A THEISTIC ARGUMENT AGAINST PLATONISM
(AND IN
SUPPORT OF TRUTHMAKERS AND DIVINE SIMPLICITY)
Predication is an indisputable part of our
linguistic behavior. By contrast, the
metaphysics of predication has been a matter of dispute ever since
antiquity. According to Plato—or at
least Platonism, the view that goes
by Plato’s name in contemporary philosophy—the truths expressed by predications
such as “Socrates is wise” are true because there is a subject of predication
(e.g., Socrates), there is an abstract
property or universal (e.g., wisdom), and the subject exemplifies the property.[1] This view is supposed to be general,
applying to all predications, whether the subject of predication is a person, a
planet, or a property.[2]
Despite the controversy
surrounding the metaphysics of predication, many theistic
philosophers—including the majority of contemporary analytic theists—regard
Platonism as extremely attractive. At
the same time, however, such philosophers are also commonly attracted to a form of traditional theism that has at its core the thesis that God is an absolutely independent being who exists
entirely from himself (a se), whereas everything else is somehow dependent on him. This central thesis of traditional theism
(which we’ll call ‘the aseity-dependence doctrine’) led philosophers and
theologians during the Middle Ages to endorse what is known as the doctrine of divine simplicity. According to this doctrine, God is an absolutely
simple being, completely devoid of any metaphysical complexity whatsoever—where
this implies not only that he lacks certain obvious forms of complexity, such
as those associated with material or temporal composition, but also that he
lacks even the minimal form of complexity associated with the exemplification
of properties. The appeal of this
doctrine is that it makes it completely clear that God does not depend on
things in any way at all, not even in
the way that wholes depend on their proper parts or that things depend on their properties (in order to
exemplify them).
One of the main conclusions
of this paper will be that Platonism is inconsistent with the central thesis of traditional theism, namely, the aseity-dependence
doctrine. The inconsistency is perhaps
clearest in the case of Platonism and divine simplicity, which is the characteristic medieval
expression of the aseity-dependence doctrine.[3] But our conclusion will be that Platonism
is, in fact, inconsistent with the
aseity-dependence doctrine itself (not merely its medieval expression),
and, hence, that merely rejecting divine simplicity is insufficient to remove
the contradiction.
In
one sense, our
conclusion should come as no surprise.
There is a rich tradition of thinkers—from Augustine right down to the
present—who have felt pressure from traditional theism to reject the existence
of Platonic forms or properties.[4] Nonetheless, our argument stands out in
important ways from other arguments in this tradition (though even if it didn’t, it would still be worth
pressing, if only because contemporary philosophers of religion seem to have
lost sight of a significant
tension that exists between traditional theism and Platonism, and hence
continue to operate as if the two
were perfectly compatible). Platonism, as we have characterized it, is a
thesis involving two components: (1) the view that a unified account of predication can be provided in terms of
properties or exemplifiables, and (2) the view that exemplifiables are best conceived of as
abstract properties or universals. Most
theistic arguments against Platonism have targeted only the second
component. What distinguishes our
argument is that it specifically targets the first. This difference is important, because it is often thought that
the inconsistency of Platonism and traditional theism can be avoided merely by
rejecting the Platonic view of properties in favor of another, such as the
Augustinian view that properties are ideas in the mind of God.[5] Indeed,
some contemporary Augustinians, most notably Thomas Morris and Christopher
Menzel, have gone so far as to suggest that such a replacement will not only
remove the original inconsistency, but also preserve the most attractive
feature of Platonism from a contemporary point of view, namely, its conception
of properties as necessary beings.
But if our argument is correct, the inconsistency
between Platonism and traditional theism runs deeper than most theistic
arguments suggest. Traditional
theists who are Platonists, therefore, cannot avoid the inconsistency merely by
dropping the Platonic conception of
properties and replacing it with another—whether
it be an Aristotelian conception
(according to which there are no unexemplified universals), some form of immanent realism
(according to which universals are concrete constituents of the things that
exemplify them), a nominalistic theory of tropes (according to which properties
are concrete individuals), or even the Augustinian account (according to which
all exemplifiables are divine concepts).[6] In fact, as we shall be at pains to show, the inconsistency will remain so
long as the traditional theist continues
in any way to endorse the first of
the two components of Platonism identified above—i.e., so long as she
offers any unified account of
predication in terms of exemplifiables, no matter how such entities are
conceived.[7]
Assuming our argument is sound, the inconsistency
can be resolved in only one of two ways: either by rejecting
traditional theism (and hence becoming either a nontheist or a nontraditional
theist) or by rejecting any unified account of predication in terms of
exemplifiables (and hence adopting either
a non-unified account of predication or a unified account that appeals to
something other than exemplifiables).
For those who want to hang on to
their traditional theism, we shall argue that our argument naturally leads to a unified account of
predication in terms of truthmakers. As will emerge, such an account of
predication is precisely what is needed to defend the traditional doctrine of divine simplicity against the
dominant objection it has faced in the last two decades. Thus, our argument for the claim that
traditional theism is inconsistent with unified accounts of predication in
terms of exemplifiables can be viewed as a theistic argument in support of both
the truthmaker theory of
predication and the traditional
doctrine of divine simplicity.
Our discussion in the paper
proceeds as follows. In Section I, we
consider some of the reasons that have been given for thinking that traditional
theism is inconsistent with
Platonism and then briefly examine the
most important recent attempt to reconcile them by appealing to some form of Augustinianism.
After these preliminaries, we lay out our argument for their
inconsistency, focusing in particular
on the inconsistency between the
traditional theist’s aseity-dependence doctrine and
the Platonist thesis (also included in many non-Platonist accounts of
predication) that a unified
account of predication can be provided in terms of exemplifiables. In Section II, we explain how the conclusion of Section I naturally leads to a truthmaker theory of
predication, which in turn provides the materials needed to defend the
traditional doctrine of divine simplicity against the dominant objection to it
in the recent literature.[8]
Traditional (western) theism has many ingredients, including among others that God is an
omnipotent, omniscient, eternal, necessarily
existing, perfectly good person. This
list is not intended not to be exhaustive (for our purposes it will be
unnecessary to provide an exhaustive list). Rather it is intended to be representative
of the sorts of things that traditional theists have said about God. In addition to the things just mentioned, there
is a further component of traditional theism, one that will be especially important to our discussion in what
follows, namely, the aseity-dependence
doctrine discussed above. That doctrine, as we will be
understanding it, may be stated as follows:
AD: (i) God does not depend on anything distinct from himself for his existing and (ii) everything distinct from God depends on God’s creative activity for its existing.
Each of the
components of AD follows straightforwardly from the traditional conception of
God as an absolutely perfect or supreme being.
Thus, (i) asserts that God lacks
a certain type of imperfection (namely, dependency on another), whereas (ii)
asserts that he possess a certain
type of perfection (namely, that associated with having creative power extending to all other existing things). Moreover, each of these components fits well not only with the traditional conception
of deity, but also with certain authoritative statements within the
tradition. Compare, for example, the
first sentence of the Nicene Creed, which also seems to presuppose that God is
the uncreated creator of all things: “We believe in one God, the Father
Almighty, Creator of heaven and earth,
and of all things visible and invisible.”[9]
Although we will be speaking in what follows of the dependence of
creatures on God’s creative activity,
we do not mean to imply by this that created things have a beginning
in time, nor even that they are
contingent beings. As we understand it,
the aseity-dependence doctrine is perfectly
consistent with there being other necessary beings besides God, provided that
they too depend on God as a created thing depends for its existing on its
creator. With all this in mind, we can state the position on which we want to
focus as follows:
T: Traditional theism (which includes AD) is true.
Our claim is that T is
inconsistent with a group of theories concerning the metaphysical implications
of predication. What these theories
have in common is that they offer a unified account of predication in terms of
exemplifiables (though they differ over whether exemplifiables are to be
conceived of as abstract Platonic entities, Aristotelian universals, concrete
immanent universals, the tropes familiar from certain forms of contemporary
nominalism, or the divine concepts of which Augustine speaks). We may state the thesis that is common to
all these theories as follows:
P: The truth of all true predications, or at least of all true predications of the form “a is F”, is to be explained in terms of a subject and an exemplifiable (however exemplifiables are themselves to be conceived).[10]
Our argument will be that the conjunction of T and P
results in a contradiction, and hence that T implies the falsity of P. Before mounting this argument, however, it
will be useful to consider both what it
is about T and P that appears to
make them inconsistent and why so many traditional theists have thought that the Augustinian
response mentioned above is sufficient to resolve the apparent inconsistency.
A. The Apparent Inconsistency of T&P and the Response of Theistic
Activism
In “Absolute Creation,” a paper originally
co-authored with Christopher Menzel, Thomas Morris identifies the source of the apparent tension between traditional theism and Platonism.
According to traditional theism, which includes the aseity-dependence
doctrine, God is the “absolute” creator of everything—that is to say, he is the
creator of everything distinct from himself.
According to Platonism, by contrast, the entities in terms of which
predications are to be explained are necessarily existing beings—namely, abstract properties or
universals—and hence not the sorts of things that appear to be capable of being
created.
In
light of this
tension, it is not surprising that many
traditional theists have been attracted to the Augustinian view
according to which Platonic universals are identical with divine concepts—that is, entities that,
despite their necessary existence, are nonetheless dependent on God as
thoughts are dependent on a
thinker. Contemporary philosophers now typically refer to this Augustinian view
as “theistic activism”, since according to it, the
existence of properties and propositions is due to the activity of the divine intellect: properties are divine concepts
resulting from God’s acts of conceptualizing and propositions are divine
thoughts due to God’s acts of thinking or considering.[11]
Now
as Morris himself recognizes, traditional theism still presents a difficulty
even for the Augustinian view:
Of course the whole project of theistic activism is to recognize some divine activity as responsible for the existence of absolutely everything distinct from God. But it would sound at least exceedingly odd to say that God creates the very properties which are logically necessary for, and distinctively exemplified within, his creative activity—properties such as his omniscience and omnipotence—to say that he creates his own nature. In fact, many people would find this suggestion incoherent or absurd. (p. 172)
Later, Morris
refers to this problem as the “circularity of God’s creating his own nature”
(p. 173) and asks:
[I]f God creates his own haecceity [i.e., his individual essence or nature], and the existence of his haecceity is logically sufficient for his existence, as is the case with any necessarily existent being, do we not have the result that on this view God creates himself? And of course, the very idea of self-causation or self-creation is almost universally characterized as absurd, incoherent, or worse. (p. 174)
Thus, as Morris
recognizes, there is a tension within theistic activism—a tension that derives
from the fact that it appears to
include an objectionable sort of
circularity. Unlike the tension between Platonism and traditional theism, however,
Morris thinks that this tension can be resolved. For the circularity in question, he maintains, is ultimately benign.
In
order to resolve the tension in question, Morris does two things. First, he presents an analogy of an eternally existing materialization machine (itself a material
object about the size of a clock radio) that produces material objects ex nihilo and sustains them in
existence, including its very own parts which it replaces from time to time
with newly produced parts.[12] He
intends this analogy to go some distance toward showing the coherence of a
thing’s essence depending on its
own creative activity. Of course, he
recognizes that the analogy is
imperfect insofar as the machine doesn’t produce the very properties it
instantiates, but only some of its
material parts. Nevertheless, he
thinks it models “in central ways what the [theistic] activist alleges about
God” (p. 176). To those who aren’t
persuaded by this response (and we count ourselves among them), he has the following to
say:
But, strictly speaking, there is no need of any such analogy to defend the implication of activism now in view. The value of the analogy is mainly heuristic, or pedagogical. It just seems to me that there is nothing logically or metaphysically objectionable about God’s creating his own nature in precisely the way indicated [by theistic activism]. (p. 176, emphasis added)
We suggest that the reason it just seems to Morris that there is no objectionable circularity is
that he isn’t clear enough about precisely what the objectionable circularity
is. In fact, Morris never gets any more explicit than he is in the passages
quoted above about the exact
nature of the damaging circularity. In
the next subsection, we will offer an
argument that provides a better target for defenders of theistic
activism. Indeed, we will say precisely what the objectionable circularity
is and provide a formal argument
for the conclusion that such circularity infects not only views like theistic activism, but any view that combines
traditional theism with a unified account of predication in terms of
exemplifiables (however the exemplifiables are themselves understood). Thus,
we will be providing
theistic activists, along with anyone
else who endorses a unified account of predication in terms of exemplifiables,
the opportunity to respond to our objection by pinpointing where our
argument goes wrong, and thus remove the need for them to rely instead on
imperfect analogies or the apparent absence of anything objectionable about
their view.
Morris’s second response to
the circularity problem is to point out that, from the fact that God’s nature
is causally dependent on God and God
is logically dependent on his nature
(in the sense that the existence of his nature entails his existing[13]),
it doesn’t follow that there is any objectionable circularity. For logical dependence, like logical
entailment, can be mutual. There is
nothing objectionable about each necessary truth entailing every other such
truth; nor is there anything objectionable about the existence of each
necessary being entailing the existence of every other such being. Hence there is no difficulty with the
suggestion that logical dependence (as Morris understands it) is not an asymmetrical relation. As for causal dependence, although it may be
an asymmetrical relation, there is no reason to think that God is causally
dependent on his nature (though of course the theistic activist is committed to
saying that God’s nature causally depends upon God). For the fact that God is logically
dependent on his nature (in the sense noted above) doesn’t imply that God is causally dependent on anything, much
less his nature. Indeed, on any view
according to which, say, the numbers two and nine are necessary beings, it will
follow that each is logically dependent (in Morris’s sense) on the other. But such a view needn’t add that the numbers
two and nine are causally dependent on each other.
We agree wholeheartedly with
Morris’s points summarized in the previous paragraph. From them we take the following lesson: In order to establish
that there is an objectionable circularity in a view like theistic activism, we
must establish not only that (a) there is a dependence relation of some sort
running in both directions between a pair of things (such as God and his nature),
but also that (b) it is the same
relation that holds in both directions and (c) the relation in question is asymmetrical. With this lesson in mind, we shall now attempt to establish that
there is a form of circularity that both meets conditions (a)-(c) and infects
the conjunction of traditional theism with
any unified account of predication in terms of exemplifiables.
Although our argument for the inconsistency of T and
P is somewhat complicated, the basic idea behind it is fairly simple. 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.[14] Notice, however, that in order to create F, God must have the property of being able to create a property. Here is where the trouble begins. For on the one hand, it would seem that this
property (i.e., being
able to create a property) must
be logically prior to God’s creating it, since God’s having it is a prerequisite for the creation of any
property. On the other hand, however,
it would also seem that this property must be logically posterior to God’s
creating it, since insofar as it is a property (or exemplifiable), it must fall
under the general principle articulated in AD, and hence be a product of God’s creative activity.
Evidently, therefore, in order for it to be true that God is the creator
of all properties, there must be a property—namely, being able to
create a property—that is both logically prior and logically
posterior to God’s creating properties.
Assuming that logical priority is an asymmetrical relation, however,
this conclusion is obviously absurd.
With this intuitive
statement in hand,[15]
we can now turn to a more precise statement of the argument, extending its scope so that it applies not
just to theistic activism, but to any unified account of predication in terms
of exemplifiables. To begin, let
us note that our argument will establish the inconsistency of T and P by
showing that their conjunction entails the following two claims, which give
rise to an objectionable circularity:
C1: God’s creating an exemplifiable is logically prior to the exemplifiable being able to create an exemplifiable.
C2: The exemplifiable being able to create an exemplifiable is logically prior to God’s creating an exemplifiable.
Notice that C1 and C2 together entail a claim of the
form “a is logically prior to b and b is logically prior to a”. Assuming once again that the relation of
logical priority is asymmetrical, the conjunction of C1 and C2 is impossible, for it involves circularity of
the sort described in conditions (a)-(c) mentioned at the end of the previous
subsection. But since T and P together entail the
conjunction of C1 and C2, the conjunction of T and P is also impossible, which
is what we are aiming to show.
Before stating the argument proper, we need to set
out the assumptions on which it relies:
A1. For any exemplifiable F, if F depends on God’s creative activity for its existing, then God’s creating an exemplifiable is logically prior to F.
A2. For any x and any action A, x’s being able to do A is logically prior to x’s doing A.[16]
A3. For any x, any y, and any exemplifiable F, if x’s exemplifying F is logically prior to y, then F is logically prior to y.
A4. x’s being able to create an F = x’s exemplifying being able to create an F.
A5. For any x and any y, if x is logically prior to y, then y is not logically prior to x.
Since the notion of logical priority plays a crucial role in these assumptions and, hence, in our argument as a whole, it requires some comment. Perhaps the best way to clarify the notion is by way of example. Consider, therefore, a whole consisting of several parts—say, an ordinary pocket watch. Its parts, we say, are logically prior to the whole of which they are the parts. Or consider a thinker and its thoughts. The thinker, we say, is logically prior to its thoughts. As these examples serve to indicate, logical priority is associated with a special type of dependence. If an object a is logically prior to an object b, then b depends for its existing on a (in a way that a doesn’t depend on b)—in fact, it depends on a in the way a whole depends on its parts or a thought depends on its thinker. This type of dependence, however, must be sharply distinguished from several other types of dependence.
First of all, logical priority must be distinguished from the type of dependence associated with being a mere necessary condition. The existence of a part is a necessary condition for the existence of the whole of which it is a part; likewise, the existence of a thinker is a necessary condition for the existence of its thoughts. Nonetheless, the logical priority of parts to wholes, or of thinkers to their thoughts, cannot be reduced to their being necessary conditions. For the relation of dependence that holds between parts and wholes and between thinkers and their thoughts is asymmetric, whereas the relation of being a necessary condition of isn’t (e.g., any pair of necessary truths is such that each member of it is a necessary condition of the other).
Secondly, logical priority must be distinguished from temporal priority. Parts are necessarily logically prior to
their wholes, but not necessarily temporally
prior to them. Suppose that there
existed an eternal pocket watch with
parts as eternally existent as the watch itself; or suppose that both the watch
and its parts had come into existence
simultaneously. In either case, the
parts of the watch would be
logically prior to the whole watch even though they wouldn’t be
temporally prior to it. Indeed, the parts of the watch would be logically prior to the whole watch
even if both existed necessarily. The same is true for thinkers and their
thoughts. According to traditional
theism, God not only exists necessarily but is also essentially omniscient. Thus, he not only exists in all possible
worlds, but also knows—and hence has the thought—in all possible worlds that 2+2=4. Nonetheless, he must still be regarded as logically prior to this
(or any other such) thought of his.
Finally, logical priority must be distinguished from entailment (or what
Morris calls ‘logical dependence’).
Although the existence of any necessary being entails the
existence of any other, not every necessary being is logically prior to every
other. Indeed, as the examples just
given are intended to make clear, logical priority is unlike entailment in that
it cannot be mutual. Although God is
logically prior to his thoughts, his thoughts are not logically prior to
him. On the contrary, they are logically
posterior to him. And this
is so despite the fact that both God and certain of his thoughts (such as that 2+2=4) are necessary beings and, hence, mutually entailing.
Is there anything more we can say about logical priority, apart from the fact that it is associated with a special type of dependence? Perhaps the most illuminating thing to say is that if a is logically prior to b, then b depends on a in such a way that a at least partially explains b whereas b is not even a partial explanation of a. Thus, the existence of the parts of a watch explain (at least partially) the existence of the watch itself, whereas the watch does nothing to explain the existence of the parts.[17] Likewise, the existence of God is at least a partial explanation of the existence of his thoughts, but not vice versa.[18]
In
light of all this, it should be clear that the relation
of logical priority is asymmetric, and, hence, that assumption A5 above is
true. Also, given P (whose conjunction
with T will be assumed for reductio in our argument), the equivalence stated in
A4 seems to be uncontroversial.
Furthermore, assumptions A1
and A2 are extremely plausible. The act
of creating seems to be logically prior to the creature (and not vice versa);
and, the having of an ability seems to
explain (at least partially), and hence to be logically prior to, the
exercise of that ability (and not vice versa).[19] It is difficult to see, therefore, how one
could plausibly deny either A1-A2 or A4-A5.
Thus, the only assumption which requires any extended comment is A3.
A3 strikes us as intuitively
plausible. In order to see why, we need to focus on the relationship
between a property and its exemplification.
In particular, we need to consider which, if either, is logically prior to the other. In our view, a property is logically prior
to its exemplification. This position
can be stated as follows:
A3*. For any x and any exemplifiable F, F is logically prior to x’s
exemplifying F.
In defense of A3*, we note, first, that an exemplifiable, F, seems to be related to the
state of affairs something’s exemplifying F in roughly the way in
which a constituent is related to that of which it is a constituent or the way
in which a proper part is
related to the whole of which it is a part.
Furthermore, it seems that constituents are logically prior to the
things of which they are constituents (and not vice versa), in much the
same way that proper parts are
logically prior to the wholes of which they are parts (and not vice versa). By
parity of reasoning, therefore, it
seems that F is logically prior to something’s
exemplifying F (and not vice versa).
Given A3*, A3 seems to
follow. For consider these three things: a, F, and b’s exemplifying F
(where F is an exemplifiable and a
and b are anything at all). Given that we know (by A3*) that F is
logically prior to b’s exemplifying
F, we may conclude the following: if b’s
exemplifying F is logically prior to a,
then F is also logically prior to a. And A3
is just that conclusion generalized.
We turn now from our assumptions to our argument. As we noted above, we will be arguing that the conjunction of T and P entails both C1 and C2. Since the relation of logical priority is asymmetrical (by assumption A5), the conjunction of C1 and C2 is impossible. Hence T and P are inconsistent. For convenience, we’ll begin by restating AD, T, P, and our five assumptions:
AD: (i) God does not depend on anything distinct from himself for his existing and (ii) everything distinct from God depends on God’s creative activity for its existing.
T: Traditional theism (which includes AD) is true.
P: All true predications, or at least all true predications of the form “a is F”, are to be explained in terms of a subject and an exemplifiable (however exemplifiables are themselves to be conceived).
A1. For any exemplifiable F, if F depends on God’s creative activity for its existing, then God’s creating an exemplifiable is logically prior to F.
A2. For any x and any action A, x’s being able to do A is logically prior to x’s doing A.
A3. For any x, any y, and any exemplifiable F, if x’s exemplifying F is logically prior to y, then F is logically prior to y.
A4. x’s being able to create an F = x’s exemplifying being able to create an F.
A5. For any x and any y, if x is logically prior to y, then y is not logically prior to x.
We will break our argument into two parts: the first
part argues that the conjunction of T and P gives us C1; the second part
derives C2 from our assumptions.
Here is the first part of
the argument:
1. T&P [assume for reductio]
2. All exemplifiables depend on God’s creative activity for their
existing. [from T][20]
3. For any exemplifiable F, God’s creating an exemplifiable is logically prior to F. [from 2 and A1]
4. C1: God’s creating an exemplifiable is logically prior to the exemplifiable being able to create an exemplifiable.[from 3]
Our argument so far depends only on A1.
Consider next the second part of our argument, which derives C2 from assumptions A2-A4:
5. God’s being able to create an exemplifiable is logically prior to God’s creating an exemplifiable. [from A2]
6. God’s exemplifying being able to create an exemplifiable is logically prior to God’s creating an exemplifiable. [from 5 and A4]
7. C2: The exemplifiable being able to createan exemplifiable is logically prior to God’s creating an exemplifiable. [from 6 and A3]
To complete our argument, we need only appeal to A5:
8. ~(4&7). [from A5]
9. ~(T&P) [from 1-8 by reductio]
In short, traditional theism implies the falsity of
all unified accounts of predication in terms of exemplifiables. The challenge, therefore, both for theistic
activists and for all other supporters of T and P, is to identify a problem
with our argument.[21]
One response to our argument is to try to maintain
traditional theism without endorsing the aseity-dependence doctrine as defined
in AD. For example, one might suggest
that that doctrine need not be understood in the strong way we define it—i.e.,
in terms of the dependence of things on God’s creative activity—but may be understood more weakly as follows:
AD*: (i) God does not depend on anything distinct from himself for his existing and (ii) everything distinct from God depends on God (though not, in every case, on God’s creative activity) for its existing.
Those who favor this weaker version of the
aseity-dependence doctrine, AD*, can then insist that traditional theism should
be understood, not in terms of T, but
rather in terms of T*:
T*: Traditional theism (which includes AD*) is true.
Once traditional theism is understood in this way,
however, the proponent of the weaker aseity-dependence doctrine can ignore our
argument above on the grounds that it fails to show that T* and P are
incompatible, even if it succeeds at showing that T and P are incompatible.[22]
We think there is some
precedent (e.g., the Nicene creed) for understanding traditional theism as
favoring the stronger version of the aseity-dependence doctrine, AD, over the
weaker AD*.[23] Nevertheless, we think an argument similar
to the one given in the previous subsection can be given for the
incompatibility of T* and P. Except for
A5, according to which logical priority is an asymmetrical relation, this
argument relies on only three assumptions (two of which are modified versions of earlier assumptions, and another of which we have already
encountered):
A1*. For any x, if x depends on God for its existing, then God’s being who he is is logically prior to x.
A3*. For any x and any exemplifiable F, F is logically prior to x’s exemplifying F.
A4*. God’s being who he is = God’s exemplifying his nature.
A3* was employed and defended earlier in accounting for the plausibility of A3. And A4* is similar to A4 insofar as it says that a gerundial phrase of the form ‘x’s being F’, which includes no explicit mention of exemplification, can be restated in terms of the exemplification of a property—i.e., in terms of a phrase of the form ‘x’s exemplifying F’. In light of P, which is being assumed for reductio in this argument as well, we take A4* to be as uncontroversial as A4.
As for assumption A1*, it
too is a modified version of its ancestor, A1.
The idea behind A1* is this: It must
be in virtue of something
about God that everything distinct from
him depends on him for its
existing. But in virtue of what? According to theistic activism, it is in
virtue of God’s creative activity
that all things depend on him. But not
according to AD*. Nevertheless, even
those who endorse AD* will, if they endorse P, agree that God necessarily
exemplifies the divine nature. And,
since it is in virtue of something
about God that all (other) things depend on him for their existing, it seems
that we can say, at the very least, that it is in virtue of God’s being who he
is—i.e., that it is in virtue of his being
divine or his exemplifying the divine nature—that all
things distinct from him depend on him for their existing.
In our previous argument, we
showed that a problematic conjunction (in that case, T and P) resulted in an
objectionably circular statement of the form “a is logically prior to b
and b is logically prior to a”.
Our new argument will show the same thing, only this time the
problematic conjunction will be T* &
P and the resulting objectionable circularity will arise from the following
two claims:
C1*: God’s exemplifying his nature is logically prior to the exemplifiable God’s nature (or being divine).
C2*: The exemplifiable God’s nature is logically prior to God’s exemplifying his nature.
Here, then, is our new argument:
1. T*&P [assume for reductio]
2. All exemplifiables depend on God for their existing. [from T*]
3. For any exemplifiable F, God’s being who he is is logically prior to F. [from 2 and A1*]
4. God’s being who he is is logically prior to the exemplifiable God’s nature. [from 3]
5. C1*: God’s exemplifying his nature is logically prior to the exemplifiable God’s nature. [from 4 and A4*]
6. C2*: The exemplifiable God’s nature is logically prior to God’s exemplifying his nature. [from A3*]
7. ~(5&6). [from A5]
8. ~(T*&P) [from 1-7 by reductio]
Thus, by slightly altering two of our original
assumptions, A1 and A4, and by appealing to A3* (used earlier to explain the plausibility of our original A3),
we’ve shown that P is incompatible not only with T but also with T*, which
includes only the weaker aseity-dependence doctrine, AD*.
Assuming the arguments in the first part of the
paper are sound—an assumption hereafter
taken for granted—traditional theists (of either the T- or T*-variety)
have no choice but to reject P, and with it any unified account of predication
in terms of exemplifiables. The reason is that, as our earlier
arguments make clear, there are
at least some divine predications
that cannot be explained in terms of
exemplifiables. Our first argument showed that
traditional theists (of the T-variety) cannot ascribe to God the property (or
exemplifiable) of being able to create an
exemplifiable. But, of course, if
this is right, then divine predications such as “God is able to create an
exemplifiable” cannot be explained by traditional theists in terms of
exemplifiables. Our second argument
established a similar conclusion, showing that traditional theists (of the
weaker T*-variety) cannot ascribe to God the property (or exemplifiable) of being divine. Once again, however, this just goes to show that predications
such as “God is divine” cannot be explained by them in terms of
exemplifiables. And perhaps there are other such
properties (or exemplifiables) that cannot be ascribed to God, and hence other
divine predications that provide
exceptions to P.
All of this presents traditional theists with a challenge—in fact, it presents them
with two challenges. The first and most immediate challenge is that of providing an account of divine
predications—or at least of those divine predications that are
problematic. But assuming such theists are also interested in
preserving a unified or systematic general theory of predication, there is also
the second challenge of explaining how divine predication relates to predication generally. In what follows, we present what we take to
be the best responses to these challenges available to traditional theists. In doing so, we not only defend a truthmaker
theory of predication, but also show that such a theory yields an understanding of the doctrine of divine simplicity that rescues that doctrine from
the standard contemporary objection leveled against it.
TM: If an
entity E is a truthmaker for a
predication P, then ‘E exists’ entails the truth expressed by P.[27]
In what follows, we will
need to speak of the relationship between a particular truthmaker and the
predication it makes true. In order to
avoid using the potentially misleading notion of entailment, we will speak
instead of truthmakers as necessitating the
truth of the predications they make true.
Here again, however, the form of necessitation we have in mind is not
causal but broadly logical.
One final observation about TM: it is
intended to provide only a partial
analysis of the notion of truthmaking.
This is important because a complete analysis of truthmaking in terms of
entailment would lead to obvious absurdities, including the claim that
necessary truths—such as 2+2=4—have
any existing thing whatsoever as their truthmakers. But if TM does not provide a complete analysis of the notion of
truthmaking, then what, in addition to entailment or necessitation, is required
for something to qualify as a truthmaker?
This is a difficult question, but one that we shall not attempt
to answer here.[28] For present purposes, it will suffice to
note that even if the fact that an entity E
necessitates the truth expressed by a
predication P does not guarantee that E is P ’s truthmaker, it
does make E a candidate—perhaps even
a prima facie good candidate—for
playing this role.
With these
clarifications in mind, it should now be
possible to appreciate the point of our suggestion, on behalf of traditional
theists, about how best to meet the basic challenge facing their view—at least
with respect to the predication “God is divine”. If traditional theists want to explain the truth of this predication
in terms of something other than properties or exemplifiables, they can do so
in terms of truthmakers. For given that
“God is divine” is a case of essential predication, and hence that God
necessitates its truth, God is already a plausible candidate for its
truthmaker. Notice, moreover, that the
same account can be given of the other problematic divine predication discussed
above, namely, “God is able to create exemplifiables”. For like “God is divine”, it too appears to
be a case of essential predication (assuming that exemplifiables are capable of
being created). But, then, as in the
case of “God is divine”, God will be a plausible candidate for its truthmaker
as well. And presumably, if there are any other divine predications that present a difficulty
for traditional theists, they can be explained in the same way.
In the end, therefore, it appears that traditional theists can answer the most
immediate challenge facing their
view. Even so, there is still a question concerning the
nature of predication in general—and in particular how to reconcile it with the account of divine predication just
given. This is the second main
challenge facing traditional theists.
Here again, however, the challenge appears to admit of a
straightforward resolution.
As we have seen, what raises trouble for traditional theists is not just Platonism, but any of a group of theories that take for granted the following thesis about predication:
P: The truth of all true predications, or at least of all true predications of the form “a is F”, is to be explained in terms of a subject and an exemplifiable.
To this point, we have suggested that, if traditional theists want to avoid the circularity problem associated with P, they ought to adopt a truthmaker account of certain divine predications (namely, “God is divine” and “God is able to create exemplifiables”). However, it seems natural to go further and to suggest that, if traditional theists want a theory to replace P, they ought to adopt a truthmaker theory of predication generally—that is a theory that, instead of P, takes for granted the following alternative thesis about predication:
P*: The truth of all true predications, or at least of all true predications of the form “a is F”, is to be explained in terms of truthmakers.[29]
By taking this extra step, and endorsing P*, traditional theists are able not only to resolve the circularity problem associated with P, but also to present this resolution as falling out of a general account of predication that is every bit as unified or systematic as P itself. In short, by taking this step, they are able to meet each of the challenges facing their view.[30]
It is important to
emphasize that the truthmaker theory of predication, as we’ve stated it at P*, is an ontologically
neutral theory of predication. According
to this theory, if a predication of the form “a is F” is true, then its
truth must be explained in terms of its truthmaker—that is, in terms of an entity (or a group of entities) whose existence
necessitates the truth of the predication in question. But
in principle, there is no restriction on the nature or ontological
category to which such an entity belongs. Hence this theory does not require us
to say that the truthmaker for “a is
F” either is or involves an exemplifiable.
Indeed, for all the theory itself says, the truthmaker for this
predication may be nothing but the single individual, a. Even so, this theory doesn’t rule out the possibility of explaining at
least some predications in terms of properties or exemplifiables. On the contrary, it actually invites such an
explanation in certain cases.
We have already
indicated that, in the case of essential predications, it is possible to take
the subject of predication itself to be the truthmaker. Thus, Socrates may be regarded as the
truthmaker of “Socrates is human”, just as God may be regarded as the
truthmaker for “God is divine”—since in each case the subject is such that it
necessitates the truth expressed by the corresponding predication. Notice, however, that the same cannot be
said for accidental or contingent predications. Socrates, for example, cannot be regarded as the truthmaker for “Socrates is wise”, since Socrates does not necessitate its truth. But then what is the truthmaker in such
cases? There is more than one way
to answer this question, but the two most common ways appeal
directly to properties or exemplifiables.
First of all, one can say, as David Armstrong does, that the truthmaker for contingent
predications are facts (or concrete states of affairs) that include properties
as constituents.[31] In that case, the truthmaker for “Socrates is wise” will be the fact that Socrates is wise, which
includes the property wisdom as a constituent. Alternatively, one can
say, as C. B. Martin does, that
the truthmaker for contingent predications are non-transferable tropes (or
concrete individual properties that are essentially dependent on the subjects
of which they are the properties).[32] In that case, the truthmaker for “Socrates is wise” will not be the fact that
Socrates is wise, but Socrates’s
wisdom—an entity such that,
in all possible worlds in which it exists, Socrates exists and is wise.
It might be thought
that the ontological neutrality of the truthmaker theory compromises our claim
that it is every bit as unified or systematic as the alternative stated at
P. After all, if the truthmaker theory
of predication can allow some predications (e.g., “Socrates is wise”), but not others (e.g., “God is divine”), to be explained in terms of
exemplifiables, then it might not seem to be a unified theory of
predication after all.
In fact, however, the ontological neutrality of the truthmaker theory merely calls
attention to the distinctiveness of the principle of unity underlying it. To
characterize an entity as a truthmaker is to characterize it in terms of a
certain function or role—that of necessitating the truth of the
predications it makes true. In this respect, ‘truthmaker’ is similar to other sorts of functional
characterization one finds in philosophy—ones that prescind, to some extent, from the intrinsic nature of
the entity being characterized. Thus,
just as functionalists in philosophy of mind claim that we can make progress in understanding mental states
(such as pain) only if we abandon the attempt to characterize them in terms of
a single ontological category (namely, physical or non-physical), so too, we
have been suggesting, traditional
theists can make progress in understanding predication in general, and
divine predication in particular, if they adopt the same sort of strategy. We call the truthmaker theory of
predication a ‘unified theory’,
therefore, not because it
explains all predications in terms of entities from a single ontological
category, but rather because it explains all predications in terms of entities
of one familiar functional kind.
We have been
emphasizing the ontological neutrality of the truthmaker theory, not only because it is
what enables traditional theists to
meet the main challenges facing their view, but also because, as we now
want to show, it is what enables them to go a considerable
distance toward rehabilitating the doctrine of divine simplicity. Since this doctrine remains one of the most
historically important and theologically influential expressions of the thesis
at the core of traditional theism (namely, the aseity-dependence doctrine), this result ought to be of
significant interest.
B. Truthmakers, Divine Simplicity, and The Category Problem
According to the traditional
doctrine of divine simplicity, God is an absolutely simple being devoid of any
form of metaphysical complexity whatsoever.
Although this doctrine has its roots in antiquity, it received its most
elaborate development and careful defense at the hands of philosophers and
theologians during the Middle Ages.
According to the medievals, this doctrine
entails not only that God lacks the sort of complexity associated
with the possession of material or temporal parts, but also that he lacks even the minimal form of complexity associated with the
possession of properties. Thus, from
the fact that God is simple, the medievals infer that God lacks any (intrinsic)
accidental or contingent properties, and hence that all true predications of
the form “God is (intrinsically) F” are cases of essential predication. And even in the case of essential
predications, the medievals take the doctrine to have fairly radical
consequences. Hence, from the truth of
“God is divine”, they infer that God is identical with his nature or divinity;
from the truth of “God is good” they infer that he is identical with his
goodness; and so on for every other such predication. And, of course, from the fact that God is identical with each of
these things, they infer that each of these things is identical to each of the
others.
Ever since the
publication of Alvin Plantinga’s Does God Have a Nature?, the literature
on divine simplicity has been dominated by the discussion of a particular
objection to its coherence. The alleged
difficulty arises from the fact that the doctrine appears to entail the absurdity that God is identical with a property or
exemplifiable. Predications such as
“Socrates is wise” are widely assumed (and rightly in our opinion) to require
the existence of things like Socrates’s
wisdom or wisdom in general—that is,
some entity that can serve as the referent for a so-called abstract singular
term, such as ‘wisdom’. (Terms such as
‘wisdom’ are called abstract singular terms because they are grammatically
singular in number and function as the abstract counterparts of concrete terms
such as ‘wise’.) But what sort of
entities could serve as the referents of abstract singular terms besides
properties or exemplifiables? Without
an answer to this challenge, we would appear to have no choice but to assume
that endorsement of a predication such
as “God is divine” commits defenders of divine simplicity (which
requires that God is identical with his divinity) to the view that God is
identical with the property of being divine. For the same reason, endorsement of divine predications such as
“God is good”, “God is powerful”, and “God is wise” will commit such theists to
the view that God is identical with the properties of being good, being
powerful, and being wise—and indeed, by transitivity of identity,
that each of these properties is identical with each of the others. And so on for every other such divine
predication.
Now why does this identification of God with
his properties seem so objectionable?
Because one of the most obvious things about God is that he
isn’t an exemplifiable. Unlike universals, tropes, or property-instances, God is a person and persons aren’t the
sorts of things that can be exemplified.
The doctrine of divine
simplicity, therefore, seems to be guilty of making a category mistake: it
places a nonexemplifiable thing, a person, into the category of
exemplifiables. Let’s call this
familiar objection to the doctrine of divine simplicity, ‘the category
problem’.
Now if the doctrine
of divine simplicity could be stated in such a way that it avoided this problem, that would be a significant result for
contemporary discussion of the doctrine.
For, as we’ve just noted, worries about that problem have been the main
focus of the recent literature on the topic.
In what follows, we will explain how the truthmaker theory of
predication presented at P*, and to which we were led by the arguments in section I, enables proponents of the doctrine to
avoid the category problem. As will
emerge, the solution is to recognize that although defenders of divine simplicity
must agree that God is identical with the referent of abstract singular terms
such as ‘God’s goodness’ or ‘God’s divinity’, they need not construe the referents of such terms as exemplifiables.
From the perspective of the truthmaker theory of predication, there is nothing problematic about saying that God is identical with his nature, goodness, power, wisdom, or any other such things. To put the point more carefully, there is nothing problematic about saying that God is identical with the referents of abstract singular terms corresponding to each of the true intrinsic predications that can be made about him. For in light of the truthmaker theory developed above, there is a straightforward answer to the challenge raised earlier: “What could the referents of abstract singular terms be if not exemplifiables?” Just as the defenders of Platonism (or, more generally, P) typically assume that properties (or exemplifiables) are what serve as the referents of abstract singular terms, so too the defenders of the truthmaker theory (or P*) can maintain that truthmakers play this role. Thus, it is open to the defender of divine simplicity to say that the truthmaker for predications such as “God is divine” is also the referent for the abstract singular term ‘God’s divinity’ or ‘God’s nature’. Indeed, if we reflect on the fact that expressions such as ‘God’s divinity’ are the abstract nominalizations of predications such as “God is divine”, we might expect them to refer to the truthmakers corresponding to such predications. For abstract nominalizations are typically introduced precisely for the sake of referring to the entities corresponding to their concrete counterparts. But if an expression such as ‘God’s divinity’ is understood in this way, then to say that God is identical with his divinity will just be another way of saying that God is identical with the truthmaker for “God is divine”. Likewise, to say that God is identical with his goodness, power, wisdom, and so on—and that each of these is identical with each of the others—will be the same as saying that there is only one truthmaker for each of the true intrinsic predications that can be made of God. Now suppose that the truthmaker in each case is God himself. Then to say that God is identical with his goodness is just to say that God is identical with God. Unlike the claim that God is identical with a property or exemplifiable, however, this claim is perfectly coherent.
The claim that God is the truthmaker for every true intrinsic predication of the form “God is F” not only provides a response to the category problem, but also seems to make the doctrine of divine simplicity attractive in certain ways. In order to see why, consider the sorts of intrinsic predications that can be made about God, beginning with “God is divine”. Like any other statement involving the predication of a thing’s nature, “God is divine” is a case of essential predication. But since God is essentially divine, his existing necessitates the truth expressed by “God is divine” (since if God is essentially divine, he will be divine in all possible worlds in which he exists). But, then, for the very same reason, God himself will be a plausible candidate for the role of the truthmaker of “God is divine”.
Now as it turns out, similar remarks apply to
other such divine predications. For as
traditional theists conceive of him, God is not only good, but essentially good
(or omnibenevolent); likewise, he is not only powerful, but also essentially
powerful (or omnipotent). Indeed, if we accept that aspect of the
traditional doctrine of divine simplicity which requires that all intrinsic
predications of the form “God is F” are cases of essential predication,[33]
then the same remarks will apply to each of
the intrinsic or non-relational predications that can be made about God. This aspect of the doctrine is, of course, controversial and
difficult to square with other aspects of traditional theism, which appear to
imply that God has intrinsic accidental properties (say, in virtue of freely
choosing to do certain things, including responding to human free
choices). Our purpose here, however, is
not to provide a complete defense of divine simplicity, but only to show that
the truthmaker theory of predication (to which one is naturally led by
the conclusions of our arguments in Section I) enables proponents of that
doctrine to avoid the problem that has dominated contemporary discussion of
it—namely, the category problem.
In the end, therefore, it
seems to us that, whatever other
difficulties the doctrine of divine simplicity might have, it can at least be
defended against the standard charge of incoherence leveled by contemporary
philosophers. Indeed, as we have
attempted to show, if one grants to the defenders of this doctrine the
(admittedly controversial) claim that all true divine intrinsic predications
are cases of essential predication, the doctrine actually becomes somewhat
appealing—at least when interpreted within the context of P*. Obviously this by itself does not give us
reason to accept the doctrine. But we
do hope it goes some distance toward showing that the doctrine deserves further
consideration than it has yet received by contemporary philosophers. At
the very least, it shows that critical reflection on the doctrine needn’t be
focused entirely on the category problem.
We have now completed the two projects we set out to
accomplish in the paper: first, to provide a theistic argument against
Platonism (as well as any other theory of predication that accepts P), and
second, to show how this argument provides support for a certain theory of
predication and, to a lesser extent, the doctrine of divine simplicity. We developed our theistic argument against
Platonism in two stages. In the first
stage, we argued for the inconsistency of Platonism with what we take to be the
proper understanding of traditional theism.
In the second stage, we argued that even if we are wrong about the
proper understanding of traditional theism, and it can be understood in some
weaker way, this is irrelevant from the point of view of its consistency with
Platonism.
Although our theistic argument against Platonism proceeded fairly straightforwardly, the support we offered for truthmaker theory and divine simplicity is more indirect. As we suggested, the denial of Platonism seems to lead in the direction of a unified theory of predication, one that does not appeal to exemplifiables. Indeed, it seems to us that once traditional theists have jettisoned P (as they must if they are to remain traditional theists), a very attractive strategy—one that enables us to preserve a unified account of predication—is to accept P* in its place, and with it the view that truthmakers are required to explain the truth of predications. By itself, of course, the truthmaker theory of predication does not support the doctrine of divine simplicity. Nonetheless, it does enable us to make some progress toward understanding it—and more importantly, to remove what has been, at least in recent years, the greatest obstacle to this doctrine’s being taken seriously by contemporary theists.[34]
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[1] For convenience in what follows, we will often speak of “true predications” as shorthand for the more cumbersome (but also more accurate) phrase “the truths (or propositions) expressed by true predications”. The latter, however, is what we always have in mind.
[2] Platonism thus involves what is often called an “abundant” (as opposed to a “sparse”) theory of properties. Of course, philosophers since Russell have been aware that there is one sort of case to which this (or any other such unified) analysis of predication cannot be said to apply, namely, predications involving the predicate ‘is non-selfexemplifiable’. As is well known, the assumption that there is a property corresponding to this predicate immediately leads to paradox (such a property must either exemplify itself or not, but in either case we get a contradiction). In what follows, we ignore this complication and continue to speak of Platonism, as well as any other theory of predication involving an abundant theory of properties, as a general or unified theory of predication, since it assumes that all predications except those leading to Russell’s paradox can be explained in terms of properties or exemplifiables. For an example of a defense of Platonism that is considered by its author to be general and unified in this sense, see van Inwagen 2002.
[3] We can state the inconsistency as follows: Whereas Platonism requires all true predications to be explained in terms of properties, divine simplicity seems to require God to be identical with each of the things that can be predicated of him (more on this below). But then, if both are true, it follows that God is identical with each of his properties and hence is himself a property—which is absurd since, unlike properties, God is a person and persons can’t be exemplified.
[4] Aquinas alludes to this tradition in the first part of the epigraph that begins this paper.
[5] Aquinas refers to this Augustinian view in the second part of the epigraph quoted at the beginning of our paper.
[6] Cf. Loux 1978 and 1998 (for Aristotelian realism), Armstrong 1978, 1989, and 1999 (for immanent realism), Campbell 1980 and 1990 (for trope theory), and Morris 1987 (for the Augustinian view).
[7] Hence, the argument will also work against those who understand predication in terms of property instances—that is, concrete individuals standing in a special relation (namely, instantiation) to the universals of which they are the instances—as well as against those who understand predication in terms of sets and conceive of sets as exemplifiables. For a property-instance conception of exemplifiables, cf. Mann 1982 and 1983; for a set-theoretical conception of exemplifiables, cf. Oliver 1996, pp. 21-25.
[8] We should
note up front that, in presenting this argument from traditional theism against Platonism and in defense of divine simplicity, we are not thereby committing
ourselves to either the falsity of Platonism or the truth of divine simplicity,
despite the fact that we are both theists.
One can always avoid rejecting
Platonism merely by availing oneself
of a version of nontraditional
theism, according to which things such as necessarily existing exemplifiables
are not dependent on God. (See Wolterstorff 1970 for a defense of such
a view.) Moreover, in the case of
divine simplicity, one would
have to do more than defend it
against the dominant contemporary objection it faces (which is all we do here)
to show that it is ultimately defensible.
[9] For further defense of the claim that traditional theism includes the aseity-dependence doctrine, see Morris 1987. Cf. the discussion of the ‘Sovereignty-Aseity Intuition’ in Plantinga 1980, pp. 28-37 and the discussion of the ‘Ultimacy Assumption’ in Leftow 1990b, pp. 584-592.
[10] Again, we ignore complications arising from Russell’s paradox. Cf. note 2 above. Here again it’s important to emphasize that when we speak of “the truth of all true predications” we have in mind the truth of the truths expressed by such predications (rather than the predications themselves).
[11] See Morris 1987. Morris reminds us that false propositions aren’t beliefs God has. They are thoughts that are considered and denied, not ones that, like true propositions, are considered and affirmed.
[12] Morris 1987, pp. 174-75.
[13] As Morris points out (1987, p. 176), this is a trivial consequence of the fact that both God and his nature are necessary beings.
[14] We discuss the notion of logical priority below.
[15] Brian Leftow has drawn our attention to his own intuitive statement of a similar argument (though his argument is for a less general conclusion). See Leftow 1990a, p. 201.
[16] Notice that A2 says that abilities are logically prior to their being
exercised (i.e., to doings). This should not be confused with the claim
that potentialities are logically prior to actualities (i.e., that x's being
possibly F is logically prior to x's being F). Our point here is not that the latter claim
is false (we aren’t taking a stand on that), but rather that A2 (on which we are
taking a stand) should be distinguished
from that latter claim.
[17] It might be objected that our claim that parts are logically prior to wholes does not hold for Morris’s materialization machine, which creates its own parts. After all, doesn’t it present us with a case of a whole explaining the existence of its parts? Not in the relevant sense. To see why not, we need to employ time indices. Using them, the more careful way to state our claim in the text is this: the existence at t of the parts of a watch partially explains the existence at t of the watch itself, whereas the existence at t of the watch does nothing to explain the existence at t of the parts. Here is the parallel claim with respect to the materialization machine: the existence at t of the parts of the materialization machine partially explain the existence at t of the machine but the existence at t of the materialization machine doesn’t even partially explain the existence at t of its parts. As we understand the example of the materialization machine, the claims in the previous sentence are true because the machine’s creating and sustaining activities are temporally prior to the created or sustained existence they produce. If we are mistaken about this, and the example is, instead, to be understood as lacking such temporal priority, then the example seems to us to be incoherent—as incoherent as the suggestion that something can cause itself to come into existence from nothing.
[18] God’s existence doesn’t itself produce the thoughts. That’s why we say God’s existence is only a partial explanation of the existence of his thoughts.
[19] Of course the having of an ability isn’t sufficient by itself to explain its exercise. Here again, therefore, we speak of only a partial explanation.
[20] We take for granted here that God isn’t an exemplifiable, from which it follows that all exemplifiables are distinct from God. Cf. Brower 2002 for discussion of this topic.
[21] Although we shall not dwell on the point here, it is worth noting that arguments parallel to the one just given might be constructed for the conclusion that traditional theism is also incompatible with abstract objects of other kinds (such as certain propositions and certain states of affairs). Our argument draws attention to the fact that a certain exemplifiable—namely, being able to create an exemplifiable—has to be both logically prior and logically posterior to God’s exemplifying it. It has to be logically posterior to God’s exemplifying it because God’s exemplifying it is a prerequisite for God’s creating any exemplifiable (and, hence, for any exemplifiable). But it also has to be logically prior to God’s exemplifying it because, as A3* makes clear, every exemplifiable is logically prior to (because it is a constituent of) its exemplification. It seems that something similar can be said with respect to propositions. Consider the proposition God is able to create a proposition. Apparently, this proposition must be both logically prior and logically posterior to its being true. It has to be logically posterior to its being true because its being true that God is able to create a proposition is a prerequisite for God’s creating any proposition (and, hence, for any proposition). But it also has to be logically prior to its being true because of a general principle, much like A3*, according to which every proposition is logically prior to (because it’s a constituent of) its being true. A similar sort of argument could be constructed in connection with the relationship between the abstract state of affairs God’s being able to create a state of affairs and its obtaining.
[22] This sort of response was brought to our
attention in discussions with Jan Cover and Michael Rea.
[23] Cf. also the references cited in note 9 above.
[24] Such philosophers standardly assume that distinct predications can be made true by the same truthmaker—so that, for example, “Socrates is human”, “Socrates is an animal”, and “Socrates is human or the moon is made of green cheese” can all have the same truthmaker (namely, Socrates), despite the fact they differ in meaning and logical form. For discussion and defense of this assumption, see Armstrong 1978, vol. 2, pp. 7-18, 52-59, and Mulligan, Simons, and Smith 1984, pp. 295-304.
[25] See, e.g., Armstrong 1997, p. 13.
[26] Bigelow 1998, p. 126.
[27] Cf. Rodrigue-Pereyra 2000, p. 260; Bigelow 1988, p. 126; Fox 1987, p. 188; and Oliver 1996, p. 69.
[28] Cf. Restall 1996 for an attempt to answer this question by appeal to “relevant” entailment, and Smith 2002 and 1999 for an attempt answer it without such an appeal.
[29] It might seem objectionable that we contrast P* with P (which is endorsed by Platonism and other theories of predication) by calling the former ‘a truth-maker theory of predication’. For P might itself seem to be a form of truth-maker theory in that, like P*, it aims to explain why certain predications are true by saying what makes them true (namely, a subject and an exemplifiable).
It is important to recognize, however, that in addition to explaining the truth of certain predications (or the truths expressed by them), P* invokes the notion of a truthmaker in another more fundamental way. The suggestion made by P* is that the most important feature common to all truth-makers for claims of the form ‘The truth expressed by predication X is true’ is just that they are truth-makers. But according to P, there is another more important feature that all such truth-makers have in common, namely, that they involve a subject and an exemplifiable. It is only because P* invokes the notion of a truth-maker in this second way that we call it (but not P) a ‘truth-maker theory of predication’.
[30] Since we are primarily concerned in what follows only with affirmative (atomic) predications of the form “a is F”, our statement of P* ignores the difficulty associated with claims such as “a is not F” and “there are no Fs”. These sorts of claims are often thought to be the undoing of truthmaker theory, since the only candidate truthmakers for them appear to be negative facts like a’s not being F and there not being any Fs. Appealing to negative facts, however, strikes many as extremely implausible. As David Lewis (1999, p. 204) points out: “It seems, offhand, that [such claims] are true not because things of some kind do exist, but rather because counterexamples don’t exist.” It is important to note, however, that we could take account of these and other related difficulties in a way that is, at least in the spirit of truthmaker theory, by modifying our account of predication as follows. First, we could divide all (atomic) predications into two sorts: (A) those (like ‘there are no Fs’) whose candidate truthmakers are negative facts (e.g., there not being any Fs) but whose denials (‘there are Fs’) are such that the candidate truthmakers for them are not negative facts but entities of some kind (namely, one or more F); and (B) those (like ‘a is F’) whose candidate truthmakers are entities of some kind (say, the individual a, or a non-transferable trope of F-ness, or the fact that a is F) but whose denials (‘a is not F’) are such that the only candidate truthmakers for them are negative facts (a’s not being F) . With this division in mind, we could then say that (A)-type predications will be true just in case there is no truthmaker for their negation and that (B)-type predications will be true just in case they have a truthmaker. In line with this, P* could then be revised as follows:
P**: All
true predications are such that either their
truth can be explained in terms of truthmakers or the falsity of their
negations can be explained in terms of the absence of truthmakers.
For further development and defense this sort of truthmaker theory, see Bigelow 1998, 128-134 and especially Lewis 2001.
[31] See Armstrong 1997 and 1989.
[32] See Armstrong 1989, esp. 116-119. For a more complete development and defense of this view, see Mulligan, Simons, and Smith 1989.
[33] See, e.g., Aquinas’s remarks in Summa
Theologiae Ia, q. 3, a. 6 for a defense of this aspect of the
doctrine.
[34] For comments on earlier drafts, we are grateful to Susan Brower-Toland, Jan Cover, Martin Curd, Brian Leftow, Trenton Merricks, Alvin Plantinga, Michael Rea, Michael Rota, William Rowe, Paul Studtmann, and Dean Zimmerman.