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]

Sure, 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.

No, I’m not saying that. Let’s assume there are 100 patterns (the actual number doesn’t matter) one could mathematically come up with to cover all decimal numbers. I’m saying the meta-pattern for one-to-one correspondence reasons would be (1, the first number of pattern 1), (2, the first number of pattern 2), (3, the first number of pattern 3), …, (101, the second number of pattern 1), (102, the second number of pattern 3), etc.

Why this and not:
(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 one-to-one correspondence is a feature two sets have or don’t have. Just like five sets of 9 is 45, no matter if you add each individual set together or multiply the sets by number of sets. It’s not a valid mathematical question to say “do these two sets have one-to-one correspondence according to method 1 but not method 2”.

I don't think I keep doing special pleading. I think you are semantically moving the words around, but aren’t adequately portraying the situation in doing so.

Because they have concluded that the universe is expanding without boundary from their observation.

Why not think they are being illogical? You are just trusting them? If not, then you should be able to explain their concept of “expanding” and how it’s about not having a boundary.

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.

No, being “reached” doesn’t mean finite, but it is a part of what it means to be a finite series. I tried to say in various ways that I felt this was part of the definition of finite/infinite, but you kept asking me to explain it differently. It was never an argument for the definition being that. I don’t think I am creating a new definition, but simply putting it in the terms you were bringing up.

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?

I’m not defining things, but working off of definitions already there. The infinite A-theory past, while containing members that are reachable, will never have the whole series completed by definition. The problem is that it must be completed before one could reach the present moment.

You are free to show the variation proof, if you want my analysis of it.

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?

The present moment is not a member of the A-theory infinite past.

[Bust Nak]

No, I’m not saying that. Let’s assume there are 100 patterns (the actual number doesn’t matter) one could mathematically come up with to cover all decimal numbers. I’m saying the meta-pattern for one-to-one correspondence reasons would be (1, the first number of pattern 1), (2, the first number of pattern 2), (3, the first number of pattern 3), …, (101, the second number of pattern 1), (102, the second number of pattern 3), etc.

Let's not assume there are 100 patterns, since the actual number does matter. Your suggestion would only work if there is a finite set of patterns. If the set is infinite, then every single integer would be used up to match the first number of each pattern. You won't be able to find a match for the second number of pattern 1, the second number of pattern 2, etc.

Because one-to-one correspondence is a feature two sets have or don’t have. Just like five sets of 9 is 45, no matter if you add each individual set together or multiply the sets by number of sets. It’s not a valid mathematical question to say “do these two sets have one-to-one correspondence according to method 1 but not method 2”.

Why this and not "because weightlifting is a feature Bust Nak and the weight have or don’t have. Just like five sets of 9 is 45, no matter if you add each individual set together or multiply the sets by number of sets. It’s not a valid weightlifting question to say “do these two sets have one-to-one correspondence according to method 1 but not method 2?”

Why not think they are being illogical?

Because they can support their claims with empirical evidence.

If not, then you should be able to explain their concept of “expanding” and how it’s about not having a boundary.

What is there to explain? There isn't any inherent relationship between expanding and boundary. I can explain why an association isn't necessary though, suggest some for me to explain away.

No, being “reached” doesn’t mean finite, but it is a part of what it means to be a finite series. I tried to say in various ways that I felt this was part of the definition of finite/infinite, but you kept asking me to explain it differently. It was never an argument for the definition being that. I don’t think I am creating a new definition, but simply putting it in the terms you were bringing up.

I’m not defining things, but working off of definitions already there. The infinite A-theory past, while containing members that are reachable, will never have the whole series completed by definition. The problem is that it must be completed before one could reach the present moment.

Why must it be completed before one could reach the present moment, when you can just reach the final member, then reach the present from that final member, regardless of whether infinite A-theory past can be completed or not?

You are free to show the variation proof, if you want my analysis of it.

1) Let X be the set (finite or infinite) of all integers < 0 that cannot be counted from to 0. (define X)
2) X is not empty (assumption)
3) Let x0 be the highest member of X (define x0)
4) Let y be the integer x0+1 (define y)
5) y can be counted form to 0 (from 4)
6) x0 can be counted from to y (from 4)
7) x0 can be counted from to 0 (from 5 and 6)
8) contradiction, therefore the assumption is false (from 1, 3 and 7)
9) X, the set of all integers < 0 that cannot be counted from to 0, is empty (from 2 and 8)
10) all integers <= 0 falls into 1 of 2 categories: can be counted from to 0, or cannot be counted from to 0 (premise)
11) a (finite or infinite) set of integers <= 0, with members of X removed, leaves a set that contains only members that can be counted from to 0 (from 10)
12) {..., 0} with members of X removed is {..., 0} (from 9)
13) {..., 0} contains only members that can be counted from to 0 (from 11 and 12)
14) an integer that can be counted from to 0, is an integer that is reachable (premise)
15) {..., 0} contains only members that are reachable (from 13 and 14)
16) all members of {..., 0} are reachable (from 15)

The present moment is not a member of the A-theory infinite past.

This is a red herring, if I can reach last Monday, a member of the A-theory infinite past, then I can reach the present moment, I made this argument a while ago.

[The Tanager]

Let's not assume there are 100 patterns, since the actual number does matter. Your suggestion would only work if there is a finite set of patterns. If the set is infinite, then every single integer would be used up to match the first number of each pattern. You won't be able to find a match for the second number of pattern 1, the second number of pattern 2, etc.

Again, this is the problem with treating infinity as a number. There will always be available members available to match, so we could never say one number doesn’t have a match. Yet you are saying you will run out of members to match. This is just more evidence that an actual infinity doesn’t make any sense.

Why this and not "because weightlifting is a feature Bust Nak and the weight have or don’t have. Just like five sets of 9 is 45, no matter if you add each individual set together or multiply the sets by number of sets. It’s not a valid weightlifting question to say “do these two sets have one-to-one correspondence according to method 1 but not method 2?”

Just because you switch some words around doesn’t mean you are saying something that makes sense. It is a valid weightlifting question to say “can Bust Nak lift this weight with the weight equally dispersed but not with all the weight to one side?” One-to-one correspondence doesn’t change because the members involved are what is being put into one-to-one correspondence. With every finite set, one-to-one correspondence doesn’t depend on the method used. So why would that change when applying the same concept of one-to-one correspondence to an infinite set?

Because they can support their claims with empirical evidence.

What empirical evidence supports expansion being defined without a boundary implication?

What is there to explain? There isn't any inherent relationship between expanding and boundary. I can explain why an association isn't necessary though, suggest some for me to explain away.

There seems to be an inherent relationship. The actual numbers don’t matter. And, remember, you are trying to argue that infinity is a number, so you’ve got to treat it like one. Call something’s measurement a 5. Expansion means going to, say, a 10, which is bigger. That thing was smaller than 10 previously, meaning it was bounded by a number smaller than 10, otherwise it would have already been 10 in size.

Why must it be completed before one could reach the present moment, when you can just reach the final member, then reach the present from that final member, regardless of whether infinite A-theory past can be completed or not?

It must be completed because of the nature of A-theory time, where one event follows another. The past must be completed before reaching the present moment. The same isn’t true of B-theory time. If the past isn’t completed, then no present.

1) Let X be the set (finite or infinite) of all integers < 0 that cannot be counted from to 0. (define X)
2) X is not empty (assumption)
3) Let x0 be the highest member of X (define x0)
4) Let y be the integer x0+1 (define y)
5) y can be counted form to 0 (from 4)
6) x0 can be counted from to y (from 4)
7) x0 can be counted from to 0 (from 5 and 6)
8) contradiction, therefore the assumption is false (from 1, 3 and 7)
9) X, the set of all integers < 0 that cannot be counted from to 0, is empty (from 2 and 8)
10) all integers <= 0 falls into 1 of 2 categories: can be counted from to 0, or cannot be counted from to 0 (premise)
11) a (finite or infinite) set of integers <= 0, with members of X removed, leaves a set that contains only members that can be counted from to 0 (from 10)
12) {..., 0} with members of X removed is {..., 0} (from 9)
13) {..., 0} contains only members that can be counted from to 0 (from 11 and 12)
14) an integer that can be counted from to 0, is an integer that is reachable (premise)
15) {..., 0} contains only members that are reachable (from 13 and 14)
16) all members of {..., 0} are reachable (from 15)

What you’ve shown is that, starting at a specific number, you can reach 0. That’s not the same thing as {..., 0} being a completed series; it’s equivalent to {X, …, 0} being a completed series.

This is a red herring, if I can reach last Monday, a member of the A-theory infinite past, then I can reach the present moment, I made this argument a while ago.

Yes, and I replied to it. It’s not a red herring. In an infinite A-theory past you won’t be able to reach last Monday, either. You’d have to complete {..., last Sunday} before reaching that date. Any previous date you choose has the same problem. This leads to the ludicrous concept that absolutely no date in the infinite A-theory past is ever reached! So, even if actual infinite made sense (I’m believing more and more that it doesn’t) an actual infinite A-theory past definitely doesn’t.

[Bust Nak]

Again, this is the problem with treating infinity as a number. There will always be available members available to match...

No, that's not correct. You will run out of room when trying to match decimals to integers. That's why the patterns you offered did not work. More importantly, it's not because we have yet to find a pattern that works, it's that it can be proven that no pattern can work, it's proven that you would run out of space when trying to match decimals to integers.

Just because you switch some words around doesn’t mean you are saying something that makes sense. It is a valid weightlifting question to say “can Bust Nak lift this weight with the weight equally dispersed but not with all the weight to one side?”

Just as it is a valid number matching question to say "can {0, ...} be matched with {-1, ...} with this pattern (n, n-1) but not with (n, n)?"

One-to-one correspondence doesn’t change because the members involved are what is being put into one-to-one correspondence. With every finite set, one-to-one correspondence doesn’t depend on the method used. So why would that change when applying the same concept of one-to-one correspondence to an infinite set?

Because there is something different between infinite sets and finite sets, that's the whole point of using one-to-one correspondence to define the size of infinite sets to begin with.

What empirical evidence supports expansion being defined without a boundary implication?

Red shift, among other stuff that goes all the way back Edwin Hubble discovered that the universe is expanding, and more importantly the rate of expanding is proportionate to the distance from the observer.

There seems to be an inherent relationship. The actual numbers don’t matter. And, remember, you are trying to argue that infinity is a number, so you’ve got to treat it like one.

I distinctively remember saying infinity is not a number like 5 is a number.

Call something’s measurement a 5. Expansion means going to, say, a 10, which is bigger. That thing was smaller than 10 previously, meaning it was bounded by a number smaller than 10, otherwise it would have already been 10 in size.

That tells you nothing about the size, or boundary of the set that contains those two numbers.

It must be completed because of the nature of A-theory time, where one event follows another. The past must be completed before reaching the present moment. The same isn’t true of B-theory time. If the past isn’t completed, then no present.

Then the concepts you are using are incoherent: You can reach the present moment form A-theory infinite past, which means the past must be completed, yet the infinite past cannot be completed, you have a contradiction. Pick one: either reaching the final member means a set is completed, or infinite sets cannot be completed.

What you’ve shown is that, starting at a specific number, you can reach 0. That’s not the same thing as {..., 0} being a completed series; it’s equivalent to {X, …, 0} being a completed series.

Never mind what is and isn't completed for now, I said that all members of {..., 0} are reachable, and that's what I have set out to prove with this deductive argument. Any comment on that much?

Yes, and I replied to it. It’s not a red herring. In an infinite A-theory past you won’t be able to reach last Monday, either.

If that's the case, then it wouldn't matter if the present moment is part of the infinite past or not, I wouldn't be able to reach it either way, so it would still be a red herring. More importantly, you would be able to reach last Monday, and I can prove it, it would take the same format as the {..., 0} proof.

You’d have to complete {..., last Sunday} before reaching that date...

Follow through with this thought, this means I must have completed {..., last Sunday}, since I can reach last Monday...

[The Tanager]

No, that's not correct. You will run out of room when trying to match decimals to integers. That's why the patterns you offered did not work. More importantly, it's not because we have yet to find a pattern that works, it's that it can be proven that no pattern can work, it's proven that you would run out of space when trying to match decimals to integers.

How can you run out of room to match things when you never run out of elements in either series? It’s illogical to run out of that which you can’t run out of. If it’s proven otherwise, then show the proof.

Just as it is a valid number matching question to say "can {0, ...} be matched with {-1, ...} with this pattern (n, n-1) but not with (n, n)?"

I agree. That’s different than asking: are {0, …} and {-1, …} in one-to-one correspondence?

Because there is something different between infinite sets and finite sets, that's the whole point of using one-to-one correspondence to define the size of infinite sets to begin with.

You aren’t using the same concept of one-to-one correspondence, though, you are changing it into something that a set can have and not have at the same time.

Red shift, among other stuff that goes all the way back Edwin Hubble discovered that the universe is expanding, and more importantly the rate of expanding is proportionate to the distance from the observer.

How does this support there is no boundary implication?

I distinctively remember saying infinity is not a number like 5 is a number.

It’s either a number or it’s not. If an infinite number is something entirely different than a finite number, then don’t call it a number. There has to be some kind of similarity; I’m not saying it is identical.

That tells you nothing about the size, or boundary of the set that contains those two numbers.

A set is not a size. A set has a size. We are saying the size of X (whether a set or something else) is 5 and then it expands to the size of 10. That thing’s boundary was 5 meters (or whatever). It wasn’t bigger than 5. Then it expanded beyond that boundary.

Then the concepts you are using are incoherent: You can reach the present moment form A-theory infinite past, which means the past must be completed, yet the infinite past cannot be completed, you have a contradiction. Pick one: either reaching the final member means a set is completed, or infinite sets cannot be completed.

You can’t just arbitrarily pick one, if that is what you are saying. The whole point is that one cannot logically reach the present moment that follows an A-theory infinite past. Sure, you can write the sentence. But you can also say “throw me the square circle over there.” It’s nonsense. You can never reach the final member of an infinite set. You can’t complete it. Infinite sets cannot be completed by their very definition.

Never mind what is and isn't completed for now, I said that all members of {..., 0} are reachable, and that's what I have set out to prove with this deductive argument. Any comment on that much?

The same one I just gave. Your proof shows that starting at -5 (or -4 or -1000 or -X where X is a finite number), one can reach 0. Or, in other words, the set {-5, -4, -3, -2, -1, 0} can be completed and the set {-4, -3, …, 0} and the set {-1000, -999, …, 0} but not the set {..., 0}

Just like your previous proof showed that starting at 0, one can complete the series {0, 1} and the series {0, 1, 2} and the series {0, 1, 2, 3}, but not the series {0, …}

If that's the case, then it wouldn't matter if the present moment is part of the infinite past or not, I wouldn't be able to reach it either way, so it would still be a red herring.

By definition, the present moment cannot be counted as part of the infinite past. They are mutually exclusive terms. You can’t have a present moment that is also a past moment in A-theory time. Yes, the present moment becomes a past moment, but is not considered present any longer to where you could say what you are trying to say above.

More importantly, you would be able to reach last Monday, and I can prove it, it would take the same format as the {..., 0} proof.

All you’d show by doing that is that starting at some finite point in the past, one could reach last Monday.

Follow through with this thought, this means I must have completed {..., last Sunday}, since I can reach last Monday...

No, you’ve got it completely backwards. You need to prove you can reach last Sunday in order to prove you can reach last Monday, not vice versa. We can reach last Monday, that's obvious because we did. But you are trying to show that we can reach last Monday assuming an infinite past. To do that you can't assume last Monday is reached as support for the ability to reach it.

[Bust Nak]

How can you run out of room to match things when you never run out of elements in either series? If it’s proven otherwise, then show the proof.

1) there is a 1 to 1 match between integers and decimals. (assumption)
2) if there is a 1 to 1 match between integers and decimals, then all decimals can be ordered into a linear sequence {r1, r2, r3, ...} (premise)
3) all decimals can be ordered into a linear sequence {r1, r2, r3, ...} from (1 and 2)
4) let r0 be a decimal number constructed thus: its first digit is taken from the first digit of r1, its second digit is the second dight of r2 and so on. (define r0)
5) let r0' be a modified version of r0 where each of its digits is shifted up once. For example, 3.69 would be modified to 4.70 using this method (define r0')
6) r0' is not r1, because their first digits are different, it's not r2 because their second digits are different and so on. (from 5)
7) r0' is not in the linear sequence {r1, r2, r3.... } (from 6)
8) contradiction, therefore the assumption is false. (from 7 and 3)
9) there is no 1 to 1 match between integers and decimals. (from 1 and 8)
10) you would run out of room if you try to match one decimal to one integer. (from 9)

I agree. That’s different than asking: are {0, …} and {-1, …} in one-to-one correspondence?

The same way "can Bust Nak lift this weight with the weight equally dispersed but not with all the weight to one side?" is different than asking "can Bust Nak lift this weight?" The analogy still holds.

You aren’t using the same concept of one-to-one correspondence, though, you are changing it into something that a set can have and not have at the same time.

No, it's something that a set can either has or does not have. Just as "can Bust Nak lift this weight?" has only one answer, I can lift it with when it's balanced, the answer is "yes, I can" despite not being able to when it's off balanced.

How does this support there is no boundary implication?

Because it is equally expanding on all direction, so either we are exactly in the center of a bounded universe, or the universe is unbounded. The former is unlikely.

It’s either a number or it’s not. If an infinite number is something entirely different than a finite number, then don’t call it a number. There has to be some kind of similarity; I’m not saying it is identical.

That's fine. There are some kind of similarity, yes, they are not identical, also yes. If it is either a number or it is not, then go ahead and tell me how similar they have to be, for infinite to be considered a number.

A set is not a size. A set has a size. We are saying the size of X (whether a set or something else) is 5 and then it expands to the size of 10. That thing’s boundary was 5 meters (or whatever). It wasn’t bigger than 5. Then it expanded beyond that boundary.

Yeah, but what if the size of X is infinite?

You can’t just arbitrarily pick one, if that is what you are saying. The whole point is that one cannot logically reach the present moment that follows an A-theory infinite past.

But I can prove otherwise, so you must pick one.

The same one I just gave. Your proof shows that starting at -5 (or -4 or -1000 or -X where X is a finite number), one can reach 0...

My proof is for showing "all members of {..., 0} are reachable," so of course it also show that starting at any finite number, one can reach 0. Judging by a later comment though, you seemed to think my proof only shows that, but not its actual conclusion as stated. No matter how many reasons you can throw at me for disagreeing with my conclusion, you were given a deductive proof. If it is logically sound then conclusion must follow. You need to actually address the proof itself, tell me which steps you disagree with, that isn't too much to ask for.

Or, in other words, the set {-5, -4, -3, -2, -1, 0} can be completed and the set {-4, -3, …, 0} and the set {-1000, -999, …, 0} but not the set {..., 0}

Just like your previous proof showed that starting at 0, one can complete the series {0, 1} and the series {0, 1, 2} and the series {0, 1, 2, 3}, but not the series {0, …}

This bit is still about completing a series, I asked you to focus on reachable for just this little bit.

By definition, the present moment cannot be counted as part of the infinite past. They are mutually exclusive terms. You can’t have a present moment that is also a past moment in A-theory time. Yes, the present moment becomes a past moment, but is not considered present any longer to where you could say what you are trying to say above.

So? It doesn't matter whether a present moment that is also a past moment or not. If last Monday is reachable, then the present moment is reachable. You accepted that much before, why do you think you need to reiterate this again?

All you’d show by doing that is that starting at some finite point in the past, one could reach last Monday.

All I'd show is this? But not all members of {..., last Monday} is reachable?

No, you’ve got it completely backwards. You need to prove you can reach last Sunday in order to prove you can reach last Monday, not vice versa...

I wasn't trying to prove I can reach last Monday with that argument though, I have the big proof for that. This part was about "complete" not "reachable." Let me formalize my argument.

1) last Monday is reachable. (premise)
2) If last Monday is reachable, then {..., last Sunday} is completable. (premise)
3) {..., last Sunday} is completable. (from 1 and 2)

[The Tanager]

1) there is a 1 to 1 match between integers and decimals. (assumption)
2) if there is a 1 to 1 match between integers and decimals, then all decimals can be ordered into a linear sequence {r1, r2, r3, ...} (premise)
3) all decimals can be ordered into a linear sequence {r1, r2, r3, ...} from (1 and 2)
4) let r0 be a decimal number constructed thus: its first digit is taken from the first digit of r1, its second digit is the second dight of r2 and so on. (define r0)
5) let r0' be a modified version of r0 where each of its digits is shifted up once. For example, 3.69 would be modified to 4.70 using this method (define r0')
6) r0' is not r1, because their first digits are different, it's not r2 because their second digits are different and so on. (from 5)
7) r0' is not in the linear sequence {r1, r2, r3.... } (from 6)
8) contradiction, therefore the assumption is false. (from 7 and 3)
9) there is no 1 to 1 match between integers and decimals. (from 1 and 8)
10) you would run out of room if you try to match one decimal to one integer. (from 9)

Focusing in on premise 2, are you saying that if there is not a 1 to 1 match between integers and decimals, then all decimals cannot be ordered into a linear sequence?

The same way "can Bust Nak lift this weight with the weight equally dispersed but not with all the weight to one side?" is different than asking "can Bust Nak lift this weight?" The analogy still holds.

So you agree that “can {0, ...} be matched with {-1, ...} with this pattern (n, n-1) but not with (n, n)?” is a different question than “can {0, …} and {-1, …} be put in one-to-one correspondence?”

No, it's something that a set can either has or does not have.

So, there is only one answer to this question.

Just as "can Bust Nak lift this weight?" has only one answer, I can lift it with when it's balanced, the answer is "yes, I can" despite not being able to when it's off balanced.

So, you give two answers to this question and yet say that it’s the same as what's above, where something only has one answer to a question?

Because it is equally expanding on all direction, so either we are exactly in the center of a bounded universe, or the universe is unbounded. The former is unlikely.

What does one’s location have to do with the size of the universe? If something is expanding in all directions, then in all directions it’s (for example) going from a 5 to a 10 in all directions and crossing the previous boundary it had.

That's fine. There are some kind of similarity, yes, they are not identical, also yes. If it is either a number or it is not, then go ahead and tell me how similar they have to be, for infinite to be considered a number.

I’m not even sure how one would judge the level of similarity. My point is simply that if they are completely different, then the same term shouldn’t be used to describe them. You have the burden to show infinity has the necessary features to properly be called a number.

Yeah, but what if the size of X is infinite?

If infinity is something that expands, then it must still expand beyond a previous boundary. That’s because of what expansion means, not because of what it means to be finite or infinite.

But I can prove otherwise, so you must pick one.

You haven’t proven otherwise.

My proof is for showing "all members of {..., 0} are reachable," so of course it also show that starting at any finite number, one can reach 0. Judging by a later comment though, you seemed to think my proof only shows that, but not its actual conclusion as stated. No matter how many reasons you can throw at me for disagreeing with my conclusion, you were given a deductive proof. If it is logically sound then conclusion must follow. You need to actually address the proof itself, tell me which steps you disagree with, that isn't too much to ask for.

I have addressed it multiple times. You keep changing the semantics, but make the same mistakes.

This bit is still about completing a series, I asked you to focus on reachable for just this little bit.

They are the same thing. To say the number 5 in this series {0, …} is reachable is to say that this series {0, 1, 2, 3, 4, 5} can be completed.

So? It doesn't matter whether a present moment that is also a past moment or not. If last Monday is reachable, then the present moment is reachable. You accepted that much before, why do you think you need to reiterate this again?

Yes, but you haven’t shown last Monday is reachable. To do that you’d have to show that {..., last Sunday} can be completed.

All you’d show by doing that is that starting at some finite point in the past, one could reach last Monday.

All I'd show is this? But not all members of {..., last Monday} is reachable?

I must be misreading you here because something seems off.

Yes, if you used the same proof, all you’d end up with is that starting at some finite point in the past, you could reach last Monday. That’s not the same thing as showing you can reach last Monday in this set {..., last Monday}

1) last Monday is reachable. (premise)
2) If last Monday is reachable, then {..., last Sunday} is completable. (premise)
3) {..., last Sunday} is completable. (from 1 and 2)

And I’m questioning the truth of premise 1 assuming an A-theory infinite past because of the very nature of an A-theory infinite past. I don’t think last Monday is reachable on an A-theory infinite past.

[Bust Nak]

2) if there is a 1 to 1 match between integers and decimals, then all decimals can be ordered into a linear sequence {r1, r2, r3, ...} (premise)

Focusing in on premise 2, are you saying that if there is not a 1 to 1 match between integers and decimals, then all decimals cannot be ordered into a linear sequence?

Yes and no. Yes, you could only place elements in a linear sequence, if and only if there is a 1 to 1 match to integers. But no, I didn't actually say "only if" in my proof because I only needed the "if" part to prove there can be no 1 to 1 match.

So you agree that “can {0, ...} be matched with {-1, ...} with this pattern (n, n-1) but not with (n, n)?” is a different question than “can {0, …} and {-1, …} be put in one-to-one correspondence?”

Sure.

So, there is only one answer to this question.

Yes.

So, you give two answers to this question and yet say that it’s the same as what's above, where something only has one answer to a question?

No? Not sure what you are talking about here. I gave only one answer, and that answer was a "yes, I can lift it," corresponding to the only one answer, "yes, there is a one-to-one correspondence" what was the second answer supposed to be?

What does one’s location have to do with the size of the universe?

Don't know, it does have something to do with its boundary though.

If something is expanding in all directions, then in all directions it’s (for example) going from a 5 to a 10 in all directions and crossing the previous boundary it had.

If you chop it up into little subsets of 5s, then sure. What if you don't know what is going from and what it is going to? All you know is little subsets of 5s are crossing the previous boundaries.

I’m not even sure how one would judge the level of similarity. My point is simply that if they are completely different, then the same term shouldn’t be used to describe them. You have the burden to show infinity has the necessary features to properly be called a number.

No, I have no such burden, not only did I not make the claim that infinity can properly be called a number, I explicit said infinity is not a number like 5 is a number.

If infinity is something that expands, then it must still expand beyond a previous boundary. That’s because of what expansion means, not because of what it means to be finite or infinite.

Never mind about infinity for now, the universe (infinite or not) doesn't have a boundary, so the concepts you are using are incompatible with the outside world, like I keep saying. Expansion need not have any implication to boundary.

You haven’t proven otherwise.

I have addressed it multiple times. You keep changing the semantics, but make the same mistakes.

That's why I keep inviting you to be explicit about which steps you have a problem with, you kept "addressing" why my proof can't possibly be correct, without addressing the proof itself. Where are the mistakes in my proof? You can give endless reasons for why the infinite past cannot be completed or talk all you want about how {X, ..., 0} isn't the same thing as {..., 0}. If you can't pin-point why my proof might be unsound, then my conclusion has to be true, which means all the reasons you gave are automatically invalidated. Give me step numbers!

They are the same thing. To say the number 5 in this series {0, …} is reachable is to say that this series {0, 1, 2, 3, 4, 5} can be completed.

It doesn't matter if they are the same thing or not, I asked you a very specific question: do you accept the conclusion of the deductive proof, "all members of {..., 0} are reachable," if not, which step do you disagree with?" Answer this question as stated, not what you think it is equivalent to. Acceptable answers take the form of either "no, and here are some steps numbers..." or "yes, I do."

Yes...

Then stop brining the question of whether the present moment is a member of the infinite past or not.

And I’m questioning the truth of premise 1 assuming an A-theory infinite past because of the very nature of an A-theory infinite past. I don’t think last Monday is reachable on an A-theory infinite past.

I will take that as confirmation that you have no issue with the validity (as opposed to soundness) of this proof for {..., last Sunday} being completable, it all hinges on the premise of reachable. So, if you could just leave completing a series aside for now and focus on solely on reachable please, that would be nice. You said I kept changing the semantics, well, here is me trying to get you to limit the semantics.

[The Tanager]

Yes and no. Yes, you could only place elements in a linear sequence, if and only if there is a 1 to 1 match to integers. But no, I didn't actually say "only if" in my proof because I only needed the "if" part to prove there can be no 1 to 1 match.

Why couldn’t decimals be put into an ordered sequence if there wasn’t a one-to-one match to integers?

So you agree that “can {0, ...} be matched with {-1, ...} with this pattern (n, n-1) but not with (n, n)?” is a different question than “can {0, …} and {-1, …} be put in one-to-one correspondence?”

Sure.

And weren’t we discussing the second question? Whether these two sets have on-to-one correspondence?

Not sure what you are talking about here. I gave only one answer, and that answer was a "yes, I can lift it," corresponding to the only one answer, "yes, there is a one-to-one correspondence" what was the second answer supposed to be?

The question is “Can Bust Nak lift this weight?” You have given “yes, I can” and “no, I can’t” with the respective caveats of “when balanced” and “when not balanced”. That’s two answers to the same question. That’s not analogical to “do these two sets have one-to-one correspondence,” which you believe has one answer only.

Don't know, it does have something to do with its boundary though.

Okay, what does it have to do with the boundary of the universe?

If you chop it up into little subsets of 5s, then sure. What if you don't know what is going from and what it is going to? All you know is little subsets of 5s are crossing the previous boundaries.

We aren’t talking about pieces of the universe, but the universe as a whole. If, analogically, the size of the universe was 5 and expanded to a 10, then the whole universe would cross the previous boundary.

No, I have no such burden, not only did I not make the claim that infinity can properly be called a number, I explicit said infinity is not a number like 5 is a number.

You have said infinity is a number (or maybe it was amount or whatever), just not a number like 5 is a number.

Never mind about infinity for now, the universe (infinite or not) doesn't have a boundary, so the concepts you are using are incompatible with the outside world, like I keep saying. Expansion need not have any implication to boundary.

Why do you think the universe doesn’t have a boundary?

That's why I keep inviting you to be explicit about which steps you have a problem with, you kept "addressing" why my proof can't possibly be correct, without addressing the proof itself. Where are the mistakes in my proof? You can give endless reasons for why the infinite past cannot be completed or talk all you want about how {X, ..., 0} isn't the same thing as {..., 0}. If you can't pin-point why my proof might be unsound, then my conclusion has to be true, which means all the reasons you gave are automatically invalidated. Give me step numbers!

Come on, I’ve addressed specific steps on numerous occasions.

It doesn't matter if they are the same thing or not, I asked you a very specific question: do you accept the conclusion of the deductive proof, "all members of {..., 0} are reachable," if not, which step do you disagree with?" Answer this question as stated, not what you think it is equivalent to. Acceptable answers take the form of either "no, and here are some steps numbers..." or "yes, I do."

We’ve already done this. Yes, the members are reachable, i.e., they are the types of numbers that can be reached given certain scenarios (like starting at 0 or whatever). Your proof either only shows that or attempts to do more and has failed in the various places I’ve said.

So? It doesn't matter whether a present moment that is also a past moment or not. If last Monday is reachable, then the present moment is reachable. You accepted that much before, why do you think you need to reiterate this again?

Yes, but you haven’t shown last Monday is reachable. To do that you’d have to show that {..., last Sunday} can be completed.

Then stop brining the question of whether the present moment is a member of the infinite past or not.

My statement was in reference to the bolded part above, the question you asked me. Yes, if last Monday is reachable, then the present moment is reachable. But you haven’t shown last Monday is reachable on an A-theory infinite past.

I will take that as confirmation that you have no issue with the validity (as opposed to soundness) of this proof for {..., last Sunday} being completable, it all hinges on the premise of reachable. So, if you could just leave completing a series aside for now and focus on solely on reachable please, that would be nice. You said I kept changing the semantics, well, here is me trying to get you to limit the semantics.

Yes, the form of your argument is valid. The problem is that last Monday being reachable hinges on which series it is a part of.

[Bust Nak]

Why couldn’t decimals be put into an ordered sequence if there wasn’t a one-to-one match to integers?

Does it matter why? All I needed for the proof is the fact that if there is a 1 to 1 match to integers, then all decimals can be ordered into a linear sequence. I'll have a go at answering that after you affirm my proof, it would rely on much of the same steps as the one here.

And weren’t we discussing the second question? Whether these two sets have on-to-one correspondence?

Yes?

The question is “Can Bust Nak lift this weight?” You have given “yes, I can” and “no, I can’t” with the respective caveats of “when balanced” and “when not balanced”.

No, there is only one answer, "yes, I can." These answers you are referring to are for answering other questions, namely, "can Bust Nak lift this weight with the weight equally dispersed?" and "can Bust Nak lift the weight with all the weight to one side?" As you pointed out above, we discussing whether these two sets have on-to-one correspondence, there is only one answer to that.

Okay, what does it have to do with the boundary of the universe?

As before, this means either the universe does not have a boundary, or we are slap bang in the exact centre of the universe. The latter is not likely.

We aren’t talking about pieces of the universe, but the universe as a whole. If, analogically, the size of the universe was 5 and expanded to a 10, then the whole universe would cross the previous boundary.

That's right, not sure what that's got to do with what I said though. It's still the case that you can't conclude anything about the boundary of the universe, just by seeing bits of it expanding from 5 to 10.

You have said infinity is a number (or maybe it was amount or whatever), just not a number like 5 is a number.

I said it was a quantity. As support for that claim, I pointed how it is used in math.

Why do you think the universe doesn’t have a boundary?

See above. Alternatively, I can answer this by saying, I think this because scientists think this.

Come on, I’ve addressed specific steps on numerous occasions.

You were talking about "completing," though. I want you to addressing specific steps with respect to "reachable," because that's the stated conclusion of the proof. You went on and on about what my proof doesn't prove, but not on its conclusion as stated.

We’ve already done this. Yes, the members are reachable, i.e., they are the types of numbers that can be reached given certain scenarios (like starting at 0 or whatever). Your proof either only shows that or attempts to do more and has failed in the various places I’ve said.

Great, you accept the starting at 0 version, can I also get an explicit answer for the ending at 0, {..., 0} version?

My statement was in reference to the bolded part above, the question you asked me. Yes, if last Monday is reachable, then the present moment is reachable. But you haven’t shown last Monday is reachable on an A-theory infinite past.

And that means whether the present moment is part of the infinite past is not a factor when deciding if it is reachable, which means you should stop mentioning it.