Another version of divine simplicity

as I promised in the comments on rock*'s last post, here are some of my
notes on divine simplicity.  If I remember correctly Aquinas seemed to
hold something like the following views:

1.  God has no proper parts
2.  God has exactly one divine attribute
3.  Amongst God's attributes are his omniscience, omnipotence and
omnibenevolence.  
4.  God is identical to his one divine attribute.  

From (2)-(4) it follows that

5.  God = God's omniscience = God's omnipotence = God's omnnibenevolence.  

Now, you might think that there is a complex God property that is
built up out of omniscience, omnipotence and omnibenevolence.
God's omniscience, omnipotence and omnibenevolence would then
just be identical to this complex God property.  However, this seems
to be ruled out by (1) and (4) above.  This is because if the God
property were built out of omni-p, omni-s and omni-b, then it would
have parts.  But that claim, along with (4) entails that God has parts. 
But, (1) says he does not.  

Here is a solution.  In my paper "A tale of two simples" I talk about a
distributional properties explanation of the following seeming
possibility:

(*) Possibly, there is an extended, heterogeneous atomic object that
occupies a region with no proper subregions.  

trypically a person who believes in extended heterogeneous simples
will connect property exemplification to regions in some way.  So, for
example, if the person believes that possibly there is a striped red and
purple atomic object, then he will say that that object has red-at-R and
Purple-at-R*.  But, this will not help to explain (*) since the atomic object
in (*) occupies a region with no proper sub-regions.  

According to the distributional properties approach, there are fully
determinate distributional properties that guarantee the seeming
heterogeniety of such a simple.  These are properties like polka-
dottedness but they are not built up out of "smaller" color properties.
Rather the smaller properties are built out of disjunctions of these
distributional properties.  

One thing that I noticed is that God seems to be heterogeneous in some
sense: he seems to be both omniscient and omnipotent.  But, God, is an
atomic object as well and there is nothing we can index his omniscience
and omnipotence to.  This situation looks rather similar to the situation
of a heterogeneous simple that occupies an atomic region of space.  So,
here is a view about divine simplicity:  

There is one God property that is like a distributional property.
Exemplifying that God property guarantees the seeming distribution
of omnipotence and omniscience.  But, there really aren't these "Smaller"
properties (except insofar as they are built up out of the disjunctions of
the fully determinate God property).  On this view God's Omniscience and
Omnipotence are just identical to this distributional property.  Moreover,
we could connect this view to a bundle theory of individuals and get that
this single God Property just is God himself.

A Non-Stupid Version of the Doctrine of Divine Simplicity (or Something Like It, at Least)

Jonathan Schaffer has recently argued that the traditional debate concerning monism was a debate concerning whether the first of the following theses is true rather than a debate over whether the second is true:

Priority Monism (PM): The world is fundamental (i.e., is a substance in the traditional sense--it does no depend on anything else for its existence), while every proper part of the world depends on the world for its existence.

Existence Monism (EM): The world has no proper parts.*

Now I think that (PM) and (EM) are both false (or at least have serious doubts about their truth), largely because I am inclined to think that "the world" is a non-denoting definite description; that is, I am inclined to say that there is no such thing as the world. Schaffer's paper is still quite interesting, however. Furthermore, my most recent reading of it made me think about whether there are any connections between Schaffer's discussion and the doctrine of divine simplicity.

The doctrine of divine simplicity is usually formulated as follows:

The Doctrine of Divine Simplicity (DDS): God has no proper parts and each of God's properties is identical to God.

(DDS) is, I think, a pretty bad view (and not just because the view that there is such a thing as God is a pretty bad view). Assuming that God exists, it does not seem implausible that God has proper parts. (One heterodox interpretation of the doctrine of the Trinity is that God has the three persons of the Trinity as proper parts, which contradicts (DDS).) Worse, if (DDS) is true, then:
-God is a property,
-God instantiates himself, and
-I instantiate God. (After all, both God has the property of being self-identical. So, if (DDS) is true, then God is identical to the property of being self-identical. But I instantiate the property of being self-identical. Therefore, if (DDS) is true, then I instantiate God.)

Now what Schaffer's paper got me wondering about is this. Consider the following thesis:

The Doctrine of Divine Simplicity* (DDS*): Every proper part of God and every property of God depends on God for its existence.

While (DDS) is the analogue of (EM), (DDS*) is the analogue of (PM). So if the traditional debate concerning monism was a debate concerning the truth of (PM) rather than the truth of (EM), then perhaps the traditional debate over the divine simplicity was a debate concerning the truth of (DDS*) rather than the truth of (DDS). Furthermore, even if the traditional debate over divine simplicity was not a debate about the truth of (DDS*) but was rather a debate about the truth of (DDS), (DDS*) is a more plausible thesis than (DDS). For one thing, suffers from none of the problems for (DDS) noted above. For another, it is strongly suggested by other, not terribly implausible, traditional views.

Take the claim that every proper part of God depends on God for its existence. As Schaffer argues, Aristotle--and presumably Aquinas as well--held that each of a living thing's proper parts is dependent upon that living thing for its existence. Thus, given the claim that God is alive, which I take to be a traditional view, it follows that every proper part of God depends on God for its existence.

Next, take the claim that every property of God depends on God for its existence. According to one traditional view, properties depend upon the schmubstances that instantiate them for their existence. (A schmubstance is a substance in Aristotle's second sense; that is, it is something that has properties (or stands in relations) but is not itself a property (or a relation).) Thus, according to this view, the property of being green depends upon the green schmubstances for its existence; this is a dependence relation that obtains between a property and a plurality. Now take any property P of God. According to this view, P depends for its existence on the schmubstances that instantiate it, bbs, and God is one of bbs. Now this doesn't quite get us to the view that P depends on God for its existence. Rather, it gets us to the view that P depends on bbs for its existence, and although God is one of bbs, another schmubstance may also be one of bbs. However, another traditional view is the view that every other schmubstance depends upon God for its existence. And the following is a plausible principle: for any x, y, and zzs, if x depends on zzs for its existence and each thing that is one of zzs is either identical to y or depends on y for its existence, then x depends on y for its existence. It follows from this principle, the claim that properties depend on the schmubstances that instantiate them for their existence, and the claim that every other schmubstance depends on God for its existence that P depends upon God for its existence. But P was an arbitrarily chosen property of God. So it follows from that principle and those two traditional (and not terribly implausible) views that every property of God depends upon God for its existence.

Putting the conclusions of the last two paragraphs together, both the claim that every proper part of God depends on God for its existence and the claim that every property of God depends on God for its existence follow from traditional, and not terribly implausible, views (plus a very plausible principle concerning pluralities and dependence). But these two claims together entail (DDS*). So (DDS*) follows from traditional, and not terribly implausible, views.


*See "Monism", available on Schaffer's website, for his argument. My formulation of existence monism differs from the formulation Schaffer gives. Schaffer's formulates existence monism as follows: For all x, x is identical to the world. My formulation is superior to Schaffer's because, at least as I interpret him, Schaffer does not take the world to be the mereological fusion of absolutely everything. Rather, he takes it to be the mereological fusion of absolutely every concrete entity. Given this, the debate concerning existence monism is, it seems to me, a debate over whether the fusion of absolutely every concrete entity has any proper parts, and thus evidence in favor of the existence of abstract entities is irrelevant to the debate. However, given Schaffer's formulation, evidence in favor of the existence of abstract entities is relevant to the debate. An alternative formulation of (EM), given that the world is the mereological fusion of absolutely every concrete entity, is: For all concrete entities x, x is identical to the world.

Necessity and Natural Species Kinds

There are some natural species kinds. for example, Tiger is a natural species kind and Kangaroo is a natural species kind. We tend to make certain claims about these species. For example, we say that Tigers are striped. Whatever the literal content of this claim, it seems we are trying to convey that the species tiger has a certain property related to being striped. For simplicity, let's restate this conveyed truth as one that is explicitly about the species tiger. We can introduce a new predicate, 'striped*' to be whatever property the species has in virtue of which it is acceptable to say that tigers are striped. Now we can explicitly say that the species tiger is striped*. One thing to point out is that it is sometimes acceptable (though perhaps not true) to say that Tigers are striped even though some tiger is not striped. Similarly, it may be true that the species tiger is striped* even though some tigers are not striped (no '*' intended). Now, I am wondering whether it is necessary that the species tiger is striped*.

Here is an argument against that position. Tigers have a certain genetic makeup. Tigers have genes G. We can introduce the new predicate 'has genes G*' to express the property that the species has in virtue of which it is acceptable to say that Tigers have genes G. So, the species tiger has genes G*. But, tigers don't all have the same genetic makeup. There is always genetic variation within a species. Indeed, although the species tiger has genes G*, it seems like there may well be a tiger that lacks genes G* in virtue of having a very slightly different genetic makeup. If more tigers had been like that particular tiger, then it would not have been true that the species tiger has genes G*. The species tiger is susceptible to small variations in genetic makeup*. Moreover, this will be true across some set of possibilities. But, small changes add up to big ones and given that what is possibly possible is itself possible, it follows that the species tiger might have had a genetic* makeup significantly different than G*. In fact, that genetic makeup* might ground the truth that the species tiger is not striped*. Hence, it might be acceptable to say that Tigers are striped, but tigers might not have been striped.

Some of you might recognize that this is related to the Salmon's argument against S5. Of course, there are various responses to that argument and those responses would probably carry over to this argument as well. But I wanted to point out one thing that might follow if we accept the argument I have just presented. It seems that we can have small genetic variations that add up to drastically differences. If that is right and we accept the kind of argument that I just presented above, then it might follow that the species tiger could have been just like the way that the species kangaroo actual is. Moreover, If the species tiger could have been like the way the species kangaroo actually is, then a particular tiger could have been just like a kangaroo. But, if it could have been just like a kangaroo, then it could also have been a kangaroo. Hence, tigers are not essentially tigers. I know this argument goes pretty quickly, but it seems rather interesting to me.