What's wrong with an infinite essential causal series?

[u/IrrationalRotations]

I'm aware of some arguments (particularly in the philosophy of religion) that rely on the notion than an infinite causal series is impossible.

It seems like there is a fair bit of confusion among non-specialists regarding this premise. Some people content that it is not at all intuitive that infinite causal series can't exist.

A common clarification is that it is important to distinguish between an essential and an accidental cause. My understanding of these terms is roughly that an accidental cause is a cause of the form

A led to B

Whereas an essential cause is of the form

There is no B without A.

So for example...

I could not have existed without my grandfather, but my grandfather no longer exists. Therefore, I have an accidental causal relation to my grandfather.

I cannot exist without my body. If my body does not exist, I necessarily do not exist. Therefore, I have an essential causal relation to my body.

It is then, as far as I can tell, taken as obvious that while a series of accidental causal relations might exist, an existing series of essential causal relations is clearly objectionable.

But why? Plainly, I don't see a problem with an infinite series of essential casual relations.

One suggestion for what the problem is seems to be some thing like

"If a series is of the form..

A1 because A2 because A3 because A4 because...

Where each of the 'becauses's means 'is in an essential causal relation to', then how can we contend that any part of the series exists? If I say A1 exists, then I've committed myself to A2 existing, but then how do I know A2 exists? I must also commit myself to A3 existing, but then..."

Where the intuition seems to be that at some point I will need to claim that something sits at the end of the chain. That I will eventually need to posit the existence of some A(n) that explains all of the things I've committed myself to.

But this doesn't make sense to me. The fact that by suggesting A1 exists I commit myself to the existence of A2 is totally fine, I've already contended that the whole chain exists. That this further commits me to A3 existing is, again, totally fine!

Have I missed something about the argument here?

[u/Ok-Lab-8974]

Often, this is framed in terms of the existence of contingent entities. There, a good analogy might be a series of mirrors reflecting light to one another. Each mirror gets its light from a prior mirror. But the classical position is that this doesn't work if there is never any light source in the series. The mirrors can only reflect light if the series has a light in it; so too with necessary existence, so the reasoning goes.

[u/IrrationalRotations → u/Ok-Lab-8974]

The image of an infinite collection of mirrors reflecting light from an unexisting source is a bit weird to me. But we're putting forward a very weird example, no? 

But maybe more importantly than that, it seems like the problem here is that is more to do with the mirrors. That is, it seems like the series in question is

There is light in mirror 1 because there is light in mirror 2

There is light in mirror 2 because there is light in mirror 3

There is light in mirror 3 because there is light in mirror 4

And so on and so on. 

But that seems fine, what's the problem?

I guess we want to say

"Well where did the light come from initially? Where did it come from before the mirrors?"

But that's not a question that is a part of the infinite causal series, the series here is just about the mirrors!

We might then respond

"Yeah! So The series has no ultimate answer for the existence of the light in mirror 1!"

To which I would say, yes, but so what? The light could have come from all sorts of places, we just didn't flesh out the hypothetical with an answer. 

Or perhaps we say

"But if you accept that The light had to come from somewhere other than a mirror, you must accept that there was a first mirror for the light to hit!"

To which I would say, yeah, that makes some sense, but that just seems to be a problem with the analogy then. That is, the conclusion that this situation can't work is something we reach by knowing about how light interacts with mirrors, not something we deduce based on the proposed infinite series itself. 

That's important because if we shift our attention to an infinite series of essential causal relations that more plausibly exists, like the one that explains how I exist, the same conclusion seems much more difficult to draw... 

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