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

[polymath257]

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.

So you are assuming that the set of causes is indexed by the natural numbers? What supports that assumption?

The more accurate translation into math is

for each x, C(x)--> exists y such that x is dependent on y

Then there is  the ambiguity of the term 'dependent'. Typically, it is equivalent to 'caused by', which assumes some sort of natural law. But it can also mean 'logically follows from', which is a very different thing.

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]. 

Here, you have used your assumption that the index set is the natural numbers. But if, for example, the index set is the set of integers, the 'proof' you have given fails. There are many mathematical situations where infinite regresses are not only possible, but necessary.

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

Since the previous step hasn't been proved, neither has this one.

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

Wait a minute. You only showed that there exists a non-contingent entity (the term 'being' usually implies that it is alive). You did NOT show that it is unique. How do you know that there are not multiple non-contingent entities? How do you know that there are not multiple such that appear every second?

Your 'proof' does not address these issues.

And, in fact, if you take dependency to be the same as causality, modern physics points out that *most* quantum events are uncaused and are thereby non-contingent.

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.]

You are showing a medieval understanding of the properties of infinite sets. I might suggest you learn a bit about them. Some aspects are counter-intuitive at first, but they are not inconsistent.

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.

OK, lets.