Monday, September 22, 2014

The Simplicity of God: Objections and Responses

This is a post discussing the objections to Step 2 in the ongoing series setting forth a proof on the simplicity of any unconditioned reality.


In the First Step of the argument for the existence of God, we established that if there exists any reality, there exists an unconditioned reality. That step established that if anyone asserts that something exists, but denies the existence of an unconditioned reality (i.e., a reality that is utterly independent of any other reality), one is caught in self-contradiction.

The Second Step of the argument establishes than an unconditioned reality, considered in itself, must be 1) without parts, 2) absolutely simple (i.e., it possesses no intrinsic or extrinsic boundaries and has no actual or potential incompatible states with any other reality) and 3) infinite. From the necessarily simple and infinite nature of an unconditioned reality, several other features--eternity, independence of the laws of physics, and immutability--followed.

Can an Unconditioned Reality be Spatial?

The only sustained criticism of the second step concerned the argument that an unconditioned reality cannot be composed of parts. The original post did not define the notion of a part, but a subsequent edit added that definition. The addition of the definition renders the objections raised superfluous. I do believe, however, that a quick reformulation of the argument as it relates to spatial extension will be useful.

Extended Spatial Realities Have Parts

A part is defined as:
any aspect belonging to a reality that is distinct in any way from any other aspect of that reality. (2.1a) 
The question, then, is does a spatial reality necessarily have parts?

If a spatial reality is extended, it has parts. For if A is a spatial reality, it means that some aspect of A has a distinct location from some other aspect of A. If A had no aspects that were distinct in terms of location, A would be a non-extended point. Thus, if a reality is extended, it is composed of parts.

Pure Unconditioned Reality Has No Parts

Can an unconditioned reality be composed of parts? We can distinguish two types of parts: parts upon which a reality depends and parts upon which a reality does not depend. Take a trivial example: my existence currently depends upon my brain. However, my existence does not depend upon my hair. I can go on existing if I shave my head, but I cannot go on existing without my brain. We can break the question down into two parts: can an unconditioned reality have parts upon which it depends? And can an unconditioned reality have parts upon which it does not depend?

An unconditioned reality clearly cannot have parts upon which it depends, for an unconditioned reality cannot be dependent upon any other reality. (1.1 and 1.3) Remember that a reality is defined as broadly as possible: if you can say of x either, "there is an x ..." or "it is not the case there's no such thing as x ...", x is a reality.

Can an unconditioned reality have parts upon which it does not depend? We've left the answer open: possibly it can. However, when we speak of "pure" unconditioned reality or an unconditioned reality considered in itself, we mean the unconditioned reality as it is independent of such parts. Thus, while we leave open the possibility that it might be in some sense true that an unconditioned reality might possess non-essential parts, we speak of unconditioned reality in itself as it is independently of these parts.

(Christians will obviously want to maintain that an unconditioned reality can take on non-essential parts, as it opens the way for the Incarnation.)

We can conclude from the above that an unconditioned reality, considered in itself, does not have parts. Thus, pure unconditioned reality is not spatially extended. (Note that nothing new from Step 2 has been introduced, the premises have just been shuffled to deal specifically with the issue of spatiality.)

What of Non-Extended Spatial Realities?

Yet there is one final possibility: though an unconditioned reality cannot be spatially extended, can it be a non-extended spatial reality? That is, can it be a point? We again answer no; for a non-extended reality to still be spatial, it must be in some way located spatially. It must be here instead of there. 

Yet for this to be true, such a reality depends upon the space in which it can be located here instead of there. A reality that is non-extended and not located in space would be extra-spatial. Thus, such a reality is necessarily conditioned. But no unconditioned reality can be conditioned. Therefore, no unconditioned reality can be a non-extended spatial reality.

We have established that pure unconditioned reality cannot be an extended spatial reality, and it cannot be a non-extended spatial reality. We must conclude, then, that if a reality is unconditioned, it is neither extended, nor located in space. To be neither extended nor located in space is to be extra-spatial. Therefore, a pure unconditioned reality is extra-spatial.

An Alternative Argument for Immutability and Extra-Temporality

Step Two offers an argument for the non-temporality and immutability of any pure unconditioned reality. However, there is an alternative proof that is, to my mind, even more effective.

One could rearrange the immutability and temporality premises and make the argument differently. A reality, to be mutable, must be able to change (by definition). To be able to change, a portion of the reality must be in a state of potentiality—i.e., not x but able to become x. Yet any reality, to exist at all, must be actually in some state. 

Therefore, a reality, to be changeable, must be in some respect actual and in another respect potential. Potentiality and actuality are two distinct aspects of a reality, distinguished by modality. It follows that any mutable reality has parts. But no unconditioned reality, considered in itself, has parts. Thus, no unconditioned reality is mutable. (2.4) 

Now, time is either a reality independent of other realities or an aspect of those realities. No unconditioned reality can have time as a condition. Therefore an unconditioned reality cannot essentially be in time. Nor can time be said to be an aspect of an unconditioned reality in itself, for unconditioned realities, in themselves, do not change. (2.4) An unconditioned reality is non-temporal in the sense that it does not depend upon time, does not change in time, and does not have its own time (in terms of a sequence of states).


Anonymous said...

I returned to step 1 and I am having trouble with the definition of a reality.

1.1 A conditioned reality is any reality whose existence depends in any way on some other reality. "Reality" is used very broadly here. It means not only material objects, but also physical laws, space, time--in short, anything that can be described as really existing.

As I understand this broad definition of reality, then the the number one is a reality. If "one" is a reality, upon what does it depend?

Thomas M. Cothran said...


It would depend on your metaphysics: a Platonist would regard "one" as a reality. A reductive materialist, arguably, would not (even with the broad definition).

This argument doesn't take any particular metaphysical stance. It works whether you think there are such things as ideal objects or not.

For example, if you are a classical materialist and believe the only realities are atoms and the void, you have a set of conditioned realities. The argument presented here would show that it is self contradictory to assert these conditioned realities exist and that there is no unconditioned reality.

If you are a Platonist of some stripe, you have a broader set of conditioned realities. The argument still works just the same.

That's the beauty of the argument: it is independent of any particular metaphysical stance about what really exists.

Anonymous said...

OK, so if I assume that "one" is a reality, then upon what does it depend?

I feel that "one" is unconditioned reality. I can't see upon what it depends.

This seems too simple to me. What am I missing?

Thomas M. Cothran said...

Perhaps you're a neo-platonist: for Plotinus, the One is the God of theism--the eternal, infinite source of all that is.

Step 1 just demonstrates that there is at least one unconditioned reality.

Step 2 deals with what an unconditioned reality is. That argument shows that an unconditioned reality is, among other things, without boundaries or incompatible states. Plotinus' "one" meets the criterion of simplicity and infinity.

But if you just mean "one" in the sense of an ordinal, it seems clear that one has boundaries two does not (or vice versa). Step 2 shows that an unconditioned reality is necessarily without boundaries of any sort. It would follow that the number one is not an unconditioned reality.

If you insist on one being a conditioned reality, you'd need to show where the logic of Step 2 breaks down. If you like, I can reshuffle the premises of step 2 to show you the argument as it relates to an ideal object like a number.

In any case, I'm not sure why you're insistent that "one" is an unconditioned reality. It seems fairly obvious that as an abstract object it depends on there being some intelligence there to think about it, and as a concrete substantiation it depends on there being some physical object of a certain structure. Even if you go the Platonist route to say that abstract objects have an existence independent of real physical things, Platonists still regard finite intelligible realities as dependent upon the divine.

Martin Cothran said...

Anonymous (and Thomas):

Is "one" being used here as one of the metaphysical transcendentals (i.e., the true, the good, being, and the one--and, according to whose list you're using, the beautiful)?

I haven't thought this through, but if it is a transcendental, then it is a universal property of being. Is a universal property of being an unconditioned reality?

Anonymous said...

I am sorry guys, but you are putting more meaning into my question than I intended.

I don't know the metaphysical "one" is, but I was meaning the number between zero and two.

I don't think one depends on anything. I think the number one is a unconditional reality. But reading your argument this must be wrong. What am I doing wrong here?

Thomas M. Cothran said...


(I'm assuming you understand the argument that unconditioned reality must be absolutely simple, infinite, etc., and are just asking how numbers can be conditioned by other realities. If it's unclear why numbers can't be unconditioned by the terms of the argument, I'd be happy to explain that too.)

If you just mean that numbers are unconditioned, let's choose a number other than one, which is a synonym for simplicity. So if we're talking just about about numbers, let's choose 10.

It seems plausible to me that 10 is only a reality under two conditions: there are 10 of something, or the notion of 10 has been abstracted by some mind. If there are 10 ducklings, for example, it seems clear that the tenness is dependent upon there being ten ducklings. If a hawk swoops down and eats one helpless duckling, there are no longer 10 ducklings. 10 in this case is dependent upon the physical world.

What of the number 10 abstracted from anything in the physical world? We can think about 10 without thinking about 10 of anything. In this case, 10 has mental rather than physical existence. I can think of a unicorn, and a world where unicorns are thought of is different than a world where unicorns aren't thought of. Yet unicorns don't physically exist, they exist only in thought. Unicorns are conditioned by thought.

Similarly, if the number 10 exists, it exists either in thought (as when I think of 10-9=1), or in the physical world (the ducklings example), or in both (if I think about the ten ducklings). But if there is no thought and no physical world, it is hard to think of 10 as real, except insofar as we are thinking of it (and thereby granting it mental existence).

The plausible answer seems to be that numbers are dependent on either physical or mental realities.