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

[Anomalocaris]

I can conceive of a square circle provided it is placed correctly in a specific non-Euclidian space.  Is it possible?  I don't know.  I'm not sure conceiving tells us much one way or the other.

The classical problem of squaring a circle is impossible in euclidian spaces. If you change the space, you change the problem.

And, for the record, it is possible to square a circle in some non euclidian frameworks.

Unless you can conceive of how something is logically possible, I don't think you've truly conceived of it in any logically meaningful sense.

Not necessarily. People conceived of airplanes centuries ago, without knowing how to make them. And still, no one can deny that it's thanks to their wild dreams and ambitions that we have airplanes today.

So someone will make allah for you because you have dreams and ambitions of being slave to allah and this “owning” atheists?

[emjay]

Unless you can conceive of how something is logically possible, I don't think you've truly conceived of it in any logically meaningful sense.

Not necessarily. People conceived of airplanes centuries ago, without knowing how to make them. And still, no one can deny that it's thanks to their wild dreams and ambitions that we have airplanes today.

But the conception in and of itself doesn't speak to the logical feasibility of an idea. Ie some ideas may turn out to be logically feasible, others may not, but the actual initial conception doesn't in and of itself speak to that feasibility, unless it directly addresses that feasibility. Ie for instance the difference between a designer who conceives not only of the thing as a whole but also how it works is addressing the logical feasibility, but a child idly imagining something is not addressing that feasibility at all.

[The Grand Nudger]

@arewethereyet

That's legit, we have documentary evidence.

[Angrboda]

@arewethereyet

That's legit, we have documentary evidence.

Negatory. That bird won't fly. It hadn't got any wings.

[The Grand Nudger]

They don't need them. They chew up rocks to create lighter than air gasses, and they hold that in a special bladder. That's why they live in caves. Those ridges along it's back along with the tail provide directional thrust and inertial control. To decrease in altitude, or if they're annoyed, they belch flame, expelling the flammable mixture.

[arewethereyet]

They don't need them.  They chew up rocks to create lighter than air gasses, and they hold that in a special bladder.  That's why they live in caves.  Those ridges along it's back along with the tail provide directional thrust and inertial control.  To decrease in altitude, or if they're annoyed, they belch flame, expelling the flammable mixture.

You have thought about this too much. 

[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.

[polymath257]

Go ahead, give me one example of something you can conceive of, and which is logically impossible to exist at the same time.

I can *conceive of* three positive integers x,y, and z and an integer exponent p>2 with x^p +y^p =z^p. But it has been discovered that such is logically impossible.

I can conceive of a finite field with non-commutative multiplication, but it also known that such is logically impossible.

I can conceive of a Fourier series for a continuous function that diverges everywhere, but, again, it is known to be logically impossible.

I can conceive of an odd perfect number, but *nobody* knows if such are logically possible or not.

I can conceive of a non-trivial zero of the Riemann zeta function that isn't on the critical line. Once again, *nobody* knows if such is logically possible or not.

At least part of the  problem is that the notion of 'conceive' is way too vague. How much detail is required to actually have a 'clear conception' of something?

[polymath257]

Go ahead, give me one example of something you can conceive of, and which is logically impossible to exist at the same time.

And more importantly for this thread, I can conceive of an infinite regress of causes. According to you, that is logically impossible (even though it is trivial if the  sequence of causes is indexed by the negative integers).

[Nishant Xavier]

Ok. So, while, I was away, I was thinking of another way the argument could be formulated: for a Being Bn, if it is contingent, it depends on a prior Being Bn-1. But Bn-1 likewise, if it too is contingent, further depends on Bn-2. And so on and so forth until we come to B1 and B0. Since we are speaking of real beings, there is no B0. Therefore, B1, the First Being, is non-contingent.

But perhaps these words "contingent" and "necessary" don't indicate too much to the average reader, though they are well known in modal logic and other fields. Very well, then, we will use simpler terminology. Let's use temporal/eternal instead. For every Being Bn, if it is temporal, it depends on a prior being in the timeline, Bn-1. Nevertheless, this series cannot go on backward to infinity (will come to why, and the objections raised in a minute), Therefore, at some point we will reach the very beginning of time, and the final temporal being, B2, will have been caused by B1. And B1, the First Being, is thus proven to be a Non-Temporal Being, an Eternal Being, the First Cause of the Universe.

Hence, Axiom I is: B1, i.e., an Eternal First Being exists, owing to whom B2 to Bn, i.e. the Sub-Set or Universe of Temporal Beings, began to exist.

This conclusion is confirmed by Empirical Science. Wikipedia says: https://en.wikipedia.org/wiki/Borde%E2%8...in_theorem

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 "The Borde–Guth–Vilenkin theorem, or the BGV theorem, is a theorem in physical cosmology which deduces that any universe that has, on average, been expanding throughout its history cannot be infinite in the past but must have a past spacetime boundary.

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