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.

[William]

[Replying to We_Are_VENOM in post #1]

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”.

I think this reasoning forgets that one is including "time" with the notion of 'eternity'...eternity is timeless.

Time as a construct involves beginnings and ends, yet some models taken seriously involve the idea that the universe will go on expanding forever and that the universe is only one of many which derive from one event, like branches from a trunk...but the 'roots' are hidden from current scientific probing.

[Bust Nak]

What is the difference between a number and an amount/size?

A number is specific, while an amount or size can be specific but does not have to be.

You can measure (1) the whole of something or (2) part(s) of something. The “edge to edge” sense is (1). Your second sense above is (2). Our discussion involves (1).

Does it? That does not seem to gel what what you say below re: sum of all windows equals the whole green house. Sounds like you were proposing that (1) is just a particular instance of (2).

So, it’s not expanding, but it’s expanding everywhere? How does the addition of “everywhere” change anything?

Or it is expanding because it is expanding everywhere? It changes what we are measuring, what is expanding, from the whole house, to the windows. It's just a matter of perspective/semantics.

If the “whole” is a series of windows, then we’re talking about the sum of all windows, rather than just one window. If all the windows in your greenhouse expand in size, then the greenhouse is also expanding in size. Changing the terms doesn’t change anything. Break up the parts all you want. If all of the parts are expanding in size, then the whole is expanding in size.

Well there you go, so you accept that expanding windows implies expanding house. So what's wrong with the idea that the infinite universe is expanding in size in this sense, without expanding in size in the infinity plus one is still infinity sense?

As for your claim, yes, I’m asking you to prove that claim. Your argument doesn’t get you there. It talks about moving through every number in every finite mathematical series. Your argument covers that when we are starting at one integer and count to another integer that we can move through every integer in that series.

That's right, starting at one integer and counting to another is what is meant by moving through that integer.

That is not the infinite series analogical to an A-theory infinite past. What are your next steps to get rid of the “starting at one integer” part?

No need to get rid of it at all. Here we are talking about the concept of moving through an integer, that doesn't change depending on the size of the series, or the existence of beginning/ends; and my proof does not reference any of these things, just the concept of moving through an integer.

But why does the second sense have anything to do with what I’m saying? I’ll grant you two senses. I’m saying I’m talking about sense (1). In sense (1), by definition, an infinite series is a process that can’t be completed. An A-theory past requires the series of past events to be completed in sense (1).

What? No, it doesn't. That's the whole point of brining up the second sense in respond to what you were saying. An A-theory past requires the series of past events to be completed in sense (2), but not sense (1). An A-theory infinite past does not require the number of past events in the series to be finite in the direction of movement at all.

[The Tanager]

A number is specific, while an amount or size can be specific but does not have to be.

Why is that true?

Does it? That does not seem to gel what what you say below re: sum of all windows equals the whole green house. Sounds like you were proposing that (1) is just a particular instance of (2).

No, (1) is doing the whole whether you measure all at once or by summing measured parts. (2) is measuring only a part whether you measure that part all at once or by summing smaller parts of that part.

Or it is expanding because it is expanding everywhere? It changes what we are measuring, what is expanding, from the whole house, to the windows. It's just a matter of perspective/semantics.

If we are talking about measuring the whole house (which we are), I see no difference between it ‘expanding’ and ‘expanding everwhere’. If they mean the same, then the problem remains. Either the universe is actually infinite in size or it is expanding; it cannot be both. You introduced “expanding everywhere” as a way to get around that and I don’t see how it does.

Well there you go, so you accept that expanding windows implies expanding house. So what's wrong with the idea that the infinite universe is expanding in size in this sense, without expanding in size in the infinity plus one is still infinity sense?

Analogically, the windows are parts of the universe. The house is the whole of the universe. So, “expanding house” is identical (the same referent) to the “infinity plus one is still infinity”. You are saying that same referent is both expanding and “without expanding” in the same sense. That’s illogical.

No need to get rid of it at all. Here we are talking about the concept of moving through an integer, that doesn't change depending on the size of the series, or the existence of beginning/ends; and my proof does not reference any of these things, just the concept of moving through an integer.

Your proof relies upon series that have beginnings and ends, so, yes, you need to show how “moving through an integer” doesn’t change depending on the existence of beginnings/ends rather than just assume it does.

What? No, it doesn't. That's the whole point of brining up the second sense in respond to what you were saying. An A-theory past requires the series of past events to be completed in sense (2), but not sense (1). An A-theory infinite past does not require the number of past events in the series to be finite in the direction of movement at all.

Why do you see senses (1) and (2) like that? Sense (2) is only part of the series (whether finite or infinite). Sense (1) is the whole of the series (whether infinite or finite). We are talking about moving through the entire infinite past (sense 1) not just part of it (sense 2).

[Bust Nak]

Why is that true?

It's self-evidently true? Consider words such as "several," it is a quantity, but not a specific quantity.

No, (1) is doing the whole whether you measure all at once or by summing measured parts. (2) is measuring only a part whether you measure that part all at once or by summing smaller parts of that part.

The universe is measurable (1) by summing measured (2) parts, but not measurable (1) by edge to edge. Still not seeing anything contradictory.

If we are talking about measuring the whole house (which we are), I see no difference between it ‘expanding’ and ‘expanding everwhere’. If they mean the same, then the problem remains. Either the universe is actually infinite in size or it is expanding; it cannot be both... Analogically, the windows are parts of the universe. The house is the whole of the universe. So, “expanding house” is identical (the same referent) to the “infinity plus one is still infinity”. You are saying that same referent is both expanding and “without expanding” in the same sense.

The universe is expanding and the universe is not expanding does refer to the same referent, namely the universe, but how are the two expanding the same sense?

Your proof relies upon series that have beginnings and ends...

No it doesn't, where do you think I have referred to a series with beginnings or ends in my proof? Do you think you cannot move through all the integers, both positive and negative? Such a series has neither a beginning nor an end.

Why do you see senses (1) and (2) like that? Sense (2) is only part of the series (whether finite or infinite). Sense (1) is the whole of the series (whether infinite or finite). We are talking about moving through the entire infinite past (sense 1) not just part of it (sense 2).

I don't understand what you are asking here. Let me just restate my case more concisely and you see if you can rephrase your objection in light of the following:

Sense 1 of complete the process: moving through a limited number of members in the direction of movement, arriving at the back end.
A theory infinite past is incompletable by definition because there are endless members in the direction of movement.

Sense 2 of complete the process: moving through all the members in the direction of movement, arriving at the back end.
A theory infinite past not incompletable by definition because a) "all" could be finite or infinite; and b) the present moment acts as the back end.

Both refers to the whole series, neither of these is limited to just part of the series.

[The Tanager]

It's self-evidently true? Consider words such as "several," it is a quantity, but not a specific quantity.

'Several’ is a non-specific way we refer to something that is a specific quantity.

The universe is measurable (1) by summing measured (2) parts, but not measurable (1) by edge to edge. Still not seeing anything contradictory.

Those are not two senses of “measure”. It’s the same sense of measure applied to different things, to the whole (1) and to parts (2). And “edge to edge” is a (1), i.e., a whole. Measuring any whole (a) all at once or (b) by summing measured parts will get you the same measurement of (1).

No it doesn't, where do you think I have referred to a series with beginnings or ends in my proof?

Premises 1, 2, and 4 involve the phrase “count from X to Y”. That’s the series.

Do you think you cannot move through all the integers, both positive and negative? Such a series has neither a beginning nor an end.

I do not think one can “move through” all the integers because that seems to me to mean the equivalent of counting to infinity, which I think is logically impossible.

I don't understand what you are asking here. Let me just restate my case more concisely and you see if you can rephrase your objection in light of the following:

Sense 1 of complete the process: moving through a limited number of members in the direction of movement, arriving at the back end.
A theory infinite past is incompletable by definition because there are endless members in the direction of movement.

Sense 2 of complete the process: moving through all the members in the direction of movement, arriving at the back end.
A theory infinite past not incompletable by definition because a) "all" could be finite or infinite; and b) the present moment acts as the back end.

Both refers to the whole series, neither of these is limited to just part of the series.

These are not two senses of “complete the process,” but one sense applied to 2 different concepts (a part of a series and the whole of a series). We are talking about applying the one sense to the whole of a series.

[Bust Nak]

'Several’ is a non-specific way we refer to something that is a specific quantity.

So what? "Several" is therefore not a quantity, therefore not a valid answer to the question of "how many?"

Those are not two senses of “measure”. It’s the same sense of measure applied to different things, to the whole (1) and to parts (2). And “edge to edge” is a (1), i.e., a whole. Measuring any whole (a) all at once or (b) by summing measured parts will get you the same measurement of (1).

That's fine, the point is still this: there is no contradiction, because you can have same sense of measure and not measure when applied to different things.

Premises 1, 2, and 4 involve the phrase “count from X to Y”. That’s the series.

Okay, if that was what you were referring to, then the proof itself serves a link from series with a start and end, to a series that does not need to have a start or end.

I do not think one can “move through” all the integers because that seems to me to mean the equivalent of counting to infinity, which I think is logically impossible.

Then which premise of my proof do you disagree with? Alternatively which step is invalid? If you accept my proof as sound, then you are forced to accept that moving through every integer is not the equivalent of counting to infinity.

These are not two senses of “complete the process,” but one sense applied to 2 different concepts (a part of a series and the whole of a series)...

Where are you reading "part of a series" from in either "moving through a limited number of members in the direction of movement, arriving at the back end" or "moving through all the members in the direction of movement, arriving at the back end?"

[The Tanager]

So what? "Several" is therefore not a quantity, therefore not a valid answer to the question of "how many?"

So let’s revisit the main point: “whether counting to the final number in an ordered infinite set of integers is a coherent mathematical concept”. Does defining ‘infinity’ as a non-specific amount show ‘infinity’ to be a coherent mathematical concept? I don’t see how it’s moved the discussion at all. You can count to the final number in an ordered set of several integers, if “several” refers to a specific, finite amount; we agree there. You are still missing the proof that you can count to the final number in an ordered infinite set of integers.

Those are not two senses of “measure”. It’s the same sense of measure applied to different things, to the whole (1) and to parts (2). And “edge to edge” is a (1), i.e., a whole. Measuring any whole (a) all at once or (b) by summing measured parts will get you the same measurement of (1).

That's fine, the point is still this: there is no contradiction, because you can have same sense of measure and not measure when applied to different things.

But we are talking about one thing, not different things. The article you brought into the discussion claimed that the measurement of the whole (1) universe was (actual) infinity and that the whole (1) universe is expanding. I’m saying those two statements about that one thing is a logical contradiction.

Okay, if that was what you were referring to, then the proof itself serves a link from series with a start and end, to a series that does not need to have a start or end.

No, it doesn’t. Premise 1 states that in a series with a start and end, you can move through the first number in that series. Premise 2 gives us this series with a start and an end: {0, 1}. Premise 3 says we can move through the number 0 in that series with a start and an end. Premise 4 says extends the series with a start and end to this: {0, 1, 2}. Premise 5 says that we can move through the numbers 0 and 1 in that series with a start and an end.

Then premise 6 just states that you can move through every number. I would say that’s true if you mean every number in a series with a start and an end. You have not made any valid logical move to either focus on a series without a start or to make a general point about all series (with or without starts or ends).

Where are you reading "part of a series" from in either "moving through a limited number of members in the direction of movement, arriving at the back end" or "moving through all the members in the direction of movement, arriving at the back end?"

Okay, I misunderstood you there. I think I understand you better now. Why not define ‘complete the process’ as simply “moving through all members,” as I have been doing? Why put those other details into the definition? When we add the other details we risk begging or confusing the questions we are trying to answer.

Your “sense 2” is less basic than my definition. Your “sense 2” is not just about completing a process, but completing a process as an A-theory past. The definition of “A-theory” doesn’t contradict the definition of “completing a process.” Thus, no logical contradiction here. But, we aren’t talking about just an A-theory past; we are talking about an A-theory infinite past. New characteristics could cause contradictions. For instance, going from a bachelor to (an analogical sense 2) Chinese bachelor isn’t a contradiction, but a new characteristic (‘being married’) could cause a contradiction: a married Chinese bachelor.

Your “sense 1” is less basic than your sense 1. Your “sense 1” completing a process of an A-theory finite past. Neither the definition of “A-theory” nor the definition of the new characteristic, “finite”, contradicts the definition of “completing a process”. Thus, no contradiction here. Although, again, this isn’t what we are analyzing; we are talking about an A-theory infinite past.

In your terminology, we need a “sense 3” of completing a process of an A-theory infinite past. We have to analyze the definition of “infinite” to see if a contradiction comes from combining it in here. Is it like “Chinese” or “married” in our analogy above? An infinite series or process is an endless process. I think there is a clear logical contradiction between an endless/incompletable process and completing/ending that process akin to being a married bachelor.

[Bust Nak]

So let’s revisit the main point: “whether counting to the final number in an ordered infinite set of integers is a coherent mathematical concept”. Does defining ‘infinity’ as a non-specific amount show ‘infinity’ to be a coherent mathematical concept?

Not by itself, but it addresses one of your objection way back when, something along the lines of, how can an endless series have a size but not a specific size. We can by defining things this way.

You are still missing the proof that you can count to the final number in an ordered infinite set of integers.

That's what my "move through" proof is for, a version for going in the opposite direction can be provided, it's takes the same form as the one provided.

But we are talking about one thing, not different things. The article you brought into the discussion claimed that the measurement of the whole (1) universe was (actual) infinity and that the whole (1) universe is expanding.

Yes? What seems to be the problem, in light of everything I said? The whole (1) universe was actual infinity (as far as NASA can tell) it's flat and boundless. The whole (1) universe is expanding - every window is getting bigger.

No, it doesn’t... Then premise 6 just states that you can move through every number.

Step 6 is not a premise, it's a conclusion based on steps 3 and 5, my premises are clearly labelled in 1, 2 and 4.

I would say that’s true if you mean every number in a series with a start and an end. You have not made any valid logical move to either focus on a series without a start or to make a general point about all series (with or without starts or ends).

Can you clarify why you think step 6 is not logically valid? Presumably you'd agree that mathematical induction is valid?

Okay, I misunderstood you there. I think I understand you better now. Why not define ‘complete the process’ as simply “moving through all members,” as I have been doing? Why put those other details into the definition?

I did that for the following reasons:

1) simply moving through all members, without the reaching the back end clause, is incompatible with the idea that that it's impossible to complete counting from 0 to infinity, since it can be proven (at least an attempt at proving, pending your challenge to the validity of the proof above) that it is possible to move through all integers from 0 upwards.

2) you accepted that when moving through the members of a set, whatever the direction of movement, forwards, backwards, zigzag, arbitrarily jumping here and there, there is still an order, so specifying "in the direction of travel" highlights the fact that the issue with direction has been resolved so we can avoid revisiting old grounds.

Having said all that, I can easily remove "reaching the back end" and "in the direction of travel." Sense 1 complete the process: moving through a limited number of members; sense 2 complete the process: moving through all the members. The argument would still be the same. Using sense 2, there is no contradiction with completing an A-theory infinite past, i.e. "cannot be complete" is not an integral part of the concept of infinity.

Your “sense 2” is less basic than my definition. Your “sense 2” is not just about completing a process, but completing a process as an A-theory past. The definition of “A-theory” doesn’t contradict the definition of “completing a process.” Thus, no logical contradiction here. But, we aren’t talking about just an A-theory past; we are talking about an A-theory infinite past. New characteristics could cause contradictions.

My sense 2 is indeed about completing a process as just an A-theory past, leaving finite or infinite unspecified. That definition of "A-theory past" (finite or otherwise), doesn’t contradict the definition of "completing a process" is exactly why I brought this particular sense of complete. You would have a point if sense 2 wasn't about just an A-theory but specifically about an A-theory finite past. A-theory infinite past is covered by just an A-theory past.

Your “sense 1” is less basic than your sense 1. Your “sense 1” completing a process of an A-theory finite past. Neither the definition of “A-theory” nor the definition of the new characteristic, “finite”, contradicts the definition of “completing a process”. Thus, no contradiction here. Although, again, this isn’t what we are analyzing; we are talking about an A-theory infinite past.

That's kinda the point, setting aside "reaching the back end" part aside for now, your definition of completing a process rules out infinite process by definition, yours is less basic than sense 2, which doesn't care if the process is finite or infinite. The only reason why you saw a contradiction between "completed the process" with infinite was because you have a different, less basic definition.

In your terminology, we need a “sense 3” of completing a process of an A-theory infinite past.

We don't need it, that's covered by sense 2, it is finite/infinite agnostic. As I pointed out in my last post, "all" could be finite or infinite.

We have to analyze the definition of “infinite” to see if a contradiction comes from combining it in here. Is it like “Chinese” or “married” in our analogy above?

It's not like that, "all" is compatible with both being finite and infinite, but "bachelor" is not married/unmarried agnostic, it is compatible only with unmarried but not with married.

An infinite series or process is an endless process. I think there is a clear logical contradiction between an endless/incompletable process and completing/ending that process akin to being a married bachelor.

There aren't 2 senses of "married," but there are 2 senses of "complete the process."

(Alternatively we can bring up another sense like "married to his job," then there wouldn't be an issue with being a married bachelor. But lets not.)

[The Tanager]

Not by itself, but it addresses one of your objection way back when, something along the lines of, how can an endless series have a size but not a specific size. We can by defining things this way.

That doesn’t address that objection. All you’ve done is describe a thing that has a specific size in a non-specific way.

Yes? What seems to be the problem, in light of everything I said? The whole (1) universe was actual infinity (as far as NASA can tell) it's flat and boundless. The whole (1) universe is expanding - every window is getting bigger.

So, you are saying that in a house made up of windows, every window can be expanding without the house expanding? If so, how is that logical? That would be like saying all 100 2 inch bricks in a line of bricks are expanding to 3 inches long while the line of bricks remains 200 inches long.

I would say that’s true if you mean every number in a series with a start and an end. You have not made any valid logical move to either focus on a series without a start or to make a general point about all series (with or without starts or ends).

Can you clarify why you think step 6 is not logically valid? Presumably you'd agree that mathematical induction is valid?

C = count from one number (i.e., starting a series there) to the next number (i.e., ending a series there)
S = move through the number you started the series at
E = move through the number you ended the series at
A = move through all numbers in the series whether or not it has a start and end

1) If you can C, then you can S
2-3) This works with the series {0, 1}
4-5) This works with the series {N, N+1} and {N+1, N+2}
6) You can A

Your conclusion is a complete non-sequitur.

My sense 2 is indeed about completing a process as just an A-theory past, leaving finite or infinite unspecified. That definition of "A-theory past" (finite or otherwise), doesn’t contradict the definition of "completing a process" is exactly why I brought this particular sense of complete. You would have a point if sense 2 wasn't about just an A-theory but specifically about an A-theory finite past. A-theory infinite past is covered by just an A-theory past.

You have two terms considered in themselves:

1. complete a process
2. A-theory past

Analogically, that is like:

1. Married
2. Chinese person

Are there any necessary contradictions between either of these? No. Have we ruled out that there could be any contradictions? No. We can further categorize Chinese people into those who are bachelors and those who are not bachelors. Once we do that, we see there is a potential contradiction between (1) and (2) above, right?

It’s exactly the same with an A-theory past. There aren’t any necessary contradictions, but we haven’t ruled out that there could be contradictions when further categorizing the types of A-theory pasts there could be. Thus, in your sense 2, we haven’t determined if there is a contradiction or not.

That's kinda the point, setting aside "reaching the back end" part aside for now, your definition of completing a process rules out infinite process by definition, yours is less basic than sense 2, which doesn't care if the process is finite or infinite. The only reason why you saw a contradiction between "completed the process" with infinite was because you have a different, less basic definition.

My definition of completing the process (“moving through all members) is the most basic definition. It rules out “completing an infinite process” in the same sense the definition of a circle rules out a figure being both a circle and a square. An A-theory infinite past must be able to be completed, if the definition of ‘infinite’ precludes such a thing, by definition, then that means we havea logical contradiction.

We don't need it, that's covered by sense 2, it is finite/infinite agnostic. As I pointed out in my last post, "all" could be finite or infinite.

It's not like that, "all" is compatible with both being finite and infinite, but "bachelor" is not married/unmarried agnostic, it is compatible only with unmarried but not with married.

You are off on the analogy. “All” could be finite or infinite just as “Chinese person” could be bachelor or non-bachelor.

There aren't 2 senses of "married," but there are 2 senses of "complete the process."

(Alternatively we can bring up another sense like "married to his job," then there wouldn't be an issue with being a married bachelor. But lets not.)

Yes, the equivocation fallacy should be avoided. I don’t see two senses of “complete the process.” What are the two senses? Your previous “senses” weren’t senses of “completing the process” any more than “bachelor and non-bachelor” are two senses of married (Chinese) people.

[Bust Nak]

That doesn’t address that objection. All you’ve done is describe a thing that has a specific size in a non-specific way.

Where are you getting this idea of an infinite set having specific size from? I asked you this before, just how many integers are there currently? (As opposed to how many there could potentially be, or what number you could potentially count to.) If I remember correctly, you told me there is a specific size, you just don't know what it is. Well, it cannot be 0, and it cannot be 1, and it cannot be 2, it cannot be any specific number.

So, you are saying that in a house made up of windows, every window can be expanding without the house expanding? If so, how is that logical? That would be like saying all 100 2 inch bricks in a line of bricks are expanding to 3 inches long while the line of bricks remains 200 inches long.

Yes, I am saying that, given an infinite house. It is logical because infinity X 1.5 is still infinity. It's not like 100 bricks expand 1.5 in size in a very important way: 200 X 1.5 is not 200.

C = count from one number (i.e., starting a series there) to the next number (i.e., ending a series there)
S = move through the number you started the series at
E = move through the number you ended the series at
A = move through all numbers in the series whether or not it has a start and end

1) If you can C, then you can S
2-3) This works with the series {0, 1}
4-5) This works with the series {N, N+1} and {N+1, N+2}
6) You can A

Your conclusion is a complete non-sequitur.

Your summary of 4-5 isn't right, you are missing the conditional if... then..., let me make the mathematical induction explicit, using your preferred terms:

4) If this works with the series {N, N+1} then this works with the series {N+1, N+2}
5.1) If (if this works with the series {N, N+1} then this works with the series {N+1, N+2}) then (if this works with the series {N, N+1} then this works with this set of series {{N, N+1}, {N+1, N+2}, ...})
5.2) If this works with the series {N, N+1} then this works with this set of series {{N, N+1}, {N+1, N+2}, ...}
5.3) If this works with this set of series {{N, N+1}, {N+1, N+2}, ...} then possible to move through all numbers in the series {N, ...}
5.4) if this works with the series {N, N+1} then possible to move through all numbers in the series {N, ...}
5.5) Possible to move through all numbers in the series series {0, ...}
6) You can A

You have two terms considered in themselves...

Are there any necessary contradictions between either of these? No... we haven’t determined if there is a contradiction or not.

Okay, let me flesh that out a bit, I have two terms considered in themselves:

1. complete a process
2. A-theory past (finite or infinite)

Analogically, that is like:

1. Married
2. Chinese person (married or not married)

By making the further categorizing explicit, we can clearly see married and not married are contradictory. Now we throw in the two senses of complete a process:

1. moving through a limited number of members
2. A-theory past (finite or infinite)

vs

1. moving through all the members
2. A-theory past (finite or infinite)

There is only a contradiction with one sense of complete a process with an A-theory infinite past.

My definition of completing the process (“moving through all members) is the most basic definition. It rules out “completing an infinite process” in the same sense the definition of a circle rules out a figure being both a circle and a square.

Only in one sense of "compete the process." I see that you have accepted that "all" could be finite or infinite, from this we can conclude that "moving through all members" does not rule out completing an infinite process in the same sense as circle rules out a square. It could only rule out an infinite process, if you have some unstated restriction in addition to that basic definition, i.e. in the "moving through a limited number of members" sense.

You are off on the analogy. “All” could be finite or infinite just as “Chinese person” could be bachelor or non-bachelor.

That's part of the point, complete the complete the process could also be finite or infinite, where as married can't be bachelor.

Yes, the equivocation fallacy should be avoided. I don’t see two senses of “complete the process.” What are the two senses?

1) moving through a limited number of members.
2) moving through all the members.

Your previous “senses” weren’t senses of “completing the process” any more than “bachelor and non-bachelor” are two senses of married (Chinese) people.

Yes, just like the example I suggested: married to his job. I repeat my previous request, lets not invoke another sense of married to allow for married bachelors. But I could go there if you insist, we can throw in the two sense of married:

1. Having a husband or a wife
2. Chinese person (married or not married)

vs

1. Heavily involved with his job
2. Chinese person (married or not married)

There is only a contradiction with one sense of married with a Chinese bachelor.

Are you insisting?