The Principle of Contingent Causation: The Impossibility of Infinite Regress.

[GrandizerII]

The Augustino-Thomistic Argument from Contingency and Necessity provides Basic Foundational Evidence for the Existence of Almighty God.

Let's define Contingency and Necessity. You, me, our parents, then theirs, the Planet Earth, etc all exist contingently, i.e. are contingent beings.

By Contingent Beings is meant a being whose existence or the existence of which is contingent, i.e. dependent on the existence of another.

Thus, you and me are dependent for our existence on the existence of our parents, all life on Planet Earth is contingent upon Earth etc.

Now, the argument may be formulated both logically and mathematically:

1. Now, every Contingent Being, by definition, is Contingent, i.e. Dependent on a Prior Being's Existence.

if we wrote it mathematically, for every Contingent Being, CB, CB(n) is dependent on CB(n-1); CB(n-1) on CB(n-2) etc.

2. But it is impossible for this series of contingent causation to go on until infinity.

Again, mathematically, this is obvious. If CB(n) is dependent on CB(n-1), and so on (and negative beings are impossible; we are speaking of real beings here. The nth Being in existence, the 2nd being etc; so also, there is no "zeroth" being; n must be a natural number here), then that can proceed back until at most Being 2, B2=CB2, contingent upon B1. [B1 cannot be contingent upon anything, since no B0, as we come to down]. 

3. Therefore, not every Being in existence is a contingent being.

4. Specifically, the First Being in Existence exists Non-Contingently. 

We already showed this above when we saw B2 is contingent upon B1, but B1 is not contingent upon any prior being, being the First Being in existence. [The only alternative to the existence of an actual first being is an infinite series of contingent beings, but that is impossible because an infinite series never ends; and if there were an actual infinite of real beings, we would never have gotten to the present moment; again, an infinite series cannot be formed by successive addition, because no matter how beings you add to each other, whether it is 1 or 1 trillion, n will always be finite. Therefore, granted that we got here, granted that we are 1 in a series of contingent beings, the number of beings in existence is finite.]

Therefore B1, the First Being, is a Non-Contingent Being, a Necessary Being, One Whose Existence is not contingent/dependent on a Prior Being.

Let's Debate.
God Bless.

I prefer the word "dependent" here instead of "contingent", since I'm now used to "contingent" meaning something different from "dependent". So what the OP labels CB, I label DB (dependent being). And as for any independent being, let's label it IB.

Now the question arises:
Must there be a First Cause in the absolute sense per the logic argued above?

The OP doesn't appear to have made an adequate case for it.

You could, for example, have multiple chains of DBs, each with some particular IB at the "root" of it. In this case, you could therefore have multiple particular IBs instead of one absolute IB (i.e., First Cause).

Of course, this doesn't mean it's a satisfying counter to the argument in the OP. The theist could respond back with something about elegant/neat explanations or the Principle of Sufficient Reason, but it's very likely that whatever argument they may make along these lines could then be used against them anyway. After all, one could point out the challenges with having the First Cause instantiating just a particular chain of DBs instead of some other chain or even instead of multiple (or even infinite) chains of DBs.