examine Craig’s reasons for rejecting theistic conceptualism. After (1) defining some key terms, I argue (2) that there is a strong and principled argument for theistic conceptualism from the nature of divine omniscience. I then argue (3) that Craig’s objections against theistic conceptualism are weak. For the most part, they are little more than straw men. I then argue (4) that Craig’s anti-realist approach to abstractions ultimately presupposes theistic conceptualism and so it isn’t a genuine alternative. Finally, I argue (5) that Craig’s preferred model of divine providence (Molinism) undermines divine aseity and so, given Craig’s unqualified endorsement of divine aseity, he should be consistent by abandoning Molinism.
1. Defining key terms
Before diving in it will be helpful to define some terms. First, there is the realism/anti-realism distinction.
In general, realism across some domain of discourse holds that some things within that domain are straightforwardly “real” in the sense that something in objective reality corresponds to them. By “objective reality” I mean that the things in question have mind-independent reality relative to all finite, non-omniscient minds. Restriction to “finite, non-omniscient minds” is necessary because nothing, not even God, is independent of God’s omniscient mind. In contrast, anti-realism across some domain of discourse denies that things within that domain are straightforwardly “real.” This is not to say that such things don’t “exist” in some sense, but it is to say that they don’t exist in the objective reality sense. Case in point: living persons vs. fictional characters. Most everyone is a realist when it comes to other people. We aren’t solipsists. We think that there really are other human beings like ourselves. But we are anti-realists about fictional characters like Harry Potter. Harry “exists” in the wizarding world of J. K. Rowling. It’s a world that her readers can imaginatively “enter” by reading her books and watching the movies. But Harry doesn’t exist in objective reality as a bona fide human being.
A closely related term, oddly not mentioned by Craig, is reductionism. Roughly speaking, whereas a realist about X affirms the mind-independent existence of X in a straightforward way and an anti-realist about X denies the mind-independent existence of X in a straightforward way, a reductionist about X affirms the existence of X but only in a non-straightforward or deflationary sense. “X exists,” says the reductionist, not in the robust way the realist supposes, but in a qualified or reduced sense. For example, with respect to mental states, realists think that mental states exist (full stop), anti-realists (aka eliminativists) deny that they exist (full stop), and reductionists think that they “exist” after a fashion, but what they really are is something else, something non-mental or quasi-mental perhaps, or maybe just something less robust than the “extreme” realism of, say, Cartesian substance dualism. For example, one type of reductionist says that mental states are token brain states, another says that they are types of brain states, yet another says that they are behavioral dispositions, and so forth.
Reductionism, in short, sits dialectically between realism and anti-realism without clearly picking a side. Here’s a theological example: Is Christ “really present” in the Eucharist? To that question nearly all Christians want to answer “yes.” But they don’t all understand that affirmation in the same way. According to the Roman Catholic doctrine of transubstantiation, the Eucharistic elements (the bread and wine) literally become the physical body and blood of Christ. That’s what they mean by “real presence.” Lutherans, in contrast, affirm consubstantiation, the view that Christ’s physical body and blood are “really present” alongside the elements. Likewise, many Reformed Christians affirm a spiritual presence view. Christ is “really present” spiritually in the elements, but not physically present in or with them (because Christ’s physical body is in heaven). And, finally, Zwinglians deny that Christ is present in the elements per se, but they believe that Christ is still “really present” in the gathering of believers (Matthew 18:20) among whom the Eucharist is observed. Despite their differences, all of these views are nominally “realist” about Christ’s presence during the celebration of the Eucharist in a way that contrasts with the clearly anti-realist position of an atheist who doesn’t think Christ, having died, even exists any more. We can arrange these views from transubstantiation on down and think of them as holding different “degrees” or “levels” of realism:
- Transubstantiation (physical and spiritual presence in the elements)
- Consubstantiation (physical and spiritual presence with the elements)
- Spiritual presence (spiritual presence in the elements)
- Zwinglianism (spiritual presence with the elements in the church gathering)
- Atheism (no presence at all)
A cursory glance at the polemics between these views will reveal that (i) views higher up the list tend to consider views lower down as “reductionist” if not anti-realist (“If you don’t affirm (a) then you deny the real presence.”); (ii) everyone but the last rejects hard-core anti-realism about Christ’s presence; and (iii) views lower on the list tend to consider views higher up as excessively realist, construing Christ’s eucharistic presence as “real” in a way that is unnecessarily inflated or even superstitious. (Note: The phrase “hocus pocus” came from Protestants making fun of the Roman Catholic position that, when the priest says “hoc est corpus meum” during the Latin liturgy, the elements “magically” become the literal body and blood of Christ.) In sum, how people apply the labels “realist,” “reductionist,” and “anti-realist” is often perspectival and political. The moral: One man’s “realism” can be another man’s “reductionism,” another man’s “extreme realism,” and yet another man’s “anti-realism.”
Moving on, Craig defines Platonism (i.e., mathematical Platonism) as the view that some “abstract” objects exist and are uncreated (p. 3). Later, in the glossary, he defines it more simply as “the view that there exist abstract objects” (p. 215). Neither characterization is apt. The issue isn’t whether abstract objects exist or not, but whether they exist independently of God. At any rate, by abstract objects (or “abstracta”), Craig means “immaterial entities which are essentially causally powerless” (p. 209) in contrast with concrete objects (or “concreta”), entities which “have causal powers, such as minds and material objects” (p. 210). He also distinguishes “heavyweight Platonism” from “lightweight Platonism.” The former takes abstracta to be “just as real” (or more real than) concreta (p. 10), whereas the latter takes abstracta to be less real than concreta because they lack objective or mind-independent existence. Again, this distinction is not apt—lacking mind-independent existence does not make something “less real.” In any case, it is only heavyweight Platonism that poses a threat to divine aseity (p. 12). Craig doesn’t make this point, but the “lightweight” variety may be regarded as a form of reductionism about abstract objects. It doesn’t reject their existence as anti-realism does, but regards them as things that exist in dependence on God.
Regarding the abstract/concrete distinction, Craig distinguishes abstracta and concreta along causal lines. This is in part because he wants the distinction to be absolute or categorical. A thing, in his mind, has to be either abstract or concrete and never both. But Craig’s approach to this distinction ignores the core meaning of “abstract.” Despite Craig’s stipulations, “abstract” is not a categorical term but a relative term. Things can be more-or-less abstract, and more-or-less concrete. This is because in its core meaning “abstract” is a verb meaning “to draw out of.” When one considers or focuses on part of a larger whole while prescinding from the rest, one has abstracted. What is thus abstracted can still have causal powers and so be “concrete” in Craig’s usage. For example, when I consider the cover of Craig’s book, or ponder the meaning of his words, I am mentally abstracting those bits from the book as a whole. Yet those bits can still affect the world causally. If I’m careless the cover of the book can give me a paper cut, and the meaning of his words can motivate me to blog about it. And I can keep on abstracting by focusing on narrower and narrower aspects of the whole that I started with. In so doing, my focus becomes more and more abstract and less and less concrete. It may reach a point where my focus is no longer on anything physical (e.g., the shape of Craig’s book). But it can still have causal effects. For example, contemplating the shape of Craig’s book may help me decide how best to package it for shipping (should I desire to do so).
So, defining “abstract” in terms of causal inefficacy is problematic at best. I agree that concreta have causal powers, but I reject Craig’s assumption that “abstract” and “concrete” (as adjectives) must be fundamentally opposed. Perhaps that is how modern mathematical Platonists construe the distinction, but properly speaking, abstractions are always drawn out of something more concrete and so can never leave the realm of the concrete wholly behind. Abstracting is something we do. It’s a function of what we mentally focus on, and so the products of abstraction are ultimately mental entities. And mental entities can be causally efficacious.
Side note #1. If there were no minds capable of considering part of something in abstraction from the rest of it, there would be no abstracta. From this perspective, mathematical Platonism is a non-starter. If abstract mathematical objects necessarily and eternally exist, then they can only do so in relation to an eternal and necessarily existent Mind. And they cannot exist independently of that Mind. If mathematical Platonism says that abstracta exist independently of all minds, including God’s, then mathematical Platonism is incoherent.
In any case, Craig concedes that not much rides on how one draws the abstract/concrete distinction (p. 6). What matters for divine aseity is whether there are things, whether abstract or concrete, that exist independently of God. Craig doesn’t put it that way, though. He says what matters is their “uncreatability, along with their necessity and eternality” (p. 6). This conflates being uncreated with being independent. They aren’t the same thing—something can be uncreated without being independent of God by virtue of being an essential aspect or facet of God’s being, like God’s wisdom, power, and divine glory.
2. Theistic conceptualism established
As noted above, theistic conceptualism is the view that numbers, concepts, propositions, and other “abstract” objects exist most fundamentally as divine ideas, i.e., as mental objects in God’s mind. This is the dominant position regarding abstracta in the Christian tradition. It’s dominant, I believe, because it stems from two core theistic commitments:
- divine aseity: As the sole foundation of reality, all necessity, actuality, and possibility is ultimately either identical to God or grounded in God. There is, thus, no possible object (concrete or abstract) that is not already in some way included in God.
- divine omniscience: If God essentially has perfect knowledge of reality, then God fully understands Himself as the ultimate source of all necessity, actuality, and possibility. There is, thus, no possible object (concrete or abstract) that is not already fully understood by God.
A straightforward implication of these two commitments is that all possible abstract objects eternally “exist” in God’s omniscient mind as divine ideas.
This is practically important as well because if we think God is perfectly provident over creation (as Craig does), then we must suppose that whatever possibilities are latent in creation have already been considered by God. If the future of creation is somewhat open-ended (as I think it is), then it is open-ended to the extent that it is by God’s deliberate design, which means that no possible developments in creation can catch God off guard, flat-footed and unprepared.
For these reasons, to deny theistic conceptualism seems to me implicitly to undermine divine aseity, divine omniscience, and/or God’s perfect providence.
3. Craig’s objections to theistic conceptualism considered
In his chapter on theistic conceptualism, while Craig does at least once characterize it in terms of divine ideas (p. 73), by far his dominant characterization (following both Plantinga and Welty) is as the view that abstract objects are divine “thoughts.” As he puts it on p. 72, theistic conceptualism “takes mathematical objects and other allegedly abstract entities to be … concrete objects, namely thoughts in God’s mind.” Craig’s talk of “allegedly” abstract objects here reflects his categorical / causal distinction between abstracta and concreta. As I’ve already discussed in §1, the causal criterion is problematic because it doesn’t allow for degrees of abstraction and concreteness. Since on my view divine ideas are both abstract (when considered in relation to the larger whole of God Himself) and concrete (when considered in themselves as realities in God’s mind), I will drop qualifiers like “allegedly” in what follows. I now consider Craig’s objections against theistic conceptualism.
3.1. Are God’s thoughts uncaused? (pp. 78–80)
Trading on the idea that a thinker’s thoughts are active products of the thinker, Craig finds it very natural to suppose that there should be a causal relation between God and God’s thoughts (p. 78). Welty, however, denies that the relation between God and God’s thoughts is causal. He doesn’t want to extend the causal thinker/thought relationship from the human context to the divine context on the grounds that God (unlike humans) is essentially omniscient and so cannot come to have (all) the thoughts He does (p. 79). Craig demures that this is only a problem “if one is a realist about properties (and other abstract objects)” since “on anti-realism” there are no properties like divine omniscience that God’s causing His thoughts would bring into being (p. 79).
In my view, the root problem here is Craig’s and Welty’s framing of the issues in terms of “thoughts” rather than “ideas.” There is pressure from human experience and language to suppose that a thinker causally produces His thoughts because thinking is an active verb, but there is no comparable pressure to suppose that minds produce ideas. Minds can simply have ideas.
That said, I think Craig is wrong to suppose that Welty’s worry about divine omniscience is only a problem for realists about abstract objects. If, as Craig urges, the thinker/thought relation is causal, then there is an explanatory moment where God is a pure thinker with no thoughts at all and thus not omniscient. In that moment God wouldn’t even know that He exists!
3.2. Does theistic conceptualism violate divine aseity? (pp. 80–84)
Welty holds that God’s “thoughts” (i.e., ideas) are uncaused and uncreated. Craig thinks this leads to problems for divine aseity. Since these thoughts “are …distinct from God in the sense that they are not identical to God, and yet they are not creatures, but are … uncreated by God … we seem to be stuck with a realm of entities which are distinct from God and uncreated by God” (p. 81). Craig worries that this violates divine aseity.
I think this is a bogus worry. Divine aseity is not, as Craig says, the view that “God is the only uncreated being” (p. 81). Rather, divine aseity says that God is the sole fundamental being. It does not preclude there being non-created, non-fundamental things, like divine thoughts (or uncreated natural divine energies). These don’t have to be caused by God. They can simply be natural expressions of God’s own uncreated being.
Craig, I submit, conflates theistic conceptualism, understood as the view that abstract objects exist as divine ideas, with the view that such objects exist “in addition to” God Himself (p. 83). But this is a mistake. To suppose that divine ideas exist as facets of or as objects internal to God’s own being is not to “add” them to God but merely to distinguish them from God as “parts” of a sort from a larger whole.
3.3. Worrying about false propositions (pp. 84–85)
Craig wonders how theistic conceptualists can handle false propositions “without attributing to God false beliefs” on the assumption that “to think that p is to believe that p” (p. 84).
This, however, is a rather stupid objection, and a transparent straw man at that, for the objection is predicated upon the ill-advised prior choice to describe divine ideas as “thoughts.” While Craig is surely right that, “the English idiom ‘thinks that’ … is virtually synonymous with ‘believes that'” (p. 85), there is no pressing reason for the theistic conceptualist to use doxastically committing language like “thinks,” “affirms,” “doubts,” or “denies” in place of doxastically neutral language like “ideates” or “conceives” in presenting his position.
3.4. Bawdy, banal, malicious, and silly thoughts (pp. 85–89)
Craig next worries that theistic conceptualism requires God to be constantly and consciously entertaining, in words quoted from Graham Oppy, “inappropriate thoughts: bawdy thoughts, banal thoughts, malicious thoughts, silly thoughts, and so forth” (p. 85). There seem to be two connected worries here: (a) that the content of God’s thoughts is sometimes “inappropriate,” that is, unbecoming of an all-wise and all-holy God, and (b) that God would have to be conscious of this inappropriate content.
Welty is, I think rightly, rather dismissive of this objection, but Craig thinks his dismissal is too quick:
[T]he problem is that if God has the full range of thoughts that we do, then He must imagine Himself, as well as everyone else, to be engaged in bawdy and malicious acts. Moreover, rather than putting such detestable thoughts immediately out of mind as we try to do, He keeps on thinking about them! (p. 86)
In response to Craig, part of the problem again lies in the gratuitous choice to describe God’s mental contents as “thoughts” rather than using the neutral and traditional language of divine ideas. One can consider an idea as a bare conceptual possibility without in any way endorsing that idea. Thus, as the omniscient ground of all possibility, God is aware of every possible idea and every possible combination of ideas, including ones that involve logical absurdities like square circles and moral absurdities like God’s being unfaithful to His promises. Combinations that involve absurdities of one sort or another God, of course, firmly and categorically rejects as intrinsically impossible. As for combinations that involve creatures doing malicious and bawdy things, God may acknowledge these as logical possibilities while still firmly and categorically rejecting them as morally impermissible. And of course, combinations that are in fact false, God firmly and categorically rejects as false.
Another part of the problem is Craig’s supposition that God’s merely being aware of such combinations, His being conscious of them, is tantamount to God’s taking a neutral stance toward combinations that God should reject or even put “immediately out of mind.” God should not, thinks Craig, “be entertaining or dwelling on bawdy or malicious thoughts” (p. 87) because to “dwell on” such ideas is not to take a negative stance toward them as seems proper. But this worry confuses having an idea with having a stance on an idea. God’s merely being conscious of an idea or combination of ideas neither entails nor precludes God’s having a stance on them. Indeed, it’s hard to see how God could take any stance on an idea unless God already has the idea in question. If God didn’t already have bawdy or malicious ideas in mind, He wouldn’t be able to reject them because He wouldn’t have any idea what He’s rejecting. In sum, Craig presents us with a false choice. God’s having ideas of things that are malicious, etc. does not in any way entail God’s taking a positive or neutral stance toward them or God’s “dwelling on” them with any stance other than firm rejection.
Finally, in regards to banal and silly “thoughts” Craig asks
Why in the world should we think that God is constantly thinking the non-denumerable infinity of banal and silly propositions … that there are? Take Welty’s own illustration of the thought that for any real number r, r is distinct from the Taj Mahal. Why would God hold such inanities constantly in consciousness? … [W]hy would he dwell on such trivialities? (p. 88)
Here again we have a straw man. God doesn’t “dwell on” trivialities in the sense of focusing attention on them to the exclusion of other, more important ideas. While Craig claims to “fully appreciate that God must have a conscious life much different than ours” (p. 89), his understanding of God’s omniscience remains quite anthropomorphic in supposing that God’s attention must be focused as ours is. But for an essentially and perfectly omniscient being there can be no distinction between focal and background awareness and thus no distinction between what God is conscious of and things God knows but is not conscious of. This is because to be omniscient is to know and understand everything—everything necessary, everything possible, and everything actual—as well as it can be known, and thus with full, simultaneous conscious immediacy. The root problem here is Craig’s merely propositional conception of omniscience (p. 86). That is, he thinks of omniscience exclusively in terms of knowledge by description or knowing that. This allows Craig to suppose that God can “know that” a proposition is true without holding that knowledge in consciousness. But this is a defective conception of omniscience. Mere propositional knowledge is not sufficient for being a maximally perfect (i.e., omniscient) knower. Perfect knowledge entails being immediately and fully acquainted with all of reality, including all possible combinations of ideas. God’s “knowing that” is an abstraction from this richer and more basic kind of knowing. Once we appreciate this, Craig’s suggestion that God might not be fully conscious of the contents of His own mind loses all plausibility.
 3.5. How can divine ideas be universals? (pp. 89–92)
Craig offers up yet another objection:
The difficulty … for conceptualism is that God’s thoughts, as concrete objects, are not universals, but particulars, and so cannot be wholly present in spatially separated objects. (p. 89)
This worry clearly trades on Craig’s categorical understanding of the abstract/concrete distinction. On this conception, divine ideas must be either abstract (and universal) or concrete (and particular). As particular ideas in God’s mind having potential causal efficacy in motivating God’s actions, divine ideas—so Craig reasons—must be concrete. Hence, they are not abstract. Hence, they are not universal, nor can they play the role that abstract Platonic universals are supposed to play.
The main problem with this objection, I submit, is Craig’s mistaken understanding of the abstract/concrete distinction. As I explained above (§1), this distinction is relative, not categorical, and it comes in degrees. To abstract is mentally to “draw out of” a larger whole while prescinding from the rest of that whole. The whole one abstracts from is relatively more concrete. And one can repeat the process by abstracting from relatively more concrete abstractions to yield relatively more abstract abstractions.
Divine ideas are thus both abstract and concrete. They are concrete as the particular ideas they are and abstract with respect to their generality, a generality that is “drawn out of” the plenum of possibilities inherent in God’s omnipotent power. For example, God’s idea of humanity is a particular, concrete idea but it is also the idea of a general kind and thus able to subsume many particular, concrete instances of humanity—you, I, Adam, and Christ, for examples. It’s the generality of divine ideas that enables them to play the role that abstract Platonic universals are supposed to play. In creating many individual humans, God projects His single idea of humanity into many instances, thereby constituting those instances as human.
Craig objects to this proposal in two ways, however. First,
God’s thought of the number 2 is about 2. But then His thought is not 2, but something distinct from 2. 2 is what He is thinking about. But He is not thinking about His thought; He is thinking about 2. Therefore, His thought cannot be 2. (p. 92)
In response, I reject the assumption that God’s idea of 2 is not identical with 2. My idea of 2 is not identical with 2, but God’s is. This is because, unlike me, God is the ultimate source of everything other than Himself. His ideas are constitutive of things whereas mine are merely representative. I also reject the idea that God is not thinking about His thoughts. Of course He is! An essentially omniscient God is always cognizant of everything. God’s idea of 2 is part of “everything,” and so God has an idea of His idea of 2. And so on. This may seem to lead to a problematic regress: For all X, God has an idea of His idea of His idea … of His idea of X. But the regress is only problematic if each stage is a distinct idea. I deny this in the case of God. For finite knowers like us higher-order thinking always requires extra effort. For me to think about my thinking of X (second-order) is harder than just thinking of X (first-order), and to think about my thinking about my thinking about X (third-order) is harder still. But not for God. As omniscient God’s second- and higher-order ideations require no extra effort because all of reality (including His own mind) is fully transparent to God (cf. Hebrews 4:13). So for God, His idea of His idea of 2 just is His idea of 2 just is 2.
Craig’s second objection is that my proposal get the explanatory order backwards:
Things are not brown because they fall under God’s concept brown … ; rather, they fall under God’s concept brown because they are brown. (p. 92)
Again, I reject this line of reasoning because it ignores the constitutive nature of God’s ideas with respect to creation. Things are not brown because they fall under my concept of brown. That’s because I’m not the source of such things. But God is. God’s concept of brown is definitive of brown. The only reason brown things exist at all is because God wanted there to be such things (or at least wanted it to be possible for creatures to produce such things). In creating (and sustaining) brown things (or the creaturely possibility of brown things), God projects His idea of brownness into them.
Side note #2: The sort of theistic conceptualism I am proposing is closely tied to Maximum the Confessor’s Logos/logoi distinction. The Logos or Word of God (John 1:1), i.e., God the Son, contains all divine ideas (the logoi). In creating (John 1:3) He projects some of those ideas into created reality. I say more about the Logos/logoi distinction in this post. Here is a quote from that post: “In sum, for Maximus, just as Christ the incarnate Logos is the bridge uniting divinity and humanity, the uncreated divine ideas or logoi are projected into creation and so are bridges that directly connect God and creation. They serve, if you will, as intentional conduits through which God structures and energetically sustains creation.”
3.6. Worries about sets (pp. 92–94)
Finally, Craig challenges theistic conceptualists with a worry about mathematical sets. He asks:
If sets are really particular divine thoughts, then how do we have any access to sets? … [The problem] is that sets, the real sets, are locked away in God’s private consciousness, so that what we talk and work with are not sets at all. (pp. 92–93)
Craig asks further why God has to be “constantly collecting things together” to constitute sets at all. What if God instead “merely imagines such collections to exist?” On this divine imagination view, thinks Craig, sets don’t exist “but are merely imagined to exist” (p. 93).
In response to this worry, a theistic conceptualist should simply reject the idea that sets and other abstractions are “locked away in God’s private consciousness.” As Maximus the Confessor (see Side note #2 above) insists, divine ideas are not “stuck” in God’s mind. They are projected into creation, not as created copies of divine ideas (Augustine’s rationes seminales) but as the divine ideas themselves. Furthermore, in creating us with rational minds, God projects into us the capacity to form sets and other abstractions. God, we might say, shares a human-sized portion of His infinite intellect with us. When we construct sets and other abstractions we actualize in our minds a conceptual possibility that God, as our omniscient creator, was already aware of. We ideate one of God’s ideas after Him.
As for Craig’s suggestion that God “merely imagines” sets to exist, I say there is no difference between God’s imagining set A and having the idea of set A. Imagined sets are not merely “imagined to exist.” If God imagines a specific set (i.e., a collection with definite membership) as opposed to simply imagining vaguely that some set or other exists, then the set God imagines exists as a mental object in God’s mind. And for an idea to exist in a mind is for the idea to exist period. After all, where else would an idea exist?
4. Anti-realist approaches presuppose theistic conceptualism
In the second half of his book (Chapters 8–10), Craig discusses and defends an eclectic package of anti-realist approaches to mathematical entities. These anti-realist approaches are fictionalism, figuralism, and pretense theory. As far as I can see, none of these has any advantage over theistic conceptualism and all of them presuppose theistic conceptualism when we shift the question to God’s perspective. What I mean is, when we shift the question from whether we should take a fictionalist, figuralist, or pretense approach to some abstract object or other to what it would mean for God to take a fictionalist, figuralist, or pretense approach to objects of that sort, we’re led right back to theistic conceptualism. But first, let me state briefly what these anti-realist approaches are.
Fictionalism takes talk about (certain classes of) abstractions to be like talk about fictional characters. In the wizarding world of Harry Potter, Harry’s owl Hedwig “exists.” But Hedwig doesn’t exist full stop. Fictional owls aren’t owls. And the activities of fictional characters aren’t real activities. Harry is described as doing things like playing quidditch and casting spells, but he doesn’t really do those things and he doesn’t really exist either, not as a person at any rate. Fictional people aren’t people. They are merely ideas in people’s minds, having no extra-mental status. With respect to (certain) abstractions, the fictionalist proposes that, like Harry and Hedwig, these too are mere mental constructs. When we talk about them we’re simply talking about our own mental creations.
Figuralism takes talk about (certain classes of) abstractions to be figurative rather than literal. On this view to talk about, say, the number of hairs on my head is not to posit the existence of numbers, but merely to employ a figure of speech. Just as we can truly say “it’s raining cats and dogs” without implying that any of our four-legged furry friends are literally falling out of the sky—all we mean by the figure is that it’s raining very heavily—so we can talk figuratively as if various abstractions exist without committing ourselves to their literal existence.
Finally, pretense theory takes talk about (certain classes of) abstractions to be examples of make believe. It’s as if we’re speaking suppositionally (“Lets pretend that …”). For example, “if we suppose or pretend that numbers exist, then the number 2 when added to itself equals the number 4.” The idea here is that we can pretend whatever we need to in order to make sense of abstract discourse without committing ourselves to the mind-independent existence of those abstractions.
Now, whatever the merits of these various anti-realist approaches—and I certainly don’t wish to deny that they have some merit, especially in contexts where we want to paraphrase away seemingly unwelcome ontological commitments—none of these approaches is in conflict with theistic conceptualism. Even if we can use these approaches to avoid positing (certain classes of) abstractions as having extra-mental existence, the abstractions still exist in our minds as mental constructs. And if they exist in our minds, then they certainly exist in God’s omniscient mind. After all, He knows our thoughts. Nor can God use these approaches to avoid commitment to divine ideas. Whether God invents a fictional scenario, pretends that such-and-such is the case, or understands the literal (non-figurative) sense of a thought expressed in figurative terms, God has ideas corresponding to the very abstractions that these approaches claim to show are merely mental. So, as far as I can see, Craig’s foray into anti-realism may be useful for defeating arguments for Platonism (the idea that abstractions exist independently of God) but not at all useful for avoiding theistic conceptualism. Indeed, for any possible concept C, God either knows that C is instantiated or knows that C is not instantiated. Either way, God has knowledge of C’s ontological status and therefore has a concept of C.
5. Craig’s Molinism presupposes theistic conceptualism and conflicts with divine aseity
Craig is a well-known advocate of Molinism, a model of divine providence which says God meticulously ordains “whatsoever comes to pass” after considering the whole range of “feasible worlds” compatible with His “middle knowledge.” For space reasons I won’t elaborate on how Molinism supposedly works here (see §1 of this post for a detailed description of Molinism). The point is that, if God is considering and choosing among entire feasible worlds, each with a complete determinate history, then God’s got to have divine ideas corresponding to everything in any of those feasible worlds. Molinism, therefore, requires divine ideas for everything that could ever have possibly come about. And so it’s hard to see how Molinism can avoid theistic conceptualism. Whichever world God actualizes, His total set of divine ideas is explanatorily prior to, and thus more fundamental than, creation.
But we also run into a problem with divine aseity here because for Molinism the specific information content of God’s middle knowledge is explicitly stated to be independent of God. Middle knowledge information exists independently of God’s nature and will and yet somehow places a contingent constraint on what God can do with His omnipotent power. The Molinist may wish to insist that this information is logically dependent on God’s natural knowledge and so exists “in” God and not apart from God, but that’s beside the point here. The issue here is that, from the outset, God finds Himself confronted and constrained by a large body of logically contingent information has its specific content independently of God. This directly conflicts with divine aseity. According to divine aseity, God is the sole fundamental being and so nothing is more fundamental than God or co-fundamental alongside God. Even if the existence of middle knowledge information depends in some sense on God, the specific content of that information does not. Moreover, God is dependent on that information because it limits what He is able to do. So, even if middle knowledge information is not more fundamental than God, it’s at least co-fundamental alongside God. The two, we might say, are co-dependent on each other. But this is enough to conclude that middle knowledge is incompatible with divine aseity.
In sum, then, given Craig’s Molinism, he should be a theistic conceptualist. But given Craig’s full-throated endorsement of divine aseity, he should reject Molinism. That wouldn’t be a basis for rejecting theistic conceptualism, however, because none of the anti-realist approaches Craig explores are in any tension with it.