This is the second step in a proof for the existence of God that has been the subject of an ongoing series. In the First Step, we deduced the existence of at least one unconditioned reality. This argument draws heavily on Robert Spitzer’s New Proofs for the Existence of God.

In the first step, we saw that if any reality exists—any reality at all—there must be at least one unconditioned reality. In this article, we will be drawing out the consequences of this with respect to simplicity. We will see that an unconditioned reality must be absolutely simple.

The term “simplicity” is a term of art. In common parlance, simplicity often means something like the lack of content or what is easily understood. We naturally consider “1”, for instance, to be simpler than the operation “1+1” or the number “32.” “Simplicity,” as we will use the term here, will not mean what is easy to understand or what lacks a richness of content. Simplicity will be used in an ontological sense to mean that which is without parts, boundaries, or incompatible states.

An Unconditioned Reality Lacks Parts

Let’s begin with the proof for the following claim:

2.1 An unconditioned reality, considered in itself, cannot have parts.

A part is defined as follows:

2.1a A part is any aspect of a reality that is distinct from any other aspect in any way.

It is important to note how broad the definition of a part is. A part could be something that exists at a different location, has a different function, or a different modality (actual instead of potential, for example).

The principle in 2.1 follows swiftly from the definition of an unconditioned reality (1.2). Consider the following indirect proof.

2.1.1 A part is either necessary to the existence of the whole, or not. (Bifurcation)

Assume an unconditioned reality, “UR.” If “UR” has a part necessary to its existence, UR depends for its existence on another reality (i.e., condition). But then UR is not an unconditioned reality. (1.2) This is a contradiction. Therefore, it cannot be the case that a reality is both unconditioned and depends for its existence on some part. Thus we can conclude:

2.1.2 An unconditioned reality cannot have a part necessary to its existence.

Now let us see if an unconditioned reality, considered in itself, can have a part on which it does not depend for its existence. Assume an unconditioned reality, “UR.” Assume that UR has a part, “p,” on which it does not depend. UR exists even if p does not. But if UR’s existence is independent of p, UR considered in itself, does not include p. Therefore we can conclude:

2.1.4 An unconditioned reality, considered in itself, is a reality independent of unnecessary parts.

This establishes 2.1. UR cannot have a necessary part. (2.1.2). If UR has an unnecessary part, that part is distinct from UR in itself. (2.1.4) Therefore, an unconditioned reality, in itself, does not have parts.

From this simple proof, we can draw several sweeping conclusions. First, an unconditioned reality cannot be a spatial reality. A spatial reality is either extended or non-extended. Any extended spatial reality has spatial extension, and any extended thing has parts. (If A is spatially extended, it must have at least two aspects that are spatially distinct from one another.)

A non-extended spatial reality is a point. It has a location in space, and is therefore limited by space, but it is not extended, and therefore has no parts. However, no unconditioned reality can be a point, for to be a point, there must be the reality of space. Any non-extended spatial reality depends upon space, and is therefore conditioned. Thus, a spatial reality either has parts (and for this reason cannot be unconditioned) or it has no parts, in which case it is conditioned by the reality of space. An unconditioned reality, considered in itself, can have neither extension nor location in space. In this sense, therefore:

2.2 An unconditioned reality, considered in itself, is not a spatial reality.

Similarly, an unconditioned reality cannot be a temporal reality. A temporal reality either consists of a duration or it doesn’t. If it is a duration, it extends through space and has parts. (For example, if A is temporal, its existence stretches from time 1 to time 2, which is distinct from the stretch from time 2 to time 3.)

What of an instant in time? If any non-extended instant exists in time, at this point in time and this point alone, it would depend upon the reality of time. But an unconditioned reality is by definition not dependent. Therefore, no unconditioned reality could be extended (because it would have parts) or non-extended (because it would be conditioned by time). Thus, we can conclude

2.3 An unconditioned reality, considered in itself, is not a temporal reality.

From 2.2 and 2.3 we know that any unconditioned reality is super- or extra- spatio-temporal. This allows the deduction of the immutability of unconditioned reality.

The proof for immutability runs as follows. Any change occurs in time: A thing has property x at time 1, and property y at time 2. However, an unconditioned reality is not a temporal reality. (2.3) Therefore an unconditioned reality, considered in itself, does not suffer change. So we can conclude

2.4 An unconditioned reality, considered in itself, is immutable.

Alternative Argument for UR’s Extra-Spatiotemporality and Immutability

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).

Note that none of this entails that an unconditioned reality could not have conditioned, non-essential parts, such as, for example, the Eastern Orthodox concept of the divine energies. Furthermore, it could be the case that an unconditioned reality could become conjoin with conditioned realities in such a way that it takes on spatially limited properties. All that is proved here is that an unconditioned reality, considered in itself, is not spatially limited, immutable, and so on.

Absolute Simplicity

We have established that an unconditioned reality, in itself, is simple in the sense that it has no parts. Let’s extend this notion of simplicity further to include its limit: absolute simplicity.

2.5 “Absolute simplicity” means that reality which utterly lacks a) boundaries and b) incompatible states with other realities.

This definition of absolute simplicity clearly turns upon the twin notions of boundaries and incompatible states. The two notions are closely connected, as a few examples will show.

Consider the boundaries of a given square: it has four equilateral sides and four right angles. The boundaries of a square conflict with the boundaries of a circle, giving rise to an incompatible state: no X can be both square and circular at the same time and in the same respect.

Note that boundaries operate as restrictions. The boundaries of a square restrict the kinds of angles a square can have qua square. No square can have a 72 degree angle.

Examples from Contemporary Physics

Let’s move from geometry to physics. One of the electron’s boundaries is its repulsion of other other electrons. An electron qua electron repulses other electron. Protons, on the other hand, attract electrons. The boundary conditions of protons and electrons conflict with one another. This means that protons and electrons are incompatible states: nothing can be both a proton and an electron at the same time and in the same respect, if for no other reason that nothing can both attract and repel an electron at the same time and in the same respect. Boundaries give rise to incompatible states.

Although a proton and an electron are incompatible states, they can interact with each other through a simpler reality—the electromagnetic field. The greater simplicity of the electromagnetic field’s state entails not only the compatibility between the electron and the field, but also permits the interaction between the electron and the proton. Beings with incompatible states or boundaries can interact through simpler realities.

The Tree of Being: An Illustration

Fr. Spitzer uses the notion of the “tree of being” as a way of representing the relations of exclusion, incompatible states, and simplicity. The tree of being is one way of illustrating the principle of simplicity, rather than being part of the argument.

A simpler reality has fewer boundaries than does a less simple reality. Spatial extension, for example, is more simple than a square, for it has fewer boundaries. Spatial extension is compatible with a square, but it is also compatible with a circle. Spatial extension is a simpler reality than the square and the circle, being compatible with both but not having the limits (boundaries) of either. Furthermore, the square and the circle, though they are incompatible states, can relate to each other through the simpler reality of the spatial field (for example, by being side by side).

We can represent these relationships of boundaries and simplicity as forming a tree:

Spatial extension
/ \
/      \
Square   Circle

Fr. Spitzer calls this the tree of being. The example he uses, however, is that of the proton and the electron. As we saw, the boundaries of the proton and the electron means that they are incompatible states. However, protons and electrons are both compatible with electromagnetic fields. Electromagnetic fields are, therefore, simpler realities in this respect, because they have fewer boundaries, and thus fewer incompatible states. Due to the greater compatibility of an electromagnetic field, lower realities can interact with one another.

This can be represented as follows

Electromagnetic field
/ \
/     \
Proton Electron

There are two ways of distinguishing realities that can be seen visually on the tree of being. One is through greater simplicity—e.g., the proton can be distinguished from the electromagnetic field by greater simplicity—and the other is through incompatible states—e.g., the proton and electron.

There are two types of simplicity: simplicity in act and simplicity in potency. Simplicity may be had by either lack or plenitude. For example, 0 is a simple reality, but its simplicity is that of potentiality or lack. It is simple, because it lacks actualities that give rise to boundaries or incompatible states. As Fr. Spitzer puts it, “Zero has no boundaries because it signifies ‘the absence of reality in which boundaries can inhere.’” Such simplicity is had in the absence of reality. Thus:

2.7 Absolute simplicity in potency utterly lacks any reality or actuality.

Simplicity in act, on the other hand, does not have boundaries because it does not have limitations on its act or power. Absolute simplicity in act, as Fr. Spitzer puts it, “would then refer to act or being without any intrinsic or extrinsic parameters, boundaries, or restrictions, that is a being capable of acting in any and all non-contradictory ways.” Simplicity in act arises as the plenitude of unbounded reality.

A simpler reality (in act) will have fewer boundaries and therefore greater compatibility or inclusivity with other realities lower in the tree of being. An absolutely simple reality is, by definition, utterly without boundaries or incompatible states, and therefore is compatible with all other realities. (The question remains, at this point, whether there is any absolutely simple reality.)

Boundaries: Intrinsic and Extrinsic

We are now reaching the latter part of Step 2, namely, the question of whether an unconditioned reality is absolutely simple. In order to approach the question of whether an unconditioned reality is utterly simple, we need to determine whether it has any intrinsic or extrinsic boundaries.

An extrinsic boundary is a boundary that separates a reality from another (external) reality. An intrinsic boundary is a boundary internal to that reality. An intrinsic boundary gives rise to parts. For example, the boundaries of my heart exclude the boundaries of my liver (in terms of spatial location, function, material composition, and so on), and so the two are distinct parts. However, we discovered that an unconditioned reality, considered in itself, does not have parts. (2.1) Therefore, an unconditioned reality cannot have intrinsic boundaries.

Can an unconditioned reality have extrinsic boundaries? That is, can an unconditioned reality have boundaries that distinguish it from other realities? The answer is no. This can be shown by the following indirect proof.

Assume that an unconditioned reality, UR, does have extrinsic boundaries distinguishing it from a given reality, R. UR and R are incompatible realities. R’s existence entails a state of ~UR, just as a square’s existence entails a state of ~circle. However, if there is a state ~UR, it must either be the case that ~UR obtains everywhere or is spatially or temporally limited. If ~UR obtains everywhere, then we have a contradiction. It can’t be the case that both UR and R exist.

But it also cannot be the case that the state of ~UR is limited to one place or time where R exists, while elsewhere there is a state UR—for then UR would be limited by space or time. But we saw that no unconditioned reality is limited spatio-temporally. (2.2 and 2.3). We can conclude that UR can have no extrinsic boundaries with any existing realities:

2.8 No unconditioned reality has extrinsic boundaries excluding any existing reality.

Notice this argument does not demonstrate that an unconditioned reality has no boundaries whatsoever, for it may have boundaries that exclude a potential entity. But this is easily proven false along similar lines. Assume UR, which has boundaries that exclude a possible reality, P. If P were possible, then it must be possible that ~UR. However, if ~UR were locally the case, it would be universally the case, as we saw above. Thus, the assumption of UR having an incompatible state with a possible reality entails the non-existence of UR, which is a contradiction. Therefore, we can conclude:

2.9 No unconditioned reality has extrinsic boundaries.

Conclusion

Now we can wrap up the argument. An unconditioned reality is necessarily without parts (2.1), outside space and time (2.2 and 2.3), and immutable (2.4). Furthermore, an unconditioned reality is absolutely simple (as defined in 2.5) because it lacks intrinsic and extrinsic boundaries (2.8 and 2.9), and is therefore absolutely simple. We can therefore conclude:

2.10 Any unconditioned reality is absolutely simple.

Furthermore, we know that there exists at least one unconditioned reality. (1.10) From 1.10 and 2.10 we can conclude:

2.11 There exists at least one absolutely simple unconditioned reality.

Finally, we know that any existing unconditioned reality must be absolutely simple in terms of act. For anything that absolutely simple in terms of potency is non-existent. (2.7) Thus, we can conclude:

2.12 There exists at least one unconditioned reality that is utterly without boundaries or incompatible states.

It is clear that an unconditioned reality must be infinite. For anything finite is so by a limitation—a boundary. But we have shown that an unconditioned reality has no boundaries. (2.5 and 2.10). Therefore:

2.13 Any unconditioned reality is infinite.

Finally, unconditioned realities must be eternal. For if they exist, but they do not exist in time (i.e., at one time but not another), then they are eternal.

2.14 Any unconditioned reality is eternal.

The jump from Step 1 to Step 2 is considerable. In Step 1 we deduced the existence of an unconditioned reality (or realities). But the nature of that unconditioned reality was left vague. We knew that it did not depend on any other reality, but little beyond that. Could a fundamental particle be unconditioned? What about the universe as a whole? Those questions were not answered in Step 1.

In Step 2 we established that any unconditioned reality is absolutely simple, is not spatial or temporal, is infinite and immutable. This means that no fundamental particle could be unconditioned, nor could any field with any sort of extension or duration. The host of physical entities are conditioned realities that ultimately depend on a reality outside time and space. Only two steps into the argument, and we’ve gone a good way toward proving the truth of theism.