A Good Infinite Regress Step of Some Cosmological Arguments

[Lawrence Crocker]

As this thread shows, discussion of the issue of completed infinities tends to gravitate towards efficient causation and the possibility or impossibility of an infinite past.

Where I think there is a possibility of a good "no infinity" argument is with respect to explanations for finite beings. I am not sure who first said something like "explanation must come to an end," but it is surely ancient. Explanations often follow efficient causation back in time, and so come to an end at some first date (whether or not time goes back farther), but explanation can also go "deeper" in the way that chemistry explains aspects of biology and physics explains chemistry. There may be another intelligible sense of something like "deeper" in the notion of explanations of "sustaining causation" as in the claims that every physical particle would blink out of existence were it not for underlying sustaining causes. If there are layers of sustaining causes in this way, then explanations based upon them must come to an end, whether or not the hierarchy of sustaining causes does. Finally, there can be a sequence of purposes based upon something like Aristotle's final cause, as was Aristotle's prime mover argument. To the extent that explanation in terms of purposes works, it too must come to an end. So there are other kinds of explanation regresses that have been used in cosmological arguments in addition to efficient cause explanation going step by step into the past .

So far as go their premise that these explanatory "regresses" must come to an end, theses arguments seem to me OK. It is putting the rest of a sound cosmological proof around the true premise that has proven difficult.

[Noax]

Can you explain what you mean by entropy? Suppose I take the set of integers ..., -4, -3, -2, -1, 0, 1, 2, 3, ...

Integers don't exhibit entropy nor the arrow of time that the asymmetry of entropy gives the states of our physical universe. But integers are a great example of the typical arguments against an infinite past. If there is an infinite past (I don't personally think there is meaning to the concept), it does not require a beginning. The integers exist despite lack of a last-one at either end. Time in this universe however behaves nothing like integers. IC seems to differ:

The universe cannot be infinite-in-the-past, at the very least: that we can know deductively.

Love to see this deduction. The same logic would prove that there must be a lowest integer.
You attempt to demonstrate that by describing integers as 'happening', but when infinity is considered, suddenly declare the term 'happening' to be something inapplicable to integers.

That may be so, although certainly life on earth has progressed from disorder to order. Why do you think that is?

Earth life is powered by an external energy source which is necessary to convert disorder to order.

if entropy is the law, then from where did the universe get this marvellous amount of energy and order from which it is now progressively declining entropically? There must have been an immense infusion of it somehow...but how?

Entropy is not the running down of energy. Energy is conserved over time, and in fact adds up to zero. But yes, physicists need models that explain/predict the 'marvelous low amount' of entropy and also the flatness of space, both seemingly improbably things.

There are actually logically only two possibilities here. Either a) the universe had a beginning, or b) the universe had no beginning.

You need to define 'had a beginning' here, and 'universe' as well. The definition of universe uwot gave is quite good for the purpose of this discussion (as opposed to 'all existence' which includes God and anything else supernatural), and I think you pretty much use that. So the question you ask seems to be an objective one (not one that is true only from a point of view), and objectively, the universe has no current state, and thus 'had a beginning' is a begging wording of the concept. You can't switch verb tense in the middle of a question. Logic does not acknowledge your 'only two possibilities'.

It seems that time as we measure it has a lower bound at the big bang, and time is part of the universe, so it is not valid to posit time outside the universe to express something like "God created ..." when there is no time for a god to do that, at least not the kind of time we know.
OK, you're up front about your biases, but you seem to be under the delusion that your arguments are evidence/proof. You have to drop the begging in order to formulate a valid argument for the necessity of a god.

[Immanuel Can]

But integers are a great example of the typical arguments against an infinite past. ... The same logic would prove that there must be a lowest integer.

Untrue. You've misunderstood here, a bit. I'll try to clarify.

Causality is not integers, because integers do not "cause" one another. But we're talking about things that cause other things, which means the effect can never happen without the cause, or before the cause. That's a crucial caveat there.

You have to add in the factor of each integer being dependent on the previous one, in other words.

Infinite integers is what we call a "conceptual infinity," which is quite possible to have, since it's not real; but causality, which is reality, posits an "actual infinity" -- i.e. a literal chain of caused events, each one dependent on the previous. And to have a real one of those is impossible, as we can deductively see for certain.

You attempt to demonstrate that by describing integers as 'happening', but when infinity is considered, suddenly declare the term 'happening' to be something inapplicable to integers.

When you say this, you come very close to seeing why your critique above was off target. For you are quite right: integers are not "happenings." But as I noted above, I only used integers as placeholders for caused events, to make thinking about the chain of causality easier: I did not imply that causality IS integers.

Logic does not acknowledge your 'only two possibilities'.

The Law of Non-Contradiction does: either a thing had a beginning, or it had none. And really, that's not even debatable, because it's basic logic. If a person doesn't understand that, his dispute really is with the whole concept of reason, not with me.

OK, you're up front about your biases, but you seem to be under the delusion that your arguments are evidence/proof.

"Biases"? Well, if you mean the things a person thinks are true, then I guess we've all got those?

But no. I was just pointing out that mathematics proves what I said. That's all. If one were to want to fight with the laws of logic and the laws of maths, then I don't know where they'd go from there. I suspect we couldn't find much out.

You have to drop the begging...

I'm sorry...I didn't "beg" anything, so far as I can see. I just presented an argument. And it wasn't one that even depended even a scratch on what you call my "biases."

[Immanuel Can]

Ah! You're still here!

Good. I was afraid we'd lost ye, Lawrence. You'd gone silent.

As this thread shows, discussion of the issue of completed infinities tends to gravitate towards efficient causation and the possibility or impossibility of an infinite past.

Yes. But I think that's perhaps a necessary preparatory kind of thing. The first blink of light is to realize that the positing of an actual infinity -- for whatever purpose -- is simply not reasonable. Once one has seen that, one can go in various directions with the realization, of course.

I think you're observation about "sustaining causation" is very, very interesting indeed. I hadn't thought of it in that "vertical" dimension, having previously focused my thought on the "horizontal" axis of time and causation.

And "purpose" causation is even more interesting. How can there be a "purpose" unless there is a Purposer? And this Purposer would, supposedly, be the final answer to the question of why the guy (human) who invented the thing (say, a computer), that serves the purpose (storing data) has that purpose anyway (why do humans invent instruments to store data) and so on. Ultimately, there would have to be a "purpose" for that whole "purpose-driven" chain. Very interesting.

So far as go their premise that these explanatory "regresses" must come to an end, theses arguments seem to me OK. It is putting the rest of a sound cosmological proof around the true premise that has proven difficult.

Well, at the very least we've got a kind of "negative" proof, don't we? We've at least disproved the idea that any explanation that posits an actual infinity, in any relevant dimension, is bound not to be true, have we not? So that would move us into the set of explanations that posit a First Cause of some kind instead.

And I'm not sure Cosmological Arguments are really designed to do more than that. Maybe the next step (positive demonstration) is not tightly deductive in the way our disproof of actual infinites is, but requires something like induction, abduction or even the supplementation of a kind of 'faith.'

[wtf]

I trust that clarifies the case I'm pointing out.

Not in the least.

You want to be able to make the claim that "Every event has a cause."

Ok. Take the integers again and let's say they represent events, and each integer's immediate predecessor is its "cause."

Now -47, does that have a cause? Yes, -48.

-44324324, does that have a cause? Yes, -4432435.

Challenge: Can you find a single event that does not have a cause? No, you can't.

So we have a model of causation such that TWO things are true:

1) Every event has a cause; and

2) There is no first cause.

Now of course you want to object, "But how did everything get started then?" It seems to me that this question makes many hidden assumptions about how time and causality work. It's a different question. A good question perhaps.

But that does not contradict my model. We wake up, look around, realize we're event -12 and we were caused by -13. Doesn't seem to be a problem. Any event we consider does in fact have a cause. That satisfies the "causist" demand that everything must have a cause. It doesn't satisfy the first-mover fans but they are always looking for a reason to invoke God.

[Immanuel Can]

You want to be able to make the claim that "Every event has a cause."

I don't need to "claim" it. It's manifestly true, and a basic axiom of science, so I just point it out.

Ok. Take the integers again and let's say they represent events, and each integer's immediate predecessor is its "cause."

Now -47, does that have a cause? Yes, -48.

-44324324, does that have a cause? Yes, -4432435.

Yes, this is right, so long as you remember we're not actually talking about integers but causal chains.

Challenge: Can you find a single event that does not have a cause? No, you can't.

Which is precisely what I said above.

So we have a model of causation such that TWO things are true:

1) Every event has a cause; and

2) There is no first cause.

No, actually. What you have done is to create only a conceptual (i.e. purely imaginative, theoretical, non-existent) regress -- and nobody, least of all me, ever said such were impossible.

But try my example of converting that concept into the real world:

Write 10. Do it, on paper, right now if you need to.
But imagine you cannot do it until you have written 9 first, so write 9...
But do not write 9 until you have first written 8,
And do not write 8 until you have written 7...
And so on, into the integers like -1, -2. Never, never write a number until you have written its previous one first.

Question: if you do as I say, when will you be able to start to write?

Answer: you never will. In theory, every one of those numbers may have a prior number. But in reality, you never get to write even one of them. That's the difference between a merely conceptual regression (like integers) and an actual regression of causes.

Hope that helps. Seriously, if you doubt me, try the experiment. I absolutely promise you, you won't be able to write even one number without breaking the rules there.

[wtf]

No, actually. What you have done is to create only a conceptual (i.e. purely imaginative, theoretical, non-existent) regress -- and nobody, least of all me, ever said such were impossible.

LOL. Moving the goalposts. You: You can't have an infinite regress of causes. Me: Yes, watch this. You: Oh I didn't mean a CONCEPTUAL regress. Me: LOL. Moving the goalposts.

You claim using sophomoric language games to figure out how the universe began is something other than conceptual? What, you have a particle accelerator in your basement along with a captive team of physicists? This entire conversation is conceptual. You agree that my example is valid, right?

Question: if you do as I say, when will you be able to start to write?

As I already explained, asking how the world got started is a completely different question. And your example incorporates many hidden assumptions about how time and causality work; assumptions that are already coming under heavy attack by modern physics. You are simply playing language games using naive and discredited ideas of time and causality.

I showed you a model of causality in which every event has a cause yet there is no first cause. How did it get started? I don't know, maybe it was always here. Maybe causality is circular. How do you know it's not? Look around you. Everything's here and everything had a cause. My model is more likely to be right than yours.

[uwot]

You want to be able to make the claim that "Every event has a cause."

I don't need to "claim" it. It's manifestly true, and a basic axiom of science, so I just point it out.

Christ in a bucket, you don't half talk some bollocks, Mr Can. In the first place, it is not manifestly true that every event has a cause; you simply can't get your head round that fact that it might not be true. But "basic axiom of science"? There are no axioms of science. That's what makes it science.

[Immanuel Can]

LOL. Moving the goalposts. You: You can't have an infinite regress of causes. Me: Yes, watch this. You: Oh I didn't mean a CONCEPTUAL regress. Me: LOL. Moving the goalposts.

Not an inch. You didn't read carefully. The talk from the start has been about "causes," which are actual. You're not aware of the difference between a concept and a reality. Cause-and-effect is a function of reality, but not of integers.

Oy vey. I suppose I'll have to refer you to the literature, because I can't make it any simpler than I already have and don't know how to make it simple enough, but maybe someone else can explain it. Try David Hilbert's mathematics.

Question: if you do as I say, when will you be able to start to write?

You're not getting it. I didn't say "Talk about doing it." You won't get the point by talking, apparently. I meant go and actually try to do it. Go for it. See what happens.

I'll talk to you about your findings afterward. But of course, if I'm right, that will never happen, since you'll never even be able to write a single number.

You'll see.

[wtf]

Not an inch. You didn't read carefully. The talk from the start has been about "causes," which are actual.

What does "causes are actual" mean? You have evidence for that claim? Or even an interpretation of the words that makes the statement sensible?

You're not aware of the difference between a concept and a reality. Cause-and-effect is a function of reality, but not of integers.

As I've said three times now, you are implicitly making hidden assumptions about causality for which you are not providing proof, nor even acknowledging that they are assumptions.

Oy vey. I suppose I'll have to refer you to the literature, because I can't make it any simpler than I already have and don't know how to make it simple enough, but maybe someone else can explain it. Try David Hilbert's mathematics.

You're name-checking Hilbert? Please supply specific citations in support of whatever it is you are trying to say.

Question: if you do as I say, when will you be able to start to write?

You're not getting it. I didn't say "Talk about doing it." You won't get the point by talking, apparently. I meant go and actually try to do it. Go for it. See what happens.

I'll talk to you about your findings afterward. But of course, if I'm right, that will never happen, since you'll never even be able to write a single number.

But this is silly. Childish. To write this post I need a computer, but to have a computer there needed to be a factory, and to have a factory there needs to be bricks and metal, and those require the earth, and those require the solar system, and now what caused the big bang? Ergo you can't write a forum post. Yet here it is. You seem to be doubling down on pretending reality doesn't exist around you.

You say there must be a first cause, but I showed a model in which every event has a cause yet there is no first cause. To write down the numeral 5 I don't need to figure out how the universe started, I just need to write down the numeral 5. The endless back-chain of causes from the numeral to the pencil to the wood to the tree to the ground to the earth is already baked in to reality. You don't know how the universe started and neither do I, but that doesn't stop either of us from going about our every day lives.

The fact that you want to deny that I can write a forum post or write down the numeral 5 shows a certain lack of seriousness in your discourse.

[ken]

Suppose the universe is modeled by the integers, ..., -3, -2, -1, 0, 1, 2, 3, ...

It will be seen that this collection of points, or instants, or whatever you prefer to call them, is unbounded but not necessarily infinite. You are making an unjustified leap from the potential infinity to the actual, as named by Aristotle. It's perfectly possible that we have each of those points of time, just not all at once.

So perhaps I wake up and I'm living at -43434. Or 5454343. I'm at some point. I'm at a finite point. There is no point of time which is infinite.

You seem to have me backward. I was presenting the case against the existence of an actual infinite.

Since you ask, let me simplify that case as much as I can.

Take out a pen.

Write the number 1.

But before you do, write 0.

But before you do that, write -1.

But not until you've already written -2.

When you've already written -3.

But not until you've written the number -4.

And so on, to infinity.

The question, then, is "When will you actually get to write the number 1? Remember, every number before must be written prior to it.

Obviously, then, you will never ever have the chance to write 1, if you play by those rules. But that is exactly what an infinite regress posits: that before any action, there has to be an infinite chain of prior causes. But if the chain is infinite, then no prior cause ever gets to take place, because the one prior to it hasn't happened yet, because the one prior to that hasn't happened yet...and so on forever.

But the point is the one prior HAS already happened, obviously. If there is some thing happening NOW, then obviously some thing happened prior, so on, infinitely. Nothing hard at all to grasp that most basic of wisdom.

IF every action is just a re-action from a prior or previous action, then an infinite chain of prior causes is obviously 'WHAT TAKES PLACE'. A chain of 'infinite causes' is what HAPPENS and is therefore 'WHAT IS'.

The point is that whether you use integers or causes, if the number prior to any number you pick is a prerequisite for the next one, and if the set is infinite, NO NUMBER EVER HAPPENS. It can't.

But obviously NUMBERS DO HAPPEN, human beings have invented them and use them, you are talking about them, so numbers MUST OF ALREADY HAPPENED. Therefore, ALL prerequisites have already taken place.

The point is there is only NOW. Whatever number is picked NOW, means the prerequisite numbers have already happened. And, whatever number picked NOW is the prerequisite for the next numbers to follow. Whatever happens NOW is the cause, for all that follows. NOW is the beginning, and was the end by the way.

Creation is continual. Always has been and always will be.

Now, I'm suggesting that if our universe is a chain of causes, just like Naturalism or Physicalism claim it is, then it cannot be infinite. It will have to start somewhere, with an Uncaused Causer, because absent that, NOTHING EVER HAPPENS according to the Naturalistic theory itself.

How unsound and invalid is that what you are suggesting here?

I think that a Naturalistic theory itself would NOT suggest that absent an uncaused causer, nothing ever happens. I would suggest otherwise. I would suggest the opposite is true because things happen there was always a cause or causer before. A natural theory of 'ALL there is' would be Every thing caused, happened be-cause of some thing else prior. That 'some thing else' has to involve at least two other things, coming together in order to create or cause 'what IS' NOW.

IF the Universe is a chain of causes, then THAT by itself it means, that can NOT start somewhere. It can NOT start with an uncaused causer, because it states it is a chain of causes, which by definition means ALL causers were caused, in an unbroken line or link of causes. There is NO suggestion anywhere that there is a missing link anywhere. There is nothing suggesting a "first uncaused causer". Nothing of the type you are trying to suggest exists, anyway. The type you are trying to suggest is a complete misinterpretation of what has been written. The 'First Causer' you are referring to is the NOW. The Being, or Creator, that exists NOW, always has Been and always will Be. What happens NOW is the Creator or Causer of ALL that follows. This Being is the reason for ALL else, that follows. Absolutely Everything happens and exists, in the infinite, NOW. This Being, who exists NOW, is the Causer, or the Creator, which is still being misinterpreted and mistaught through religion by the way, but anyway this Being is the Cause for Everything. Everything happens Be-Cause of NOW. NOW can, and does, exist for-ever and for infinitely. NOW has always existed be-cause of what happened be-fore, and, NOW will always keep existing be-cause it is the first caused cause be-fore the future.

I trust that clarifies the case I'm pointing out. I wasn't the one who invented it, but it seems quite right to me. It means that there is no actual infinity of causes.

[/quote]

It may seem quite right to you, but when looked at fully it is a rather silly view of what actually IS. You did not really clarify anything other than to yourself that your own already held belief is right. But all you are really doing is trying anything you can to fit anything in with your mistaught view of how God created Everything. What you have said here does NOT mean that there is no actual infinity of causes at all. Your view, that what you are suggesting about there is a chain of causes that is finite, which fits in with Naturalism or Physicalism claims is laughable at the best. What you have said here is just an attempt at trying to fit what is right, in with your already held distorted view of how God is the first causer. I, on the other hand, have (partly) shown HOW a 'God' can create Everything and how this can still fit in with any scientific view of nature and/or with natural occurrences. If, every action causes a reaction, then that causes or creates an infinite NOW, with NO first uncaused cause(r).

Seriously, how can you even think, let alone try to propose, there be a chain of causes that is NOT infinite?

How could there be a first uncaused causer in a chain of causes?

If every action causes a reaction, then even a big bang type reaction was obviously caused by an action. To Me, what that (prior) action was is pretty obvious, but this will not even be looked at, let alone confirmed, until people stop believing that the big bang was the start or the beginning.

[ken]

As this thread shows, discussion of the issue of completed infinities tends to gravitate towards efficient causation and the possibility or impossibility of an infinite past.

Where I think there is a possibility of a good "no infinity" argument is with respect to explanations for finite beings.

If you are talking about human beings being a finite being, then that is sadly part of the reason WHY human beings think the Universe MUST also have to be finite. Human beings have a propensity to see other things behaving in the same way they themselves do. (There is a word for this propensity, but I forget it now. Something like 'amorphosizing'.) Anyway, human beings, individually and on a whole, appear to have had a beginning and are seen as having an ending also, so human beings will assume and see in ALL other things that they also must have had a beginning and will have an ending to, including the Universe, Itself. But there is absolutely no evidence that the Universe did start and will end. The saying, "In the beginning", in relation to the Universe, Itself, is just a common phrase, which has caught on. Some people to this day still say that as though it is the Truth.

I am not sure who first said something like "explanation must come to an end," but it is surely ancient. Explanations often follow efficient causation back in time, and so come to an end at some first date (whether or not time goes back farther), but explanation can also go "deeper" in the way that chemistry explains aspects of biology and physics explains chemistry. There may be another intelligible sense of something like "deeper" in the notion of explanations of "sustaining causation" as in the claims that every physical particle would blink out of existence were it not for underlying sustaining causes. If there are layers of sustaining causes in this way, then explanations based upon them must come to an end, whether or not the hierarchy of sustaining causes does.

Why MUST explanations come to an end?

Why do you say explanations MUST come to an end? One of the first things in discovering and learning HOW ALL things work, is discovered and learned in HOW you, yourself, work. So, WHY do you think/believe, and say "Explanations MUST come to an end"?

For every thing that happens there is a cause AND a why. Just because you may not be able to see and know them yet does NOT mean that that is the end, so they MUST come to an end. Also, just because a statement like, "explanation must come to and end", is ancient is NO reason that it is then true.

I have followed back the WHY questions and have been able to answer ALL of them, providing Me with A reason, the cause and the why, for Everything, which by the way fits a perfect picture.

Finally, there can be a sequence of purposes based upon something like Aristotle's final cause, as was Aristotle's prime mover argument. To the extent that explanation in terms of purposes works, it too must come to an end. So there are other kinds of explanation regresses that have been used in cosmological arguments in addition to efficient cause explanation going step by step into the past .

So far as go their premise that these explanatory "regresses" must come to an end, theses arguments seem to me OK. It is putting the rest of a sound cosmological proof around the true premise that has proven difficult.

If, as you say, explanatory regresses MUST come to an end is a true premise, then there MUST be some kind of evidence and proof for this.

Your alleged "true premise" has not been proven yet. Thus probably the very reason a sound cosmological proof around the supposed "true premise" of "explanations must come to an end" IS difficult, maybe impossible, to prove.

Name one or ALL of the explanations that supposedly and allegedly are at their end, which by the way would be the proof and evidence needed that 'explanation MUST come to an end', and, if you are truly interested, then I can show you HOW that is NOT the end.

IF you are truly interested in the idea that the Universe could be infinite, then that can be easily shown. If, however, you want to and/or are believing that the Universe is finite, then no amount of proof and/nor evidence can show you otherwise.

[ken]

But integers are a great example of the typical arguments against an infinite past. ... The same logic would prove that there must be a lowest integer.

Untrue. You've misunderstood here, a bit. I'll try to clarify.

Causality is not integers, because integers do not "cause" one another. But we're talking about things that cause other things, which means the effect can never happen without the cause, or before the cause. That's a crucial caveat there.

You have to add in the factor of each integer being dependent on the previous one, in other words.

Infinite integers is what we call a "conceptual infinity," which is quite possible to have, since it's not real; but causality, which is reality, posits an "actual infinity" -- i.e. a literal chain of caused events, each one dependent on the previous. And to have a real one of those is impossible, as we can deductively see for certain.

But I certainly can deductively see an actual real infinity. I see it very possible to have a literally unbroken chain of caused events. In fact I have not yet seen how it could be possible to have the opposite. How could it be possible to have a literally broken chain of caused events.

Can you provide an example and/or an explanation of how an uncaused causer could have caused a chain of caused events? So that I could at least take a look at that.

OK, you're up front about your biases, but you seem to be under the delusion that your arguments are evidence/proof.

"Biases"? Well, if you mean the things a person thinks are true, then I guess we've all got those?

Yes every adult human being has things they think are true. But are the things that you "think" are true, really beliefs instead?

If so, then those beliefs cause a confirmation biases point of view, which is what appears to be being expressed by you here.

Do you believe that a first causer, called God (or whatever else), caused or created the Universe, or do you just think this is true?

Your honest answer here will provide more insight for others.

But no. I was just pointing out that mathematics proves what I said. That's all. If one were to want to fight with the laws of logic and the laws of maths, then I don't know where they'd go from there. I suspect we couldn't find much out.

Mathematics certainly does NOT prove what you have been saying at all. Mathematics certainly does NOT prove that a first causer created everything. Mathematics certainly does not prove any "God", which you perceive and believe is true. In fact the type of "God" you perceive, will be found could NOT exist. Anyway, maths also certainly does NOT prove that your "God" caused everything.

But I know that the 'God' that I am proposing, and HOW that 'God' creates every thing, can be proven scientifically, logically, and probably also with the help of mathematics. By the way this 'God' also fits in with every religious and spiritual perspective also.

You have to drop the begging...

I'm sorry...I didn't "beg" anything, so far as I can see. I just presented an argument. And it wasn't one that even depended even a scratch on what you call my "biases."

[/quote]

To Me, your whole argument is invalid and unsound anyway. To Me, your whole argument is a great example of confirmation biases, and how they play a huge part in forming views, whenever a person already has and holds a belief.

You are right in that your argument was not one depended upon your biases, but your invalid and unsound argument was surely constructed and made up because of your biases.

I will be able to use the above as more proof and evidence for what it is that I want to say and express.

[ken]

You want to be able to make the claim that "Every event has a cause."

I don't need to "claim" it. It's manifestly true, and a basic axiom of science, so I just point it out.

You do realize that 'every event' means absolutely ALL events have a cause, therefore there could NOT be a first cause without a prior cause to that, right?

How can you argue that 'EVERY event has a cause', and even say it is manifestly true, and a basic axiom of science, in one sentence (premise), but in the very next sentence (premise) dismiss that first sentence (premise) wholeheartedly and state that, "But there actually is one event that does not have cause"?

The two just do not logically follow on from each other.

Ok. Take the integers again and let's say they represent events, and each integer's immediate predecessor is its "cause."

Now -47, does that have a cause? Yes, -48.

-44324324, does that have a cause? Yes, -4432435.

Yes, this is right, so long as you remember we're not actually talking about integers but causal chains.

Challenge: Can you find a single event that does not have a cause? No, you can't.

Which is precisely what I said above.

So we have a model of causation such that TWO things are true:

1) Every event has a cause; and

2) There is no first cause.

No, actually. What you have done is to create only a conceptual (i.e. purely imaginative, theoretical, non-existent) regress -- and nobody, least of all me, ever said such were impossible.

But try my example of converting that concept into the real world:

Write 10. Do it, on paper, right now if you need to.
But imagine you cannot do it until you have written 9 first, so write 9...
But do not write 9 until you have first written 8,
And do not write 8 until you have written 7...
And so on, into the integers like -1, -2. Never, never write a number until you have written its previous one first.

Question: if you do as I say, when will you be able to start to write?

Answer: you never will. In theory, every one of those numbers may have a prior number. But in reality, you never get to write even one of them. That's the difference between a merely conceptual regression (like integers) and an actual regression of causes.

Hope that helps. Seriously, if you doubt me, try the experiment. I absolutely promise you, you won't be able to write even one number without breaking the rules there.

You can even try another experiment by not doing some thing, until you do some thing prior to it. Never, never do some thing until you have done the thing previous to that one.

Question: if you do as I say, when will you be able to start to do anything?

Answer: you never will. I absolutely promise you, you will not be able to do one thing.

BUT, that does NOT prove anything one way or the other. That is just an experiment telling you not to do some thing until you do some thing prior, ad infinitum.

[Immanuel Can]

What does "causes are actual" mean? You have evidence for that claim? Or even an interpretation of the words that makes the statement sensible?

Ah. I thought so. I figured out afterward that you were unfamiliar with the phrase "actual infinite." My apologies...I thought you were aware of the term. I'll explain.

A "conceptual" infinite is one that doesn't really exist but can be imagined to exist. Take pi, for example: it can be thought about, but cannot actually be calculated. Nobody has ever seen all the digits in pi, and because it's infinite, nobody ever will. But we can think about the idea of pi.

In contrast, an "actual" infinite is one that actually exists in the real world. Such a thing cannot happen. A "causal regress" is a combination of real-world causality and an infinite timespan. That combination is just not possible, because each "cause" must happen before the next one does.

As I've said three times now, you are implicitly making hidden assumptions about causality for which you are not providing proof, nor even acknowledging that they are assumptions.

Science. Science believes in causal explanations for every event that has a beginning. In other words, it assumes that things never "just start to happen for no reason." If we do believe such things happen, we are believers in magic, not science. Science looks for causality. If it finds none, it cannot get any grip on the thing in question, because it has to answer "why." If there is no causality, there is no "why" to ask about.

Fortunately for science that hasn't happened yet, so far as we know. There are things for which science does not yet know a cause; but in every case where it has assumed causality and then pursued it to an answer, it has found it. So science itself depends on causality.

Science does have assumptions, and causality is one of them. But causality is a very secure one. We know of nothing that has started to happen that did so without a cause.

You're name-checking Hilbert? Please supply specific citations in support of whatever it is you are trying to say.

Google "David Hilbert mathematician," if you wish more.

Question: if you do as I say, when will you be able to start to write?

You're not getting it. I didn't say "Talk about doing it." You won't get the point by talking, apparently. I meant go and actually try to do it. Go for it. See what happens.

I'll talk to you about your findings afterward. But of course, if I'm right, that will never happen, since you'll never even be able to write a single number.

But this is silly. Childish. To write this post I need a computer, but to have a computer there needed to be a factory, and to have a factory there needs to be bricks and metal, and those require the earth, and those require the solar system, and now what caused the big bang? Ergo you can't write a forum post. Yet here it is. You seem to be doubling down on pretending reality doesn't exist around you.

You've just restated exactly what I'm saying. Since things have "begun to happen," they are not uncaused. That is precisely my point. And it proves beyond any reasonable doubt that the universe is not infinitely old. That's also the point.

There are those around who want to say the universe never had a beginning. Aristotle thought that, and a few people today still believe it. But you can see they are mathematically wrong. At least, I trust you can see it now.

The fact that you want to deny that I can write a forum post or write down the numeral 5 shows a certain lack of seriousness in your discourse.

I don't deny you can do it. You've misunderstood there. I deny that if the universe were infinitely old you could do it. But, as I say, the universe is not infinitely old, as causality demonstrates. The fact that you can write the number 5 at all proves it conclusively, because if your writing was "caused" by a prior event (at point 4), which was caused by a prior event (at point 3) and so on infinitely, you would never ever arrive at point 5 and be able to write that number down...which is just what my little experiment of writing the numbers shows you beyond any reasonable doubt.

What you did when you wrote the number 5, in actuality may have been a free action on your part, or may have been part of a causal chain, just as the Naturalist or Physicalist would say -- I won't contests that claim for a minute here -- but either way, it was not part of an infinite causal chain. That's the one idea we can rule out absolutely. At some point, a "will" or "cause" from outside of the causal chain, one that does not itself have a cause, had to break into history and start the chain.

That's the whole point here.