Thursday, July 24, 2014

Step 1 in the Argument for God's Existence: Clarification and Responses

By Thomas Cothran

This is a part of the ongoing series setting out an argument for the existence of God. For an overview of the series, click here. The numbers (e.g., 1.3) refer to the premises. The “1” in 1.3 refers to Step 1, and the “3” refers to the third premise. To see the premises, review Step 1.

Before moving on to the second step in the argument for the existence of God, let us expand on the claim that an infinite series of conditioned realities necessarily does not exist. This turned out to be the most controversial part of the argument for commentators on this blog. First, we will consider in more detail the notion of infinite series, then we will consider some objections.

The question is whether an infinite series of conditioned realities can exist without an unconditioned reality. We begin with the assumption that there exists an infinite set of conditioned realities, but no unconditioned realities. We will show that an infinite number of conditioned realities without an unconditioned reality entails the non-existence of any realities whatsoever.

Let’s start this time with an illustration, and then proceed to the argument. It is important to remember that by signifying different stages, what is being signified is not necessarily different moments in time, but a conditioned reality along with its conditions. What is meant is not so much a sequence as particular relations of dependence. CR2 is before CR1 as a condition precedes the conditioned in the causal order. It may be the case that a condition precedes the conditioned in time; but this is not something that needs to be resolved here.

Stage 1 Stage 2 Stage 3 Stage 4…
Conditioned reality in question CR1 CR2 CR3 CR4…
Conditions that must be fulfilled for Conditioned Reality to Exist CR2 exists & CR2’s conditions are fulfilled CR3 exists & CR2’s conditions are fulfilled CR4 exists & CR4’s conditions are fulfilled CR5 exists & CR5’s conditions are fulfilled….
Present CR’s existential conditions met? No No. No No…
Previous CR’s existential conditions met? No No No No…

Take a look at Stage 1. CR1 is the conditioned reality in question. In order for it to exist, its condition must exist. (1.1 and 1.3) CR2 is the condition of CR1. Thus, if CR2 does not exist, CR1 does not exist.

But there is an objection. Why can we not represent the relations of conditions as CR1 if CR2, CR2 if CR3, CR3 if CR4…., and then simply posit CR2 as existing, leaving aside the question whether its own condition is fulfilled, and thus posit CR1’s conditions as being met? That is to say, why can’t we consider [CR1 if CR2] in separation from [CR2 if CR3], or indeed, the rest of the infinite series? In the lowermost row in the chart above, why is it that we say that at Stage 2, the previous conditioned reality (CR1) has unmet conditions?

The answer, put simply, is that CR1’s condition is not met until CR2’s condition is met, and CR2’s condition’s condition, and so on to infinity. That is, not only must it be the case that, if CR1 is to exist, its condition, CR2, must exist. It must also be the case that CR2 is a conditioned reality (since we have excluded any unconditioned realities), and therefore CR2’s condition must be met.

It will not do for us to say that CR1s condition is met by simply assuming the existence CR1’s condition, CR2, leaving for later the question of whether CR2’s conditions are met. For we have also assumed the existence of an infinite series of conditioned realities each conditioning another. For every conditioned reality in the chain, insofar as it is causally prior, is a condition of CR1. And the consequence of this is that at no point is any condition of any conditioned reality met.

Assume that CR1’s condition, CR2, has unmet conditions. If CR2’s conditions for existence are unmet—as they are at Stage 2—CR2’s conditions for existence has not yet been met. (1.1 and 1.3) If CR2’s condition has not been met, CR1’s condition has not been met for the simple reason that CR1’s existence hinges on CR2. (1.3) Therefore, it is necessary to posit not only the existence of CR1’s condition; it is equally necessary to posit that condition’s condition being met. And, at Stage 2, one cannot do this. Thus, at Stage 2, neither CR1 nor CR2’s condition has been met.

Does positing the existence of CR1’s condition’s condition solve the problem? That is to day, does positing CR3 meet the conditions of CR1 and CR2? The answer is no, and for the same reasons. CR3 cannot be posited without co-positing that CR3’s conditions are met. Thus, at Stage 3, the conditions for CR3, CR2, and CR1 remain unmet.

You can see from the chart that no matter which stage you pick (i.e, no matter which conditioned reality is in question) neither that reality nor the realities prior to it have had their conditions met. It doesn’t matter whether you’re looking at CR 51 or CR 1,029,348,203. For every single conditioned reality in the sequence (and there are an infinite number of them) it will both be true that their existential conditions will be unmet, and that all the conditioned realities prior to them will likewise have unmet existential conditions. Every single one. And for no conditioned reality with an unmet condition can exist. (1.1 and 1.3) Therefore, on the assumption of an infinite causal regress, no conditioned reality exists.

The reason for this is simple. It is impossible to derive a non-conditional statement from a series of conditionals, no matter how many conditional you posit. Contrast:
A if B
Therefore A
A if B
B if C
C if D
D if E
At no point in the second example can the conclusion “A” be drawn. “B if C” does not justify the conclusion “A”, and no additional conditional premise (e.g., “C if D”)can do so unless it posits something as unconditioned.

Barry Miller puts it this way:
“The point, an it is a purely logical one, is that conditionals can be piled up ad infinitum without the slightest chance of a categorical conclusion ever being inferable from them. If, from the conditional ‘[A] if [B], we want to infer [A], then besides the conditional, we need the categorical [B] as well. It is the the lack of any such categorical in the above series that makes it impossible on logical grounds to assert categorically ‘[A] exists.’” Miller, “The Contingency Argument” 369.
The important point is that the relations of conditions to each other is not so simple as, for example, CR1 exists if CR2 exists. It must also be the case that CR2’s conditions are fulfilled. And we know that CR2’s conditions will have further conditions, each themselves conditioned, ad infinitum. CR1’s conditions are then “nested” rather than linear. That is to say that it the series should not be expressed like this:
[CR1 if CR2] & [CR2 if CR3] & [CR3 if CR4] …
So much as this:
CR1 if (CR2 if [CR3 if {CR4 if |…|}])
The relations of conditions to what they condition in an infinite set of conditioned realities is not a matter merely of the two conditioned realities taken at a time. The “if” in “CR1 if” cannot be resolved without resolving the future “ifs”—as the second way of noting the series shows.

For example, CR1’s “if” is conditioned not only on CR2, but on CR2’s conditions, and the conditions of those conditions, and the conditions of the conditions of those conditions to infinity. Thus, for CR1 to exist, it is never simply a matter of assuming that CR2 exists and leaving the other CRs to be considered later. CR1 has an infinite number of conditions, each of which is a conditioned reality, none of whose conditions are achieved.

And since none of those conditions are never achieved, no conditioned reality in the infinite set can exist without the existence of an unconditioned reality.

Further Objections

Singring, in the comments objection, raises the following objection: The argument “implicitly assumes that the conditional realities 'arise' in some causal sequence, that is ordered in time - e.g. one reality existing before another.”

This objection is certainly well motivated, for we are accustomed to think of causes as arranged in temporal sequences: first my grandfather exists, then my father exists, then I exist. We customarily think of effects as following causes in time. However, there are good reasons to believe that effects can be simultaneous with causes, as both Thomist metaphysics and quantum physics purport to show.

The argument presented here, however, does not depend on any particular view of how causes and effects are related to time. “Before” and “after” refer to relations of dependence, not points in time. Thus, the argument does not preclude eternally existing conditioned entities; it just says these eternal conditioned realities must depend on an unconditioned reality. (Aquinas famously argued that philosophical considerations could not show that the world had a starting point in time.)

Art, raising a very different objection, states that the argument is the same thing as Zeno’s paradox. I admit that this claim mystifies me. Two arguments are the same if they have the same premises and conclusion. Zeno’s paradox shares not a single premise with this cosmological argument. Nor are the conclusions the same. Zeno’s paradox concludes that change with respect to place is impossible. The cosmological argument isn’t concerned with that question.

Furthermore, the arguments are not about the same thing. Even the notions of infinity are different. The cosmological argument considers the question of an infinite number of realities. Zeno’s paradox, on the other hand, deals with an entirely different kind of infinity: the infinite divisibility of a single magnitude.

Finally, Zeno’s paradox is advanced to support the view that no conditioned realities exist. Zeno was a Parmenidean. But this is rejected in our argument by premise 1.4. The arguments are different in what they argue, why they argue it, what they conclude, and even what they are about. At the points they do touch, they are contradictory.

No comments: