Does the impossibility of an infinite regress prove God exists?

Question

I'm strictly discussing one aspect of God: God as the First Cause. I am excluding all other qualities of God defined by any religion or belief system -- including the notion of God as a sentient being. For the scope of this question God could be nothing more than an inanimate construct that is the source of all things. My question rephrased: "Does the impossibility of an infinite regress prove the universe has an ultimate source?"

Thomas Aquinas decided the answer to this question was Yes ( as can be seen is his Argument of the First Cause ). Yet he makes the faulty assumption that this being must be God as defined by religion. Notice how my question differs.

There have been many similar arguments throughout history such as The Cosmological Argument and Kalam's Argument. My question, however has nothing to do with the identity of this First Cause. For that, see this question. I am only asking if we can logically determine if there is one, or not.

For my argument to be successful an Infinite Regress must be impossible. If anyone has a valid argument against this, please share. My argument supporting the impossibility of an infinite regress is as follows:

An infinite regress proposes an explanation, but the mechanism proposed stands just as much in need of explanation as the original fact to be explained. It is literally an infinite series of propositions where each proposition relies on the previous proposition. It is equivalent to saying:

"Each and every single human being was created by a human being before them"

According to this logic there can be no "first" human or even an origin for the species. Is this not a logical fallacy that is impossible? If this is, in fact, impossible as I suppose then the law of causality and the causal chain itself breaks down at a type of singularity that must be outside of it. With what we know from science and The Big Bang this would possibly be the influence that caused the Big Bang. This is in very much agreement with science because we now believe time itself started with the Big Bang, and causality depends on time existing. The only way to arrive at a timeless state is to go "before" the Big Bang.

Special pleading is an argument with an unjustified exception. Given the above, is this exception justified? Does the very fact that an infinite regress is impossible justify this exception?

Answer 1

Most answers are misinterpreting your question. Whether it be space-time itself, the multi-verse, or the Flying Spaghetti Monster you would like to know if something had to first exist for infinity due to the problems with infinite regression.

If we assume the Big Bang Theory is correct, then there is no "before" the Big Bang in the usual sense of the word "before". If something caused the Big Bang, that something is outside of time and - for the lack of a better word - "infinite" or always having existed from at least our limited vantage point.

Because this entity is outside of our timeline, it could be viewed as a "first cause" or "prime mover". This doesn't mean this entity itself wasn't created by something else in its own separate timeline; but for logic to prevail: If we keep going back, traversing possibly multiple timelines from possibly multiple universes, it all ultimately has to fall back on one cause, outside of all the other timelines, thus being infinite from their vantage points.

This singularity must in fact exist given the logic above. As you noted, this doesn't mean it is a personal being like a God, or even anything more than an inanimate object for our purposes, but we have sufficient evidence that it's out there, or was at one point in "time".

Answer 2

It's no solution to postulate a primordial source as a remedy against infinite regress. The concept of a primordial source prompts at once the question for its cause. To say it is "causa sui" - the answer of Christian philosophy - does not answer the question but rejects it.

My conclusion: We must not overestimate the power of pure reasoning. Instead, we must restrict ourself to the insight that today certain cosmological questions have no answer.

Answer 3

This is very similar to Thomas Aquinas' second 'way'. Aquinas was a 13th century catholic philosopher and wrote Quinque viæ, five ways to God. The second is The Argument of the First Cause.

The five ways are controversial and very debatable. Richard Dawkins famously criticised them in The God Delusion. He claims it is a form of special pleading to say that everything except god must have a cause. This is a fallacious argument where something is an exception to a general rule, while the exception isn't justified. In your case, you don't justify why god can be an exception to your first premise that everything is caused.

Also, you don't justify your second premise, that an infinite regress is impossible. It doesn't seem to be very compatible with the Big Bang, however, it isn't impossible once you refute that theory. For more info, see eternal return.

Answer 4

OK, I'm going to have a go at this.

An argument can go 3 ways:

• A circular path.
• Infinite regress.
• Hmm... let's just call it stop condition for now.

Circular arguments

These are outright nonsense. A thing cannot prove itself.

Oil floats on water because oil floats on water.

Nonsense. The premises are right, but the argument is nonsense. Compare with:

Oil sinks in water because oil sinks in water.

Takeaway: for an argument to be reasonable, the premises have to be reasonable, and the argument valid.

Infinite regression

Let me give you an argument to tinker of:

For each number X, there exists a number Y, such that Y = X + 1.

Try to stop that regression train.

"Each and every single human being was created by a human being before them"

This is an infinite regression alright, but it's nonsense as well - humans don't create other humans. Biological processes 'do'. We are merely hosts for a biological phenomena.

You have to be careful when using the word create. Does a carpenter create chairs? Language is fuzzy and abstract - a carpenter merely converts one form to another. The end result can be seen as having been 'created', but really, its just about cutting wood and assembling it in a particular way.

Now you'd be a famous person had you managed to prove that infinite regress is impossible. For all we know, perhaps the most empirically tested paradigm we have is cause and effect - break it once and science will be reduced to a pile of nonsense.

All these talks about initial singularity are based on general relativity, which is by many seen as fit to explain the early universe as Newtonian physics was explaining the orbit of mercury (both are phenomenal theories of unprecedented utility, but neither is all-encompassing).

Notwithstanding, lets play along - lets just assume that infinite regress is nonsense.

Stop condition

A stop condition can be many things. An axiom or justified belief, for example.

Now stop conditions are not evil. In fact, they are highly practical. Consider this:

The amputated limb of a human will not regrow. Why? Because no such case has ever been observed.

(The skeptics will surely have their say on this, but this is manageable alright.)

The commutative low for addition is another axiom that serves us right.

Anyhow, with circular reasoning being nonsense, and infinite regress out of the question, all you have shown is that arguments must stop at some stop condition. Let's put this to the test:

There is at least one day a year where not a single person on this planet is having sex. Why? Because god exists.

OK, we have a stop condition, it's even god itself. But is the argument valid? Is it reasonable?

Now consider this argument:

Given that circular reasoning and infinite regress is nonsense, there must be a stop condition.

OK. Seems like a reasonable argument, but note that this in itself depends on an axiom - that there are only 3 ways an argument can go. But lets assume the 3 way axiom is reasonable.

Now you argue:

Given that infinite regress is nonsense, god must exist.

If this argument is valid, so is this:

Given that infinite regress is nonsense, love is red.

You have asserted that:

God is only the first cause.

And so one might argue:

A love that is red is only the first cause.

It's a bit unfair to take a word like god, the semantic of which is fairly understood, and demote it to something that only constitutes a first cause. What's the point doing this? The concept already has a title - first cause.

Imagine I walk in the street and this girl walks to me and say:

Hey, god exists.

And I go, really? And then she goes:

Yes, but its not the god you think of, it just another label for the first cause. God is just another label.

It's 3AM, so I'm unsure how much sense this makes. Probably not much. But I hope this helps.

Possibility vs practicality

In light of your comments, I'd like emphasis a point that so far may have been implicit.

I believe your line of reasoning is this: If we'd have to regress ad infinitum, we'd get nowhere. This is absolutely right.

To make it as bold as I can, knowledge depends on stop-conditions. Euclid's proof of the infinitude of primes is a proof alright, but only for being based on some mathematical axioms, which are its stop condition. We must stop somewhere on our way in, in order to get results back out.

But this doesn't make infinite regress impossible, it is simply impractical.

Alice

By way of analogy, consider you walk in the woods and suddenly see a door. You open it and see stairs. A white rabbit pops from the bushes and says:

Howdy! These stairs go down forever. You can go down if you fancy, but they never end.

Now. Would going down the stairs be impossible or impractical? If the stairs are indeed infinite, would it be impossible for a thrown ball to fall down infinitely?

Impossibility

If it is impossibility we debate, then cause and effect couldn't serve as a better example - we have all the evidence in the world such principle is in effect. We haven't got a single evidence that there is an effect without a cause. In other words, infinite regress seems much more reasonable (possible) than any 'natural' stop condition.

The same principle is in effect elsewhere (forgive a few leaps):

• We are having this discussion using a language.
• We have acquired it through experience.
• An experience which is the results social formation of shared abstractions.
• Society itself was shaped by evolution.
• Which takes us back to the big bang, which is currently as far as we can empirically test our knowledge. The big bang is forced upon us at the moment same as the notion of the sun orbiting earth was forced upon our ancestors before they had the tools to conclude otherwise (in other words, before further regression was possible).

On the nature of science

As a closing remark, I hope we have a shared understanding that science is not concerned with deriving at absolute and independent truths - science is about adopting the most rigorous tools at our disposal to approximate patterns.

Answer 5

Keelan's answer is very good. I see no reason to give Dawkins the final say on the issue.

Infinite regress does not prove God exists. Nothing proves the existence of God, The Flying Spaghetti Monster, the Invisible Pink Unicorn, Russell's Teapot, nor the Multiverse.

But believers in God simply end the recurring sequence of regression regarding causality with God. Because of the defined nature of God, the question of infinite regress need not be answered. The regress ends with God.

And Dawkins may complain that it's special pleading, but that's the whole point of God. It is appropriate that God is the exception to the generally accepted rule of causation. That's the purpose of the construction of the notion of God.

Answer 6

Despite the good answers above (especially by the resident Kantians), as far as I can tell the problem here lies more with the concept of causality than with the red herrings "god" and "infinity."

This triumvirate, "god-infinity-causality" is so primal and interdependent it is very difficult to define one as "prior to" the other two. But for us moderns, it is probably more fruitful to look at "causality."

Kant suggests that the universe may well be fully determined, as the physics of his day implied. There may well be this physical-mechanical version of the principle of sufficient reason.Nonetheless, it may also be "too complex," if one prefers that phrase, to have any affect on what human consciousness can grasp.

We are free from such determination because we can never possibly "know" otherwise. It is beyond "knowing" to know the totality of the cause of what is "known." In other words, noumenal. In Kant's crucial distinction, we may "think about" such things, but never "know" them. Ultimate "causes" fall into this category and generate illusions.

Hegel goes further. He notes, almost as an aside in the "Logic," that causality is a retrospective selection. It must be. One can only define a "cause" after one has defined an "effect." So in rational consciousness and representation, "causes" follow "effects." This is, in part, a defense of teleology, hence its theological implications.

In a more mundane vein, Althusser attempts to correct the materialist version of historical causation with "overdetermination." Given some "effect" the "causes" are infinitely divisible and dispersed, hence infinite. (Historically, who is more "causally effective," Napoleon or Napoleon's mother?)

My point is this. Your problem has to do with a view of "causality" that is simplistically additive and reductive. You assume by "regressing" or going backwards we should somehow arrive at and identify fewer and fewer "causes" until only one is left. This is a crude model that even science is in the process of discarding.

Answer 7

So does impossibility of an infinite regress "prove" God? You have made it a condition that we have to reject the possibility of an infinite regress. Given that, the answer would be yes. (On assumption that by God you mean the first cause and prove is not prove).

If an infinite causal chain is impossible it must terminate somewhere. Someone/Something has to knock the first domino. I think here you/we just beg the question here. If causal chain is not infinite, it must have a starting point. And that will be a cause (because the chain is causal). Hence it will be the first cause (because there would be no cause prior to that).

Or -

P1) Infinite causal chain is impossible.

P2) A non-finite chain has a starting point.

A1) Causal chain has a starting point.

A2) First cause exists.

However I think that is not what you mean because you justify condition that you laid down. So I assume you are also interested in finding whether an infinite regress is possible.

To add however, I would say the reason why there has to be a first cause would be as follows -

Suppose there is a following causal chain and we are at n -

........ -> a -> b -> c -> d -> e -> f -> g -> h -> ........... -> n

We don't know whether the chain is finite or infinite. We can't say for the end. But from our perspective in reverse direction an infinite chain must have no starting point and a finite chain must have one.

There can be just these two possibilities for a linear chain.

Let us assume that 1/x_N denotes the probability of occurence of an event N given that its cause has already occurred.

From Probability Theory, we can say that 0 <= 1/x_N <= 1. ^*a

So what is the probability of the occurrence of the event n?

Well it would be simply product of probabilities of all events prior to event n and of event n itself. ^*b

Now if number of events or points were indeed infinite (not tending to infinite) then such probability would be an actual zero. ^*c

But we know that event n actually occurred (if our senses are reliable and events really occur).

Hence there cannot be an infinite chain of causally related events.

This is, I guess, a pretty neat "proof by contradiction".

A way to avoid it could be that there are infinitely many worlds and our world is just one such among them. But any calculations on infinity are absurd to begin with. So that conclusion would probably forever be a speculation (still possible because if infinite regress can exist, then maybe infinite worlds can too).

If however number of events in the causal chain are finite, then as such there is no problem in occurrence of event 'n'. Such an event could occur even if there was just one world because probabilities of all events at the position of n would be almost as low or even that any outcome would have to occur. But if probability is zero, such event is never possible. As infinite chain can be extended infinitely, no event on causal chain would take place.

Where however would this fail?

Well some such conditions I listed above which are necessary for the proof. For example such "proof" will fail if the chain is circular. Then this proof will have no meaning.

Also if causal events are not actually dependent, or probabilities do not actually exist, this proof would be invalid. They may look ridiculous but are at least possible (We should remember we are talking about infinite regress here, so almost anything is possible).

*a - One can argue that probability of the events could be 0 or 1. But we know that event 'n' has occurred (so it can't be 0) and event 'n' is not unique consequence of event 'm' (so it can't be 1). These are again two assumptions. But remember even if event 'm' surely leads to event 'n', event 'a' would not lead surely to event 'n' and an infinite would have same number of such long distance events as short ones.

*b - N may depend on more than one event. But we can uniquely point out its predecessor. Extrapolating that such was always true, even when we were not there, all points on causal chain exist singly for a world.

*c - Such calculation is absurd, because reciprocal of infinity is not defined (because infinity is not a number) but I think that is a fair assumption considering we are presupposing that such infinite chain occurs and going uncoventional any way. But that is one weakness I would say.

Answer 8

The first part of your statement, "impossibility of regress," is false. Although there might be regressions that are impossible, there is at least one that is possible. The one that is possible, is the one that depends on (is a function of) time. If you regress to the point where time does not exist (stops, ends, etc.), then the regression goes to infinity!
If the first part were true, that in itself would "be God," because it could be used to prove that anything (therefore everything) exists!

Answer 9

I haven't read all the answers so forgive me if this is a repetition.

Positing a First Cause of any kind causes insurmountable logical problems. The only way around these problems is to adopt the traditional idea of a 'causeless cause'. This refers to the idea of our Origin being causal simply by being what it is, such that there is no original causal action or intention. The idea is far too subtle to explain here and it takes some pondering to grok it.

We see this idea in Lao Tsu when he explains the laws of heaven and Earth as following ineluctably 'Tao being what it is' and if you read around Zen you'll find widespread mention of this 'causeless cause'. The moment we say there was an original cause we are in trouble but a causeless cause (once carefully defined) makes sense and allows us to escape from the usual problems.

So even with a very loosely defined 'God' as a First Cause the problem is not solved. The problem is with the idea of a First Cause, not with who or what we assign it to. .

Answer 10

In string theory they posit the big bang as a collision between surfaces in a multidimensional space. It seems if there is the possibility of a static (timeless) reality, external to this one but able to have caused it, there could be such a first cause. How to think about a time before time is tricky though.

Buddhist thought simply accepts infinite beings, in infinite realms, for a infinite time. In the Brahmajala Sutta (in part 40, of https://www.accesstoinsight.org/tipitaka/dn/dn.01.0.bodh.html) Buddha explains how a deity can come to think they are a creator, but how in fact they face the same fundamental problems as all beings. This may be pointing to the idea that causation itself is a state of mind, an unawakened state, and that as long as a previous causevs searched for the next previous link in the chain can be found, but that only gives us the truth of the lack of any inherent nature, that everything we ordinarily experience is conditioned and dependent.

Answer 11

We know we are here at this point in space-time. The law of Causation is used to explain how we got here, receding as far back in time to The Big Bang. The expanse of time from the start of The Big Bang up to this moment now; though lengthy( 13 billion years ), is a finite amount of time.

Because space-time, by definition, exists only within our universe, there would be no “time” for something to exist “before” the Big Bang, however, that doesn’t explain why The Big Bang happened to begin with.

Although something cannot exist “before” the Big Bang, we can imagine an entity existing “outside” of it in higher dimensions than the ones our universe are bound to. In hyperspace and hyper-time this entity could be the reason the Big Bang happened. Being in hyper-space-time this entity would appear infinite from our perspectives.

This entity could be a part of an infinite “hyper”-causal-chain that always existed. It would be a true infinite regress, however, that still doesn’t explain why the whole set exists in the first place. An ultimate “cause” isn't the word we are looking for because causality has only been seen within our current space-time. We need an ultimate-un-contingent-hyper-necessity. That’s what we'll call it: U.U.H.N. This title, at least avoids most of the problems with naming it a “first cause”.

This “thing” then, has just been shown to be absolutely necessary, given the fact that we can look around and conclude that We know we are here at this point in space-time