God Must Exist: Infinite Regression is Impossible

[We_Are_VENOM]

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First off, by "universe", I mean all physical reality govern by natural law. This would include universes that we know/don’t know about.

1. If God does not exist, then the universe is past eternal.

Justification: We know that the universe exist, and if there is no transcendent supernatural cause, then either

A. the universe either popped into being, uncaused, out of nothing.
B. OR, it has existed for eternity.

I think we can safely remove posit A from the equation (unless there is someone who thinks it is a plausible explanation).

Let’s focus on posit B.

Based on posit B, we need not provide any naturalistic explanation as to the cause of our universe, considering the fact that the term “universe” applies (as mentioned earlier) to all physical reality, which means that any naturalistic explanation one provides is already accounted for as “eternal”.

And if God does not exist, then physical reality (the universe) is all there is, and thus must be eternal.

2. If the universe is not past eternal, then God exists.

Justification: If the universe (all physical reality) is NOT eternal, then it had a beginning.

Since natural law (mother nature) cannot logically be used to explain the origin of its own domain, then an external, supernatural cause is necessary.

If “nature” had a beginning, one cannot logically use nature to explain the origin of nature, and to do so is fallacious.

So, where nature stops, supernatural begins.

3. The universe is not past eternal.

Justification: If the universe is past eternal, then the causal chain of events (cause and effect) within the universe is infinite. But this is impossible, because infinity cannot be traversed or “reached”.

If the past is eternal, that would mean that there are an infinite amount of “days” which lead to today. But in order for us to have “arrived” to today, an infinite amount of days would have to be traversed (one by one), which is impossible, because infinite cannot be “reached”.

Consider thought analogy..

Sandman analogy: Imagine there is a man who is standing above a bottomless hole. By “bottomless”, of course if one was to fall into the hole, he would fall forever and ever and ever.

Now, imagine the man is surrounded by an infinite amount of sand, which is at his disposal.

Imagine if the man has been shoveling sand into this hole for an infinite amount of time (he never began shoveling, or he never stopped shoveling, he has been shoveling forever).

Imagine if the man’s plan was to shovel sand into the hole until he successfully filled the sand from the bottom, all the way to the top of the hole.

How long will it take him to accomplish this? Will he ever accomplish this task? No. Why? Because the sand is bottomless, so no matter how fast he shoveled, or how long he shoveled, the sand will never reach the top.

So lets put it all together…

The sand falling: Represents time travel, and the trajectory of the sand falling south of the top represents time traveling into the past, which is synonymous with past eternity.

The man shoveling: Represents the “present”, as the man is presently shoveling without halt. This is synonymous with our present causal reality. We are presently in a state of constant change, without halt.

Conclusion: If the sand cannot reach the bottom of the hole (because of no boundary/foundation) and it can’t be filled from the bottom-up to the present (man), then how, if there is no past boundary to precedent days, how could we have possibly reached the present day…if there is/was no beginning foundation (day).

However, lets say a gazillion miles down the hole, there is a foundation…then the hole will be filled in a finite amount of time, and it will be filled from the bottom-up.

But ONLY if there is a foundation.

Likewise, we can only reach today if and ONLY IF there is a beginning point of reference, a foundation in the distant past.

4. Therefore, an Uncaused Cause (UCC) must exist: As explained, infinite regression is impossible, so an uncaused cause is absolutely necessary.

This UCC cannot logically be a product of any precedent cause or conditions, thus, it exists necessarily (supplementing the Modal Ontological Argument).

This UCC cannot logically depend on any external entity for it’s existence (supplementing the Modal Ontological Argument).

This UCC is the foundation for any/everything which began to exist, which included by not limited to all physical reality…but mainly, the universe an everything in it.

This UCC would also have to have free will, which explains why the universe began at X point instead of Y point...and the reason is; it began at that point because that is when the UCC decided it should begin...and only a being with free will can decide to do anything.

This UCC would have to have the power to create from nothing (as there was no preexisting physical matter to create from, before it was created).

So, based on the truth value of the argument, what can we conclude of the UCC?

1. It is a supernatural, metaphysically necessary being
2. A being of whom has existed for eternity and can never cease existing
3. A being with the greatest power imaginable (being able to create from nothing)
4. A being with free will, thus, a being with a mind

This being in question is what theists have traditionally recognized as God. God exists.

In closing, I predict the whole "well, based on your argument, God cannot be infinite".

My response to that for now is; first admit the validity of the presented argument, and THEN we will discuss why the objection raised doesn't apply to God.

[The Tanager]

Well, if there is a good reason to drop said ideas, then yes. And before you ask, good reasons to drop your ideas were given: scientists and mathematicians have better ideas than yours.

Reasons were given. I shared why I don’t think they are good ones. It has nothing to do with the science and math of those scientists and mathematicians, but the philosophy.

It's different because space can be expanding without the whole thing getting bigger.

How? Explain it, don’t just say it’s the case.

Think integers vs decimal numbers. There are infinitely many decimal numbers between each pair of consecutive integers.

How does this support your claim? The number of decimal numbers between each pair of consecutive integers is identically infinite.

Two sets are the same size if there is a one-to-one correspondence, so the question is, is there a one-to-one correspondence? "Yes" is the only correct answer.

I’m contesting there is one-to-one correspondence. I showed that you can correspond numbers in a way where one set has 1 number that doesn’t correspond. This casts doubt on whether there is true one-to-one correspondence.

I am sticking to my original answer: that scientists are seriously considering it, is enough to justify that it is a rational concept.

Okay, appeal to authority, especially when that authority is spilling over into a discipline that the supposed authority isn’t an authority in (i.e., philosophy) isn’t enough for me.

You are missing the all important "only" qualifier here. A series contains certain numbers that are countable as a number is not the same thing as saying that whole series is countable as a series, because it might also contain numbers that are not countable as a number. But a series that only contains numbers that are countable as a number is the same thing as saying that whole series is countable as a series.

I didn’t miss that qualifier. Containing only numbers that are countable is not the same thing as every number in a particular series being counted in that series.

Just as a wall containing red bricks doesn't mean the wall is red, there might be blue bricks mixed in; but a wall containing only red bricks, is a red wall.

A wall containing only 8 inch long bricks is not an 8 inch wall.

It's synonymous. Just as a wall that contains only red bricks, means the whole thing is a red wall, even though a brick is red is a distinct idea from the wall is red. I kept asking you, what does moving through a series even mean, if not being moving through each and every single one of its members? Because that's what it means to me.

Let’s distinguish reaching a number and counting it to try to get at the difference. You are teaching your daughter the numbers, so you write out 0 to 10 on a piece of paper from left to right. You start at 0, say it, then move your finger to the 1 and then say it. Then your finger reaches 2 on the page and then you count it.

A number being countable means that if you reach it in the series, you will be able to count it. A series being countable means that you must both reach every number and count every number. The first is a potential characteristic, while the second involves an actual case. The problem with an infinite series is that you can’t reach every number (because it goes on without end), so that you can’t count it.

[Bust Nak]

Reasons were given. I shared why I don’t think they are good ones. It has nothing to do with the science and math of those scientists and mathematicians, but the philosophy.

I checked on The Oxford Dictionary of Philosophy, infinity is defined as "the unlimited; that which goes beyond any fixed bound. Exploration of this notion goes back at least to *Zeno..." (I have to subscribe to see more.) There isn't a standard Philosophy definition for "boundary" or "size." So why yours and not scientists' or mathematicians' definitions?

How? Explain it, don’t just say it’s the case.

By having space expanding, meaning the distance between two points is getting bigger, yet the universe does not have a boundary.

How does this support your claim? The number of decimal numbers between each pair of consecutive integers is identically infinite.

So there are more decimal numbers then integers, infinitely more. Therefore there are different sizes of infinities. That's how it support my claims.

I’m contesting there is one-to-one correspondence. I showed that you can correspond numbers in a way where one set has 1 number that doesn’t correspond.

That's moot because I have showed that you can correspond numbers in a way where is a one-to-one correspondence. If there is a way, then there is a way, doesn't matter how many other ways fail.

Okay, appeal to authority, especially when that authority is spilling over into a discipline that the supposed authority isn’t an authority in (i.e., philosophy) isn’t enough for me.

Philosophers thought the universe was eternal before scientists discovered red-shift as evidence for the big bang. Their authority is secondary when it comes to the real world.

I didn’t miss that qualifier. Containing only numbers that are countable is not the same thing as every number in a particular series being counted in that series...

Let’s distinguish reaching a number and counting it to try to get at the difference. You are teaching your daughter the numbers, so you write out 0 to 10 on a piece of paper from left to right. You start at 0, say it, then move your finger to the 1 and then say it. Then your finger reaches 2 on the page and then you count it.

A number being countable means that if you reach it in the series, you will be able to count it.

A series being countable means that you must both reach every number and count every number. The first is a potential characteristic, while the second involves an actual case...

So a sufficiently long finite series (1 sextillion members for example) would not be countable, because no one, not even with the help of today's super computer, with has actually reach every number one after another? Surely you don't mean that by "actual case," please clarify your criteria for a countable series so that it includes all finite series.

[The Tanager]

I checked on The Oxford Dictionary of Philosophy, infinity is defined as "the unlimited; that which goes beyond any fixed bound. Exploration of this notion goes back at least to *Zeno..." (I have to subscribe to see more.) There isn't a standard Philosophy definition for "boundary" or "size." So why yours and not scientists' or mathematicians' definitions?

I don’t see why you think they are different. Even one-to-one correspondence isn’t a definition of size, but how we can tell if two things have the same size.

By having space expanding, meaning the distance between two points is getting bigger, yet the universe does not have a boundary.

The distance between two points necessarily has a boundary, though.

So there are more decimal numbers then integers, infinitely more. Therefore there are different sizes of infinities. That's how it support my claims.

How are there more decimal numbers than integers? Are you saying they can’t be put in one-to-one correspondence?

That's moot because I have showed that you can correspond numbers in a way where is a one-to-one correspondence. If there is a way, then there is a way, doesn't matter how many other ways fail.

It’s not moot. If you ask a question and get two conflicting answers, you can’t just ignore one of those.

Philosophers thought the universe was eternal before scientists discovered red-shift as evidence for the big bang. Their authority is secondary when it comes to the real world.

Any scientist saying the universe is eternal is making a philosophical claim, including but not limited to their belief that their equations accurately portray reality.

So a sufficiently long finite series (1 sextillion members for example) would not be countable, because no one, not even with the help of today's super computer, with has actually reach every number one after another? Surely you don't mean that by "actual case," please clarify your criteria for a countable series so that it includes all finite series.

No, I would say 1 sextillion is countable. Any finite number is countable because of the very nature of what it means to be finite, whether or not you, I, or a super computer has actually reached that number.

The "actual case" is about the very nature of infinity and how you can't have reached every member of an unending series. If you can't have reached every member of the series, then you can't have counted every member. That is, the series is not fully countable. If the series is not fully countable, then the series isn't fully moved-through-able.

[Bust Nak]

I don’t see why you think they are different. Even one-to-one correspondence isn’t a definition of size, but how we can tell if two things have the same size.

There is a different because you think size implies a boundary.

The distance between two points necessarily has a boundary, though.

That's fine, so what's wrong with stating that the universe is expanding because space between any two points is expanding again?

How are there more decimal numbers than integers? Are you saying they can’t be put in one-to-one correspondence?

Exactly.

It’s not moot. If you ask a question and get two conflicting answers, you can’t just ignore one of those.

That's moot because there is only one correct answer: there is a one-to-one correspondence. "You can't get a correspondence if you try to do it in this particular order," doesn't invalidate this answer, nor validate any other answer to the question, "is there, or isn't there?"

Any scientist saying the universe is eternal is making a philosophical claim, including but not limited to their belief that their equations accurately portray reality.

You can say that for every scientific claim. If that counts as philosophical, then scientists are philosophers, as they used to be categorised as. As philosophers, they would still be the relevant authority.

No, I would say 1 sextillion is countable. Any finite number is countable because of the very nature of what it means to be finite, whether or not you, I, or a super computer has actually reached that number.

That's fine, but that doesn't answer my question. I didn't ask if the number "1 sextillion" is countable or not. I asked if the series {0, ..., 1 sextillion} is countable or not. I want to what makes a series countable, if every number in the series having the property "countable," wasn't enough to qualify.

The "actual case" is about the very nature of infinity and how you can't have reached every member of an unending series...

When you say "actual case," you were taking about mere possibility to have reached every members? If possibility is enough, then why did you reject my proof for appealing to the potential characteristic of being reached? I am not seeing the difference between "potential characteristic" of can reach, and the "actual case" can have reached.

[The Tanager]

There is a different because you think size implies a boundary.

No, I think growing in size implies there was a previous boundary that was surpassed. If an actual infinite can exist, then it would be a size without a boundary and, because of that, could never grow in size.

That's fine, so what's wrong with stating that the universe is expanding because space between any two points is expanding again?

That means the space between two points is expanding beyond what its previous boundaries were. If the “distance between two points” is the way you are referring (literally or metaphorically) to the extent of the universe, then the universe would be expanding beyond its previous boundaries.

Exactly.

But isn’t there an infinite amount of decimal numbers between 1 and 2? And isn’t there an infinite amount of integers?

That's moot because there is only one correct answer: there is a one-to-one correspondence. "You can't get a correspondence if you try to do it in this particular order," doesn't invalidate this answer, nor validate any other answer to the question, "is there, or isn't there?"

But I’m contesting that there is one-to-one correspondence. You take one arbitrary method and seemingly get an answer that is affirmative. I take another arbitrary method and get an answer that is in the negative. That should cause one to question if there really is one-to-one correspondence. Your method could simply be fooling us into thinking there is one-to-one correspondence when there is not.

You can say that for every scientific claim. If that counts as philosophical, then scientists are philosophers, as they used to be categorised as. As philosophers, they would still be the relevant authority.

My point is not about whether they are authorities on the subject or not (some scientists are trained/good philosophers; some aren’t), it’s about how we test their claims. If they were talking about science, rebuttals should be scientific. I’m not a scientist and I’m not making scientific rebuttals. I am comfortable making philosophical rebuttals to their philosophical points. When the philosophical critiques are made, I’m saying it doesn’t matter that they are scientists or philosophers; I’m saying let’s discuss the reasons.

That's fine, but that doesn't answer my question. I didn't ask if the number "1 sextillion" is countable or not. I asked if the series {0, ..., 1 sextillion} is countable or not. I want to what makes a series countable, if every number in the series having the property "countable," wasn't enough to qualify.

Yes, that series is countable. Not just because all of the numbers are countable types of numbers, but because all of those numbers can also be reached going through the series.

When you say "actual case," you were taking about mere possibility to have reached every members? If possibility is enough, then why did you reject my proof for appealing to the potential characteristic of being reached? I am not seeing the difference between "potential characteristic" of can reach, and the "actual case" can have reached.

Because that proof didn’t show that an infinite series has that potential characteristic.

[Bust Nak]

No, I think growing in size implies there was a previous boundary that was surpassed. If an actual infinite can exist, then it would be a size without a boundary and, because of that, could never grow in size.

Hence infinity + 1 = infinity? What's the problem again?

That means the space between two points is expanding beyond what its previous boundaries were. If the “distance between two points” is the way you are referring (literally or metaphorically) to the extent of the universe, then the universe would be expanding beyond its previous boundaries.

Hence the universe is expanding? That's the point.

But isn’t there an infinite amount of decimal numbers between 1 and 2? And isn’t there an infinite amount of integers?

Yes and yes. Since there is a one-to-one correspondence between integers and natural numbers, but isn't one between decimals and natural numbers, we can conclude that some infinities are larger than others.

But I’m contesting that there is one-to-one correspondence. You take one arbitrary method and seemingly get an answer that is affirmative. I take another arbitrary method and get an answer that is in the negative.

Which mean the only correct answer to the question, is there a one-to-one correspondence, is "yes, there is." That you cannot get a one-to-one correspondence in a particular manner does not change the fact that there is a one-to-one correspondence. Again, the question to "is there a way to match them?" would only be a "no" if there is exactly zero way of getting a match. There is at least one, therefore the answer is "yes."

That should cause one to question if there really is one-to-one correspondence. Your method could simply be fooling us into thinking there is one-to-one correspondence when there is not.

Maybe it is fooling us, but pointing out that you can't get a match if you do things in an another way isn't enough to cast doubt. Just as the fact that I can't bench-press with unbalanced weight doesn't cast doubt over whether I can bench-press 100lb or not. You have to attack the proposed one-to-one correspondence itself.

My point is not about whether they are authorities on the subject or not (some scientists are trained/good philosophers; some aren’t), it’s about how we test their claims. If they were talking about science, rebuttals should be scientific. I’m not a scientist and I’m not making scientific rebuttals. I am comfortable making philosophical rebuttals to their philosophical points. When the philosophical critiques are made, I’m saying it doesn’t matter that they are scientists or philosophers; I’m saying let’s discuss the reasons.

Then don't make any scientific rebuttals. What's the problem with just accepting that the scientific data is consistent with an infinite universe and move on?

Yes, that series is countable. Not just because all of the numbers are countable types of numbers, but because all of those numbers can also be reached going through the series.

So why isn't {0, ...} countable when all of those numbers are both countable types of numbers, but can also be reached going through the series?

Because that proof didn’t show that an infinite series has that potential characteristic.

Along the same line of questioning as above, why isn't showing that all members are of countable type, and can also be reached going through the series, enough to show that the series itself has that potential characteristic?

[The Tanager]

No, I think growing in size implies there was a previous boundary that was surpassed. If an actual infinite can exist, then it would be a size without a boundary and, because of that, could never grow in size.

Hence infinity + 1 = infinity? What's the problem again?

That if this is not growing in size, then by definition, it is not expanding. Thus, the universe couldn’t be not growing in size and expanding. Thus, the logical contradiction I’ve been talking about and you’ve been disagreeing with.

Hence the universe is expanding? That's the point.

Thus, it’s growing in size and, by definition, has expanded beyond a previous boundary, which an actually infinite universe cannot have had, by definition. Thus, the logical contradiction I’ve been talking about and you’ve been disagreeing with.

Yes and yes. Since there is a one-to-one correspondence between integers and natural numbers, but isn't one between decimals and natural numbers, we can conclude that some infinities are larger than others.

Why isn’t there one-to-one correspondence?

Which mean the only correct answer to the question, is there a one-to-one correspondence, is "yes, there is." That you cannot get a one-to-one correspondence in a particular manner does not change the fact that there is a one-to-one correspondence. Again, the question to "is there a way to match them?" would only be a "no" if there is exactly zero way of getting a match. There is at least one, therefore the answer is "yes."

I’m saying that a different method with the exact same members leading to not having one-to-one correspondence calls into question that your arbitrary approach truly gives us a “yes”. This is attacking the proposed one-to-one correspondence itself. I don’t think your method truly gives us a match. It uses the illogical nature of actual infinity to trick you into thinking there is a match.

Then don't make any scientific rebuttals. What's the problem with just accepting that the scientific data is consistent with an infinite universe and move on?

Because it’s not a scientific claim, but a philosophical one. It’s not the scientific data I’m contesting, but what philosophers are claiming based off of that scientific data.

So why isn't {0, ...} countable when all of those numbers are both countable types of numbers, but can also be reached going through the series?

Because you can’t fully go through that series since it never ends. Going through the series, by definition, would mean completing the whole series, reaching the end.

[Bust Nak]

That if this is not growing in size, then by definition, it is not expanding. Thus, the universe couldn’t be not growing in size and expanding.

So the universe isn't growing in size and expanding, but space is. That's easy enough to reconcile, isn't it?

Thus, it’s growing in size and, by definition, has expanded beyond a previous boundary, which an actually infinite universe cannot have had, by definition.

Yes, the boundary being any two points you care to pick out in the universe. There is nothing contradictory about space expanding when you are measuring two points, and the universe not having boundary.

Why isn’t there one-to-one correspondence?

Because there is exactly zero way to match every decimals to one natural number.

I’m saying that a different method with the exact same members leading to not having one-to-one correspondence calls into question that your arbitrary approach truly gives us a “yes”.

Why would it? Appealing to my analogy again, using a different method with the exact weights lead to me not being able to lift them, yet that does not call into question that my arbitrary approach of lifting those same exact weight truly give us a "yes."

This is attacking the proposed one-to-one correspondence itself. I don’t think your method truly gives us a match.

You can demonstrate that my method does not truly give us a match by telling me which number does not have a match, using my method. Pointing out a number that does not have a match using your method just doesn't cut it.

Because it’s not a scientific claim, but a philosophical one. It’s not the scientific data I’m contesting, but what philosophers are claiming based off of that scientific data.

What claim are you referring to exactly here? "The observable data is consistent with an infinite universe" sounds scientific enough to me.

Because you can’t fully go through that series since it never ends. Going through the series, by definition, would mean completing the whole series, reaching the end.

Now we are making progress. Recall if you will, a few months ago, I said there were two senses of "completing a series," 1) simply moving through all members, and 2) going through all members and then reaching the end. You asked me why I added "reaching the end" bit to your most basic definition of "complete the process" and I told you the basic definition of "complete" allows for the possibility of completing an infinite series that never ends. Which conflicts with your contention that "cannot be completed" is an integral part of the concept of infinity. (We also spoke about two senses of "bachelor" if that helps jog your memory.)

That lead me to present a proof to show that you can indeed move through all members of {0, ...}. So after all that, it seems you do want the move complex "and then reaching the end" definition of "completing a series." Can I call that much resolved then? You accept that since you can move through all members of an infinite series, the additional criteria of "reaching the end" is required to maintain your contention that an infinite series that doesn't end, cannot be completed by definition?

If so then we can move on: While some infinite series does not end, other does end, namely the ones that do not have a beginning, {..., 0} for example. The {0, ...} proof would serve as a primer for the variation with no beginning but an end.

[The Tanager]

So the universe isn't growing in size and expanding, but space is. That's easy enough to reconcile, isn't it?

Space is a part of the universe, not separate from it in which the universe is contained. But even assuming it wasn’t, you’d still have the exact same problem.

Yes, the boundary being any two points you care to pick out in the universe. There is nothing contradictory about space expanding when you are measuring two points, and the universe not having boundary.

If we are just talking about two points within the universe, then how does this address the size of the whole universe, which is what we are talking about, not part of the universe?

Because there is exactly zero way to match every decimals to one natural number.

Why not? Why can’t we match them this way (1, ½), (2, ⅓), (3, ⅔), (4, ¼), etc.?

Why would it? Appealing to my analogy again, using a different method with the exact weights lead to me not being able to lift them, yet that does not call into question that my arbitrary approach of lifting those same exact weight truly give us a "yes."

The difference that makes the analogy fail is that the weightlifting scenario is talking about two separate characteristics (lift weight arranged in way X and lift weight arranged in way Y), while the one-to-one correspondence is talking about the exact same characteristic (do these two sets have it). Different methods leading to different answers as to whether two sets have a characteristic or don’t calls that characteristic into question.

What claim are you referring to exactly here? "The observable data is consistent with an infinite universe" sounds scientific enough to me.

That an infinite universe can be expanding. This is a logical question based on what those words mean. Logic is a branch of philosophy, not science.

Now we are making progress. Recall if you will, a few months ago, I said there were two senses of "completing a series," 1) simply moving through all members, and 2) going through all members and then reaching the end. You asked me why I added "reaching the end" bit to your most basic definition of "complete the process" and I told you the basic definition of "complete" allows for the possibility of completing an infinite series that never ends. Which conflicts with your contention that "cannot be completed" is an integral part of the concept of infinity. (We also spoke about two senses of "bachelor" if that helps jog your memory.)

You said that, but didn’t successfully support that the basic definition of “complete” allows for the possibility of completing an infinite series that never ends. Thus, I have no reason to believe these 2 senses exist. Moving through ALL members is equivalent to “reaching the end” where “end” refers to either extreme, not just the back end.

You accept that since you can move through all members of an infinite series, the additional criteria of "reaching the end" is required to maintain your contention that an infinite series that doesn't end, cannot be completed by definition?

So, from what I just wrote above, I don’t accept that this is an additional criteria.

[Bust Nak]

Space is a part of the universe, not separate from it in which the universe is contained. But even assuming it wasn’t, you’d still have the exact same problem.

Space, as part of the universe, has many boundaries but the universe does not. How is that a problem?

If we are just talking about two points within the universe, then how does this address the size of the whole universe, which is what we are talking about, not part of the universe?

Part of the universe is expanding, you tell me, what does that tell you about the size of the whole universes, if anything at all? If it does not address the size of the whole universe, then you can just completely ignore "the universe is expanding" claim. The only reason we say the universe is expanding, is because we can see space expanding.

Why not? Why can’t we match them this way (1, ½), (2, ⅓), (3, ⅔), (4, ¼), etc.?

You can't get a one-to-one match this way because most decimal numbers, pi for example, cannot be represented as a fraction.

The difference that makes the analogy fail is that the weightlifting scenario is talking about two separate characteristics (lift weight arranged in way X and lift weight arranged in way Y), while the one-to-one correspondence is talking about the exact same characteristic (do these two sets have it). Different methods leading to different answers as to whether two sets have a characteristic or don’t calls that characteristic into question.

Why this and not "the difference that makes the analogy fail is that the weightlifting scenario is talking about the exact same characteristic (lift-able by Bust Nak), while the one-to-one correspondence is talking about the two separate characteristics (match members arranged in way X and match members arranged in way Y?) In other words, what makes "lift weigh arranged in way X" and "lift weight arranged in way Y" two separate characteristics but "match members arranged in way X" and "match members arranged in way Y" the same characteristic? Sounds like special pleading to me.

The offer is still open, to show me a number that is in {-1, …} that couldn't be matched to {0, …} using my method.

That an infinite universe can be expanding. This is a logical question based on what those words mean. Logic is a branch of philosophy, not science.

So does adding 1 to infinity count as expanding? If so, then it can, if not then it can't. It's just a matter of how you define things, as far as philosophy goes.

You said that, but didn’t successfully support that the basic definition of “complete” allows for the possibility of completing an infinite series that never ends...

That's what the proof is for, it proved that all members {0, ...} are countable types of numbers, and all can be reached going through the series. That's the basic definition of "complete," right? You did give these two things as the reason why finite series can be complete, after all. When then I ask you why {0, ...} still don't qualify despite sharing these two factors with finite series, you said it's because one cannot reach the end. That makes "reaching the end" an additional criteria. Failing to meet an additional criteria doesn't mean my proof failed to meet the basic definition of "complete."

... “reaching the end” where “end” refers to either extreme, not just the back end.

While we are here, if "end" refers to either extreme, then why pick out one of them as the end to be reached? After all, one end of {0, ...} can be reached trivially by counting 0.