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.

[polymath257]

Belacqua

Implicit in your argument is that a "being" of some sort or other caused anything.

No, that's not what the argument says. 

It sounds as if you are anthropomorphizing the First Cause by calling it a being, with the indefinite article. The First Cause is not a being, it is being. 

Not according to the OP. furthermore, 'existence' is a property, not a thing.

Too many people think of the First Cause like a big guy who decides to pull the levers to start things going. It's nothing like that. It is the thing which must be the case in order for anything else to be the case. There must be being in order for any contingent thing to be. There can be nothing essentially prior to being, because that thing would require being to be, and that's a paradox. 

OK, so the universe of spacetime 'simply exists'. It is being itself.

The word "cause," in these arguments, is not the same as the modern English word. It is the translation of the Greek αἰτία. The αἰτία of X includes all the things which must be the case in order for X to be the case. 

Which assumes some sort of physical laws to produce the dependence.

[Belacqua]

It's also a pure assertion that an infinite regress is impossible or even really a problem when discussing the universe. For all we know the universe is part of the regress.

It's not pure assertion. There are arguments against infinite regress. 

The arguments might be good or bad, but you'd have to know what they are in order to judge them.

Here is a brief outline:

https://plato.stanford.edu/entries/infinite-regress/

[polymath257]

In the instant that you admit the possibility that this non-contingent cause could be a natural event you'll find that you have no argument. Your religion requires One Being complete with capitalization. Philosophy does not.

Nishant might disagree with me on this, but as I understand the Thomist argument, it does not posit an event that happened in the past. 

Again, people read it that way because the word "cause" in English refers to an efficient cause -- the thing that pushed the first domino so that all the other dominoes fell. It's different in Aristotelian and Thomist arguments, however. They aren't talking about the Deist God, who makes the universe, winds it up like a clock, and walks away. Their God is necessary to sustain the universe in being, continuously. 

So when asking about a cause of X, we have to ask "what has to exist in order for X to exist?" Then we get a chain of essential, not temporal, causation. So for our sun to exist, we need hydrogen (among many other things). If our sun disappeared, hydrogen would still exist, but if hydrogen disappeared, our sun would disappear too. That's what is meant by "essentially prior." 

This is the case because the sun is made from hydrogen from a process involving natural laws.

So our sun needs hydrogen, hydrogen needs subatomic particles, subatomic particles need this and that and the next thing. Eventually you get to a "deepest" level. What does physics call it these days? Space/time? Matter/energy? I'm not sure. But of course for space/time to be, there must be being, which is what the philosophers call the First Cause. 

Well, we may or may not have found any fundamental particles. Electrons and quarks, along with several bosons are the most fundamental we have found. But that is composition, not causality.

Why must there be a separate 'being' for spacetime to exist? maybe spacetime is a non-dependent entity ( I much prefer this to 'first cause' since we are taking about dependency, not cause).

Your argument is still relevant, in that scientists can still posit that the deepest level, the one thing that is necessary for everything else to exist, is natural. We could argue that being itself, which is necessary for space/time to be, is itself natural. But I don't think this argues against a First Cause. It just claims that we should call the First Cause natural. And I don't think theologians would have any problem with that - the natural/supernatural distinction is notoriously tricky. 

If the universe as a whole is a non-dependent entity (which makes sense because all known causes or dependencies are within the universe), then it would be the 'first cause' in your system, right?

As always, to associate this First Cause with the Christian God requires many other arguments, which aren't addressed in the Five Ways.

There are also the issues that an infinite regress is NOT a logical contradiction nor has the uniqueness of a 'first cause' been shown.

[Belacqua]

This is the case because the sun is made from hydrogen from a process involving natural laws.

I'm curious why you thought you needed to tell me this.

What have I said which indicates that I don't understand it, or believe otherwise?

[arewethereyet]

No matter how interested I am in a thread, Bel can always quash that interest.

It's a gift.

[no one]

Bel is the anti awty.

[The Architect Of Fate]

It's not pure assertion. There are arguments against infinite regress. 

Actually it is a pure assertion i'm am aware of all the so called argument none of the address the issue of an  infinite regress they waffle on some outlining point instead then pretend they adressed the issue 

The arguments might be good or bad, but you'd have to know what they are in order to judge them.

Except they aren't really arguments against an infinite regress at all.

Here is a brief outline:

Again i know what they say and they never get around to the actual regress they waffle on some outlining point instead then pretend they addressed the issue.

[brewer]

To my knowledge no one has provided evidence that infinate regress can't exist. The only 'argument' christians provide is used to postulate (suggest or assume the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief) the existence of a god.

When will christians learn that nobody can argue a god into existence. Continued discussion to attempt to justify/validate their 'belief' is pointless. Unless they are only talking to themselves. But then most already believed the imaginary before the argument, once again ....... pointless.

[The Grand Nudger]

Correct. As you would find in the link Bel offered, infinite regress has been argued to be incompatible with specific analytical positions and particular metaphysical ideologies or principles - but a difficulty for systems that people use to organize their thoughts or assert their beliefs is not a problem for the universe. It's our problem. There are and have always been things that do exist and are a problem for us or some other belief we hold. As I said pages and pages ago, in this arguments against infinite regress are appeals to consequence. If infinite regress existed, that would be bad -for whatever x the arguer holds dear-. I actually agree with this and it is troubling, but, ofc... it doesn't follow that because a thing would be inconvenient to a cherished belief that thing must not exist.

It's a wonder to me that the faithful mine dead and dead-end arguments from antiquity when pursuing the case for their gods. We've gotten much better at arguing since saint tommys failed attempt at syncretism, and we know a hell of alot more about the world we live in. A god informed by better arguments and by greater and more accurate data sets would seem to be preferable, to me. I suppose it might not end up looking like the god they wish existed - the central trouble that the religious often have and what..to me..indicates a deplorable shallowness in their beliefs...but hey..whatever. Like infinite regress, that's our problem, not a gods problem.