There’s a common argument often used to “prove” that God must exist. It generally starts with the assertion that there can be no infinite regression of causality, meaning that if we go back in time and watch all the events unfold, all the causes that created their effects, then at some point there must be this first cause which can’t itself have been caused. The argument for this premise is false.
The argument that there can’t be an infinite series of past events goes something like so:
- Assume that there is an infinite series of past events.
- There is an event infinitely long ago.
- It would take an infinite amount of time to get from that point to this point in time.
- Ergo the premise is false.
Step two is the flaw in the argument. If there’s an infinite series of events stretching back in time, this does not mean there is a particular event that was infinitely far back. In fact, that statement is utterly incoherent.
To explain this, I think it worthwhile to consider a mathematical equality:
.999… == 1
At first glance it seems to be intuitively false. How can .999… be the same value as 1? Well, it’s true. Here’s the proof:
1 / 3 = .333…
1 = 3/3 = (1+1+1)/3 = 1 / 3 + 1/3 + 1/3 = .333… + .333… + .333… = .999…
I have to admit that when I first ran into this proof I asked the utterly inept question, “What about the last .000…1? Doesn’t 1 – .999… = .00….1 with a 1 infinitely far in the back?”
Truth is that there isn’t one! Thinking that there is fails to understand infinite regressions. If the sequence terminated then it would not be infinite. There’s no final anything…no infinitely far back 1.
The same is true for infinite sequences of causality or time. Pick any infinitely far back point in time and there’s an infinite sequence of time before it. Not only that, but you’ll find that if you pick any point of time in the past…ANY point in time…the sequence is no longer infinite; there in a defined length between any two points in time.
Another way to think about it is to recognize that it’s question begging. If there’s a point in time infinitely far back, and the sequence itself is infinite, then that point in time also could never be reached, ergo it’s not there either. So by using that point as a premise the conclusion is question begging.
Not to say that there IS an infinite series of causes all the way back for eternity in the past, but there could be. There’s nothing to conclude that it couldn’t be that way.
I think though that this probably isn’t the case. The arrow of time hypothesis makes some sense to me and if it’s true then time doesn’t work like we think it does, we just observe it as a linear progression of events because entropy dictates it’s the only way that actually is observable…thinking creatures can only perceive the sequence of time in correlation with increasing of entropy. There actually IS no past or future, only our perception of one. If this is true then the question itself makes no sense.
Crazy Eddie's Brain 
Most of the first cause arguments are not arguing for a finite past, but rather for a non-derivitave cause in a hierarchy of causes. The classic example is of a hand moving a stick moving a rock, and reasoning from rock to hand: if the rock is only moving because the stick is pushing it, and the stick is only moving because something else is pushing it, then there cannot be an infinite number of sticks, because then there would be no hand and thus nothing to push the rock.