.
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.
God Must Exist: Infinite Regression is Impossible
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Re: God Must Exist: Infinite Regression is Impossible
Post #751When scientists talk about the universe expanding and the universe being an actual infinite in size, they are talking about its spatial dimensions.
Then, (1, 0.01), (2, 0.001), (3, 0.0001), (4, 0.00001), and so on? With both sets being infinite, you'll never run out of numbers to match.
You said that you could lift a certain weight, not tied to any particular method. My restricting the method that can be used changes the question. Being two different questions, it's fine to get two different answers. Are these 2 sets in one-to-one correspondence is the same question that we get two different answers to.Bust Nak wrote: ↑Wed Sep 21, 2022 12:39 pmWhy 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.
Philosophy is not just about definitions. It is also about how definitions interact with each other. Adding onto a dimension does count as expanding. An actual infinite can't expand (or it would have crossed a previous boundary marker, which contradicts infinity being unbounded). Thus, when dealing with actual infinity, on its own terms, and seeing it lead to such contradictions, we should come to the conclusion that it's an illogical concept.
The basic definition of "complete" is that all are/can be reached, yes. Your proof shows that all the members are countable types of numbers when they are reached. The problem is that all the members of an infinite/unending series cannot, by definition, all be reached. You will always have more to reach. Thus, an infinite series can't be completed.
You picked that example, not me. You, I think, are trying to show that {0, ...} is completable because you think it will then be easy to prove that {..., 0} is completable. You need the latter because we are talking about an infinite past.
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Re: God Must Exist: Infinite Regression is Impossible
Post #752Yes, they are, no seeing how that answers my question. What is the problem here?The Tanager wrote: ↑Fri Sep 23, 2022 11:55 am When scientists talk about the universe expanding and the universe being an actual infinite in size, they are talking about its spatial dimensions.
Still won't work, every integer (n) has been matched to 0.1 ^ n+1. There is no room for 1.01 or 0.02. You can't get a one-to-one correspondence. That's why we can say the set of decimal numbers is larger than the set of natural numbers.Then, (1, 0.01), (2, 0.001), (3, 0.0001), (4, 0.00001), and so on?
Why this and not "you said you could get a one-to-one correspondence, not tied to any particular method. My restricting the method that can be used changes the question. Being two different questions, it's fine to get two different answers. Can Bust Nak lift a certain weight is the same question that we get two different answers to," still looks like special pleading to me.You said that you could lift a certain weight, not tied to any particular method. My restricting the method that can be used changes the question. Being two different questions, it's fine to get two different answers. Are these 2 sets in one-to-one correspondence is the same question that we get two different answers to.
Pick one, you can't have both, exactly because it causes a contradiction. Either adding to infinity count as expanding, or infinity can't expand.Philosophy is not just about definitions. It is also about how definitions interact with each other. Adding onto a dimension does count as expanding. An actual infinite can't expand (or it would have crossed a previous boundary marker, which contradicts infinity being unbounded).
Why is actual infinity the illogical concept instead of expanding means crossed a previous boundary marker the illogical concept?Thus, when dealing with actual infinity, on its own terms, and seeing it lead to such contradictions, we should come to the conclusion that it's an illogical concept.
No, it showed that all the members can be reached, look at the step 16 of proof again: "you can move through all members of {0, ...} " It's not a conditional statement, if reached then countable.The basic definition of "complete" is that all are/can be reached, yes. Your proof shows that all the members are countable types of numbers when they are reached.
That's provably incorrect. All the members of {0, ...} can be reached.The problem is that all the members of an infinite/unending series cannot, by definition, all be reached.
Yes, I think it's easy to prove. But that doesn't seem to address my point. You accept that some unending series does indeed have an end, and that it can be reached?You picked that example, not me. You, I think, are trying to show that {0, ...} is completable because you think it will then be easy to prove that {..., 0} is completable. You need the latter because we are talking about an infinite past.
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Re: God Must Exist: Infinite Regression is Impossible
Post #753The problem is that whether you use the term “universe” or “space” (i.e., the spatial dimensions of the universe), that thing can’t be expanding, yet not growing in size.
No problem. You’ve still got more members to keep matching. Switch it up, if that’s throwing you off. (1, 0.01), (2, 1.01), (3, 0.02), (4, whatever other pattern you want to throw in there), throw in whatever other patterns you have, and then restart the pattern with whatever natural number you left off with.
Bust Nak wrote: ↑Mon Sep 26, 2022 11:14 amWhy this and not "you said you could get a one-to-one correspondence, not tied to any particular method. My restricting the method that can be used changes the question. Being two different questions, it's fine to get two different answers. Can Bust Nak lift a certain weight is the same question that we get two different answers to," still looks like special pleading to me.
If you can show that one-to-one correspondence is the same kind of thing that lifting a weight is, then perhaps you have something here. Your analogy simply assumes this is the case. Being able to lift the weight is just as much about the method being used as it is an intrinsic feature of the weight and how strong you are. Why think one-to-one correspondence isn’t simply an intrinsic feature of the two sets in relation to each other?
Yes, I choose that infinity can’t expand. Thus an actual infinite universe or space can’t expand.
No, “actual infinity expanding” is shown to be illogical here (not “actual infinity”) because of what actual infinity and expansion both mean.
You are still conflating the countability of a number and the countability of a series. Your proof only shows that, starting at 0, you can reach a finite number, or (in other words) you can count the series {0, …, X}. You can replace X with any countable number and all you’ve got is a finite series. You don’t have this {0, ...}.
I accept that {0, …} has one end/side (we call it the beginning). The zero in this series {0, …} can be reached, yes. That does not mean that the series is completed; once you reach the zero, you’ve got to keep going.
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Re: God Must Exist: Infinite Regression is Impossible
Post #754It's not expanding though... according to your concept of expand.The Tanager wrote: ↑Mon Sep 26, 2022 12:46 pm The problem is that whether you use the term “universe” or “space” (i.e., the spatial dimensions of the universe), that thing can’t be expanding, yet not growing in size.
No, there isn't. EVERY ONE has been matched to a decimal of the from 0.1 ^ n+1. Those not of that form, such as 1.01 and 0.02 does not have a match.No problem. You’ve still got more members to keep matching.
That pattern won't work either, now 0.001 doesn't have a match. There are no pattern to that could work, there is exactly zero way to match one integer to one decimal number.Switch it up, if that’s throwing you off. (1, 0.01), (2, 1.01), (3, 0.02), (4, whatever other pattern you want to throw in there)
But you are assuming they are not, when every you say I can turn around and ask why this and not... hence the charge of special pleading.If you can show that one-to-one correspondence is the same kind of thing that lifting a weight is, then perhaps you have something here. Your analogy simply assumes this is the case.
We know it is just as much about the method being used as it is an intrinsic feature of the two sets in relation to each other because you've pointed out one method of trying to matching members that leave one member without a match, and I have pointed out another method that does produce a one-to-one correspondence.Being able to lift the weight is just as much about the method being used as it is an intrinsic feature of the weight and how strong you are. Why think one-to-one correspondence isn’t simply an intrinsic feature of the two sets in relation to each other?
As the top, then the universe isn't expanding.Yes, I choose that infinity can’t expand. Thus an actual infinite universe or space can’t expand.
That's fine, no harm discard that concept.No, “actual infinity expanding” is shown to be illogical here (not “actual infinity”) because of what actual infinity and expansion both mean.
Not so, we are talking about the countability of a number, I said nothing of the countability of a series as far as this little part of our conversation goes. Focus on just countability of a number before moving on please. My proof has shown that all members of {0, ...} can be reached. We can decide what that means in turns of countability of a series later. You claimed that all the members of an infinite/unending series cannot all be reached. That claim is demonstrably incorrect, regardless of whether that means the series itself is countable of not. Can you accept that much before moving on?You are still conflating the countability of a number and the countability of a series.
What that in mind, what exactly are the criteria of a series being countable. So far you said:I accept that {0, …} has one end/side (we call it the beginning). The zero in this series {0, …} can be reached, yes. That does not mean that the series is completed; once you reach the zero, you’ve got to keep going.
1) all members are of countable type.
2) all members can be reached.
3) the end can be reached. Which end?
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Re: God Must Exist: Infinite Regression is Impossible
Post #755Expanding and growing in size are synonyms in my conception, so how is it not expanding, yet growing in size?
My designation accounted for that pattern and every other pattern you want to make a part of the ordering of pairs.
You brought up the analogy to support your claim. You’ve got the burden to show that the analogy is accurate in the way you are using it. I’m questioning that.
Bust Nak wrote: ↑Mon Sep 26, 2022 1:36 pmBeing able to lift the weight is just as much about the method being used as it is an intrinsic feature of the weight and how strong you are. Why think one-to-one correspondence isn’t simply an intrinsic feature of the two sets in relation to each other?
We know it is just as much about the method being used as it is an intrinsic feature of the two sets in relation to each other because you've pointed out one method of trying to matching members that leave one member without a match, and I have pointed out another method that does produce a one-to-one correspondence.
My point is that the weight lifting question is about three features: a truth about (1) the weight, a truth about (2) your strength, and a truth about (3) the method you are using to lift the weight. One-to-one correspondence concerns a truth about (1) a relation of members of two sets. These don’t seem analogous.
Then why disagree with me when I say the universe either isn’t expanding or it isn’t an actual infinite?
Bust Nak wrote: ↑Mon Sep 26, 2022 1:36 pmNot so, we are talking about the countability of a number, I said nothing of the countability of a series as far as this little part of our conversation goes. Focus on just countability of a number before moving on please. My proof has shown that all members of {0, ...} can be reached.
I have already agreed, multiple times, that all numbers are countable.
Bust Nak wrote: ↑Mon Sep 26, 2022 1:36 pmWe can decide what that means in turns of countability of a series later. You claimed that all the members of an infinite/unending series cannot all be reached. That claim is demonstrably incorrect, regardless of whether that means the series itself is countable of not. Can you accept that much before moving on?
No, I’ve claimed (and tried to clear up the misunderstanding) that an infinite/unending series cannot be completed (i.e., having all of its members counted/reached).
For 3) the end(s) would be a subset of 2), since a series doesn’t have members and then some additional ending beyond those members. I’m not sure if there are more than these two criteria or not.
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Re: God Must Exist: Infinite Regression is Impossible
Post #756It can't, so we can say it's not growing in size.The Tanager wrote: ↑Mon Sep 26, 2022 2:25 pm Expanding and growing in size are synonyms in my conception, so how is it not expanding, yet growing in size?
What do you mean by "every other pattern" though, when there is exactly ZERO pattern that can get you a one to one correspondence, let alone other ones?My designation accounted for that pattern and every other pattern you want to make a part of the ordering of pairs.
I've done that by turning everything you said around with a why this and not... demonstrating that there are no relevant differences.You brought up the analogy to support your claim. You’ve got the burden to show that the analogy is accurate in the way you are using it.
Why this and not "my point is that the matching elements question is about three features: a truth about (1) the series, a truth about (2) the method you are using to match the elements. Lifting weight concerns a truth about (1) a relation between me and the weights?My point is that the weight lifting question is about three features: a truth about (1) the weight, a truth about (2) your strength, and a truth about (3) the method you are using to lift the weight. One-to-one correspondence concerns a truth about (1) a relation of members of two sets.
Because I wasn't using your concept of expanding. I was using the one from mathematicians and scientists, which is compatible with an expanding infinite universe.Then why disagree with me when I say the universe either isn’t expanding or it isn’t an actual infinite?
Not what I asked you, this is the claim under dispute: all members of {0, ...} can be reached. Affirm it explicitly please.I have already agreed, multiple times, that all numbers are countable.
We can talk about that later, after you concede that all members of {0, ...} can be reached.No, I’ve claimed (and tried to clear up the misunderstanding) that an infinite/unending series cannot be completed (i.e., having all of its members counted/reached).
I don't understand what you are trying to say here. {0, ...} doesn't have members and then some additional ending beyond those members, what is the implication as to reaching the end of {0, ...}?For 3) the end(s) would be a subset of 2), since a series doesn’t have members and then some additional ending beyond those members. I’m not sure if there are more than these two criteria or not.
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Re: God Must Exist: Infinite Regression is Impossible
Post #757Then what are you disagreeing with?
You match 1 with pattern A, then 2 with pattern B, then 3 with pattern C, and so on.
You’ve tried to, yes.
Bust Nak wrote: ↑Tue Sep 27, 2022 4:37 amWhy this and not "my point is that the matching elements question is about three features: a truth about (1) the series, a truth about (2) the method you are using to match the elements. Lifting weight concerns a truth about (1) a relation between me and the weights?
Because that isn’t accurate. One-to-one correspondence isn’t a truth about the series, but only it’s relation to another series. Your lifting weight scenario takes into consideration your strength, the amount of the weight, and a particular method.
What is their concept of “expanding”?
Bust Nak wrote: ↑Tue Sep 27, 2022 4:37 amNot so, we are talking about the countability of a number, I said nothing of the countability of a series as far as this little part of our conversation goes. Focus on just countability of a number before moving on please. My proof has shown that all members of {0, ...} can be reached.
I have already agreed, multiple times, that all numbers are countable.
Not what I asked you, this is the claim under dispute: all members of {0, ...} can be reached. Affirm it explicitly please.
In your quote you went from talking about a number being countable. You asked me to focus on just countability of a number. You then brought in the word “reached”, implying you were using these as synonyms. So, I answered about countability.
But if you mean that all members of the series are not just reachable, but reached in that particular series, then your proof certainly has not shown that. What it has shown is that the members are reachable and countable kinds of things, generally speaking, and that finite series are reachable/countable in their entirety.
The end/side of a series isn’t something extra, or in addition to, all of the members. If we say all members of the series can be reached, then this includes the ends/sides, if there are any. [For instance, in this series {0, …}, ‘0’ is a member, a member that is an end/side]. Thus, if ‘2) all members can be reached’ is true, then ‘3) the end can be reached’ must be true as well.
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Re: God Must Exist: Infinite Regression is Impossible
Post #758Your preference as to concepts/definition used with regard to an expanding infinite universe.
Ah huh, sounds to me like you are saying pattern A can only produce a partial match between the members of the two series, same for pattern B, pattern C and so on. Sounds to me like you are saying that there isn't a single pattern, not even one, that can match every decimals number to one natural number. Can I get an affirmation?You match 1 with pattern A, then 2 with pattern B, then 3 with pattern C, and so on.
Right, and until you can point out a relevant difference, the analogy stands.You’ve tried to, yes.
By series I meant the plural form, both series. The matching numbers scenario takes into consideration the series {-1, ...}, the series {0, ...}, and a particular method, just like the lifting weights scenario takes into consideration me, the weight and a particular method.Because that isn’t accurate. One-to-one correspondence isn’t a truth about the series, but only it’s relation to another series...
Getting bigger without implications as to boundaries.What is their concept of “expanding”?
Okay, then I'll take this as your affirmation that all members of {0, ...} can be reached.In your quote you went from talking about a number being countable. You asked me to focus on just countability of a number. You then brought in the word “reached”, implying you were using these as synonyms. So, I answered about countability.
Then perhaps you should adjust the criteria for what makes a series countable, with respect to the difference between reachable and reached in that particular series. Last I checked with you, they were:But if you mean that all members of the series are not just reachable, but reached in that particular series, then your proof certainly has not shown that.
1) all members are of countable type.
2) all members can be reached.
And there may not be a 3) re: ends are included in 2).
As thing stands now, {0, ...} ticks the first two boxes. What exactly does "reached in that particular series" mean, bearing in mind that some members of very large finite series hasn't been reached in the sense of a actual iterative process.
Great, we can say {0, ...} ticks the all the boxes. All members of {0, ...} can be reached, therefore the end can be reached.The end/side of a series isn’t something extra, or in addition to, all of the members. If we say all members of the series can be reached, then this includes the ends/sides, if there are any. [For instance, in this series {0, …}, ‘0’ is a member, a member that is an end/side]. Thus, if ‘2) all members can be reached’ is true, then ‘3) the end can be reached’ must be true as well.
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Re: God Must Exist: Infinite Regression is Impossible
Post #759Bust Nak wrote: ↑Wed Sep 28, 2022 5:27 amAh huh, sounds to me like you are saying pattern A can only produce a partial match between the members of the two series, same for pattern B, pattern C and so on. Sounds to me like you are saying that there isn't a single pattern, not even one, that can match every decimals number to one natural number. Can I get an affirmation?
Yes. There isn’t a single pattern, but multiple patterns that, put together, should be able to match every decimal to a natural number, because of the very nature of infinity.
Which I believe I’ve done. You obviously disagree.
Bust Nak wrote: ↑Wed Sep 28, 2022 5:27 amBy series I meant the plural form, both series. The matching numbers scenario takes into consideration the series {-1, ...}, the series {0, ...}, and a particular method, just like the lifting weights scenario takes into consideration me, the weight and a particular method.
It’s not about the number of entities involved or else me and you lifting the weight together would throw off the analogy. Here’s another way to try to get at what I see as the disanalogy:
You’ve got:
(1a) the members of set 1 and the members of set 2
This is equivalent to you’ve got:
(2a) Bust Nak, a weight, a lifting method (or no lifting method specified).
From this we ask our questions:
(1b) Do these two sets have one-to-one correspondence?
(2b) Can Bust Nak lift the weight?
In (1) the “method” you're talking about is what we bring in to try to answer (1b), while in the weight lifting scenario, it’s a part of (1a). That’s the disanalogy I’m talking about.
And why do you think this is the concept as scientists mean ‘expanding’?
Bust Nak wrote: ↑Wed Sep 28, 2022 5:27 amIn your quote you went from talking about a number being countable. You asked me to focus on just countability of a number. You then brought in the word “reached”, implying you were using these as synonyms. So, I answered about countability.
Okay, then I'll take this as your affirmation that all members of {0, ...} can be reached.Then perhaps you should adjust the criteria for what makes a series countable, with respect to the difference between reachable and reached in that particular series. Last I checked with you, they were:But if you mean that all members of the series are not just reachable, but reached in that particular series, then your proof certainly has not shown that.
1) all members are of countable type.
2) all members can be reached.
And there may not be a 3) re: ends are included in 2).
As thing stands now, {0, ...} ticks the first two boxes. What exactly does "reached in that particular series" mean, bearing in mind that some members of very large finite series hasn't been reached in the sense of a actual iterative process.
I think 2) is redundant, so I’d say something like:
1) all members are countable/reachable
2) all members in a particular series are counted/reached
The first is a truth about individual members. The second is a truth about the series as a whole, shown by the emphasis on “all”. The nature of “finite” means that 2) will be true. Not because we’ve actually counted that far, but because of what it means to be finite. To be infinite means the series goes on forever, that all members are not reached.
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Re: God Must Exist: Infinite Regression is Impossible
Post #760Sure, but that's not a one-to-one match is it? The integer 2 has one decimal matched to it via pattern A (0.001), a second decimal matched to it via pattern B (0.02), then a third decimal matched to it via pattern C and so on. It's one-to-many.The Tanager wrote: ↑Wed Sep 28, 2022 1:33 pm Yes. There isn’t a single pattern, but multiple patterns that, put together, should be able to match every decimal to a natural number, because of the very nature of infinity.
Why this and not:It’s not about the number of entities involved or else me and you lifting the weight together would throw off the analogy. Here’s another way to try to get at what I see as the disanalogy:
You’ve got:
(1a) the members of set 1 and the members of set 2
This is equivalent to you’ve got:
(2a) Bust Nak, a weight, a lifting method (or no lifting method specified).
From this we ask our questions:
(1b) Do these two sets have one-to-one correspondence?
(2b) Can Bust Nak lift the weight?
In (1) the “method” you're talking about is what we bring in to try to answer (1b), while in the weight lifting scenario, it’s a part of (1a).
(1a) the members of set 1 and the members of set 2, a matching method (or no matching method specified)
(2a) Bust Nak, a weight.
In (2) the “method” you're talking about is what we bring in to try to answer (2b), while in the one-to-one correspondence scenario, it’s a part of (1a)? It's the same old special pleading.
Because they have concluded that the universe is expanding without boundary from their observation.And why do you think this is the concept as scientists mean ‘expanding’?
So far so good, {0, ...} ticks that box.I think 2) is redundant, so I’d say something like:
1) all members are countable/reachable
2) all members in a particular series are counted/reached
The first is a truth about individual members.
So by "reached" you actually mean finite, which trivially means infinite cannot be "reached." What was the point with all the argument re: complete and moving through all elements, when all you needed to do is to point out you've defined terms in such a way to produce a tautology? I am not going to argue against a tautology, suffice to say I am not happy with how you define things, much like I don't like how expanding means a boundary to you.The second is a truth about the series as a whole, shown by the emphasis on “all”. The nature of “finite” means that 2) will be true. Not because we’ve actually counted that far, but because of what it means to be finite. To be infinite means the series goes on forever, that all members are not reached.
Either way, we can leave this part of the conversation as resolved, and go right back to the start of this debate, does that mean you've also also defined things in such a way that while the present moment as reachable, but not reached, or do you still want to see the variation proof that all members of {..., 0} are countable/reachable?
Further more, does it matter that the present moment is not reached but is reachable in the iterative sense? Isn't reachable enough to justify the possibility of an A-theory infinite past?