God Must Exist: Infinite Regression is Impossible

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God Must Exist: Infinite Regression is Impossible

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Post by We_Are_VENOM »

.

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.
Venni Vetti Vecci!!

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Re: God Must Exist: Infinite Regression is Impossible

Post #521

Post by The Tanager »

TRANSPONDER wrote: Wed Nov 24, 2021 5:27 pmThat's the problem. A near -nothing is still something and requires an origin and thus a creator. The problem there is that a creator requires a creator.

What is it about being a creator that logically requires being created? Definitionally, it’s only the created that requires a creator. A creator could be created, of course, but nothing logically requires it to be created.
TRANSPONDER wrote: Wed Nov 24, 2021 5:27 pmThe only way out of this impasse is to posit an entity with the power to create but which wasn't created itself (which is as counter - intuitive as one could wish) or the idea of something that didn't need to be created which can only be nothing, which reasonably can be infinite in both time and space, where Something rationally can't be. And that has to be posited as a nothing that can naturally generate energy which of course is matter doing something, or rather matter is energy Not doing something.

I don’t see how it is more counter-intuitive than things popping out of nothing. If the above are the two options, then I think the first is obviously the better choice. The idea of something which can only be nothing is either tautological (where “nothing” is a “something”) or illogical (where “nothing” is the absence of “something”). A true “nothing,” in the traditional sense, cannot reasonably be infinite in time or space.
TRANSPONDER wrote: Wed Nov 24, 2021 5:27 pmYou rightly point up that energy sounds like Something but I make the point that it is near enough nothing that maybe it doesn't need to be deliberately created. It requires less to pop out of nowhere than a god, at least.

It seems to me that nothing and something are the two options. If you think there are shades within the somethings of the world, then what is it about those natures that call for the difference you need here between a “near enough nothing” something and a [“far from nothing”?] something?

Classical theism isn’t about a god popping out of nowhere. I don’t think anything can pop out of nowhere, so there needs to be an eternal something that didn’t pop out of nowhere that gave rise to the universe.

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Re: God Must Exist: Infinite Regression is Impossible

Post #522

Post by The Tanager »

brunumb wrote: Wed Nov 24, 2021 10:06 pmBut then again, you have to remember that the eternal material something works in mysterious ways. ;)

As I tell the theists who use this line, there is a difference between something being unknown or even unknowable and our belief clearly being contradicted by stuff that is known. Mystery is a good descriptor of the first kind and a cop out for the second kind.

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Re: God Must Exist: Infinite Regression is Impossible

Post #523

Post by Bust Nak »

The Tanager wrote: Mon Nov 29, 2021 9:10 pm If this is repeating your earlier claim about who has the burden here, I don’t think I have the burden of showing “why not both.” You have the burden of showing why both. To argue that I have the burden of showing why not both is akin to a theist shifting the burden to the atheist by saying “why couldn’t theism be the answer to X?”
If you find an atheist who says that theism couldn't be the answer, then the theist is not shifting the burden to the atheist by asking him why not.
The question under consideration is whether infinity can be a boundary and a value that is reached. Giving an example of a number that can be both does nothing to prove whether infinity can be both.
You said it isn't both, it's your job to explain why it isn't both, the entire reason I invited you to this thread in the first place all that time ago, was that you made the claim that infinite regression was impossible. I already did more than the bare minimum required of me, by showing that "both" is not trivially mutually exclusive.
I see a “limitless amount of stars” as an unbounded concept (i.e., a boundary idea), not a value that can be reached.
So if you don't need infinity as a value that can be reached for there to be a limitless amount of stars, why would you need infinity as a value which can be reached for an A-theory infinite past, a limitless amount of past events?
You absolutely have something to do for step 1. You have to make sure a previous action was completed, one that wouldn’t have been completed unless a different previous action was completed, so you’ve also got to make sure that previous action was completed...which wouldn’t have been completed unless a different previous action was completed, so you’ve also got to make sure that previous action was completed...ad infinitum.
Meh, that's just semantic: A plain reading of the rule says I have to do something; but in another sense I don't, because it's already been completed. As I pointed out last post, the very act of writing a number down automatically completes the next step 1, I don't need to make sure it was completed, it automatically was. Do you accept my point that doing a step 2 automatically completes the next step 1?
The pre-writing step to writing, say, the number 3 will never end because pushing the question back a step goes on for infinity...
Why wouldn't it end? It ends the very moment it starts, when the number 2 was written down. The fact that there are infinite scope more pairs of steps, doesn't mean that each pairs of 2 steps wouldn't end. I think I see what the sticking point is - the sequence enforced by your rule is ...1, 2, 1 ,2 ,1 ,2...; here you seemed to suggesting that it's ...1, 1, 1... for ever and ever... then 2, 2, 2... Had it been the latter, then I would have accepted that it would be impossible to write any number down.

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Re: God Must Exist: Infinite Regression is Impossible

Post #524

Post by The Tanager »

Bust Nak wrote: Mon Nov 29, 2021 10:06 pmYou said it isn't both, it's your job to explain why it isn't both, the entire reason I invited you to this thread in the first place all that time ago, was that you made the claim that infinite regression was impossible. I already did more than the bare minimum required of me, by showing that "both" is not trivially mutually exclusive.
If you are simply claiming I can't prove (with 100% certainty) infinite regression is impossible, I certainly agree with that and didn't mean to imply differently. My standard is what is most reasonable. I’ve shared why infinity as a value doesn’t make sense to me. Could there still be a reason that makes sense of it? Sure. You have offered none, though. You just keep saying “there’s still a chance”. I’m going with what I see as most reasonable in informing my beliefs.
Bust Nak wrote: Mon Nov 29, 2021 10:06 pmSo if you don't need infinity as a value that can be reached for there to be a limitless amount of stars, why would you need infinity as a value which can be reached for an A-theory infinite past, a limitless amount of past events?

I see “limitless amount of stars” as a concept, not a value. There are still an actual finite/limited number of stars. It’s just that the number of stars can’t be capped at a certain value. We don’t need infinity as a value for this scenario.

In the exact same way, I can envision an A-theory past that had 200,000 members or 72,000,000 members or any finite number of members/events. That’s not what you mean when talking about an infinite past or regression, though, right? No, an infinite regression requires infinity to be a value.
Bust Nak wrote: Mon Nov 29, 2021 10:06 pmMeh, that's just semantic: A plain reading of the rule says I have to do something; but in another sense I don't, because it's already been completed. As I pointed out last post, the very act of writing a number down automatically completes the next step 1, I don't need to make sure it was completed, it automatically was. Do you accept my point that doing a step 2 automatically completes the next step 1?

Only if the previous step 1 has already been done, which it can’t have, because of the rule and nature of infinity as a value (if such a thing could exist). You are correct, the only way it works is if one doesn’t make sure the previous step 1 was completed and just automatically assumes it was. That’s begging the question, though, not showing it can be done.

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Re: God Must Exist: Infinite Regression is Impossible

Post #525

Post by Bust Nak »

The Tanager wrote: Fri Dec 03, 2021 5:01 pm If you are simply claiming I can't prove (with 100% certainty) infinite regression is impossible, I certainly agree with that and didn't mean to imply differently. My standard is what is most reasonable. I’ve shared why infinity as a value doesn’t make sense to me. Could there still be a reason that makes sense of it? Sure. You have offered none, though.
I offered dictionary says "value" is synonymous with "quantity" and the fact that you accept infinity as a quantity as a good reason. And conceptually limitless yet limited in actuality make less sense than just conceptually limitless.
You just keep saying “there’s still a chance”. I’m going with what I see as most reasonable in informing my beliefs.
That's one reason I seek out opponents who go as far as to say it's impossible. "There is still a chance" is a much easier position to defend.
I see “limitless amount of stars” as a concept, not a value. There are still an actual finite/limited number of stars. It’s just that the number of stars can’t be capped at a certain value. We don’t need infinity as a value for this scenario.

In the exact same way, I can envision an A-theory past that had 200,000 members or 72,000,000 members or any finite number of members/events. That’s not what you mean when talking about an infinite past or regression, though, right? No, an infinite regression requires infinity to be a value.
How is this not a trivial self-contradiction? Conceptually there is limitless stars, yet in actuality there is a limited amount of stars?! Your concept doesn't match reality, perhaps adjust your concept. How can there not be an actual infinite amount of stars in an infinite universe?
Only if the previous step 1 has already been done, which it can’t have, because of the rule and nature of infinity as a value (if such a thing could exist).
Can you try and put that in a syllogism? I just don't see why rule and nature of infinity as a value (especially when you are granting that such a thing could exist for the sake of argument) would mean the previous step 1 couldn't been done already.
You are correct, the only way it works is if one doesn’t make sure the previous step 1 was completed and just automatically assumes it was. That’s begging the question, though, not showing it can be done.
I am offering you alternatives, there is no self-contradiction from what I can see, that is at worse an attempt at showing that it can be done, it's your job to rule out my alternatives. More to the point, I am not begging the question, since you've granted me that I eternally exist, and that infinity as a value could exist. I get these presumptions for free.

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Re: God Must Exist: Infinite Regression is Impossible

Post #526

Post by The Tanager »

Bust Nak wrote: Mon Dec 06, 2021 5:30 amI offered dictionary says "value" is synonymous with "quantity" and the fact that you accept infinity as a quantity as a good reason.

I didn’t accept infinity as a quantity, in the narrower sense of that word, where it is a synonym of value.
Bust Nak wrote: Mon Dec 06, 2021 5:30 amAnd conceptually limitless yet limited in actuality make less sense than just conceptually limitless.

Why? What’s hard about thinking that there is no limit to how many stars could exist, but a finite value of actual stars existing at one moment in time? There are a certain amount of stars, but there could have been more than that. How much more? There is no limit to how many more.
Bust Nak wrote: Mon Dec 06, 2021 5:30 amThat's one reason I seek out opponents who go as far as to say it's impossible. "There is still a chance" is a much easier position to defend.

You asked me here to have a go at proving that it is impossible to traverse an actual infinite, not to show that an infinite regression was impossible.
Bust Nak wrote: Mon Dec 06, 2021 5:30 amHow can there not be an actual infinite amount of stars in an infinite universe?

What does it mean for the universe to be infinite?
Bust Nak wrote: Mon Dec 06, 2021 5:30 amCan you try and put that in a syllogism? I just don't see why rule and nature of infinity as a value (especially when you are granting that such a thing could exist for the sake of argument) would mean the previous step 1 couldn't been done already.

I’ll give a quick stab at one::

P1. If the number of actions within step 1 of a rule does not end, then one cannot move onto step 2 of that rule. [Definition]
P2. If something is an actually infinite set, then the amount of members within that set does not end. [Definition]
P3. The amount of actions (i.e., members) within step 1 of our rule is an actually infinite set. [Definition]
P4. Therefore, there is no end to the amount of members within the set of actions within step 1 of our rule. [From 2, 3]
P5. Therefore, one cannot move onto step 2 of our rule. [From 1, 4]
Bust Nak wrote: Mon Dec 06, 2021 5:30 amMore to the point, I am not begging the question, since you've granted me that I eternally exist, and that infinity as a value could exist. I get these presumptions for free.

Those aren’t the question being begged. I grant your eternality and infinity as a value. The question being begged is that an eternally existent being would be able to finish step 1. If infinity is a value, then we can’t reach the end of it.

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Re: God Must Exist: Infinite Regression is Impossible

Post #527

Post by Bust Nak »

The Tanager wrote: Sat Dec 18, 2021 5:43 pm I didn’t accept infinity as a quantity, in the narrower sense of that word, where it is a synonym of value.
Why goes back to one of my original question, why not? When seemingly every enquire I tried, we end up agreeing on the the concept of "quantity," yet reject the word "value" as if there is something different between them. I don't think there are different conceptually, the dictionary says they are synonym. I press you on the differences and you introduce features that seems to me is applicable to both, so I ask you, why not both. It still appears that "why not" is that because you want them to be different.
Why? What’s hard about thinking that there is no limit to how many stars could exist, but a finite value of actual stars existing at one moment in time? There are a certain amount of stars, but there could have been more than that. How much more? There is no limit to how many more.
Okay, there is miscommunication here. That is not what an infinite universe filled with stars entails though. I was talking about stars that currently exists, a snap shot if you will. Rewind to my original question, I asked you how many stars there are, not how many there could be. What doesn't make sense is that "there is no limit to how many stars that currently exists, yet there is a finite value of stars actual stars existing at this moment in time." Which in my mind, translate to there is an infinite amount of stars, yet there is a finite number of stars."

To illustrate what doesn't make sense further, imagine a sock drawer:
a) There are 2 pairs of socks, there is room for more pairs. This makes sense.
b) There are at least 2 pairs of socks, there could be more. This too make sense.
c) There are 2 pairs of socks, there could be more. This doesn't, there are either 2 pairs, or there aren't 2 pairs.
What does it mean for the universe to be infinite?
Boundless and "flat" i.e. you don't loop back by going in one direction. Throw in the presumption that stars are some what evenly spaced out in the universe. That means there is a unlimited amount of stars, AKA an actual infinite amount of stars.
You asked me here to have a go at proving that it is impossible to traverse an actual infinite, not to show that an infinite regression was impossible.
Well, this: "I think the focus should be on whether the natural universe could be eternal. I don't think it could" was the original statement that lead me to invite you to the debate. That sounded a lot like the equivalent of "infinite regression was impossible."
P1. If the number of actions within step 1 of a rule does not end, then one cannot move onto step 2 of that rule. [Definition]
P2. If something is an actually infinite set, then the amount of members within that set does not end. [Definition]
P3. The amount of actions (i.e., members) within step 1 of our rule is an actually infinite set. [Definition]
...
Stop right there, the amount of actions (i.e., members) within step 1 of our rule is a finite set. It takes a finite number of actions to complete step 1. I could call it 1 action: write a number down; I could call it 2 actions: pick up a pen, move it on paper; I could call it more actions, but it's not infinite. The number of step 1s is infinite, not the same thing as step 1 being infinite.
Those aren’t the question being begged. I grant your eternality and infinity as a value. The question being begged is that an eternally existent being would be able to finish step 1.
That's not even an assumption. I have literally written the number 5 on a an A4 right on my desk to make the point that even I, a very finite being, can in fact finished a step 1.

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Re: God Must Exist: Infinite Regression is Impossible

Post #528

Post by The Tanager »

Bust Nak wrote: Wed Jan 05, 2022 11:31 amWhy goes back to one of my original question, why not? When seemingly every enquire I tried, we end up agreeing on the the concept of "quantity," yet reject the word "value" as if there is something different between them. I don't think there are different conceptually, the dictionary says they are synonym. I press you on the differences and you introduce features that seems to me is applicable to both, so I ask you, why not both. It still appears that "why not" is that because you want them to be different.

The distinction I’ve tried to make is between (1) being a quantifiable kind of thing and (2) having a specific quantity/value. Infinity speaks to there being no limit to the quantity that could be reached by that quantifiable kind of thing, i.e., (1) with a finite (2). At any specific moment, the thing being quantified will have a specific, determinate, finite quantity; it’s just that more could be added.

You are either saying infinity can be a (2) as well or that I can’t prove infinity can’t be a (2). Either way, my point is that some new information will need to be brought in to make infinity have that second sense, where it can be a (2). I see no mathematical reason to think this is the case.
Bust Nak wrote: Wed Jan 05, 2022 11:31 amOkay, there is miscommunication here. That is not what an infinite universe filled with stars entails though. I was talking about stars that currently exists, a snap shot if you will. Rewind to my original question, I asked you how many stars there are, not how many there could be. What doesn't make sense is that "there is no limit to how many stars that currently exists, yet there is a finite value of stars actual stars existing at this moment in time." Which in my mind, translate to there is an infinite amount of stars, yet there is a finite number of stars."

Yes, a miscommunication. I don’t think infinity can apply to how many stars there currently are. Assuming it could, we get the various absurdities that would follow, which we’ve been talking about in various ways.

This is what you just said sounds like, to me:

A: How many stars are there right now?

B: No limit.

A: That’s not a number/value/quantity but a statement that we can’t limit what that number could be. We agree there are stars and that stars are quantifiable kinds of things, so how many are there right now?

B: We call the value infinity.

A: But what does that mean? It seems like just a term that assumes there is a quantity but doesn’t actually give a value to it.

B: It means that there is no limit to how many stars currently exist.

A: Yes, but that’s not a number/value/quantity, but a statement that we can’t limit what that number could be.
Bust Nak wrote: Wed Jan 05, 2022 11:31 amWell, this: "I think the focus should be on whether the natural universe could be eternal. I don't think it could" was the original statement that lead me to invite you to the debate. That sounded a lot like the equivalent of "infinite regression was impossible."

Maybe they are related. Do you believe an actual infinite can be traversed? I thought you've said you don't think it can but I think you'd have to say it can be traversed to think an infinite regression within an A-theory temporal world could exist.
Bust Nak wrote: Wed Jan 05, 2022 11:31 amStop right there, the amount of actions (i.e., members) within step 1 of our rule is a finite set. It takes a finite number of actions to complete step 1. I could call it 1 action: write a number down; I could call it 2 actions: pick up a pen, move it on paper; I could call it more actions, but it's not infinite. The number of step 1s is infinite, not the same thing as step 1 being infinite.

No, step 1 is infinite. Before writing a specific number down (say, the number 5)...which is step 2...you have to do step 1, which includes these parts: (1) write down the number 4, and (2) write down the number 3, and (3) write down the number 2, and (4) write down the number 1, and so on. Since the prior numbers you will have to write down go on for infinity, the number of parts of step 1 will be infinite. Thus, you will never complete step 1.
Bust Nak wrote: Wed Jan 05, 2022 11:31 amThat's not even an assumption. I have literally written the number 5 on a an A4 right on my desk to make the point that even I, a very finite being, can in fact finished a step 1.

If all you’ve written down is the number 5, then you clearly haven’t finished step 1 because you have to have written down the number 4 before you can write down the number 5.

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Re: God Must Exist: Infinite Regression is Impossible

Post #529

Post by Bust Nak »

The Tanager wrote: Fri Jan 07, 2022 3:51 pm The distinction I’ve tried to make is between (1) being a quantifiable kind of thing and (2) having a specific quantity/value. Infinity speaks to there being no limit to the quantity that could be reached by that quantifiable kind of thing, i.e., (1) with a finite (2). At any specific moment, the thing being quantified will have a specific, determinate, finite quantity; it’s just that more could be added.

You are either saying infinity can be a (2) as well or that I can’t prove infinity can’t be a (2). Either way, my point is that some new information will need to be brought in to make infinity have that second sense, where it can be a (2). I see no mathematical reason to think this is the case.
I gave you an example of how a value can be both - the following 0, 1, 2, 3, 4, 5. In one sense I have not reached the boundary 6, yet I have reached it by counting 6 numbers in another sense, so why couldn't the same apply to infinity? Doesn't this count as a mathematical reason to think this is the case?
Yes, a miscommunication. I don’t think infinity can apply to how many stars there currently are. Assuming it could, we get the various absurdities that would follow, which we’ve been talking about in various ways.

This is what you just said sounds like, to me:

A: How many stars are there right now?

B: No limit.

A: That’s not a number/value/quantity but a statement that we can’t limit what that number could be. We agree there are stars and that stars are quantifiable kinds of things, so how many are there right now?

B: We call the value infinity.

A: But what does that mean? It seems like just a term that assumes there is a quantity but doesn’t actually give a value to it.

B: It means that there is no limit to how many stars currently exist.

A: Yes, but that’s not a number/value/quantity, but a statement that we can’t limit what that number could be.
And that seems like an awful lot of hoops to jump through when you could have just accepted yes, infinity is quantity (AKA value) but isn't a specific quantity (AKA value.) It's still problematic to me that stars are quantifiable things, there is no limit to them, yet infinity does not apply to how many there are.
Maybe they are related. Do you believe an actual infinite can be traversed? I thought you've said you don't think it can but I think you'd have to say it can be traversed to think an infinite regression within an A-theory temporal world could exist.
It depends on what "traversed" mean, relating to what "reached" means. Earlier I said by counting 0, 1, 2, 3, 4, 5. I have not reached the boundary 6, yet I have reached it by counting 6 numbers. In one sense I have not traversed 6 because I have not reached 6; in other sense I have traversed 6 by counting 6 numbers. I believe the same applies to actual infinite, actual infinite can be traversed without ever reaching the boundary infinity.
No, step 1 is infinite. Before writing a specific number down (say, the number 5)...which is step 2...you have to do step 1, which includes these parts: (1) write down the number 4, and (2) write down the number 3, and (3) write down the number 2, and (4) write down the number 1, and so on.
So there is only one step 1: write down all the numbers less than 5? As opposed to ...step 1: check if number 3 is written down; step 2: write 4 down; loop back to step 1: check if number 4 is written down; step 2 write 5 down.

If there is only one step 1, why did you speak of a previous step 1? Why did you referred to it as "pre-writing cognitive step" when here you are taking about actually writing numbers down? Either way, if there is only one step 1, then let me go back to an earlier premise...
P2. If something is an actually infinite set, then the amount of members within that set does not end. [Definition]
Why this and not, "If something is an actually infinite set, then the amount of members within that set either does not start, or does not end, or neither start nor end?

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Re: God Must Exist: Infinite Regression is Impossible

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Bust Nak wrote: Mon Jan 10, 2022 4:46 amI gave you an example of how a value can be both - the following 0, 1, 2, 3, 4, 5. In one sense I have not reached the boundary 6, yet I have reached it by counting 6 numbers in another sense, so why couldn't the same apply to infinity? Doesn't this count as a mathematical reason to think this is the case?

This shows that numbers can be used as boundary concepts, but with infinity we are going the other way round, trying to see if a boundary concept can also be a number. At best, your example says it is logically possible. That’s not a mathematical reason or any other kind of rational reason to think the same thing that applies to numbers does apply to infinity. Logical possibility isn’t good enough in my book.

A fence is a boundary concept, but it’s not a number. Does this count as proof that infinity can’t be a number? Of course not. The question is whether infinity is only like a fence or is also a number. We agree infinity, as defined, can act like a fence to numbers. The additional info we disagree on is whether it is also a number itself. I see no reason to believe it is a number in addition to it’s fence-like quality.
Bust Nak wrote: Mon Jan 10, 2022 4:46 amAnd that seems like an awful lot of hoops to jump through when you could have just accepted yes, infinity is quantity (AKA value) but isn't a specific quantity (AKA value.)

Why is making a distinction between a quantifiable kind of thing and a quantity “an awful lot of hoops to jump through”? What is the difference you see between being a quantity/value and a specific quantity/specific value? How is that different than my distinction?
Bust Nak wrote: Mon Jan 10, 2022 4:46 amIt's still problematic to me that stars are quantifiable things, there is no limit to them, yet infinity does not apply to how many there are.

Why is that a problem? Stars are the types of things that can be quantified. There is no limit to what the quantity could be, but the quantity they actually are is a specific quantity because that is how quantity works, 1 or 2 or 3 or 4 or so on, even if that quantity is 'infinity'. But, at that point, this infinity is a specific quantity and not a boundary concept (even if it can be used as a boundary).
Bust Nak wrote: Mon Jan 10, 2022 4:46 amIt depends on what "traversed" mean, relating to what "reached" means. Earlier I said by counting 0, 1, 2, 3, 4, 5. I have not reached the boundary 6, yet I have reached it by counting 6 numbers. In one sense I have not traversed 6 because I have not reached 6; in other sense I have traversed 6 by counting 6 numbers. I believe the same applies to actual infinite, actual infinite can be traversed without ever reaching the boundary infinity.

I mean ‘traversed’ in the sense of reaching that boundary point. I mean the number you start counting with is arbitrary, right? Why not count 1, 2, 3, 4, 5? Or 3, 4, 5? Then you would not have reached 6 in either sense. Or count this way: -5, -4, -3, …, 4, 5? There you have reached and passed 6.
So, perhaps there is an equivocation going on. The boundary is a different concept than the number of numbers you counted before reaching that boundary. Even if they share the same name or even mathematical value, those concepts are distinct ones, where the ‘6’ is being used in equivocal ways in spite of its value.

By definition, being infinite means having no end, no limit, right? I don’t see how one can traverse the whole set and reach the boundary, the end, the limit of a something that has no end or limit. How can something without an end have that end (which isn't there) reached?
Bust Nak wrote: Mon Jan 10, 2022 4:46 amSo there is only one step 1: write down all the numbers less than 5? As opposed to ...step 1: check if number 3 is written down; step 2: write 4 down; loop back to step 1: check if number 4 is written down; step 2 write 5 down.

If there is only one step 1, why did you speak of a previous step 1? Why did you referred to it as "pre-writing cognitive step" when here you are taking about actually writing numbers down? Either way, if there is only one step 1, then let me go back to an earlier premise...

No, there isn’t just one step, but I think you are speaking to a better way to formulate the steps. Step 1 is to check to see if you have already written down all the numbers prior to 5. If so, you can move to step 2 and write the number 5 down. If not, then you’ve got to write those prior numbers down. Each previous number will have its own, identical, 2-step process.
Bust Nak wrote: Mon Jan 10, 2022 4:46 amWhy this and not, "If something is an actually infinite set, then the amount of members within that set either does not start, or does not end, or neither start nor end?

In this context we know there is a beginning. Not a beginning to the set considered in itself necessarily, but how we are going about using it. If you are writing the number 5, our step 1 will begin with checking if the number 4 is written down. If not, we will then have to see if 3 is written down. If not, we will have to see if 2 is written down. Since the numbers are infinite, the numbers we will have to make sure are written down first will never end, we will never reach a number and say, alright, there are no more numbers to check.

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