Cosmological argument vs. LDS infinite regress

[changed]

What is mind? No matter. What is matter? Nevermind.

LOL! cute.

Yet scientists are beginning to think about how the properties of each universe are set when they are created in String Theory. Vibrating strings give rise to the possibility that such properties can be changed. For example, what would a universe be like if the gravitational constant were just a little higher or just a little lower thsn ours?

strings are a long way from being "fact" - but if you want to go that route, vibrating strings are still a "something" not a "nothing". Things can change form, but do not blink in and out of existence. everything that now exists has always existed in one form or another. There is no origin, there is no grand beginning.

Yes, the "fine tuning problem" what if the atomic force were different? etc. etc.

I love wiki's explanation of fine tuning:

http://en.wikipedia.org/wiki/Fine-tuned_universe

3 Possible scientific explanations

3.1 Multiverse

3.1.1 Bubble universe theory

3.1.2 Alien design

LOL! The multiverse - everything would exist given enough universes (including God BTW so they have not disproven ID) in any event, the multiverse will never be proven - totally hypothetical philosophy - so I don't know why they have it under "scientific" explanation LOL!

"Alien design" - now there is one that is getting closer. God lives on another planet, so I guess you could call him an alien.

.

[changed]

Any appeal to free will to justify the existence of evil must ultimately fail since any decision that any of us make can have its causal chain traced back to its ultimate origin, God as First Cause.

Free will - an inependent will - can only exist if part of you is independent and uncreated. Only a self-existent being with no creation can have a free will.There is no causal chain to its ultimate origin with a self-existent beings.

29 Man was also in the beginning with God. Intelligence, or the light of dtruth, was not created or made, neither indeed can be.

30 All truth is independent in that sphere in which God has placed it, to act for itself, as all intelligence also; otherwise there is no existence.

31 Behold, here is the agency of man, and here is the condemnation of man; because that which was from the beginning is bplainly manifest unto them, and they receive not the light.

(Doctrine and Covenants | Section 93:29 - 31)

The agency of man comes because we were not created - because part of us is self-existent.

the King Follett sermon starts:

The Immortal Intelligence

I have another subject to dwell upon, which is calculated to exalt man; but it is impossible for me to say much on this subject. I shall therefore just touch upon it, for time will not permit me to say all. It is associated with the subject of the resurrection of the dead—namely, the soul—the mind of man —the immortal spirit. Where did it come from? All learned men and doctors of divinity say that God created it in the beginning; but it is not so: the very idea lessens man in my estimation. I do not believe the doctrine; I know better. Hear it, all ye ends of the world; for God has told me so; and if you don’t believe me, it will not make the truth without effect. I will make a man appear a fool before I get through; if he does not believe it. I am going to tell of things more noble.

We say that God Himself is a self-existing being. Who told you so? It is correct enough; but how did it get into your heads? Who told you that man did not exist in like manner upon the same principles? Man does exist upon the same principles. God made a tabernacle and put a spirit into it, and it became a living soul. (Refers to the Bible.) How does it read in the Hebrew? It does not say in the Hebrew that God created the spirit of man. It says, “God made man out of the earth and put into him Adam’s spirit, and so became a living body.”

The mind or the intelligence which man possesses is co-equal [co-eternal] with God himself. I know that my testimony is true; hence, when I talk to these mourners, what have they lost? Their relatives and friends are only separated from their bodies for a short season: their spirits which existed with God have left the tabernacle of clay only for a little moment, as it were; and they now exist in a place where they converse together the same as we do on the earth.

I am dwelling on the immortality of the spirit of man. Is it logical to say that the intelligence of spirits is immortal, and yet that it has a beginning? The intelligence of spirits had no beginning, neither will it have an end. That is good logic. That which has a beginning may have an end. There never was a time when there were not spirits; for they are co-equal [co-eternal] with our Father in heaven.

I want to reason more on the spirit of man; for I am dwelling on the body and spirit of man—on the subject of the dead. I take my ring from my finger and liken it unto the mind of man—the immortal part, because it had no beginning. Suppose you cut it in two; then it has a beginning and an end; but join it again, and it continues one eternal round. So with the spirit of man. As the Lord liveth, if it had a beginning, it will have an end. All the fools and learned and wise men from the beginning of creation, who say that the spirit of man had a beginning, prove that it must have an end; and if that doctrine is true, then the doctrine of annihilation would be true. But if I am right, I might with boldness proclaim from the housetops that God never had the power to create the spirit of man at all. God himself could not create himself.

Intelligence is eternal and exists upon a self-existent principle. It is a spirit from age to age and there is no creation about it. All the minds and spirits that God ever sent into the world are susceptible of enlargement.

The first principles of man are self-existent with God. God himself, finding he was in the midst of spirits and glory, because he was more intelligent, saw proper to institute laws whereby the rest could have a privilege to advance like himself. The relationship we have with God places us in a situation to advance in knowledge. He has power to institute laws to instruct the weaker intelligences, that they may be exalted with Himself, so that they might have one glory upon another, and all that knowledge, power, glory, and intelligence, which is requisite in order to save them in the world of spirits.

This is good doctrine. It tastes good. I can taste the principles of eternal life, and so can you. They are given to me by the revelations of Jesus Christ; and I know that when I tell you these words of eternal life as they are given to me, you taste them, and I know that you believe them. You say honey is sweet, and so do I. I can also taste the spirit of eternal life. I know that it is good; and when I tell you of these things which were given me by inspiration of the Holy Spirit, you are bound to receive them as sweet, and rejoice more and more.

[Mudcat]

It is premise 3 that I question. What exactly is the property of an infinite set consisting of an infinite number of finite elements that logically entails that said set cannot act as first cause? I don't understand what is meant by operating "within infinity not in tandem with infinity".

Hey John,

Thanks for your thoughts.

Emphasis mine. Probably better stated as

3. If infinity exists, then an infinite number of finite causes can not create a solution to how they came to be, because a finite cause or effect is not infinite.

Many LDS would object to the idea that the elements are indeed finite since LDS doctrine is that all of us are eternal in nature. I don't think that addresses the argument you are presenting here. Eternal nature isn't sufficient for an element to be eternally capable of being a causal agent. And it seems to me that, per LDS doctrine, at some point in the past we had to be acted upon before we were enabled to act. Certainly others could disagree. This concept does address the question of why anything exists at all, setting aside causal chains for the moment. The LDS idea is that everything, including us, is eternal. In this sense, no infinite regression is needed, everything simply is. The First Cause is the eternal brute fact of the universe.

Emphasis and underline mine. This would seem logical. However, if all things are infinite then it would seem that all things are without causation. This doesn't make sense, if we assume their is some sort of divine plan to "do" things.

But the argument goes beyond mere existence. Since caused elements do exist, there must be a causal chain (premise 1). The flaw in the argument, specifically premise 3, is the insistence on viewing the elements within the infinite set individually rather than the set as a whole. Another way to express this premise would be to state: No one (finite) element of the set could be causa sui (per premise 2), therefore the entire set is incapable of being causa sui. Again, I believe this is a non-sequitur. Why must this be the case? Sets often have properties that none of the individual elements inside them possess. Sticking with infinity, the set of all real numbers from 1 to 2 is infinite, yet each single number composing the set is finite.

Using your example of the infinite set of numbers between 1 and 2, we could look at the set and say it is infinite within the set. Since the only thing we could say is that it begins with 1 and ends with 2 and any number between 1 and 2 exists within the set.

However, it would be impossible to determine the next number in the sequence if the set is infinite. For all practical purposes the number that follows 1 in this set, doesn't exist.

Regardless, in order to view the infinite set as a set, we have to close the set between 1 and 2 or whatever suits your fancy. We have assigned a distinct beginning and end. How would the situation be able to be addressed within the set, if the set were completely open?

[Mola Ram Suda Ram]

In eternity (infinity) there can be no first cause only is. First causes can only be at a point in infinity. It has no meaning when infinity is discused as a whole.

I think this is an important point. I discussed this a little in my last post. Since we can't comprehend eternity or infinity (unless you are Chuck Norris) then it is impossible to put an absolute on it.

[Vance]

Mudcat: As to what caused God to cause us after an infinity of non causality. I think he did it himself.

Nice speculation but it is really just a bunch of hand waving, because we are back to my original issue.

So what changed to cause God to change Himself? And what caused that change? Or in other words what is the real first cause?

[changed]

delete sorry - fritzing comp.

[changed]

And it seems to me that, per LDS doctrine, at some point in the past we had to be acted upon before we were enabled to act...

I think this was another reason for the fall... you don't have agency in what you cannot make an informed choice on - would you rather eat a boger or a lijjtrap? At this point, it is 50/50, until you put it in your mouth and eat them, you don't know what either are. Informed choice can only be made after the fact, after you gain experience... The first step in anything is taken in ignorance, without experience, and therefore without agency... I think our mortal birth is a transgression because it is getting spirits into something they have no experience with, and therefore do not have complete agency on.

I think it is a transgression to "act upon" a being with free will... God allows us to act for ourself, rather than forcing us into anything, rather than acting upon us... someone has to push us into the first step though, it seems a transgression is needed to give us our first experiences in things.

[changed]

Mudcat: As to what caused God to cause us after an infinity of non causality. I think he did it himself.

Nice speculation but it is really just a bunch of hand waving, because we are back to my original issue.

So what changed to cause God to change Himself? And what caused that change? Or in other words what is the real first cause?

I think this whole thread is missing the rather big point that time does not exist beyond the veil...

8 ... all is as one day with God, and time only is measured unto men.[/i]

(Book of Mormon | Alma 40: 8 )

no time, no before/after, no cause/effect.

Hard to think of existing without time, but it seems this is how God lives...

"I could notbe what I am now if I had not been what I was then"

the then and now sort of merge into one another, all creating who we are. Past/present/future are all linked to one another, and so I guess you could say they all exist simultaneously.

Are you fam with LaPlace Demon? http://en.wikipedia.org/wiki/Laplace's_demon

In the history of science, Laplace's demon is a thought experiment involving a hypothetical "demon" envisioned in 1814 by Pierre-Simon Laplace such that if it knew the precise location and momentum of every atom in the universe then it could use Newton's laws to reveal the entire course of cosmic events, past and future.

Does determinism take away free agency? I don't think it does. The point is not "if" the future is set in stone, but rather "who" sets it in stone. God knows everything, knows the future, so the future must be set in stone. We set our own future in stone through, so it is our agency. God knowing and causing are two different things... God knows, we cause, our agency...

Anyways, If God knows everything, then I guess that is determinism, which means the past/present/future already exist... there is no what was, or what will be - there is simply what is... no cause/effect before/after...

from LaPlace Demon -

The entire course of cosmic events can be found/are recorded in a single moment... in every single moment..

[Brade]

Apologies ba81,

I neglected your post in preference to others that were a bit easier to cipher through. Also, I hate being debunked so early on in the thread. Regular party pooper you are .

However, I grant you, you have debunked the argument as presented and from what I can tell, you are the only one who has done so. If I knew your address I would send you some cookies.

As you alluded to, there are a number of unstated premises. Obviously they operate on assumption. So removing assumptions, I will restate.

1. Based on any evidence we have, all things observable are finite and caused.

2. It is impossible for anything that is finite to cause itself.

3. If infinity exists, then an infinite number of finite causes can not create a solution to how they came to be, because they operate within infinity not in tandem with infinity.

4. Therefore, for anything to be, a First Cause (or something that is not an effect) must exist that is infinite.

What do you think?

Hey Mudcat, thanks for the cookies thought. Unfortunately, I don't think your revised argument fairs any better than the original. I think the same sort of criticism can be mounted against the validity of the revised argument that I mounted against the original. Also, the premises seem to muddy the waters a bit more; perhaps that's just a wording issue.

In any event, here's a form of cosmological argument that is most certainly valid and also happens to have clear premises:

P1 Everything that has a beginning of its existence has a cause of its existence.

P2 The universe has a beginning of its existence.

C1: Therefore, the universe has a cause of its existence.

P3: If the universe has a cause of its existence then that cause is God.

C2: Therefore, God exists.

You might already be familiar with this argument form. It's recently been championed by William Lane Craig, and it's a sort of Kalam Cosmological Argument. P2 is the first controversial premise and a discussion about it ought to lead into discussions about set theory, and there does seem to a be a good case against Craig's applications of intuitive notions of arithmetic to infinite sets. Infinite set theorists would argue that those intuitive notions don't hold for infinite sets, whether real or imaginary, and thus if we are dealing with infinite sets, the prima facie absurdities brought out in stories like Hilbert's Hotel and the Library Story are not actual absurdities.

Moving on from that, even if Craig overcomes objections from set theorists he still has the difficult task of showing that if the universe does have a cause of the necessary being sort, that that case (i.e. "First Cause") is the personal God of traditional Christianity. In my view, this is just as problematic, or perhaps even more so, than the set theory problems.

Let me expand on that last bit for a moment. Notice that in P3 there is a use of the expression "God." Most people will probably just make an assumption about the meaning of that expression; probably even unconsciously. So it's likely that a lot of people will see this argument and interpret the conclusion as being something about the traditional Christian God. But, nothing in the argument supports that move. The argument only deals with a sufficient and necessary existing cause, and P3 might just as well use the expression "Zazzleprod" in place of the expression "God." In other words, from the argument, the only thing that the expression "God" can mean is some sufficient and necessary existing cause; that's it.

The argument could be modified so that the expression "God" means the traditional Christian God, but that will require quite a bit more substance. I do think Craig has taken up that task, but I'm not sure how successful he's been.

[wenglund]

He guys,

While you are at it, could you also solve the chicken and egg conundrum. I'm sure it will go a long way in helping abate the problem of world hunger and perchance bring us out of the recession.

Thanks, -Wade Englund-

[Brade]

He guys,

While you are at it, could you also solve the chicken and egg conundrum. I'm sure it will go a long way in helping abate the problem of world hunger and perchance bring us out of the recession.

Thanks, -Wade Englund-

Actually, using the algorithm I came up with for the solution to the chicken/egg conundrum I was also able to figure out a way to make instant scrambled eggs using only air (of any quality). This might be of some use in solving world hunger.

[changed]

Chicken or the egg? Neither came before the other - it is a tie. Both were formed out of what eternally exists, of what has no begining.

[BCSpace]

He guys,

While you are at it, could you also solve the chicken and egg conundrum. I'm sure it will go a long way in helping abate the problem of world hunger and perchance bring us out of the recession.

Thanks, -Wade Englund-

Yes. Because of evolution, the egg came first. In fact, because of the infinite regress of Gods, I think we can safely say that the egg (or it's analog) has always come first in the case of every creature.

[Mola Ram Suda Ram]

Yes. Because of evolution, the egg came first.

WEll if you go that route niether came first.

[Mudcat]

Free will - an inependent will - can only exist if part of you is independent and uncreated. Only a self-existent being with no creation can have a free will.There is no causal chain to its ultimate origin with a self-existent beings.

The agency of man comes because we were not created - because part of us is self-existent.

You seem to be saying only uncreated beings can have free will, because there was nothing to cause their existence.

The obvious implication would be that a created be created with free will, because he was created. If it is possible for God to literally create a being, why would it then be impossible for him to allow his creation to have free will?

[Mudcat]

Mudcat: As to what caused God to cause us after an infinity of non causality. I think he did it himself.

Nice speculation but it is really just a bunch of hand waving, because we are back to my original issue.

So what changed to cause God to change Himself? And what caused that change? Or in other words what is the real first cause?

Well, I thought I was fairly clear I don't have a clue. Sorry for the misunderstanding.

Aside from God, the only other being that might know the answer to that is Chuck Norris.

[Brade]

If it is possible for God to literally create a being, why would it then be impossible for him to allow his creation to have free will?

I don't think it's impossible for one being to create another being where the created being has free will. The possibility of that, however, is going to turn on the properties of the being doing the creating and the properties of the world into which the created being is created.

[BCSpace]

Yes. Because of evolution, the egg came first.

WEll if you go that route niether came first.

The only exeption to the egg comming first could be the First Cause of all First Causes (multiple Gods, multiple universes).

[changed]

You seem to be saying only uncreated beings can have free will, because there was nothing to cause their existence.

The obvious implication would be that a created be created with free will, because he was created. If it is possible for God to literally create a being, why would it then be impossible for him to allow his creation to have free will?

If you are created, if you have a beginning, through the cause/effect net, everything can be traced back to your origin and therefore all of your actions are a result of how you were created.

Robots as an example. Everything they do can be traced back to their program/programmer.

Those who think they were created blame God for everything, why didn't you make me smarter? faster? nicer? etc. etc... yes - if you were created, then all your traits were given to you by your creator.

only a self-existent being has free will, has no origin that all of their actions can be traced back to.

God is cleaning up a mess He did not create. That is selfless. That is loving.

Our imperfections are another proof that God did not create us.

[Vance]

Mudcat: Aside from God, the only other being that might know the answer to that is Chuck Norris.

Finally!!! A real answer.

I wonder if we can get everyone to accept this newly revealed "fact".

[changed]

Did anyone post all the pre-existence scripts yet? Just for those who are not LDS... from an old file of mine

Does the bible teach that God made everything? I do not think that it does.

John 1:

1 IN the beginning was the Word, and the Word was with God, and the Word was God.

2 The same was in the beginning with God.

3 All things were made by him; and without him was not any thing made that was made.

Does not say God and Jesus were alone, nor does it say they created everything -

â??That was madeâ? â?? IF it was made, He made it. However, some things are not madeâ?¦

made does not mean ex-nihlo creation. I make a cake, but not out of nothing... make it with flour, eggs, sugar...

God did not create everything. God did not create Himself. God did not create evil. He is all powerful â?? what He is surrounded by He can control, but there is no need that He created it from nothingâ?¦ He is forming, organizing, reformingâ?¦ If He created it there would be no need for reform. No evil, no lost souls.

Isaiah 64:8 But now, O LORD, thou art our father; we are the clay, and thou our potter; and we all are the work of thy hand.

The potter did not make the clay â?? he only forms what already existsâ?¦

Does it say God created man from nothing? It does not â??

Gen 2:

7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.

8 And the LORD God planted a garden eastward in Eden; and there he put the man whom he had formed.

Formed â?? is different than created from nothingness â?? formed, organized, changed what was already thereâ?¦ then â??breathedâ? life into Adam, not created, breathed it in, placed it inâ?¦.

There are actually 2 different accounts of the creation in Gen, Chapter 1 gives one account, chapter 2 gives another account in which the creative days are given a different order. Here is chapter 2, in which Adam is created (7) before the garden of Eden (vs . Atheists use this as one example where the Bible contradicts itself. I see it as describing two different creative periods, one in heaven â??the generations of the heavensâ? and one on earth - seems pretty clear that chapter 2 is discussing formation/organization in heaven, before spirits were placed in the Earthâ?¦ see vs 5. â?¦ first He forms Adamâ??s spirit, then He places the spirit in a formed body in Edenâ?¦

4 These are the generations of the heavens and of the earth when they were created, in the day that the LORD God made the earth and the heavens,

5 And every plant of the field before it was in the earth, and every herb of the field before it grew: for the LORD God had not caused it to rain upon the earth, and there was not a man to till the ground.

6 But there went up a mist from the earth, and watered the whole face of the ground.

7 And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.

8 And the LORD God planted a garden eastward in Eden; and there he put the man whom he had formed.

9 And out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden, and the tree of knowledge of good and evil.

Our birth was not our beginningâ?¦

Jeremiah 1:5 Before I formed thee in the belly I knew thee; and before thou camest forth out of the womb I sanctified thee, and I ordained thee a prophet unto the nations.

We existed before the foundation of the world.

Eph 1: 4 According as he hath chosen us in him before the foundation of the world, that we should be holy and without blame before him in love:

Job 38: 4 Where wast thouâ?¦

7 When the morning stars sang together, and all the sons of God shouted for joy?

We are sons and daughters of God â??

Psa 82: 6 I have said, Ye are gods; and all of you are children of the most High.

we were there â?? we shouted for joy.

Ecc 12: 7 Then shall the dust return to the earth as it was: and the spirit shall return unto God who gave it.

â??returnâ? means coming to a state that we have previously been to â?? not â??comeâ? as if it were our first experience, but â??returnâ?

Zech 12:1 â?¦the LORD, which stretcheth forth the heavens, and layeth the foundation of the earth, and formeth the spirit of man within him.

He â??formedâ? our spirit before He placed us here on Earth. We call him our â??Heavenlyâ? Father because He is literally the father of our spiritâ?¦ spirit not created from nothingness, formed out of intelligences that God found Himself surrounded by.

[Mudcat]

If you are created, if you have a beginning, through the cause/effect net, everything can be traced back to your origin and therefore all of your actions are a result of how you were created.

Robots as an example. Everything they do can be traced back to how they were programmed.

only a self-existent being has free will, has no origin that all of their actions can be traced back to.

Lets say I created a rather advanced robot series. They looked just like humans, were programmed with the same desires, capable of learning, understood that there is good and evil. In fact lets say part of their programming was that they actually were programmed to believe they were human and also that they could choose whatever suited them.

Say after a few years, we noticed that the robots chose bad acts and good acts at varying points. A lot of it seemed to do with the people they were around, life experiences and so forth. Let's say one robot was raised as a Mormon and did lots of good things. Another was raised by some militant Islamists and decided to blow himself up in an embassy attack.

Now it seems rather obvious if these robots weren't here, they would have no power to do anything since they wouldn't have existed. I am with you that far. These bots didn't choose to be created.

But how can you say they didn't have free will.

[johndoe]

If it is logically impossible to create a world with beings given free moral choice without at least one being committing an evil action. And the presence of free will outweighs the existence of evil. Then is their really a problem of evil.

Yes, there really is a Problem of Evil.

Assuming you accept the traditional, classical assertions about the nature of God, including that He is absolutely omniscient, then we must necessarily live in a deterministic universe.

1. God is omniscient in an absolute sense.

2. Since 1., God infallibly knows the outcome of all our future decisions.

3. Since 1., our universe is deterministic.

4. Since 3., the outcome of all our decisions is determined by the initial conditions of the universe coupled with whatever actions are taken by causative agents (God) outside the universe which have an effect on our universe.

5. God is the only casual agent outside our universe having a causative effect on it.

6. God is absolute First Cause.

7. Since 4., 5. and 6., God determines the outcome of all our decisions.

8. We decide to do evil.

9. Since 7. and 8., God determines that the evil we do exists.

10. God is responsible for the evil we do.

Note that free will doesnâ??t enter into the picture. In any case, the Arminian has to define what he means by â??free willâ? since the classical assumptions about Godâ??s nature, namely that included in 1. above, require a deterministic universe. So only a compatibilist free will could be possible, which most Arminians do not accept (this is the logical contradiction). But even compatibilist free will doesnâ??t escape the argument above. The typical theodicy argues that free will requires that we choose evil in some cases. Why? Do beings in heaven possess free will? Does the perfected Christian have free will? If so, then we have an example of free beings who do not choose evil. It would interesting to see a proof of the assertion that at least one being must actually choose evil in order for all beings to be free in a morally relevant sense. Why couldn't God create all beings such that they are capable of actually choosing between good and evil but always choose good?

If such beings in heaven do not have free will, then why is free will a surpassing good? This is the crux of the issue. It would be very difficult to argue that compatibilist free will in this belief system, by which created beings are free to choose between good and evil according to natures and environments that God chose for them, provides a value that outweighs the negative effect of the existence of evil.

[mfbukowski]

Well, I think the problem is that few consider the possibility of other universes.

I'm confident that is the case in most cases.

They still have to answer the question as to what came before as much as we. The problem for them is that they have nothing before God whereas we have "infinite regress". In other words, they must answer the question first whereas we might not have to answer it at all. Looking at it from this perspective one realizes that creedal Christianity is not speaking about infinity at all but is quite finite and limited.

Exactly! And in most cases, all these "problems" are simply misunderstandings about what the subject of the conversation is. I would say that the OP itself is in that category. What suffers most from these misunderstandings is "christian unity" if that can ever become a reality.

[johndoe]

Hey John,

Thanks for your thoughts.

Emphasis mine. Probably better stated as

3. If infinity exists, then an infinite number of finite causes can not create a solution to how they came to be, because a finite cause or effect is not infinite.

This assumes that an infinite set cannot be composed of an infinite number of finite elements (or that such a set isn't "really" infinite), which simply isn't true.

Emphasis and underline mine. This would seem logical. However, if all things are infinite then it would seem that all things are without causation. This doesn't make sense, if we assume their is some sort of divine plan to "do" things.

I was actually arguing that the LDS idea of infinite existence doesn't address the argument based on observation of caused events. I think we agree here.

Using your example of the infinite set of numbers between 1 and 2, we could look at the set and say it is infinite within the set. Since the only thing we could say is that it begins with 1 and ends with 2 and any number between 1 and 2 exists within the set.

However, it would be impossible to determine the next number in the sequence if the set is infinite. For all practical purposes the number that follows 1 in this set, doesn't exist.

Regardless, in order to view the infinite set as a set, we have to close the set between 1 and 2 or whatever suits your fancy. We have assigned a distinct beginning and end. How would the situation be able to be addressed within the set, if the set were completely open?

You seem to be saying that an open-ended set cannot be infinite, which again, just isn't true. I think you are having problems understanding my response to your argument because you still are holding fast to an intuition which requires you to look at each element of the set individually rather than the set as a whole. The set of the infinitely regressing causes/effects is not bounded by finite bookends, at least at its "beginning". So in this sense, if you were to say that the set is infinite "within the set", it is important to realize that the set itself is not finitely bounded. Maybe I'm still not understanding what you mean.