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]

Where are you getting this idea of an infinite set having specific size from?

What I said was that “several” is a non-specific way that we use to describe something that has a specific size (10, 11, 23, etc.). I wouldn’t use “several” to refer to the number of integers that exist.

But let’s grant that “several” is a non-specific size. If it’s like every other use of “several”, then we don’t do math on “several”. Yes, we can say “several” minus 10 is still “several,” but that’s really doing math on different numbers where, say, ‘several’ is 23, we subtract 10 to get 13, and then we call 13 “several” as well. If “infinite” is like that, then we also don’t do math on “infinite”.

If it’s not like every other use of “several”, then the question is still open on whether we can do math on it or not. But you can’t just beg the question in favor of us being able to do math on it. It’s your burden to show that math can be done on it, not my burden to show it can’t be done.

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

I said it was not a particular or determinate size, but that this is different from saying it’s size is zero. It seems here that “non-specific” might just be a synonym of “non-finite/infinite.” I thought you were bringing in “non-specific” as a way to support your claim that we can do math on actual infinite amounts. Just renaming the term doesn’t do that, it doesn’t move the discussion forward, we are just translating it into different terms.

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

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

But “all windows” is equivalent to “the whole house”; those are synonyms. So, all windows are expanding, but the whole house is not expanding. The same referent is both expanding and not expanding in the same sense of “expanding”.

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

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

That wasn’t clear to me, but thanks for clarifying. There may need to be some more clarifying. I don’t see why you are moving to “sets of series”. Isn’t counting an infinite number of sets the same as just counting infinite numbers, at least for our intent here?

C = count from one number (i.e., starting a series there) to the next number (i.e., ending a series there)
C1 = count from 0 to 1
C2 = count from N to N+1
C3 = count from N+1 to N+2

Here we are just talking about counting in individual series. But then you bring in counting multiple series (“sets of series”). So, I guess I’ll use M for those:

M = count the numbers in more than one series
M∞ = count the numbers in an infinite number of series

S = move through the number you started the series at
E = move through the number you ended the series at
A = move through all numbers in the series whether or not it has a start and end
B = move through all numbers in the series that starts at 0 and has no end

This seems to be your argument:

1) If you can C, then you can S
2) You can C1
3) Therefore, you can S1
4) If you can C2, then you can C3
5.1) If (if you can C2, then you can C3), then (if you can C2, then you can M∞)
5.2) If you can C2, then you can M∞
5.3) If you can M∞, then you can A
5.4) If you can C2, then you can A
5.5) You can B (based off the premise that if you can A, then you can B…I agree that is true)
6) Therefore, you can A (how is this different than 5.4)?

While I’m not sure premise 4 is true, I think you can C2 and C3. I can count from N to N+1. And I can count from N+1 to N+2, but it’s not because I can count from N to N+1, it’s because of C being true. Still, how do you support 5.1 as a true premise? Just because I can count from 0 to 1 and 1 to 2, this doesn’t mean I can count all possible series of that sequential nature. How do you make that jump?

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

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

Analogically, that is like:

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

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

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

vs

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

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

No, analogically, we have this:

1. Married
2. Chinese person (bachelor or non-bachelor)

Using “non-bachelor” as a synonym for married should not make us think there is no contradiction. Neither should saying “move through all members” instead of “completing the process”. They mean the same thing. Once we analyze further what a non-bachelor is, then we see it conflicts with ‘married’. I think the same thing happens with what it means to complete a process and how ‘infinite’ describes a never ending process. At this point we see it is illogical to complete a never ending process.

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

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

As I said earlier, I don’t think those are two senses of ‘complete a process,’ but competing definitions where the second one is better.

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

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

vs

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

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

Are you insisting?

No, I’m definitely not. Those are two distinct, valid meanings for “married”. Your ‘sense’ of “moving through a limited number of members’ is a wrong definition for ‘completing the process’ because you are applying the real meaning ‘move through all members’ in a specific situation, ignoring other valid applications, rather than giving a definition of a distinct, valid use of the term.

[Bust Nak]

What I said was that “several” is a non-specific way that we use to describe something that has a specific size (10, 11, 23, etc.). I wouldn’t use “several” to refer to the number of integers that exist.

But let’s grant that “several” is a non-specific size. If it’s like every other use of “several”, then we don’t do math on “several”. Yes, we can say “several” minus 10 is still “several,” but that’s really doing math on different numbers where, say, ‘several’ is 23, we subtract 10 to get 13, and then we call 13 “several” as well. If “infinite” is like that, then we also don’t do math on “infinite”.

That's fine, I don't need infinite to be a number, just conceptually a quantity.

It’s your burden to show that math can be done on it, not my burden to show it can’t be done.

That's fine too, as I point to Georg Cantor doing math with infinity. Or any suitable math text book listing the properties of infinity, including things like infinity + 1 = infinity. You have argued that they are not treating infinity as a number when mathematicians do that, but there is no question that they do indeed do math with it.

I said it was not a particular or determinate size, but that this is different from saying it’s size is zero. It seems here that “non-specific” might just be a synonym of “non-finite/infinite.” I thought you were bringing in “non-specific” as a way to support your claim that we can do math on actual infinite amounts. Just renaming the term doesn’t do that, it doesn’t move the discussion forward, we are just translating it into different terms.

Well I don't know why you felt you need to point out that it's different from saying its size is zero. There are definitely at least one integer. By "non-specific" I mean it's not any one integer. It can be, but need not be infinite. My point was that you answered infinite, but if by that you meant there is no limit as to the number of integers there could potentially be, you are answering a different question. And by "infinity" you don't mean zero or any other particular or determinate size, you are left with a non-specific quantity, but a quantity non-the-less.

But “all windows” is equivalent to “the whole house”; those are synonyms. So, all windows are expanding, but the whole house is not expanding. The same referent is both expanding and not expanding in the same sense of “expanding”.

How is it the same sense? Given the same referent, is "several + 10 is still several, so not expanding" contradictory with "13 + 10 is expanding to 23" to you?

That wasn’t clear to me, but thanks for clarifying. There may need to be some more clarifying. I don’t see why you are moving to “sets of series”. Isn’t counting an infinite number of sets the same as just counting infinite numbers, at least for our intent here?

I think so, at least very close, if not exactly the same, that's why I didn't feel the need to add many explicit steps in my original proof.

E = move through the number you ended the series at

I didn't ask you this before, I'll ask now. Why do you need E? I don't see that appear anywhere in your summary.

A = move through all numbers in the series whether or not it has a start and end
B = move through all numbers in the series that starts at 0 and has no end

As I mentioned before, an almost identical proof can be provided for moving through all numbers in a series with no start and ends at 0, combine the two conclusions to get series with no start and/or end. But lets leave that aside until we resolve this version of the proof first. In light of this, I've modified the last few steps.

1) If you can C, then you can S
2) You can C1
3) Therefore, you can S1
4) If you can C2, then you can C3
5.1) If (if you can C2, then you can C3), then (if you can C2, then you can M∞)
5.2) If you can C2, then you can M∞
5.3) If you can M∞, then you can B
5.4) If you can C2, then you can B
5.5) You can B
6) pending the no start version, you can A.

While I’m not sure premise 4 is true, I think you can C2 and C3. I can count from N to N+1. And I can count from N+1 to N+2, but it’s not because I can count from N to N+1, it’s because of C being true.

That's fine, but it doesn't matter why you can C3, I just need to formulate it as a conditional statement for iterative case in mathematical induction. Logically given that can_C3 is true, we can trivially conclude if can_C2 then can_C3. See the truth table of the if...then... operator.

Still, how do you support 5.1 as a true premise? Just because I can count from 0 to 1 and 1 to 2, this doesn’t mean I can count all possible series of that sequential nature.

You just told me you can C2, isn't that just another way of saying, you can count all possible series of that sequential nature? Which series with the sequential nature {N, N+1} where you can't count from the first integer to the second integer?

How do you make that jump?

1) if can_C2 then can_C3 (premise)
2) Let X be the set of all series with the sequential nature {N, N+1} that cannot be counted. (define X)
3) X is not empty. (premise)
4) Series with the sequential nature {N, N+1} can be ordered by the integer N, e.g. {1, 2} is lower than {5, 6}, both are lower than {14, 15}. (premise)
5) Let X0 be {X, X+1}, the lowest member of X. (define X0)
6) The sequence {X-1, X} is lower than X0, the lowest member of X. (from 4 and 5)
7) Therefore the sequence {X-1, X} is not a member of X. (from 6)
8) Can count from X-1 to X (from 2 and 7)
9) Can count from X to X+1 (from 1 and 8)
10) X0 is not a member of X (from 2 and 9)
11) Contradiction, therefore some of the premises are false. (from 5 and 10)

Which ones are you gonna discard? The premise in 1) is the given starting point, the one in 4) looks solid. That leaves the premise in step 3). The set of uncountable series of the form {N, N+1} is empty. in other words, just because you can count from 0 to 1 and 1 to 2, you can count all possible series of that sequential nature.

Once we analyze further what a non-bachelor is, then we see it conflicts with ‘married’. I think the same thing happens with what it means to complete a process and how ‘infinite’ describes a never ending process. At this point we see it is illogical to complete a never ending process.

How is illogical when you already said "all" is compatible with both finite and infinite? Does that not trivially mean the "moving through all members" allows for moving through an infinite amount, and therefore endless members?

As I said earlier, I don’t think those are two senses of ‘complete a process,’ but competing definitions where the second one is better.

But that's the one I use, that's the one where it is compatible with completing a never ending process.

Your ‘sense’ of “moving through a limited number of members’ is a wrong definition for ‘completing the process’

Not my sense, I was just trying to make explicit your contention that completing the process implicitly exclude moving through an unlimited number of members, i.e. in same sense circle rules out square. Perhaps this attempt would be more to your liking:

1. completing an non-endless process
2. A-theory past (finite or infinite)

Once we analyze further what infinite is, then we see it conflicts with complete the process.

vs

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

No contradiction with A-theory infinite past with complete the process.

[The Tanager]

That's fine, I don't need infinite to be a number, just conceptually a quantity.

“Several” is a term that tells us something about a quantity, rather than being the quantity itself, so the problem remains, if you are saying (actual) ‘infinite’ is the same kind of thing as ‘several’.

That's fine too, as I point to Georg Cantor doing math with infinity. Or any suitable math text book listing the properties of infinity, including things like infinity + 1 = infinity. You have argued that they are not treating infinity as a number when mathematicians do that, but there is no question that they do indeed do math with it.

As I’ve said, they are assuming it is a number or quantity, and then seeing what mathematical operations would result in. The question we are discussing here, specifically, is whether it is a number or quantity.

Well I don't know why you felt you need to point out that it's different from saying its size is zero.

Because if I said “it doesn’t have a size” one could think I mean it’s size is zero rather than no particular or determinate size.

There are definitely at least one integer. By "non-specific" I mean it's not any one integer. It can be, but need not be infinite.

Which you need to establish as a sentence that actually makes sense. All known quantities have a corresponding integer (or fraction of an integer). We can’t just say (if we want to be rational beings) “Well, maybe, there could be a quantity without a corresponding integer, so let’s build our beliefs off of that possibility unless you prove otherwise.”

My point was that you answered infinite, but if by that you meant there is no limit as to the number of integers there could potentially be, you are answering a different question. My point was that you answered infinite, but if by that you meant there is no limit as to the number of integers there could potentially be, you are answering a different question.

Yes, “potential infinite” is an answer to another question, but it may also be the best answer to your question. I don’t think numbers or quantities exist as independent things outside of minds, so how many currently exist would depend on how many are being thought of by minds (we could even say how many have been thought of in all of history). Saying there are an infinite amount of integers, to me, means saying that minds could always think of more, not that they are actually thinking about an actual quantity of integers. Infinity is a concept that states a fact about quantities, not a quantity itself.

How is it the same sense? Given the same referent, is "several + 10 is still several, so not expanding" contradictory with "13 + 10 is expanding to 23" to you?

Absolutely! “Several + 10 is still several” is expanding. It’s a bigger “several”. Using the same term has simply fooled you into thinking, “Oh, it must not be expanding.” The somewhat vague, non-specific word you used to refer to the quantity you had before and after didn’t change, but the size of the quantity certainly did from 13 to 23. Exact same sense of “expanding” in both cases.

I didn't ask you this before, I'll ask now. Why do you need E? I don't see that appear anywhere in your summary.

I just included the different ideas, knowing not all would be used in our discussion.

5.1) If (if you can C2, then you can C3), then (if you can C2, then you can M∞)

how do you support 5.1 as a true premise? Just because I can count from 0 to 1 and 1 to 2, this doesn’t mean I can count all possible series of that sequential nature.

You just told me you can C2, isn't that just another way of saying, you can count all possible series of that sequential nature? Which series with the sequential nature {N, N+1} where you can't count from the first integer to the second integer?

C2 is where you start at a number and end at the very next number.
C3 is where you start at a number and end at the very next number.
M∞ is where you start at a number and don’t end, but still count all the numbers.

So, how does the ability to start at one number and end at the next, mean one can start at one number and just keep going without ever ending, yet count all the numbers that never end?

Which ones are you gonna discard? The premise in 1) is the given starting point, the one in 4) looks solid. That leaves the premise in step 3). The set of uncountable series of the form {N, N+1} is empty. in other words, just because you can count from 0 to 1 and 1 to 2, you can count all possible series of that sequential nature.

Yes, starting at one number you can always reach the next number and stop there. How does this help you get to starting at counting one series and then counting all the other numbers in an infinite number of series, much less not starting at one number and counting all the other numbers in an infinite number of series?

How is illogical when you already said "all" is compatible with both finite and infinite? Does that not trivially mean the "moving through all members" allows for moving through an infinite amount, and therefore endless members?

How is it illogical when you agree that “Chinese person” is compatible with bachelor and non-bachelor? Does that not trivially mean adding “married” to a description of their reality is something both bachelors and non-bachelors can do?

No, there is a logical contradiction there. Why? Because ‘married’ (the addition) contradicts ‘bachelor’ (the previous category that we were okay with). So, if ‘complete the process/move through all members’ (the addition) contradicts ‘infinite/unending process’ (the previous category that we were okay with), then there is a logical contradiction there as well.

But that's the one I use, that's the one where it is compatible with completing a never ending process.

Does “a never ending process” contradict with “a process being completed”? If so, then how does changing the terms used but meaning the exact same thing change that?

If all snow is white and thus contradicting being a black thing, then how does changing “white” to “flueger” (while meaning the exact same thing) keep it from still contradicting being a black thing?

[Diogenes]

I've never understood how this 'argument' ever got traction a 1000 years ago, let alone now.

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”.

That the universe is not past eternal is simply an assumption, an unfounded claim. So is the justification, the claim that "infinity cannot be 'reached.' Again, this is just an unfounded claim, and one that redefines "infinity" as "finite," its opposite.
That a debater cannot conceive of the infinite speaks to the claimants' limitations, not to the argument for infinity

Another major flaw in the argument is that, even if, all other aspects of the argument are assumed to be correct, the argument then takes a GIANT STEP along Assumption Road to declare the uncaused cause must be God. And not only a god, but one with a personality, a mind, a god that just happens to fit whatever the one who argues picks as a favorite definition of 'God.'

But there is another enormous problem with the argument. It starts by claiming there is no infinity, then claims there IS an infinite, the "uncaused cause," or 'God.' The 'uncaused cause' can be the universe itself (in one form or another) rather than this 'God.' And THAT is an alternative that requires fewer assumptions.

[Willum]

Okay, draw a square.
Make another squre from the midpoints of the larger square.
Do the same for that square… now do it for an infinite regression.

What is the total exposed area of all the infinite boxes, including lines?
The area of the original box.

What is the area of all the boxes?
That is the length squared of the box, times two.

Here: l^2 * (1/2 + 1/4 + 1/8 +…

=

l^2 * 1/(1-1/2)

- l^2 cancel… multiplying 1*1 = 1, -1/2*1 = -1/2, cancelling the next term, and so on.

Any REAL infinite regression ALWAYS yields a finite result.

An increasing progression, 1 + 2 + 3 +… must conclude before too long as well.

If it doesn’t it’s an fictitious result, like a god.

Best regards,

[Bust Nak]

“Several” is a term that tells us something about a quantity, rather than being the quantity itself, so the problem remains, if you are saying (actual) ‘infinite’ is the same kind of thing as ‘several’.

I am saying actual infinite is conceptually a quantity.

As I’ve said, they are assuming it is a number or quantity, and then seeing what mathematical operations would result in. The question we are discussing here, specifically, is whether it is a number or quantity.

At least affirm that they are doing math with it, even with the caveat that it's presumed to be a quantity. As for assuming it, you could say mathematicians are making assumption about the real world when they defined infinity the way they do, but they are not assuming infinity is a quantity, they have define it that way.

Because if I said “it doesn’t have a size” one could think I mean it’s size is zero rather than no particular or determinate size.

So "how many integers are there" is an incoherent question, asking the size of something that does not have a size? Later on you spoke of the quantity of integers, how can there be facts about the size of something that doesn't have a size?

Which you need to establish as a sentence that actually makes sense. All known quantities have a corresponding integer (or fraction of an integer). We can’t just say (if we want to be rational beings) “Well, maybe, there could be a quantity without a corresponding integer, so let’s build our beliefs off of that possibility unless you prove otherwise.”

I am sticking to my old answer. It's not the case that all known quantities have a corresponding integer, we know of at least one that isn't - infinity. How many integers are there is a coherent question. The answer is a quantity, the answer is not a particular integer, the correct answer is infinite.

Yes, “potential infinite” is an answer to another question, but it may also be the best answer to your question. I don’t think numbers or quantities exist as independent things outside of minds, so how many currently exist would depend on how many are being thought of by minds (we could even say how many have been thought of in all of history). Saying there are an infinite amount of integers, to me, means saying that minds could always think of more, not that they are actually thinking about an actual quantity of integers. Infinity is a concept that states a fact about quantities, not a quantity itself.

Same kind question as above, is "quantity of integers" even a thing in you book, when supposedly the set of integers doesn't have a size? Can you do math with the quantity of integers, given this fact re: can always think of more about this quantity?

Absolutely! “Several + 10 is still several” is expanding. It’s a bigger “several”.

Great, so in the same way, the universe is expanding both in the infinite + 1 is still infinite sense, and every window is expanding sense. There goes the expanding and not expanding objection. Where is the contradiction?

C2 is where you start at a number and end at the very next number.
C3 is where you start at a number and end at the very next number.
M∞ is where you start at a number and don’t end, but still count all the numbers.

No. M∞ is still talking about series with the sequential nature {N, N+1}, e.g. {1, 2}, {15, 16}, or {125, 127} and so on, each one starts at a number and ends at the very next. Starting at a number and not ending only appears from step 5.3) onwards.

So, how does the ability to start at one number and end at the next, mean one can start at one number and just keep going without ever ending, yet count all the numbers that never end? ... How does this help you get to starting at counting one series and then counting all the other numbers in an infinite number of series, much less not starting at one number and counting all the other numbers in an infinite number of series?

I don't understanding what is going on here, on the one hand you seemed to have accepted my defence of 4) and 5.1), on the other you don't see how I get from starting at counting one series, then to counting all other series of the same form, then on to counting a series with infinite number of members. I've presented a deductive proof, if the premises hold and the steps are valid, then the conclusion follows. Follow the proof step by step, that's how.

Look, let me present a more concise version of the proof, I am dropping the beginning part with S since you have accepted moving through a member of set and counting from one integer to the next is the same thing given the context of counting numbers. I am also condensing things like can_C1 to just C1 with the following updated definitions:

C1 = can count from 0 to 1
C2 = can count from N to N+1
C3 = can count from N+1 to N+2
M∞ = can count series of the form {X, X+1} for all X >= N
B = can count the series {0, ...} i.e. a series that starts at 0 and has no end

1) If C2 then C3 (premise, see defence of step 4)
2) If (if C2 then C3) then M∞ (premise, see defence of step 5.1)
3) M∞ (from 1 and 2)
4) C1 (premise)
5) If (M∞ and C1) then B (premise)
6) B (from 3, 4 and 5)

With the two problematic premises out of the way, which remaining ones are you still not sure about? Presumably that leaves the one in step 5? I can't see you challenging the validity of the proof.

How is it illogical when you agree that “Chinese person” is compatible with bachelor and non-bachelor? Does that not trivially mean adding “married” to a description of their reality is something both bachelors and non-bachelors can do?

That's a false analogy. Look carefully again at what I actually asked: How is illogical when 'all' is compatible with both finite and infinite? "All" is analogous to "married," the definition we are checking compatibility with; "A-theory past" is analogous to "Chinese person," the entity we are checking; "bachelor and non-bachelor" is analogous to "finite and infinite" the properties of the entity, which we are previously okay with, Chinese person can indeed be bachelor or a non-bachelor; A-theory past can indeed be infinite or infinite.

A such, the analogous question would be: "how is it illogical when 'married' is compatible with bachelor and non-bachelor?" The answer would then be "no, it isn't compatible." Except you can't use that answer for the question I asked, why? Because "all" (the addition) does not contradicts "infinite" (the previous category that we were okay with).

Does “a never ending process” contradict with “a process being completed”?

It depends what "a process being completed" mean. That's why it's so important to pin point the two meanings:

"A never ending process" contradicts with "completing an non-endless process."
"A never ending process" does not contradicts with "moving through all the members."

[Bust Nak]

Any REAL infinite regression ALWAYS yields a finite result.

An increasing progression, 1 + 2 + 3 +… must conclude before too long as well.

What do you think of the mathematical series 1 + 1/2 + 1/3 + 1/4 + ...? Is that infinite regression or increasing progression?

If it is an infinite regression then is it a fake one? If it is an increasing progression then why must it conclude before too long?

[Willum]

[Replying to Bust Nak in post #577]

What’s special about it that you should ask?

The point has been made.
Infinite regression exists, and even has applications in real life.

According to the op, this means God doesn’t exist.

But that is only for yourself, the author of the post.

God doesn’t exist, but not for that reason.

[Bust Nak]

[Replying to Willum in post #578]

I asked because it's not clear which series qualify as infinite regression and which don't. 1 + 1/2 + 1/3 + 1/4 + ... looks a lot like 1 + 1/2 + 1/4 + 1/8 + … but only the latter yields a finite result.

But what I am more interested in, is why you think a divergent series "must conclude before too long."

[The Tanager]

At least affirm that they are doing math with it, even with the caveat that it's presumed to be a quantity.

I’ve affirmed this multiple times.

As for assuming it, you could say mathematicians are making assumption about the real world when they defined infinity the way they do, but they are not assuming infinity is a quantity, they have define it that way.

‘Actual infinity’ didn’t involve real world assumptions in its creation at all. Only afterwards did philosophers of mathematics, like Hilbert, start to think about whether it fits in the real world.

So "how many integers are there" is an incoherent question, asking the size of something that does not have a size? Later on you spoke of the quantity of integers, how can there be facts about the size of something that doesn't have a size?

I think it’s coherent. I’m saying the answer of “infinity” is a concept akin to “there could always be more” or “it’s an unending amount.” If that is what you mean by infinity being a quantity but not like the number 2, then okay. If you mean something else, explain it.

Great, so in the same way, the universe is expanding both in the infinite + 1 is still infinite sense, and every window is expanding sense. There goes the expanding and not expanding objection. Where is the contradiction?

You were previously saying it wasn’t expanding in the infinite +1 is still infinite sense, though.

I don't understanding what is going on here, on the one hand you seemed to have accepted my defence of 4) and 5.1), on the other you don't see how I get from starting at counting one series, then to counting all other series of the same form, then on to counting a series with infinite number of members. I've presented a deductive proof, if the premises hold and the steps are valid, then the conclusion follows. Follow the proof step by step, that's how.

I never accepted 5.1; I asked you how you supported it.

C1 = can count from 0 to 1
C2 = can count from N to N+1
C3 = can count from N+1 to N+2
M∞ = can count series of the form {X, X+1} for all X >= N
B = can count the series {0, ...} i.e. a series that starts at 0 and has no end

1) If C2 then C3 (premise, see defence of step 4)
2) If (if C2 then C3) then M∞ (premise, see defence of step 5.1)
3) M∞ (from 1 and 2)
4) C1 (premise)
5) If (M∞ and C1) then B (premise)
6) B (from 3, 4 and 5)

With the two problematic premises out of the way, which remaining ones are you still not sure about? Presumably that leaves the one in step 5? I can't see you challenging the validity of the proof.

I don’t accept premise 1 (although I do accept that you can count from any number to the next number). I don’t accept premise 5. I don’t understand how being able to count from 0 to 1, from 1 to 2, from 578 to 579, etc.(i.e., always starting at a particular number and always ending at a particular number) leads to being able to count a series in which you start at a particular number, but which never ends. Every iteration of your attempt to move to a series of the nature (1, 2, 3, ….) has had the same lack of support for doing so.

How is it illogical when you agree that “Chinese person” is compatible with bachelor and non-bachelor? Does that not trivially mean adding “married” to a description of their reality is something both bachelors and non-bachelors can do?

That's a false analogy. Look carefully again at what I actually asked: How is illogical when 'all' is compatible with both finite and infinite? "All" is analogous to "married," the definition we are checking compatibility with; "A-theory past" is analogous to "Chinese person," the entity we are checking; "bachelor and non-bachelor" is analogous to "finite and infinite" the properties of the entity, which we are previously okay with, Chinese person can indeed be bachelor or a non-bachelor; A-theory past can indeed be infinite or infinite.

A such, the analogous question would be: "how is it illogical when 'married' is compatible with bachelor and non-bachelor?" The answer would then be "no, it isn't compatible." Except you can't use that answer for the question I asked, why? Because "all" (the addition) does not contradicts "infinite" (the previous category that we were okay with).

No, ‘married’ is not analogous to ‘all’ but to ‘complete a process’. We aren’t checking the definition of 'all', but of ‘complete a process’. ‘All' is a part of A-theory pasts and Chinese people. Here are the terms in analogy:

1. Complete a process
2. All A-theory pasts
2a. Finite
2b. Infinite

1. Married
2. All Chinese people
2a. Non-bachelor(ette)
2b. Bachelor(ette)

1 and 2, in both, don’t necessarily contradict. 1 and 2a, in both, don’t contradict. 1 and 2b, in both, do contradict by how they are defined.

Does “a never ending process” contradict with “a process being completed”?

It depends what "a process being completed" mean. That's why it's so important to pin point the two meanings:

"A never ending process" contradicts with "completing an non-endless process."
"A never ending process" does not contradicts with "moving through all the members."

Those aren’t two meanings/sense of ‘complete a process’; only the second one is a definition. Saying the first one is a definition of ‘a process being completed’ is like saying ‘brown cat’ is a definition of ‘cat’. No. It’s a sub-category, an example, of the term we are trying to define.