## 1. Stating the Question



The main question we will address in this article is: Does God
*ground* the existence of necessarily existing abstract
objects? It is perhaps a more general question than a question one
might at first ask: Did God create necessarily existing abstracta? But
it is the main question that philosophers who have written about the
relation between God and abstract objects have sought to answer.



Over the last two decades, philosophers have done a great deal of work
on the notion of grounding (see, e.g., Fine 2001, Rosen 2010, Audi
2012, Schaffer 2009 Koslicki 2012 and the Stanford Encyclopedia entry
on
 grounding).
 It is thought by many currently working on issues in the metaphysics
of grounding that grounding is a primitive, *sui generis*
relation. In particular, it is not to be understood as a supervenience
or causal relation. How are we then to understand what it is?
Philosophers point to particular cases where it is instanced:
Dispositional properties are grounded in categorical properties, the
mental is grounded in the physical, the semantic is grounded in the
non-semantic, features like smiles or surfaces are grounded in facts
about bodies, and so on. To this point, one might think that grounding
talk can be captured by our ordinary notion of
 supervenience.[3]
 But Fine (2001) claims that Socrates' singleton set is grounded
in Socrates; yet, necessarily one exists just if the other does. Thus
our ordinary modal notion of supervenience won't capture this
case of grounding. If we assume (as many in the grounding literature
do) that the other cases of grounding are of the same sort as the
Socrates-singleton case is, then our ordinary notion of supervenience
won't capture them either. 



Our discussion of the question of God's grounding the existence
of necessarily existing abstracta bears on the general conversation
about the nature of grounding. *First*, we can note that our
divine grounding case stands alongside the Socrates-singleton case in
showing that ordinary supervenience won't capture the grounding
relationship properly. For instance, suppose we say that God grounds
the existence of the number 2. We then can note that, necessarily God
exists just if 2 does (that is, each exist in every possible world).
According to ordinary notions of supervenience, the number 2
supervenes on God, and conversely. But we are to think that God
grounds the existence of 2, and not vice versa. *Second*, we
have here in the case of divine grounding of abstracta a case where
the grounding relationship *is* typically spelled out in other,
familiar terms (and thus isn't *sui generis*). As we will
see, a number of different philosophers who think that God grounds the
existence of necessarily existing abstract objects think that God does
so in a *causal* manner. Others think that the grounding takes
place in that necessarily existing abstracta are *identical
with* divine mental states. 



One might look at those who claim that God causes necessarily existing
abstract objects or that they are identical with divine mental states
as not asserting that God grounds the existence of necessarily
existing abstracta. But as we will see, each of these sorts of
theorists really *is* saying that God grounds the existence of
necessarily existing abstract objects. Thus, it might be better to cast our
lot with those who are skeptical that there is a *sui generis*
grounding relationship that metaphysicians investigate. Or, if there
is such a relationship in some cases of grounding, it isn't
present in all cases of grounding (it isn't
"univocal"--see Hofweber 2009 and Daly 2012 for
discussion). After all, it is perfectly sensible to recast "Do
necessarily existing abstract objects depend on God?" as
"Are necessarily existing abstract objects grounded in
God?"



However we think of the dependence relationship between God and
necessarily existing abstract objects, we will want to insist that on
it God is somehow more fundamental than necessarily existing abstract
objects.
 Fundamentality (Stanford Encyclopedia entry)
 is an asymmetric relationship. Thus we will construe those who think
that God grounds the existence of necessarily existing abstracta as
claiming that God is more fundamental than necessarily existing
abstracta, and not conversely. 


## 2. Why Might Someone Believe God Grounds the Existence of Necessarily Existing Abstract Objects?



There are at least two sorts of reasons why someone might be inclined
to think that God grounds the existence of necessarily existing
abstract objects. The first sort of reason involves central religious
texts in monotheistic faiths like Judaism, Christianity, and Islam.
Roughly, this sort of reason consists in these texts' assertions
or suggestions that God has created everything. If God created
everything, it must be that God has created necessarily existing
abstract objects, as well. Thus, God grounds the existence of these
abstract objects. For instance, there are statements in the Hebrew
Bible such as Psalm 89:11: "The heavens are yours, the earth
also is yours; the world and all that is in it--you have founded
 them".[4]
 Also in the Hebrew Bible is Nehemiah 9:6: 



> 
> 
> And Ezra said: "You are the Lord, you alone; you have made
> heaven, the heaven of heavens, with all their host, the earth and all
> that is on it, the seas and all that is in them. To all of them you
> give life, and the host of heaven worships you". 
> 
> 
> 



In the New Testament, there are passages like John 1:1-1:4: 



> 
> 
> In the beginning was the Word, and the Word was with God, and the Word
> was God. He was in the beginning with God. All things came into being
> through him, and without him not one thing came into being. (The Word
> [*logos* in Greek] to which John refers is Jesus of Nazareth)
> 
> 
> 
> 



Paul states in Colossians 1:15-16, 



> 
> 
> He [Jesus] is the image of the invisible God, the firstborn of all
> creation; for in him all things in heaven and on earth were created,
> things visible and invisible, whether thrones or dominions or rulers
> or powers--all things have been created through him and for
> him.
> 
> 
> 



One of the most important documents for Christian faith outside the
Hebrew Bible and New Testament, the
 Nicene Creed
 of 325, says "We believe in one God, the Father almighty, maker
of all things visible and invisible". The Niceno-Constantinopolitan Creed of 381,
 a modification of the older Nicene Creed of 325 that is used by the
western Church begins similarly, "We believe in one God, the
Father almighty, maker of heaven and earth, of all things that are
visible and invisible".



According to the Qur'an, "God is the Creator of all
things; He has charge of everything; the keys of the heavens and earth
are His" (39:62-63). The Qur'an also says,
"This is God, your Lord, there is no God but Him, the Creator of
all things, so worship Him; He is in charge of everything "
 (6:102).[5]




These reasons from authoritative religious texts may not be taken to
be conclusive, however. One may take these sorts of texts seriously as
an adherent to faiths they define and still hold that God
doesn't have creative control over necessarily existing abstract
objects. For instance, Peter van Inwagen (2009) argues that the
universal quantifier in claims like that of the Nicene Creed
"maker of all things visible and invisible" is implicitly
restricted to include only those things that are capable of being
created. Necessarily existing abstract objects cannot enter into
causal relations and thus can't be created. But it is worth
noting that philosophers who think that if there are necessarily
existing abstract objects, God must have some sort of control over
them (e.g., Craig 2016) point to texts like those cited above for
justification for this view.



There is a second sort of reasoning that may lead someone to think
that God grounds the existence of necessarily existing abstract
objects. That is by way of *perfect being theology* (see Morris
1987a, 1987b and Nagasawa 2017 for
discussion). Perfect being theology is a way of theorizing *a
priori* about God that goes back at least to Anselm of Canterbury.
One begins with the claim that God is the greatest possible being, and
from there one can derive attributes that God must have. This method
is one way of arriving at God's being omnipotent, omniscient,
and perfectly good. Anselm himself famously thought that via perfect
being theology he could conclude that God existed. For our purposes
here, we are to imagine two conceptually possible beings: One being
has grounds or explains the existence of necessarily existing abstract
objects, and the other doesn't. We are to see that the being
that grounds these abstracta is greater than one who doesn't,
and thus we are to conclude that God (the greatest possible being) has
control over necessarily existing abstract objects. Sometimes the
intuition that the former being is greater than the latter is put in
terms of God's *aseity*, or independence from all other
entities. A being with maximal aseity is greater than one without it
(other things being equal); and if necessarily existing abstract
objects don't depend on God, God lacks maximal aseity.



There likely would be little objection to reasoning to divine
grounding of necessarily existing abstracta in the above way, *if
it were thought that God could have control over these sorts of
abstracta*. However, someone might concur with van Inwagen that
abstracta can't enter into causal relations, and say that the
only way that abstracta might be grounded in God is via causation. Or
someone might think that the idea of a necessarily existing object
depending on *anything* is
 incoherent.[6]
 If one took either of these positions, one would deny that the being
who grounds necessarily existing abstract objects was greater than the
one who didn't. (Just as she would deny that a being who can
make a square circle is greater than one who can't--there
can't be a being who can make a square circle.)



We have noted two sorts of reasons why a theist might think that God
grounds the existence of necessarily existing abstract objects. We
turn to a discussion of some different answers to our central
question: Does God ground the existence of necessarily existing
abstract
 objects?[7]
 Each of the next two sections will begin with a list of views and
will follow with considerations for and against
 each.[8]


## 3. God's Grounding Abstract Objects I: Views on Which Necessarily Existing Abstracta Are All Grounded in God



The views discussed in this section are as follows:



**Theistic Voluntarism:**   

Necessarily existing
abstracta are caused to exist by God's will (or some other
normally-contingent divine faculty). Example: Descartes.


**Theistic Emanationism:**   
 Necessarily existing
abstracta are caused to exist by some non-contingent divine faculty
(e.g., the right sort of divine cognition). Example: Leibniz,
Morris-Menzel (1986).


**Theistic Mentalism (without Divine Simplicity):**  

Necessarily existing abstracta are identical with divine mental
states, and God isn't simple. Example: Welty (2014).


**Theistic Mentalism (with Divine Simplicity):**  

Necessarily existing abstract are identical with divine mental states,
and God is simple. Examples: Augustine, Aquinas.



### 3.1 Theistic Voluntarism



According to the theistic voluntarist, necessarily existing abstract
objects depend on the divine will, or some other contingent feature of
God. This is famously the view of Descartes. In a letter to Mersenne
(27 May 1630), Descartes says:



> 
> 
> You ask me by what kind of causality God established the eternal
> truths. I reply: by the same kind of causality as he created all
> things, that is to say, as their efficient and total cause. For it is
> certain that he is the author of the essence of created things no less
> than of their existence; and this essence is nothing other than the
> eternal truths. I do not conceive them as emanating from God like rays
> from the sun; but I know that God is the author of everything and that
> these truths are something and consequently that he is their author.
> (Descartes 1991: 25)
> 
> 
> 



Descartes makes the same sorts of claims in his public writings, as
well (e.g., in the reply to the Sixth Set of Objections (also from
Mersenne)). This view seems to take seriously that God truly is
maximally powerful; he even has volitional control over things like
numbers, properties, and states of affairs. Indeed, even more than
with views like theistic emanationism is God in control of abstracta
on this view. According to the theistic voluntarist, God could have
made different--or no--abstracta like propositions,
properties, and states of affairs. God is in control of abstracta like
God is in control of any other object: Their existence is subject to
God's will.



Of course, the seriousness with which the theistic voluntarist takes
divine aseity and sovereignty is also the source of problems for the
view. If God could have failed to make the number 2, in what sense is
2 a necessary being? One might try to weaken the voluntarist view, by
claiming that 2 is only weakly necessary: God had to create it, but it
is possibly...possible that it not exist. All worlds that are
accessible to the actual world have 2 existing in them. But some of
these worlds have a somewhat-different divine will relative to the
existence of 2 (maybe God somewhat-reluctantly wills the existence of
2 in them). And possible relative to those sorts of worlds (or
relative to worlds possible to those worlds, etc.) are worlds in which
God doesn't will that 2 exist. The key here is that the claim:
*Necessarily, 2 exists* comes out true on this picture; 2
exists in every possible world relative to the world of evaluation
(the actual world). But there are possibly...possible worlds in
which God doesn't will the existence of 2. The voluntarist can
say that abstracta depend on the will of God, and yet really do exist
necessarily (just don't say in every possible world, *full
stop* (see Plantinga 1980: 95 ff. for further discussion)).



Of course, this suggestion risks two sorts of problems. The first is
that it doesn't take divine sovereignty seriously enough.
Imagine a being who could--in a world possible relative to the
actual world--make it the case that 2 doesn't exist. That
being might be thought to be more powerful than a being that only
possibly...possibly could do this. And Descartes (in places, at
least) seems to have this intuition; and thus plumps for a God who
could make it the case that 2 didn't exist.



The second concern is that it abandons S5-type modal logic, in which
anything that is necessary is necessarily necessary. This is thought
by many to be the appropriate system of modal logic to describe the
way actual modality
 is.[9]
 So there are concerns from both sides for this reply to the objection
to voluntarism. On the one hand, it might be thought not to take
divine power seriously enough. On the other, it might not make
abstracta "necessary enough".



One reason why Descartes is famous for holding to theistic voluntarism
view is because so few others in the history of theological thought
hold to it. And perhaps the main reason why no one else holds to it is
because many judge that the theistic voluntarist isn't able to
account for the absolute necessity of necessarily existing abstracta.
These are objects that if they exist should exist in every possible
world, full stop; and once one allows for that, it makes it very
difficult to see how it could be up to God's will that these
exist. Rather, if they are up to God; one winds up with a view like theistic emanationism. We
turn to it.


### 3.2 Theistic Emanationism



According to the theistic emanationist, necessarily existing abstract
objects are caused to exist by some non-contingent feature of divine
activity. The standard feature the emanationist appeals to is divine
cognitive activity of some sort. So, the theistic emanationist will
say something like that the number 2 exists because of God's
cognitive activity. She will go on to say (and this is how the view is
distinct from a theistic voluntarist view) it is not possible
(it's true in no possible world, full stop) for God's
cognitive activity in this respect to be other than it is. Thus, the
theistic emanationist can hold that abstracta really exist in every
possible world, full stop (allowing that God does, too). 



One example of a theistic emanationist is Leibniz. In his
*Monadology* he says:



> 
> 
> 43. It is also true that God is not only the source of existences but
> also that of essences insofar as they are real, that is, the source of
> that which is real in possibility. This is because God's
> understanding is the realm of eternal truths, or that of the ideas on
> which they depend; without him there would be nothing real in
> possibles, and not only would nothing exist, but also nothing would be
> possible.
> 
> 
> 
> 44. For if there is a reality in essences or possibilities, or indeed
> in eternal truths, this reality must be grounded in something existent
> and actual, and consequently, it must be grounded in the existence of
> the necessary being, in whom essence involves existence, that is, in
> whom possible being is sufficient for actual being. (Leibniz 1714
> [1989: 218])
> 
> 
> 



Here Leibniz seems to suggest that necessarily existing abstracta are
grounded in divine cognitive activity. It's not clear exactly
how to characterize the relation between the cognitive activity and
the existence of the abstract objects, but saying that the former
causes the latter to exist seems appropriate given his language. 



Thomas Morris and Christopher Menzel (1986) also are theistic
emanationists. They invoke explicitly causal language in setting out
their view, which they call "theistic activism".



> 
> 
> So our suggestion is that the platonistic framework of reality arises
> out of a creatively efficacious intellective activity of God. It is in
> this sense that God is the creator of the framework. It depends on
> him. (1986: 356)
> 
> 
> 



They continue later:



> 
> 
> Let us refer to this view, the view that a divine intellectual
> activity is responsible for the framework of reality, as
> "theistic activism". A theistic activist will hold God
> creatively responsible for the entire modal economy, for what is
> possible as well as what is necessary and what is impossible. The
> whole Platonic realm is thus seen as deriving from God. (1986:
> 356)
> 
> 
> 



And on the next page:



> 
> 
> God's creation of the framework of reality...is an activity
> which is conscious, intentional, and neither constrained nor compelled
> by anything independent of God and his causally efficacious power.
> (1986: 357)
> 
> 
> 



Theistic emanationism allows the theist to take seriously the claims
of religious documents that God creates everything (indeed, the name
of Morris/Menzel's paper is "Absolute Creation"),
and it avoids the problems that beset theistic voluntarism. It has
virtues. But it has problems of its own. First, some philosophers
claim that God *already* has to have critical properties in
order to be able to cause abstracta to exist. The theistic
emanationist claims that God causes properties such as *being
omniscient*, *being omnipotent*, *existing
necessarily*, *being able to cause abstracta to exist*, and
*having cognitive activity* to exist. She also claims that God
causes his own haecceity, *being God*, to exist. However, to
claim this is to get the dependence relationship backwards, one might
charge. Surely, God's being able to cause abstract objects to
exist must be posterior to his having properties like the ones
mentioned above. And if God has these properties, they must exist.
But, the proponent of this theory is committed to the existence of
properties being posterior to God's causing them to exist. Thus,
the objection concludes, theistic emanationism is false (see Leftow
1990, Davison 1991, Davidson 1999, Bergmann and Brower 2006 for
discussion of this sort of objection).



This sort of argument has seemed to many to be decisive. However,
there is a response that the theistic emanationist can give at this
point. It might be claimed that although God's ability to cause
abstracta to exist is logically dependent on his having certain
properties, it is not causally dependent. The account would be
problematically circular only if God's ability to cause
abstracta to exist were causally dependent on his having certain
properties, and his having these properties were in turn causally
dependent on his having caused these properties to exist. There is a
circle of logical dependence here (as there is between any two
necessary truths), but there is no circle of causal dependence (see
Morris and Menzel for this sort of reply).



The opponent of theistic emanationism might make the following retort.
Certainly, the above response is right in that if there is a problem
of circularity, it is one of causal circularity. Earlier, we saw that
there for the theistic emanationist is a one-way causal relationship
between God's cognitive activity and the existence of abstracta
such as *being the number two*. We can say that the necessary
existence of *being the number two* (or any abstract object)
causally depends on God's having the cognitive activity that he
does. Or, perhaps we might say that the necessary existence of
*being the number two* causally depends on God's being
omniscient, omnipotent and existing necessarily. However, the entities
on which being the number two causally depends are themselves
properties. On what do they causally depend? It seems that on the
emanationist account they wind up causally depending on themselves.
But this is incoherent, one might charge.



Even if the emanationist successfully replies to this first problem
for the view, there is a second, and perhaps more serious objection to
the view. We will call this objection "the bootstrapping
objection" (see Leftow 1990, Davidson 1999, Bergmann and Brower
2006, and Gould 2014b for discussion of this sort of objection). We
can put the concern this way (following Davidson 1999). To cause
something to exist is to cause its essence (or, in the terminology of
Plantinga 1980, its *nature*) to be exemplified. Suppose God
creates a certain table which has as a part of its essence *being
red*. Then God causes the property *being red* to be
exemplified by the table when he creates it. Consider the property
*being omnipotent*. The property *being exemplified by
God* is contained in its essence. So, God causes the property
*being exemplified by God* to be exemplified by *being
omnipotent* in causing *being omnipotent* to exist. Similar
to the manner with which God causes *being red* to be
exemplified by the table in exemplifying the table's essence,
God causes *being omnipotent* to be exemplified by himself.
But, surely God can't cause the property *being
omnipotent* to be exemplified by himself: How can God make himself
omnipotent? Furthermore, one might think that God's omnipotence
should be causally prior to his causing properties to exist. However,
on this occasion it is not. Then, if one does think that God's
omnipotence should be causally prior to his causing properties to
exist, this would be an instance of causal circularity. This sort of
argument will work for other properties like *being omniscient*
or *having divine cognitive activity* (although the causal
circle may be more difficult to establish with the former, and the
implausibility of self-exemplification may be more difficult to
establish with the latter).



Furthermore, consider God's haecceity, the property *being
God*. The property *being necessarily exemplified* is
contained in the essence of this property. So, when God causes his
haecceity to exist, he causes the property *being necessarily
exemplified* to be exemplified by his haecceity. Just as God
causes *being red* to be exemplified by the table when he
causes it to exist, God causes *being God* to be exemplified
necessarily. However, one might well think this incoherent. Indeed, it
seems this is the divine causing his own existence: God is pulling
himself up by his own bootstraps.



The theistic emanationist needs to address these sorts of concerns
about bootstrapping, and it is not clear how that could be done.


### 3.3 Theistic Mentalism (without Divine Simplicity)



One sort of theistic mentalism is the view that necessarily existing
abstract objects are divine mental states, and that God isn't
 simple.[10]
 On this view, God is distinct from his mental states, and abstracta
are identical with these mental states. One proponent of this view is
Welty (2014). He says



> 
> 
> I maintain that [abstract objects] are *constitutively*
> dependent on God, for they are constituted by the divine ideas, which
> inhere in the divine mind and have no existence outside
> it...[Abstract objects] are necessarily existing, uncreated
> divine ideas that are distinct from God and dependent on God. (2014:
> 81)
> 
> 
> 



Why might someone adopt theistic mentalism? One could make the
following sort of case. Thoughts (e.g., sentences in the language of
thought) are capable of representing the world as being a particular
way. Propositions are capable of representing the world as being a
particular way. Why do we need both of these sorts of intentional
entities? We can simply identify propositions and thoughts, and we get
a simpler ontology.



Of course, there is a problem here. If the thoughts we speak of here
are human thoughts, there are continuum-many true propositions, and
finitely many human thoughts. Also, there are propositions true in
worlds where there are no human thoughts. So we can't identify
propositions and human thoughts. But we don't have this problem
with divine thoughts. God, we may grant, exists necessarily. And God
has sufficiently many mental states to stand in for true propositions
(see Plantinga 1980, 1982).



If we identify propositions with divine thoughts, we have enough of
them in all possible situations. And one has one fewer kind of thing
if one admits only thoughts (divine and otherwise) rather than
thoughts *and* propositions. But there are reasons to think
there are *both* thoughts and propositions and that the two
shouldn't be identified, even if one identifies propositions and
divine thoughts. The most straightforward reason is that thoughts are
a different kind of entity from propositions. The former are concrete,
and the latter abstract. Furthermore, it's worth noting the
conceptual role propositions play. They are the sorts of things that
can be affirmed, doubted, believed, and questioned. They can be true
and false, necessary and possible. It is said by some that they are
sets of possible worlds; and by others that they are composite
entities, made up of properties and relations, and perhaps concrete
individuals. It's not at all clear that thoughts, especially
divine thoughts, satisfy any of these conceptual roles.



We also should ask about other necessarily existing abstracta. What
sorts of mental entities are they? Do they relate to one another, as
concrete mental tokens, in the right sort of way such that they mirror
the ways that Platonic states of affairs, propositions, properties,
relations, and numbers relate to each other? 



What these considerations suggest is that theistic mentalism may
actually be a sort of nominalism about abstract objects, in the way
that Plantinga (2003: ch. 10) says Lewis' (1986) conception of
possible worlds is a sort of nominalism about possible worlds. At
best, we have concrete things that play the roles of necessarily
existing abstract objects. (And the theistic mentalist has a great deal
more work in specifying concrete divine mental particulars such that
we have all the requisite role-players among the various sorts of
necessarily existing abstract objects. It is presumably not enough to
say that propositions are divine thoughts and leave it at that.)



Let us return to the initial motivation for theistic mentalism: There
are two sorts of intentional objects (propositions and thoughts), and
it would be a simpler metaphysic to identify tokens of the two sorts.
To assess this, we must ask if the tokens of the two sorts are enough
like each other to be identified. That is, simplicity isn't the
only consideration relevant here. After all, Spinoza's
metaphysic (necessarily there is one object that is exactly as it is
in the actual world) is maximally simple, yet has few proponents
within western philosophy. Furthermore, if we are able to explain the
intentionality of one of these sorts of entities by its relation to
the other, it will seem less mysterious that we have two classes of
intentional entities. That is precisely what many want to say about
the intentionality of thoughts vis-a-vis that of propositions:
Thoughts derive their intentionality by standing in the right sort of
relation to propositions. So, the reason why my thought is a thought
that grass is green is because it has the propositional content
*that grass is green*. The proposition *that grass is
green* has its intentionality intrinsically.


### 3.4 Theistic Mentalism (with Divine Simplicity)



Theistic mentalism with divine simplicity is the view that necessarily
existing abstracta are identical with divine mental states, and that
God is simple. Because God is simple, each abstract object is
identical with God and thus each other. This is a view held most
famously by Augustine and
 Aquinas.[11]
 Because this is a mentalist view, the criticisms leveled in the
section on theistic mentalism without divine simplicity will apply
here. In addition, the person who accepts divine simplicity alongside
her divine mentalism also will face
 criticisms of divine simplicity.
 Plantinga (1980) is perhaps the *locus classicus* of
contemporary criticism of divine simplicity. He argues that according
to divine simplicity, God is identical with his attributes and has
(all of) his attributes essentially. But, he argues, God isn't
an attribute; and God has many different attributes. (For discussion
more sympathetic to divine simplicity, see Mann 1982; Stump and
Kretzmann 1985; Leftow 1990; Stump 1997; Wolterstorff 1991; and
Bergmann and Brower 2006.) The sorts of difficulties that Plantinga
has raised have seemed decisive to many. (It is beyond the scope of
this essay to evaluate them, however.) This isn't to say that
they can't be met. But the theistic mentalist who accepts divine
simplicity has, *prima facie*, a great number of difficulties
with her view.


## 4. God's Grounding Abstract Objects II: Views on Which There Aren't Necessarily Existing Abstract Objects that All Are Grounded in God


* **Theistic Platonism:** There are necessarily
existing abstract objects, and none of them are grounded in God.
Example: van Inwagen (2009).
* **Theistic Nominalism:** There are no necessarily
existing abstract objects. Example: Craig (2016).
* **Mixed View 1: Mentalism-Platonism:** Example: Gould
and Davis (2014).
* **Mixed View 2: Anti-Bootstrapping Emanationism:**
Any abstracta that create "bootstrapping" problems
aren't grounded in God. Theistic emanationism is true of the
others.


### 4.1 Theistic Platonism



According to the theistic Platonist, there are at least some
necessarily existing abstract objects (e.g., propositions, properties,
relations, numbers, and states of affairs), and the existence of all
of the necessarily existing abstracta is not grounded in God. Peter
van Inwagen (2009) is a paradigm case of a theistic Platonist. As we
saw earlier, van Inwagen argues that if necessarily existing abstract
objects were grounded in God, they would be caused to exist by God.
But necessarily existing abstracta can't enter into causal
relations. So they aren't grounded in God. He says:



> 
> 
> In the end, I can find no sense in the idea that God creates free
> abstract objects [things like propositions, relations, numbers,
> properties, etc.], no sense in the idea that the existence of free
> abstract objects in some way depends on the activities of God. (Recall
> that, although I believe that *all* abstract objects are free,
> that is not a position that I am concerned to defend in this chapter.)
> And that is because the existence of free abstract objects depends on
> nothing. Their existence has nothing to do with causation...
> Causation is simply *irrelevant* to the being (and the
> intrinsic properties) of abstract objects (2009: 18).
> 
> 
> 



Van Inwagen takes his most serious challenge to be from religious
texts that he, as a Christian, thinks are authoritative. He speaks
particularly of the beginning of the Niceno-Constantinopolitan Creed,
which begins, "I believe in one God, the Father almighty, maker
of heaven and earth, of all that is seen and unseen". He thinks
here that the quantifier in "all that is seen and unseen"
is restricted to things that are capable of entering into causal
relations and thus are capable of being created. As van Inwagen points
out, there are other authoritative Christian texts in which a
universal quantifier is read in a restricted manner (e.g., Matthew
19:26 "for God all things are possible"; see also Luke
1:37, Mark 10:27). No such passage should be taken as a prooftext for
a Cartesian view of omnipotence. Rather, the quantifier is read in a
restricted manner. Similarly, the quantifier is restricted in the case
of the beginning of the Niceno-Constantinopolitan Creed.



It is worth noting that van Inwagen's argument here is slightly
different from one that often occurs around these sorts of texts.
Often, there is discussion as to whether the writers of the
authoritative texts had in mind things like necessarily existing
abstracta (e.g., Wolterstorff 1970: 293; Morris and Menzel 1986: 354).
To the person who says that the writers of these texts didn't
have, say, structured propositions in mind when they claimed God
created everything; it is pointed out that neither did they have in
mind (clearly-created) things like quarks and bosons (e.g., Davidson
1999: 278-279). Rather, van Inwagen argues that a text like the
beginning of the Niceno-Constantinopolitan Creed has to be read in a
restricted manner if it is to avoid asserting impossible propositions.
And this seems the right way to go for the theistic Platonist. It is
very difficult to discern the scope of the universal quantifier in the
usage of writers from nearly 2000 years ago. (This is apart from
questions about the connection between intention and semantic
content.)



Van Inwagen's main focus is on authoritative texts like the
Niceno-Constantinopolitan Creed. But we noted earlier a second sort of
reason for adopting a view on which any necessarily existing abstract
objects depend on God. That second sort of reason is perfect-being
theology. Again, the line of reasoning is that a being who is such
that necessarily existing abstracta depend on it is greater than a
being on whom they don't depend. And God is the greatest
possible being. It is clear what van Inwagen would say at this point:
It's not possible for necessarily existing abstract objects to
depend on anything. Thus, *being an x such that necessarily
existing abstracta depend on x* is not a great-making property.
That this isn't a great-making property is the sort of thing the
theistic Platonist needs to say to the perfect-being defender of
divine grounding of necessarily existing abstracta. It must be that
these things can't depend on God or anyone else. (One may or may
not adopt Inwagen's particular argument that they
can't.)



Thus, if the theistic Platonist thinks there are good arguments that
necessarily existing abstract objects can't be grounded in God,
she will have reason to do two things. First, she will have reason
read the relevant universal quantifications in authoritative texts as
restricted. Second, if she accepts the sort of reasoning in perfect
being theology; she will have reason to insist that *being an x
such that necessarily existing abstracta depend on x* is not a
great-making property (any more than *being able to create a square
circle* is).


### 4.2 Theistic Nominalism



The theistic nominalist doesn't think there are necessarily
existing abstract objects. She may or may not think if there were
necessarily existing abstract objects, they would be grounded in God.
For instance, William Lane Craig (2016) who is a theistic nominalist;
thinks that were there necessarily existing abstracta, they would have
to be grounded in God. (We presumably should count Craig as someone who thinks there are true counterpossibles.) But one can imagine someone who thinks that if
things like numbers and properties did exist, theistic Platonism would
be a plausible view to adopt. It is worth noting that very
few--if any--of the realists about necessarily existing
abstracta who are theists are themselves realists *because*
they are theists. Rather, they are realists about necessarily existing
abstracta for other sorts of reasons (e.g.,
 indispensability arguments,
 arguments that we quantify over them with true sentences, or arguments that true sentences (e.g., that 2+3=5)
require them as truthmakers (see Rodriguez-Pereyra (2005) for a
defense of truthmakers). Van Inwagen himself believes in necessarily
existing abstract objects because he thinks that we are committed to
true existential quantifications over them (e.g., van Inwagen 2014:
ch. 8). There is nothing in particular the theistic nominalist needs
to say *qua* theist about the existence of necessarily existing
abstracta that any other
 nominalist
 doesn't need to say. One advantage of theistic nominalism is
that it allows one to avoid some of the sorts of difficult maneuvers
that those who believe God grounds the existence of necessarily
existing abstract objects wind up performing. Another advantage of
theistic nominalism is that it allows one, if she wishes, to avoid
debates about the semantics of universal quantifiers in ancient
religious texts. Of course, theistic nominalism is open only to those
who find plausible nominalistic replies to standard arguments for
realism about necessarily existing abstracta. Craig himself thinks
that he can give replies to these standard arguments for realism
(2016: ch. 3, 6,
 7).[12]



We turn now to two "mixed views", views on which different
types of abstracta stand in different grounding relations to God. Both
of them try to bracket abstracta having to do with God (e.g.,
God's own attributes), and to say that God doesn't ground
those. But God grounds all the other necessarily existing
abstracta.


### 4.3 Mixed View 1: Mentalism-Platonism



On this view, propositions are identical with divine mental states;
and properties and relations not exemplified by God are independent of
God, a la theistic Platonism. This is the view of Gould and Davis
(2014). They say, "Thus, abstract objects exist in two realms:
the divine mind and Plato's heaven " (2014: 61). They
decline to say in this particular essay whether mentalism or Platonism
is true of other sorts of abstract objects (e.g., numbers, states of
affairs, possible worlds). So what we have in Gould and Davis is an
initial sketch of a proposal. They are motivated by bootstrapping
worries for theistic activism (itself an emanationist view). They
think that they can evade bootstrapping objections by having some
abstracta be identical with divine mental states, and having the
others not grounded in God. Their own name for this view is
"modified theistic activism".



It is perhaps strange that, having started with theistic activism (an
emanationist view) and its bootstrapping worries, they wind up with a
part-mentalist view. It would seem that they could have kept some
abstracta causally grounded in God, and others independent of God (see
 Mixed View 2,
 below). Also, this first Mixed View will face objections of the sort
faced by theistic Platonism; viz. that it doesn't take divine
aseity seriously enough, and that it must read the quantifiers in the
relevant religious texts in a restricted manner. Furthermore, it is
peculiar that propositions wind up as divine mental states, but
properties and relations wind up independent of God. One natural
understanding of propositions is that they are structured entities,
made up of properties and relations. Another is that they are sets of
possible worlds. The former understanding seems unavailable to Gould
and Davis, and the latter would seem to involve having *sui
generis* primitive possible worlds identical with divine mental
states. But at that point, why not just be a thoroughgoing theistic
mentalist? After all, bootstrapping isn't a concern for the
mentalist. Furthermore, bootstrapping worries arise with abstracta
other than properties. For instance, consider the proposition *God
is omnipotent*. In any possible world it exists, it is true. That
is, it has *being* *true* as part of its essence. But
then, if God causes it to exist, God causes it to be true. So we have
the same sorts of bootstrapping concerns as we did with a property
like *being omnipotent*.


### 4.4 Mixed View 2: Anti-Bootstrapping Emanationism



This is a view designed wholly to avoid bootstrapping worries that
affect theistic emanationism. It *really is* a sort of modified
theistic activism, and it may actually be the sort of view Gould and
Davis (2014) would like to hold. The idea is this: Ascertain the
necessarily existing abstracta that cause bootstrapping problems
(e.g., *being God, being omnipotent*, etc.) for the
emanationist. Those exist independently of God. All other necessarily
existing abstracta are causally grounded in God in the way the
theistic emanationist thinks abstracta are grounded in God. 



So far as I can tell, no one holds this first mixed view. Perhaps the
reader is thinking that that is because it is obviously *ad
hoc*: The sole motivation for the two classes of abstracta in the
theory is avoidance of bootstrapping worries. This is too strong, I
think. There is a *reason* why certain abstracta create
bootstrapping problem. That reason is that they have to do with God in
a way that other abstracta that don't cause bootstrapping
problems don't. So why not say that Leibniz or Menzel and Morris
are right about all the non-God related abstracta? To put it another
way, why not be an emanationist about all the abstracta one can be an
emanationist about--those that don't have to do with God?




That said, there is at least a whiff of ad-hocness here. The
motivation for this theory presumably would be that of perfect being
theology. For the proponent of this first mixed view must think that
the quantifiers in relevant religious texts are actually restricted.
They aren't *as* restricted as the theistic Platonist
thinks they are. But she will agree with the theistic Platonist that
it's false that all (read the quantifier wide open) entities are
created by/depend on/grounded in God. It's worth pointing out
that it's not clear how to delineate precisely those abstracta
that lead to bootstrapping problems and those that don't. The
best one can do seems to be to say that those that cause bootstrapping
problems don't depend on God, and all others God causes to
exist. But presumably for each necessarily existing abstract object,
either it gives rise to bootstrapping problems, or it doesn't.
So there should be two non-overlapping classes of abstract objects at
hand here, even if we're not able to specify more descriptively
which abstracta are in which class.



It would be better if the emanationist could find a cogent reply to
bootstrapping concerns. But if she can't, she may plump for
being an emanationist about all abstracta save those having to do with
God.