(h/t to Monica Harmsen, our former President and current Historian. Sign reads "It's easy to be an atheist when you don't think about where everything (including God) came from.")
The pamphlet that I was handed has, amongst its 40 (40!) footnotes, an explanation of the fallacy of infinite regress that I will quote (stretched across 2 footnotes):
"Positing (infinite) prior dependencies to account for subsequent ones is not the solution: it is the problem. Fn. 11 [so, going off of footnote 11, which reads...] E.g. no matter how many dominos you add to a line or group, they will never "fall" by themselves because every faller is completely dependent upon its prior. That's why dominos only fall when some outside force makes it happen. All the more so with domino existence. See also Tyson & Goldsmith Origins pg. 44 [link], Vilenkin pg. 204 [no link to page, but some discussion and Amazon has notes for p. 204], Scientific American pg. 50 (inset) [link], F. Collins The Language of God 2006 pg. 54-67 [no suitable link]. Plus, using various interpretations of quantum mechanics and/or special/general relativity and/or singularity theories (no mass = no thing) to ignore that and/or negate the fallacy of infinite dependent regress and the necessities of source/production is a composition fallacy, category mistake, and a red herring. (Craig pgs 150-156)."I don't know why the Scientific American article is referenced. Best guess is that the inset says "Expansion probably accelerated early in cosmic history as well, erasing almost all traces of the preexisting universe, including whatever transpired at the big bang itself," and thus that's just like arguing that the universe had an infinite prior universes. It's not clear that was the intent behind the statement though. The reference to Tyson and Goldsmith is just for a quote of them off-handedly positing that there might be multiverses or that the universe popped into existence from nothing we could see.
The important thing here is that it's being claimed that asserting there is an infinite number of explanatory events is inherently fallacious – in particular this preacher asserted that it's a "vicious infinite regress," which I can only satisfactorily define as a regression that posits new explanations to account for a cause, explanations that themselves require explanations. There are two main points to be made here:
Let's say that I know a mathematical rule is true for the number 1; I can also show that if it is true for some natural number n, then it is true for the successor n + 1. Thus, since 1 satisfies the rule, so does 2 (n + 1 when n = 1), and then 3, and then 4, so on. Each number suffices the next. This is mathematical induction, and is in a sense a form of infinite regress.
This analogy isn't quite complete; it's more like infinite progress, not infinite regress. Each satisfactory number implies the next, but what we're actually trying to better understand is a cause/effect chain in reality, where it is not knowing the cause that allows us to presume the effect, but rather that knowing the effect allows us to presume the cause.
Induction is a form of self-referential thinking, and we can use that type of thinking to come up with a much better analogy: take for example the Fibonacci sequence, which goes 0, 1, 1, 2, 3, 5, 8, 13, so on, with each number being the sum of the two prior. We are often satisfied with starting with zero, but if I was to ask "what are the first 3 numbers in the sequence that satisfies N = M + L, where M and L are the immediate and secondary predecessors, and we know 5, 8, 13 are in order in that sequence?"
Why would you say (0, 1, 1), aside from an a priori assumption that the Fibonacci sequence is the only sequence that satisfies that condition? In fact, that the sequence even has a beginning? We know we can count forward – we can count backward too: 13, 8, 5, 3, 2, 1, 1, 0, 1, -1, 2, -3, 5, -8, 13, -21, etc. Negative numbers are not part of the Fibonacci sequence, BUT they do satisfy the sequence's element predictor. So I can say that the sequence isn't started by (0, 1, 1), but by (-21, 13, -8). I would be completely correct. I would be completely correct too to say that it has no beginning.
Let's put this in terms of cause and effect: given an event and given that an event implies a specific cause, that cause also being an event, there follows an infinite series of causes. The only way this statement is false or void is if there is a conceptual change in how cause and effect work anywhere along the chain (take, for instance, the beginning of the universe and thus the beginning of time), or if an event does not at all predict a specific cause. If I cannot say for certain that there was a particular cause for an event, then the universe is ultimately non-deterministic and we would, so it seems to me, inadvertently solve our question of whether or not there's a specific deity; and if the chain is broken because we can't demonstrate a possible way of knowing how cause extends past a certain point in time, we run into my second point:
Limits on observation: we can guess but we cannot know
In the case of the universe we have a very fundamental problem: we cannot actually observe to the point of the Big Bang, nor model before it nor arbitrarily close to it. There is a horizon past which we have no way to determine whether or not there could be an infinite regress; regress is a proposition, but not demonstrated.
Take our lovely domino analogy. We can see back 100 dominos – what was before then? Well maybe it's God; maybe it's another domino, maybe it's a billion dominos, maybe it's a volcano that knocked one over and a domino that initiated the volcano before that, or maybe it's just turtles all the way down or dominos all the way back.
Back to Fibonacci: if I had no conception of negative numbers (this was, in fact, something that persisted for some time until they were invented by the Chinese maybe some ~2200 years ago), I would not be able to conceive past zero, and thus would not be able to tell you that a possible start to the sequence I talked about before is (-21, 13, -8). My conceptual horizon, hopefully easily understood as analogous to an observational horizon, does NOT imply that the sequence is bounded on the lower end.
If the elements in a sequence can be deterministically and mechanistically tied to each other, then not only does our lack of ability to observe a definitive start compel us to have infinite regression as an open possibility, it makes it a logically self-consistent one, and a rather appealing one in that it doesn't require an outside explanation.
And you simply won't find people who say that there is definitively a multiverse, or that there are definitively an infinite vacua in which universes form (this seems to be what Vilenkin talks about), or that the universe for sure arose out of nothing. I would be gravely mistaken to call myself even an amateur on these subjects, but if I may: these ideas are hypotheses that mechanistically describe how one universe leads to another, or more, and are internally consistent with concepts we understand in cosmology. They are still being explored; most will probably never be experimentally verified. But the infinite regress some of them rely on is nothing more than self-referntial. We do not require some new unexplained mechanism, which would cause the regress to be "vicious" and thus unsatisfactory.
I would tentatively say, right now writing this on my own without other people to bounce ideas off of, that a general deity is not any more or less out of the question than the above-listed hypotheses. Again, we have limits on our observation, so we cannot actually say if there was a "first cause" and what that might be if there even was one. We must say we do not know (at least, I'll say that as a non expert).