5

5

Divine Conceptualism

Another version of realism about mathematical objects is considered: divine conceptualism, the view that objects normally taken to be abstract are actually thoughts in the mind of God. Whether conceptualism solves the challenge to divine aseity is unclear, since God’s thoughts seem to be objects not identical to God and must therefore be regarded as created by God, in which case the bootstrapping objection dogging absolute creationism rears its ugly head. Conceptualism can avoid the bootstrapping problem, since the conceptualist can hold that God, prior to His conceiving properties, for example, is as He is without exemplifying properties. While conceptualism holds promise for the theist, a number of worries about the adequacy of divine thoughts as substitutes for abstract objects nonetheless arise. Identifying propositions with God’s thoughts, for example, seems to saddle us with purely private propositions. Taking sets to be God’s collectings seems to violate the Axiom of Extensionality that sets have their members essentially. Such worries, though not knock-down objections, should motivate theists to explore more seriously the wide variety of anti-realist solutions to Platonism’s challenge to divine aseity.

Absolute creationism proffers the easiest solution to the challenge posed by Platonism to divine aseity, but it is not the historic Christian position. Rather, as we have seen, the Church Fathers, if not the biblical writers themselves, embraced a different solution: divine conceptualism. This view also dominated medieval thought and receded only with the advent of modernity. Like absolute creationism, divine conceptualism is a realist view of mathematical objects, but it is a non-Platonic realism. That is to say, it takes mathematical objects and other allegedly abstract entities to be, in fact, concrete objects, namely, thoughts in God’s mind.

As Figure 1 displays, there are other versions of non-Platonic realism on offer, but these were subjected to such withering criticism by the nineteenth-century mathematician and philosopher Gottlob Frege that such views are scarcely taken seriously today. Frege’s objections to psychologism, which takes mathematical objects to be thoughts in human minds, do not, however, touch divine conceptualism. The necessity, plenitude, and intersubjectivity of mathematical objects may be impossible to square with psychologism, but they constitute no obstacle to identifying such objects with thoughts of God. That Frege could simply overlook what had historically been the mainstream theistic position with respect to putative abstract objects is testimony to how utterly detached nineteenth-century philosophical thinking had become from the historic Christian tradition.1

(p.73) Conceptualism

With the late twentieth-century renaissance of Christian philosophy, divine conceptualism is once again finding articulate defenders. For example, Al Plantinga, the most influential theist philosopher writing today, has lately endorsed divine conceptualism. He locates himself in the Augustinian tradition ‘in thinking of numbers, properties, propositions and the rest of the Platonic host as divine ideas’.2 Plantinga does not always clearly differentiate divine conceptualism from absolute creationism. But he says that ‘perhaps the most natural way to think about abstract objects…is as divine thoughts’.3 Specifically, he advocates construing propositions as God’s thoughts, properties as God’s concepts, and sets as God’s collections.4 By so construing propositions, properties, sets, and the like, Plantinga means to safeguard divine aseity, since God’s thoughts depend causally upon God. ‘According to classical

versions of theism, sets, numbers and the like…are best conceived as divine thoughts. But then they stand to God in the relation in which a thought stands to a thinker. This is presumably a productive relation: the thinker produces his thoughts. It is therefore also a causal relation.’5 In that case, such objects do not exist independently of God, but depend causally upon Him, so that God exists uniquely a se.

Unfortunately, Plantinga’s endorsement of divine conceptualism amounts to little more than a nod in its direction. But a fuller development of a conceptualist viewpoint is to be found in Greg Welty’s defence of what he calls ‘theistic conceptual realism’ concerning propositions and possible worlds.6 As a realist, Welty is

entirely (p.74) sympathetic to Indispensability Arguments for the existence of propositions and possible worlds. In

fact, upon inspection, almost all of Welty’s arguments for the reality of propositions and possible worlds are various incarnations of the Indispensability Argument.7 If we reject, as I think we should, the soundness of the Indispensability Argument, then the nerve of Welty’s case for divine conceptualism will be cut. Divine conceptualism might remain a coherent option for the classical theist for meeting Platonism’s challenge, but it will not be philosophically incumbent upon him.

The key to Welty’s case for conceptualist realism over against Platonic realism (as well as other non-Platonic realisms) is the intentionality of propositions and possible worlds. Intentionality is the property of

being aboutsomething or of something. It signifies the object-directedness of something. Our thoughts, for example, have intentionality. Welty draws our attention to two characteristics of thoughts’ intentionality:

Thoughts have intentionality, which is to say they exhibit the two characteristics of ‘directedness’ and ‘aspectual shape.’…

Directedness is the ‘apparently relational structure’ of intentionality, due to the fact that every intentional state is ‘about’ something else. A thought is always a thought ‘of’ something.…

Aspectual shape denotes ‘the perspectival or fine-grained nature of intentionality.’ Objects of intentional states are ‘always apprehended in a certain way.’ So, for instance, my thought that Lewis Carroll authored Alice in Wonderland is not only about Lewis Carroll, but also picks him out in a certain way, namely, as ‘Lewis Carroll’ (the bearer of that name). Thus, it would not be correct to report my thought as being that Charles Dodgson

authored Alice in Wonderland.8

(p.75) Welty argues that propositions also exhibit intentionality. For only if propositions are about the world can they be true/false and believed/disbelieved. Welty calls a proposition’s having a truth value its alethicity (from the Greek aletheia, or truth), and he calls a proposition’s being the potential object of a person’s attitudes like belief and disbelief its doxasticity (from the Greek doxa or opinion). As this is a very important point for our study of abstract objects, I quote Welty at length:

Once we recognize the intentionality of propositions, we can see that alethicity is a corollary of it. That is, the fact that proposition p has a truth-value (and indeed can have a truth-value) presupposes the intentionality of p. For it is only because p is about something—represents it as being a certain way—that p is susceptible to

either correctly or incorrectly representing something to be the case, that is, being true or false. Thus, p’s capacity to be truth-valued presupposes p’s intentionality. The ‘aboutness’ of p is what enables it to make a claim, and it is the fact that it makes a claim that entails that it can be true or false.…

… what has been said here of alethicity can also be said on behalf of doxasticity. It too presupposes intentionality. It is only because propositions make claims, and represent something to be the case, that we can either agree or disagree that it correctly represents what it claims to represent. This agreement or disagreement is constituted by our believing or disbelieving the proposition in question.9

But Welty observes the following difference between our thoughts’ intentionality and the intentionality exhibited by abstract propositions. Our thoughts are intrinsically intentional—we think about things or of things. By contrast, abstract objects are not intrinsically intentional. They have at best an extrinsic or derivative intentionality by being the objects of doxastic attitudes.

In virtue of our acquaintance with our own thoughts, we are already committed to the reality of thoughts. So if propositions can be taken just to be thoughts rather than abstract objects, we shall have (p.76) a more economical or parsimonious ontology as a result, and therefore, Welty thinks, a theory which is more likely to be true.

Welty similarly argues that possible worlds—whatever they are, metaphysically speaking—must have intentionality because they are about how the world could be. Moreover, possible worlds discourse represents not only the world as a whole, but also particular objects in the world. For they represent ways in which, for example, Hubert Humphrey might be. The representative function of possible worlds requires that they have intentionality. As Welty says, ‘If they are…ways the World (or universe) could be, then they are about the World, representing it as such-

and-such’, and so have intentionality.10

Again, Welty argues that the intentionality of possible worlds is better explained by conceptualism than by other forms of realism. He explains,

If spatiotemporal particulars derive their intentionality from the intentionality of thinkers, why should it be any different for the intentionality of abstract simples?

…Perhaps the reason why neither of these theories is particularly illuminating on this matter of representation is because something fundamental has been left out: the intrinsic intentionality of thoughts, from which all other intentionality is derived.11

Since the intentionality of possible worlds is ultimately derivative from persons, a kind of thing to which we are already ontologically committed, conceptualism, by identifying possible worlds with thoughts of a certain kind, enjoys the advantage of being simpler than both Platonist and other anti-Platonist realisms. Welty says:

If indeed the entities posited by set-theoretic nominalism, linguistic nominalism, and realism ultimately receive their status as representations in virtue of the intrinsic intentionality of thoughts, then the fortunes of these three positions are tied to those of conceptualism itself. In short, advocates of these three positions—initially advertised as distinct alternatives to conceptualism—are implicitly committed to some version of conceptualism anyway, because in each case the status of possible worlds as representations requires the conceptual activity of thinkers. In that case conceptualism would truly be the only game in (p.77) town, and its chief alternatives would be parasitic upon its

adequacy, and therefore superfluous.12

Such parasitic alternatives will not survive the application of Ockham’s Razor. Thus, Welty sees conceptualism as the best realist theory of possible worlds.

Having argued that conceptualism is the best form of realism about propositions and possible worlds, Welty proceeds to argue that propositions and possible worlds are, respectively, to be identified with divine thoughts of various sorts. With respect to propositions, Welty observes that, although some thoughts have alethicity and doxasticity, not all do. For example, my mere thought of the letter B is not true or false or capable of being believed; but my thought that B is a letter of the alphabet is. God’s thoughts, which stand in for the Platonist’s propositions, will be thoughts that exhibit alethicity and doxasticity. By contrast, possible worlds have neither alethicity nor doxasticity and therefore are not propositions. Rather, they are divine thoughts of a different sort. Welty distinguishes narrow intentionality (which entails alethicity and doxasticity) from broad intentionality (which entails a capacity to represent). ‘Possible worlds are broadly intentional entities even if they are not narrowly intentional entities. They exhibit directedness (they are about the universe) and aspectual shape (they are fine-grained in their

aboutness), but they fall short of alethicity and doxasticity.’13They are God’s thoughts of how the world might have

been.

Because of God’s omniscience, omnipotence, and metaphysical necessity, divine conceptualism, in contrast to human psychologism, can satisfy the conditions of plenitude and necessity with respect to propositions and possible worlds. Once we have God’s thoughts, abstract objects like propositions and possible worlds become superfluous.

So on Welty’s view, propositions and possible worlds are not abstract objects, but rather are concrete entities, namely, divine thoughts of different sorts.14 By denying the existence of uncreated, abstract objects, Welty would preserve divine aseity.

(p.78) Conceptualism and Divine Aseity

Conceptualism will be an attractive view for theists who feel the force of realist arguments for abstract objects and yet who want to preserve classical theism’s commitment to God as the sole ultimate reality. Indeed, conceptualism is historically the mainstream position among Christians, Jews, and Muslims. It is the position that I assumed I would eventually adopt when I began this study. But does conceptualism succeed in safeguarding divine aseity? The answer is unclear.

Are God’s Thoughts Uncaused?

One of the peculiar features of Welty’s conceptualism is that he takes God’s thoughts to be uncreated.15 In order to avoid the bootstrapping problem that threatens absolute creationism, Welty denies that the relation between God and His thoughts is causal. He believes that absolute creationism ‘succumbs in the end to a series of successful objections, primarily because it construes the dependence relation between God and abstract objects in terms

of causation (more specifically, creation).’16 But Welty’s version of theistic conceptual realism rejects absolute

creationism’s causal, creative dependence relation and merely posits an identity relation between God’s thoughts and propositions and possible worlds.17 Welty admits that a causal account is ‘a very plausible account of

the thinker/thought relation in human beings’.18 But he refuses to extend such a model to God’s case.

Such a refusal strikes me as both implausible and ad hoc. As Paul Gould and Richard Davis point out in response to Welty, ‘the relation between a thought and a thinker is most naturally understood as a productiverelation: the thinker produces his thoughts’.19 So God’s thoughts are plausibly taken to be produced by God. Thinking, after all, is

something that God does; it is an activity, even if timeless, in (p.79) which God is engaged. The result of such activity is God’s thoughts. That plausibly suffices for a causal relation. So far as I can see, Welty offers no reason why the relationship between God and His thoughts should not be characterized as a causal relationship—apart from the fact that conceptualism would then become susceptible to the same bootstrapping problem that attends absolute creationism:

there is a serious question as to whether the thinker/thought model ought to be extended from the human context with which we are most familiar, to the divine context. Ought we to hold that God literally creates or causes his thoughts? Does this not imply that God creates his own attribute of omniscience (since divine omniscience is constituted by the thoughts in question)? If so, then we are in for a real shocker: the problems about God creating himself or creating his nature would not just be an unfortunate quirk of theistic activism, but would attach to traditional theism itself. This is probably as good a reason as any to resist extending the thinker/thought model—

construed in any causal sense—to the divine context.20

I think that it is worth observing that the bootstrapping problem will attach to theism, given a causal account of the thinker/thought relation, only if one is a realist about properties (and other abstract objects). Since on anti-realism there is no such object as omniscience, God’s causing His thoughts, as we do ours, does not bring His properties into being. If there is a problem here, it is a problem only for realists.

But would, as Welty fears, the affirmation of the causal dependence of God’s thoughts upon God, in fact, render conceptualism susceptible to the bootstrapping problem? I think not. For that problem arises, not, as Welty thinks,

from the causal dependence thesis, but rather, as we saw in our discussion of absolute creationism, from the Platonist’s ontological assay of things.21 Consider Bergmann and Brower’s intuitive statement of the bootstrapping objection:

If a view such as theistic activism is true, then every property (or exemplifiable) will be a product of God’s creative activity. But this implies the general principle that, for any property F, God’s creating F is a prerequisite for, and hence logically prior to, F. Notice, however, (p.80) that in order to create F,God must have the property of being able to create a property. Here is where the trouble begins.22

Where the trouble begins for the absolute creationist is where the conceptualist should part company with him. For on divine conceptualism, universals are neither subsistent objects in the world nor constituents in things, but rather thoughts in God’s mind. Thus, logically prior to God’s conceiving them, there are no universals. That does not imply that, apart from God’s conceptions, there are no wise men and no brown dogs, but just no wisdom and

no brownness. Thus, the conceptualist should insist that it is false that in order to conceive a property F, God must have the property being able to conceive a property. To be sure, in order to conceive F,God must be able to conceive a property, but He need not have the property being able to conceive a propertyin order to be able to conceive a property.

As we have seen, what is at stake in the bootstrapping objection is not the (causal) dependence of God’s thoughts upon God, but rather one’s ontological assay of things. Platonism offers an ontological assay of things in terms of substances and properties which are exemplified by those substances. By rejecting the Platonist’s ontological assay, the conceptualist may hold coherently that logically prior to His conceptions, God is as He is without standing in an exemplification relation to properties, and that He then produces properties by conceiving them. But, then, as we saw in our discussion of absolute creationism, much of the motivation for realism is undermined.

God’s Thoughts as Uncaused Objects

Suppose we do hold, as Welty does, that God’s thoughts are uncreated entities. Has the threat of Platonism then really been removed? Have we not merely substituted uncreated, concrete entities for uncreated, abstract entities? Welty does not directly address this worry. He does claim that his theistic conceptual realism violates neither divine

sovereignty nor divine aseity. But his defence of that claim fails to satisfy the present worry. With respect to God’s sovereignty, Welty (p.81) says: ‘Since it is not clear that these thoughts are distinct from God in the sense of being creatures, it is not clear that God’s “inability” to think something other than these thoughts—i.e., put these thoughts out of existence—somehow violates his sovereignty (since sovereignty ranges over what God has created).’23 True, on Welty’s model, God’s thoughts are not distinct from God in the sense of being creatures because Welty has

denied that the relation between God and His thoughts is one of causation or creation, so God’s thoughts cannot be creatures. But that is precisely the problem. They are entities which are distinct from God in the sense that they are not identical to God, and yet they are not creatures, but are entities uncreated by God. Even if we agree with Welty that God thinks some of His thoughts necessarily, still we seem to be stuck with a realm of entities which are distinct from God and uncreated by God.

So why does this not violate divine aseity? Welty replies, ‘on TCR, abstract objects are not created…, and so the aseity question does not arise. God has (at least some of) the thoughts he has, because of his essential omniscience about himself (in particular, about his power). Thus, the possession of these thoughts by God is rooted in something

that has traditionally been ascribed to God.’24 This response seems to be addressing a quite different worry, namely,

why God has the thoughts He essentially has. But the doctrine of divine aseity affirms that God is the only uncreated being. The concern is that, by postulating a realm of concrete entities which are uncreated by God, Welty’s conceptualism has violated divine aseity. If that is the case, then the problem which motivates our inquiry remains unsolved.

Still, I think that we have to admit that there remains intuitively a sense, difficult to articulate, in which divine thoughts existing ‘inside’ God do not seem to violate divine aseity as do uncreated, Platonic, abstract objects existing ‘outside’ God. But how are we to make sense of the metaphorical, spatial language of ‘inside’ and ‘outside’ God? I have spoken of God’s being the Creator of everything that exists apart from God. Abstract objects, if they exist, are somehow part of the world in a way that God’s thoughts are not. If the world did not exist, there would be neither concrete nor abstract objects in the world, but God and His thoughts would still exist.

(p.82) Brian Leftow explicates his claim that God is ‘the Source of All that is “outside” him’ as follows:25

GSA. For all x, if x is not God, a part, aspect, or attribute of God, or an event, God makes the creating-ex-nihilo sort of causal contribution to x’s existence as long as x exists.

Unfortunately, Leftow does not define his terms. What counts as a part of God? We might take the persons of the Trinity to be parts of God which, though not God in the sense of identity, exist acceptably a se. But God’s thoughts are not parts of God in that sense. Leftow also does not tell us what an aspect is. Could God’s thoughts be taken to be aspects of God which exist acceptably a se? Perhaps, though Leftow himself takes God’s thoughts to be

mental events.26 Leftow later walks back his claim that events are exceptions to creation out of nothing.27 He holds

that God’s thoughts are, in fact, caused by God. Attributes of God would include omnipotence, omniscience, omnipresence, and the like. Oddly, Leftow’s statement of GSA might be construed by the Platonist to allow that the abstract entities which are God’s properties do exist acceptably a se. We saw that absolute creationists Gould and Davis want simply to exempt God’s attributes from being created by God in order to stave off the bootstrapping objection and so would be happy with GSA’s exempting attributes. Such an interpretation would be contrary to Leftow’s intention, but it underlines the difficulty of explaining what it means to differentiate between things ‘inside’ and ‘outside’ God.

The anti-realist might plausibly claim that we can cut this Gordian knot by denying that divine thoughts are objects or things that really exist. That is not to deny that God is thinking. Rather, it is to claim that thoughts are just one more example of our inveterate tendency towards nominalization and reification. For example, we are planning to go to the beach tomorrow and so speak of our plans for tomorrow, we hunt deer in the fall and so speak of our deer- hunting in the fall, we hesitate when learning of the proposed restructuring and so speak of our hesitations about the proposal, without thinking that we are thereby ontologically committing ourselves to entities of these sorts.

Similarly, God thinks that Columbus discovers the New World in 1492, and so we speak of God’s thought that Columbus discovers the (p.83) New World in 1492. There is no more reason to add thoughts to our ontological inventory of things than hesitations or plans. If the realist points to our quantifying over divine thoughts and the impossibility of paraphrasing away such quantifying expressions, then, as we shall see, the anti-realist may call into question the customary criterion of ontological commitment that delivers so inflationary an ontology.

The anti-realist will hold that God thinks all the things that the conceptualist says He does, but the anti-realist will not reify God’s thinking into objects which exist in addition to God Himself. Anti-realism about God’s thoughts

removes the need to distinguish between objects which exist ‘inside’ God and those which exist ‘outside’ God, since God’s thoughts are not objects. Neither are His attributes, of course. Aspects of a thing—like the southern exposure of one’s house or a person’s health or financial status—are paradigm examples of abstractions that do not really exist. That leaves only undetached parts as things in their own right, and even that is controversial.28 We can, if we like, leave God’s concrete parts as real objects which are exempt from God’s creating everything other than Himself

without compromising divine aseity. For plausibly, if something creates non-successively all its parts, it creates itself, which, apart from its apparent metaphysical impossibility, would render God a created being if He creates His parts. So God cannot create His parts, and yet, being parts of God, these objects are clearly not examples of things existing a se apart from God. If we maintain that undetached parts are not really existing objects, so much the better!

The anti-realist theist may thus espouse a stronger version of (GSA), namely,

GSA*. For all x, if x is not God or a concrete part of God, God makes the creating-ex-nihilo sort of causal contribution to x’s existence as long as x exists.

This thesis yields a greater concept of divine aseity and so of God. If we go this route, however, then conceptualism is just misconceived. It foists upon the theist an inflated ontology of mental events which we have no good reason to embrace. Indeed, Welty’s own appeal to (p.84) ontological economy would cut against adopting conceptualism, with its added kind of entity, namely, mental events or thoughts.

Worries about Conceptualism

If the theist feels the force of arguments for realism about mathematical objects, propositions, and so on, conceptualism might seem, in light of the bootstrapping objection, to be a more attractive option than absolute creationism. Still, conceptualism is not entirely worry-free. For the question remains whether mathematical objects and other objects normally taken to be abstract can plausibly be construed as concrete objects, namely, divine thoughts.

Take propositions, for example. How will conceptualists handle false propositions? Conceptualists had better not say that God entertains only true thoughts. Otherwise, only true propositions exist, which is insufficient for the reality of the full range of propositions. We need divine thoughts which stand in for all the false propositions as well. But how is this to be done without attributing to God false beliefs, in contradiction to the doctrine of divine omniscience?

In the case of true thoughts, conceptualists can hold that, for any true proposition p, God thinks that p. But in the case of a falsehood, we cannot let p stand for a false proposition. For to think that p is to believe that p. We might try to avoid the problem by saying that, in the case of false propositions, God thinks that p is false. But the problem here is that God’s thought, then, is not p, but the quite different proposition that p is false. Thus, ontologically, there really is no thought that p, where p is false, for God would not think such a thing. So there really is, contrary to realism, no proposition p in the case that p is false. But then how can God think that p is false, if there is no such thing?

In response to this worry, the conceptualist can claim that thinking, as he uses the word, encompasses a variety of doxastic attitudes, such as believing, hoping, fearing, and so on. Morris and Menzel, who, as I explained, do not clearly differentiate absolute creationism from conceptualism, distinguish God’s beliefs from God’s thoughts: ‘We have characterized propositions as God’s thoughts. Some of those thoughts are contingently true, some are contingently false. (p.85) The latter, of course, are not among God’s beliefs, since God is omniscient.’29 Menzel later expands on this distinction:

God necessarily thinks and conceives, and moreover, necessarily thinks and conceives the same things. Note that this is not to say that God necessarily believes (and hence knows) the same things; what God believes will depend in part on contingent facts, e.g., how many people there are at any given moment. However, the thought ‘There

are n people,’ for any given n, is conceived by God regardless of whether or not it is true.30

This explanation makes it evident that the English idiom ‘thinks that’ is misleading in the context of conceptualism, for the phrase in ordinary language is virtually synonymous with ‘believes that’. ‘God conceives that’ is less misleading, for we can grasp the propositional content of, for example, questions and commands without believing

them. In the case of false propositions, perhaps we should say that God doubts or denies that p. God’s denying that p, like His believing that p, thus suffices for the existence of p—assuming, of course, that all one’s doubts and beliefs are consciously held.

Aye, but there’s the rub! Conceptualism requires that God be constantly entertaining actual thoughts corresponding to every proposition and every state of affairs. But this seems problematic. Graham Oppy complains that ‘it threatens to lead to the attribution to God of inappropriate thoughts: bawdy thoughts, banal thoughts, malicious thoughts, silly thoughts, and so forth’.31 Welty treats this concern somewhat dismissively. He responds,

An omniscient God has knowledge of the full range of thoughts that we humans can have and will have. We don’t surprise Him by our ‘bawdy thoughts, banal thoughts, malicious thoughts, silly thoughts, and so forth’ (105). His holiness is assured, as He doesn’t intend these thoughts as we intend them. He is like the parent who already knows all the ways the child can go astray.32

(p.86) This response fails to do justice to the objection. The problem, as I understand it, is not that we surprise God by our inappropriate thoughts. Rather, the 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! Of course, God does not intend to do these things; nevertheless, He thinks about them constantly, which does seem to impugn His holiness. The apostle Paul advises, ‘whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is gracious, if there is any excellence, if there is anything worthy of praise, think about these things’ (Phil. 4.8). Are we really to imagine that God does not exemplify this practice Himself, but also entertains and dwells upon the sorts of thoughts Oppy mentions?

The conceptualist might try to alleviate this difficulty by distinguishing, as Welty does, between the different sorts of thoughts God has. Welty, it will be recalled, distinguished God’s thoughts which are propositions from His thoughts which are ways the world might be. Omniscience is normally defined in terms of propositional knowledge: an omniscient person must know every true proposition and believe no false proposition. First-person knowledge is usually taken to be non-propositional knowledge. For example, God does not know or believe that He is Himself

Napoleon, even though He knows the same proposition that Napoleon knows when the emperor asserts, ‘I am Napoleon’.33 Thus, the conceptualist is not committed to God’s entertaining the bawdy or malicious first-person thought that I am engaged in , for such first-person, non-propositional knowledge is not demanded by

omniscience. At most, He would have the less salacious thought God is engaged in and knows that to be false and impossible. What He believes is that God is not engaged in , which is a true thought and describes an actual state of affairs. Even if God has the first-person belief that I am not engaged in , the conceptualist need not think that such beliefs are beliefs consciously held by God, since it is only their propositional content which

needs (p.87) to be a conscious thought of God. In other words, God need not be taken to be actually thinking of these first-person beliefs and states of affairs. That would go some way towards alleviating the worry that conceptualism would require God to be entertaining and dwelling on bawdy or malicious thoughts.

One way of putting this point is to say that what Welty calls the aspectual shape of a thought does not always correspond to the aspectual shape of the proposition expressed by that thought. For example, the thought that I am making a mess has a different aspectual shape than the proposition John Perry is making a mess. God can know the propositional content of Perry’s thought without His thought’s having the same aspectual shape as Perry’s thought. God need not have the thought that I am making a mess in order to grasp the propositional content that Perry grasps when he thinks that I am making a mess.

But the fact that thoughts and the propositions which they express can come apart in their aspectual shape raises even deeper problems for the conceptualist. God’s thoughts have an aspectual shape that is uniquely His and is plausibly different from their propositional content. But if we say that propositions just are God’s thoughts, we are no longer able to distinguish between the aspectual shape of a proposition and the aspectual shape of a divine thought having that propositional content. A first-person divine thought like I am the God of Israel is, then, a proposition. Since God has first-person thoughts, identifying God’s thoughts with propositions commits us to the existence of purely private propositions which are incommunicable by God to us. At most, we could grasp a proposition like Yahweh is the God of Israel; but that is not the same proposition as I am the God of Israel. Indeed, God may never entertain the oblique thought that Yahweh is the God of Israel, so that there is no such proposition.

First-person beliefs are just the proverbial camel’s nose. Paraphrastic strategies for dealing with unwanted ontological commitments, including commitment to abstract objects, major on distinguishing propositional content from the way it comes to expression in our thoughts and language. To take a simple example, the thought The number of people killed in the attack was 66 and the thought 66 people were killed in the attackhave, on the customary criterion of ontological commitment, different ontological commitments. The former commits us to the reality of the number 66, whereas the latter, using the numerical term adjectivally rather than substantively, lacks such a (p.88) commitment. So which one is God’s thought? If God thinks both, what are His ontological commitments? The ontological commitments of the former cannot be annulled by paraphrasing it as the latter, for the paraphrase cannot be said to give the propositional content of the thought, since according to conceptualism, both divine thoughts just are propositions. Suppose Charles Chihara and Geoffrey Hellman are correct, that the

commitment to mathematical objects in the thought 2 + 2 = 4 can be successfully paraphrased away,34 and suppose

that God thinks 2 + 2 = 4. Then we are stuck with mathematical objects regardless of the success of the paraphrases. The conceptualist might welcome commitment to mathematical objects, but this same approach will wind up committing us to holes, lacks, and other unwanted commitments of ordinary language if God has, indeed, in Welty’s words, ‘the full range of thoughts that we humans can have and will have’.

In short, distinguishing between the aspectual shape of a proposition and the aspectual shape of thoughts expressing it, as first-person thoughts almost force us to do, is a Trojan Horse for conceptualism, raising all sorts of difficulties that make conceptualism much less attractive than it at first appears. Thoughts may not be well-suited to be identified with propositions and possible worlds after all.

We have been reflecting on the problems raised by the ascription of bawdy and malicious thoughts to God. What about banal and silly thoughts? Here we see another unattractive feature of conceptualism’s identification of propositions with God’s thoughts. Why in the world should we think that God is constantly thinking the non- denumerable infinity of banal and silly propositions or states of affairs 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? Or consider false propositions like for any real number r, r is identical to the Taj Mahal. Why would God keep such a silly thought constantly in consciousness, knowing it to be false? Obviously, the concern is not that God would be incapable of keeping such a non-denumerable infinity of thoughts ever in consciousness, but rather why He would dwell on such trivialities.

(p.89) Welty moves far too hastily from the fact that God is omniscient to the conceptualist view that all that God knows is occurrent in consciousness. He writes, ‘if God is omniscient then at the very least, for any possible way something could be, God knows whether or not he could bring it about. This is sufficient for God to have thoughts that match the infinity of propositions that there must be.’35 God’s infinite knowledge is, however,

clearly not sufficient to guarantee that there are the actual mental events needed by the conceptualist. As Welty rightly puts it, ‘This argument assumes, of course, that in God’s case p> entails p>.’36Oddly, Welty says nothing to justify this crucial assumption. No reason is given for the assumption that in God’s case, unlike my case, the knowledge that 2 + 2 = 4 requires a conscious mental event or thought with that content. Obviously, we know vastly more than we occurrently believe. For example, I know the multiplication table up to 12, but I am not now thinking

thoughts like 2 × 3 = 6 or 7 × 8 = 56. Why should God’s case be any different? Now I fully appreciate that God must have a conscious life much different than ours. Still, the proliferation in God’s conscious thought of the silly and banal beliefs necessary for divine conceptualism seems pointless and makes conceptualism a less attractive option.

We have been reflecting on the problems posed by identifying propositions and possible worlds with God’s thoughts. What about properties? The main reason for construing properties as abstract universals rather than as particulars is the need for an entity that can be wholly located in diverse places.37 The Platonist’s ontological assay of the rose

and of the fire truck includes redness as an ontological constituent of each. In contrast to property instances (tropes), properties as universals are taken by realists to be wholly present in all the things exemplifying them. The difficulty, then, 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.90) So Gould and Davis protest:

For Welty, divine thoughts are not abstract; they are concrete. Therefore, we submit, Welty is a nominalist. By way of contrast, we think being a universal is a sufficient condition on being abstract (ontologically speaking), [footnote 4: We think being a universal, being non-spatial, being non-essentially spatio-temporal are sufficient conditions for

some object X to be abstract] hence it is best to think of divine thoughts (i.e., propositions) and divine ideas (i.e., concepts) as abstract objects.38

Gould and Davis certainly represent the mainstream position in saying that concrete objects cannot be universals, in view of the inability of concrete objects to wholly exist simultaneously in different places. It does not follow, however, as they assert, that we should adopt the strange view that God’s thoughts are abstract objects.39 We may, if

we wish, take God’s ideas or concepts to be the abstract content of God’s thoughts, but God’s thoughts cannot be abstract objects, since they are mental states or events.

Oddly, Welty seems to concede what I take to be the thrust of Gould and Davis’s critique. He asks, ‘If another sufficient condition for [abstract object]-status is “being a universal,” and that means being “multiply- instantiable,” that is, “one and the same object would need to be multiply located,” then are divine mental events multiply located? I can’t make sense of this.’40 Welty cannot make sense of God’s thoughts’ being multiply

located, which, he seems to admit, excludes them from being universals. How then will the conceptualist make sense of properties as God’s thoughts?

Will it help to appeal to exemplification as an account of how properties are constituents of things? J. P. Moreland reports that ‘Throughout history, the overwhelming majority of realists have agreed that quauniversals, properties are the sorts of things that (p.91) enter other things by way of the nexus of exemplification.’41 On this view, ‘Universals are literally in their instances, but they are not in the spatiotemporal location of those instances and the former are in the latter by means of a primitive non-spatiotemporal tie of predication.’42 Indeed, says Moreland, ‘it is entirely unclear how a property can be a constituent of a particular (e.g., a concrete particular, a moment, or an event) without doing so by way of exemplification’.43 On the traditional realist view, properties are abstract objects which exist independently of their instances and exist ‘in’ their instances, not spatiotemporally, but by being exemplified by particular things.

So could the conceptualist say of divine thoughts what the Platonist says of abstract universals: particulars stand in some sort of relation to God’s thoughts in virtue of which particulars are the way they are? An immediate problem for the conceptualist is that, if properties are God’s thoughts, then particulars must exemplify God’s thoughts. But a

concrete object does not seem to be the sort of thing that is exemplifiable any more than it can be a universal, since concrete objects are particulars and particulars are not exemplifiable, but rather exemplify.44 Accordingly, God’s thoughts cannot be properties.

But perhaps the conceptualist could say that divine thoughts can play the role of properties. In substituting God’s thoughts for properties, Plantinga has suggested that particulars stand to God’s thoughts in a relation analogous to exemplification.45 He appeals to Frege’s notion of ‘falling under a concept’ as the relation in which particulars stand to God’s thoughts. Thus, all brown things fall under (p.92) God’s thought of brown. Things which are brown resemble each other in virtue of falling under the same concept.

Intriguing as this suggestion might be, it is problematic. In the first place, concepts are not plausibly construed as concrete objects, for they are shared by multiple thinkers in a way that thoughts are not. Concepts seem to be part of the content of our thoughts. As such, they are plausibly abstract objects, if they exist at all.

Moreover, as mental states, thoughts are characterized by intentionality—being about things—not by things’ falling under them. My thought of redness is about redness; it is not itself redness, nor do things fall under it. This problem can be generalized. 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.

Furthermore, substituting the notion of falling under a concept for exemplifying a property seems to get the explanatory order backwards.46 Things are not brown because they fall under God’s concept brown, in the way that things are brown because they exemplify brownness; rather, they fall under God’s concept brown because they are

brown. Thus, the relation of falling under a concept cannot do the work of exemplification. If this is right, then the conceptualist who wants God’s thoughts to play the role of properties still has plenty of work cut out for him, if his view is to commend itself as an attractive option for theists.

Finally, consider mathematical sets. Plantinga suggests that sets be taken to be God’s mental collectings.47 But this raises a problem. If sets are really particular divine thoughts, then how do we have any access to sets?48The

question here is not whether I have a causal (p.93) connection with sets.49 Rather, it 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. When I collect into a unity all the pens on my desk, that ‘set’ of pens is not identical, it seems, with the set constituted by God’s collecting activity. Since we have two collectings and since sets are God’s particular collectings, the ‘set’ I form is not identical to the set of all pens on my desk. But if sets are determined by membership, how could they not be identical, since they have the same members?

And again, we might wonder, why would God be constantly collecting things together in the way demanded by the conceptualist? Perhaps the conceptualist might say that God is constantly engaged in such collectings in order to provide the subject matter for the full range of set theoretical truths, including alternative set theories. But what if God merely imagines such collections to exist? As we shall see, a pretence theoretical approach to various set theories is a very plausible interpretation of set theory, one that enjoys support in the community of mathematicians. It has been said that God is a mathematician. Perhaps God is also, in fact, a pretence theorist. Imagining is, after all, a type of thinking. We saw that in order to secure divine thoughts that are false propositions, the conceptualist cannot take ‘thinking’ to be synonymous with ‘believing’. So suppose that God pretends that sets exist in order to provide the subject matter for various set theories. In that case, we can admit that God does have thoughts about all the various set theoretical objects, but we cannot coherently identify His thoughts with sets, for sets on this view do not exist, but are merely imagined to exist. Given the coherence of pretence theory, there is no motivation to move beyond anti-realism to realism about sets as divine thoughts. Indeed, this conclusion can be extended: other abstract objects, especially possible worlds, may be (p.94) plausibly taken to be merely imagined by God. A pretence theoretical approach gives the conceptualist his divine thoughts but precludes our identifying God’s thoughts with sets, possible worlds, propositions, properties, and so on.

In short, all sorts of worries arise when we reflect upon the conceptualist identification of objects typically taken to be abstract with God’s thoughts. While by no means knock-down objections to conceptualism—indeed, I think that conceptualism remains one option for the theist wrestling with the challenge posed by abstract objects to divine aseity—these worries should motivate the theist to look seriously at the wide variety of anti-realist solutions to the challenge before acquiescing too easily to the traditional conceptualist viewpoint.

Concluding Remarks

Although the conceptualist view of abstract objects has historically been the mainstream Christian position, it is not incumbent upon us. Even if biblical writers like the author of the prologue to John’s Gospel presupposedsuch a view, they did not teach such a view as Christian doctrine, any more than they taught, for example, the generally presumed geocentrism. What they taught is that God alone is uncreated and that everything that exists apart from God has been created by Him. The task of articulating a view that does justice to this commitment, while meeting the challenge posed to it by Platonism, is left to the Christian theologian. Moreover, even among the Middle Platonists and Church Fathers who held that abstract objects are ideas in the mind of God, it is far from clear that a heavy metaphysical commitment to objects was intended. We saw that for Philo, the intelligible world may be

thought of as either formed by the divine Logos or, more reductively, as the divine Logos itself as God is engaged in creating.50 The second formulation (p.95) is quite compatible with an anti-realist view, for the anti-realist does not deny that persons think about numbers, properties, possible worlds, and so on. We also saw that among the Church

Fathers, it was sometimes denied that things existing in God’s mind have a ‘substantial’ existence, in contrast to things that exist extra-mentally for God. Anti-realists have no objection to lightweight talk of objects or thoughts in the mind of God.

We saw further that if we do make a metaphysically heavyweight commitment to the reality of divine thoughts as stand-ins for mathematical objects, propositions, properties, and so on, then it is at best unclear that conceptualism succeeds in safeguarding God’s status as the sole ultimate reality. For if these objects are held to be causally independent of God, then it would seem that God’s status as the sole ultimate reality has been abandoned. If we hold that they are causally dependent on God, then, if we are to avoid the bootstrapping objection, it seems that we must reject the Platonist’s ontological assay of things, which tends to remove the motivation for realism.

Finally, we saw that the conceptualist’s identification of allegedly abstract objects with divine thoughts is not exactly worry-free. In many cases, God’s thoughts seem ill-suited in various ways to play the roles traditionally played by abstract objects.

All this goes to place a question mark behind realism about abstract objects. Why be a realist in the first place? Perhaps absolute creationists and divine conceptualists have been much too uncritical in their acceptance of the

Indispensability Argument for realism about mathematical objects and their ilk. Perhaps Christian theists need to take a good look at anti-realist alternatives to Platonism.

(13) Ibid., 150.

(16) Ibid., 192.

(17) Ibid., 210.

(18) Ibid., 193.

(24) Ibid., 226.

(25) Brian Leftow, God and Necessity (Oxford: OUP, 2012), 20. (26) Ibid., 302–3.

(27) Ibid., 76–7.

(36) Ibid., 222.

(43) Ibid., 125.

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