Grounding Infinity

From An Infinite Chain to a First Cause

I want to consider a common objection to a First Cause based on the prospect of an infinite regress. In debates about the nature of reality, people sometimes suggest that if there is an infinite regress of causes, then there is no First Cause. In this post, I will suggest a reason to think the opposite is so. Specifically, I will offer a reason to think that if there is an infinite regress of causes, then there is a First Cause.

Before I get to my argument, it will help to distinguish between a grounded infinite and an ungrounded infinite. A grounded infinite is an infinite causal sequence that is grounded in something prior to (or beyond) the sequence itself. For example, we could imagine an infinite sequence of dominos that depends for its existence on an infinite domino table. In this case, the infinite sequence of dominos has no first member, but the domino sequence depends on something outside the sequence. By contrast, an ungrounded infinite sequence is an infinite sequence that does not depend on anything beyond the sequence itself.

This distinction between a grounded infinite and an ungrounded infinite helps display why the existence of an infinite chain does not automatically rule out the prospect of a First Cause. While an infinite chain has no first cause within it, it might still be grounded in something beyond it. In light of this possibility, it remains an open question (at the outset) whether an infinite chain of causes might depend on a foundational (“first”) cause.

The Dependence Argument

Here I offer The Dependence Argument for a First Cause:

1. Dependence Principle: Any total of dependent things depends on a prior cause.

2. No-Circularity: The total of all dependent things cannot depend on a prior dependent cause.

3. Therefore, there is a non-dependent cause (First Cause).

A few clarifications. First, for the sake of simplicity, here I am using the term ‘cause’ in a broad sense to include anything that could be a condition, ground, or source of something else. Second, a First Cause would be a cause that does not depend on any prior condition, ground, or source. We may call it “the Foundation.”

I consider premise (2) to be true by definition of what I mean by “prior.” A prior condition is not included among the things it is a condition of. For example, a chicken could be a prior condition of an egg that it lays, but it cannot be a prior condition of all chickens.

I will give two quick reasons in support of (1). First, from reason: it may seem intuitively evident that mere dependent things cannot, by their dependence, add up to an independent totality. To illustrate, suppose you saw an infinite chain of dependent turtles hanging in the air. You might think that this chain could not just exist on its own, but would depend on some prior conditions to explain how it got there or why any of those turtles exist at all. This thought, one might think, applies equally to any dependent things of any number. Mere dependent things, one might think, cannot just exist on their own, but add up to a total that depends on something prior. This may seem so by reasoning about the nature of the case.

Second, from experience: (1) successfully predicts a wide range of data. There are many instances of totals of dependent things that depend on prior conditions, and there are no (known) exceptions. For example, an infinite chain of turtles didn’t appear uncaused in front of you before you started reading this post, just as (1) predicts. If (1) is true, there also won’t be an infinite chain of turtles appearing uncaused before you finish reading this. If this further prediction comes true, that will be additional evidence for (1).

Objections

To further clarify what is at stake, I will now consider some objections. (I may add to this section based on comments from readers.)

Objection 1. It’s impossible for an infinite regress of causes across infinite time to have a cause. Here’s why: a cause must exist earlier than its effects, but nothing could be earlier than infinite time.

Reply. That’s consistent with my argument. Suppose an infinite regress of causes cannot have a cause (per the objection). And suppose I’m right that an infinite regress must have a cause (per the Dependence Argument). Then it simply follows that there cannot be an infinite regress of causes. This result reveals an interesting fruit of the objection (if we grant the objection), but it doesn’t show anything wrong with the argument itself.

Objection 2. Each member of an infinite chain already has an explanation.

Reply. That’s also consistent with my argument. The Principle of Dependence applies to totals (plurals) of dependent things. For example, if each chicken is explained by a prior chicken (ad infinitum), we can still ask why there is that total group of chickens (or why there are any chickens, for that matter).

To elaborate, consider the Hume-Edwards principle that there is no need for an explanation beyond the explanations of each member of a group. For example, if there is an explanation of why each Eskimo is at a certain corner, we need not have a further explanation of why they are all there together. Reflecting on this case might tempt us to think that an infinite regress needs no explanation beyond the individual explanations of the members.

However, the cases that motivate the Hume-Edwards principle are all cases where the total explanation of the group goes outside the group to be explained. For example, the explanation of eskimos at a corner is external to those eskimos being at that corner. But now consider that the case of an infinite chain is precisely a case where an explanation of each member does not thereby provide an external explanation of the chain. Hence, in the case of an infinite chain, an explanation of each member does not suffice to explain the chain or remove the need for a further explanation.

This result is precisely what the dependence principle predicts: chains of dependent things, whether finite or infinite, depend on something external. So rather than undermine my argument, I think the cases that support the Hume-Edwards principle actually support my argument.

Objection 3. Our observations about local, finite cases do not give us reason to extrapolate to infinite cases.

Reply. First, it is not true in general that we cannot say anything about infinite cases. For example, we can say that we did not experience infinitely many chickens appearing from nowhere 5 minutes ago.

Second, and more fundamentally, while infinity may be weird and unusual, that by itself is not a reason to restrict the principle of dependence. Compare: I have inductive evidence that unicorns won't snap into being on my front porch tomorrow, and the unusualness of infinity doesn't leave me agnostic about whether infinitely many unicorns will appear then. My evidence applies just as well to the infinite case.

Finally, I’m not aware of any competing principle that better accounts for the wide variety of cases of dependence. At the risk of being overly dramatic, the inductive evidence for the principle of dependence is so pervasive that I don't think there is anything better supported in science (note: evidence for a more modest principle is also evidence for the general principle that predicts it). So if there are independent reasons to restrict the principle, it seems to me that they'd have to be very strong for me to consider them to have tipped the scales. So far, I’ve seen no competing principles with anywhere near the same predictive success.

Final Note

You might not be convinced, and that’s okay. My goal here isn’t so much to show that there must be a First Cause. Rather, I want to help clear away a certain barrier to the prospect of a First Cause based on infinite regresses. I hope you can see why the prospect of an infinite regress does not by itself undermine every reason one might have to think there is a foundation of reality (a First Cause).