God Must Exist: Infinite Regression is Impossible

Argue for and against Christianity

Moderator: Moderators

Post Reply
User avatar
We_Are_VENOM
Sage
Posts: 720
Joined: Wed Aug 12, 2020 2:33 am
Has thanked: 30 times
Been thanked: 20 times

God Must Exist: Infinite Regression is Impossible

Post #1

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!!

User avatar
The Tanager
Prodigy
Posts: 3054
Joined: Wed May 06, 2015 11:08 am
Has thanked: 11 times
Been thanked: 41 times

Re: God Must Exist: Infinite Regression is Impossible

Post #451

Post by The Tanager »

Bust Nak wrote: Mon Sep 27, 2021 7:50 amLimited and not limited a true dichotomy, this holds trivially because it takes the form of A or ¬A. If there are exceptions, it would be because of some misunderstanding of what the two categories means (maybe something along the lines of infinity is not really the same as not limited,) there is no getting around that the simple A and ¬A.

But not all dichotomies necessarily apply in all situations. I could come up with a dichotomy of, say, taller than you vs. non-taller than you but this doesn’t mean it applies to every situation. Me liking the Chicago Cubs is neither taller than you nor non-taller than you.
Bust Nak wrote: Mon Sep 27, 2021 7:50 amUsed both ways as in a mathematic construct like the root of -1 and as a limit? That's fine, both way it is treated as a quantity though.

Why do you think infinity as a limit is treated as a quantity?
Bust Nak wrote: Mon Sep 27, 2021 7:50 amWhy not? There is still two: a height that is a real thing and the height that isn't a thing. Where as my stance just has height.

What do you mean “the height that isn’t a thing”? Both ways have the concept of height and a concept about what kinds of things height can be applied to and what it can’t.
Bust Nak wrote: Mon Sep 27, 2021 7:50 am
Then isn’t there either a contradiction or an equivocation going on? An end for an unending line (logical contradiction). Or this ‘infinity’ being limited and, therefore, not infinite (equivocation).

I don't think so, math is quite well defined, even if it might not gel well with intuition.

Perhaps it would help to look at the sources you are using for this.
Bust Nak wrote: Mon Sep 27, 2021 7:50 amNo no no, it is very much possible because traversing an actual infinite past, is not reaching infinity. Only the latter is impossible. As I keep pointing out, there is no such thing as reaching infinity or counting to infinity when traversing the infinite past because every single past event is a finite gap away from any other past event. Why do you keep equating "traversing infinity" with "reaching infinity," when you have acknowledge that every past even is a finite time away from the present? There is nothing in an actual infinite past that is infinitely far away, so how can there be any sort of reaching infinity involved? Infinitely many integers, all of them finite, it's very easy to understand when it comes to the number line, apply the same principle to the time line.

If the infinite past is like the number line, then the present moment is outside of and after the number line. So, you’d have to complete the number line before the present moment could occur. If you complete the number line (the infinite past) have you completed a finite or infinite amount of events?.
Bust Nak wrote: Mon Sep 27, 2021 7:50 am
Let series 1 = (1)
Let series 2 = (1, 2)
...
Let series 17 = (1, 2, 3, …, 17)
...

Let series Z = (series 1, series 2, series 3, …) which is equivalent to (1, 2, 3, …). That’s fine.
Let series 1 = (5)
Let series 2 = (4, 5)
...
Let series 17 = (-11, …, 3, 4, 5)
...

Let series Z = (..., series 3, series 2, series 1) which is equivalent to (…, 3, 4, 5).

....

I don't understand what you are referring to by changing how series Z looks. I don't think I am changing how series Z look at all. Do you still accept that series Z, which is defined as (series 1, series 2, series 3, ...) is equivalent to (1, 2, 3, ...)? If so, what look is changed?

How did we form series Z the first time? We took each specific case that fit a model (where we both started with and ended with a finite number), noted that there are an infinite number of such cases, and then added those cases all together to form a new set. Series Z was not itself a specific case that fit the previous model.
Bust Nak wrote: Mon Sep 27, 2021 7:50 amYes, and how many of those numbers, that you can count to and from, are there?

A potentially infinite number of numbers.
Bust Nak wrote: Mon Sep 27, 2021 7:50 amSo why would (1 + 1+1 +1 + ...) be impossible, if it is different from the iterative process? Only the iterative process of reaching infinity is impossible.

Why do you think that? What is the sum of (1+1+1+1+...)?
Bust Nak wrote: Mon Sep 27, 2021 7:50 amI am not saying you start at infinity at all. I am saying that since it is possible to start at any number and count to 5 therefore you don't have to start at all. That's what the (X... 3, 4, 5) is possible + intermediate steps therefore (... 3, 4, 5) is possible argument was for. We are just hammering out the detail of said intermediate steps.

But the previous steps in your logic are all dependent upon starting at a particular number. You haven’t shown the reasoning that allows you to move from that to getting the same results by not starting at a particular number.

User avatar
We_Are_VENOM
Sage
Posts: 720
Joined: Wed Aug 12, 2020 2:33 am
Has thanked: 30 times
Been thanked: 20 times

Re: God Must Exist: Infinite Regression is Impossible

Post #452

Post by We_Are_VENOM »

JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am While not holding your "uncaused cause" to the same criteria.
And why isn't my uncaused cause held to the same criteria? See OP.
JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am We observe the universe exists. We can therefore conclude it might well be its own "uncaused" entity.
I already gave reasons as to why the universe cannot be uncaused.
JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am We don't need to, have no need to, add the extra god step into the equation.
Not only do we need to, we did.
JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am Your inability to see the failures in your OP, and further argumentations based thereupon, are reflected in your inability to understand opposing arguments.

We observe the universe to exist. That fact alone 'allows' us to consider the universe its own "uncaused cause".
LOL. So, let me see if I have this correct..

1. The universe exists.
2. Therefore, the universe is its own "uncaused cause".

Text book example of a non sequitur.

And I will just leave it there, respectfully. See ya around, Joey :handshake:
Venni Vetti Vecci!!

User avatar
Diogenes
Student
Posts: 35
Joined: Sun May 24, 2020 12:53 pm
Location: USA
Has thanked: 8 times
Been thanked: 18 times

Re: God Must Exist: Infinite Regression is Impossible

Post #453

Post by Diogenes »

[Replying to We_Are_VENOM in post #450]
The argument is held up by a Special Pleading, which is supported by a Special Pleading.
Under that, it's Special Pleadings all the way down. :)

Bust Nak
Savant
Posts: 9217
Joined: Mon Feb 27, 2012 6:03 am
Location: Planet Earth
Has thanked: 73 times
Been thanked: 82 times

Re: God Must Exist: Infinite Regression is Impossible

Post #454

Post by Bust Nak »

The Tanager wrote: Mon Sep 27, 2021 8:37 pm But not all dichotomies necessarily apply in all situations. I could come up with a dichotomy of, say, taller than you vs. non-taller than you but this doesn’t mean it applies to every situation. Me liking the Chicago Cubs is neither taller than you nor non-taller than you.
Right, and I am saying it's you job to show that it doesn't apply here.
Why do you think infinity as a limit is treated as a quantity?
Because the limit to quantity must also be a quantity.
What do you mean “the height that isn’t a thing”?
Infinite height.
Both ways have the concept of height and a concept about what kinds of things height can be applied to and what it can’t.
Okay, in that sense your concept about what kinds of things height can be applied to is more complicated than mine, due to the extra clause of finite vs infinite.
Perhaps it would help to look at the sources you are using for this.
Here is a source about infinity in general, https://www.britannica.com/science/infinity-mathematics
Here is one about limits, https://www.intmath.com/differentiation ... iation.php
Here is one about lines meeting at infinity, https://www.britannica.com/science/projective-geometry
If the infinite past is like the number line, then the present moment is outside of and after the number line. So, you’d have to complete the number line before the present moment could occur. If you complete the number line (the infinite past) have you completed a finite or infinite amount of events?
An infinite amount of events.
How did we form series Z the first time? We took each specific case that fit a model (where we both started with and ended with a finite number), noted that there are an infinite number of such cases, and then added those cases all together to form a new set. Series Z was not itself a specific case that fit the previous model.
That's right, still not sure what you are getting at, series Z was not presented as a series that fits the model (1, 2, 3, ... X). Recall if you will, one of my earlier claim, (1, 2, 3, ... X) and (1, 2, 3, …) are different concepts, the point was one implies the other. Building series Z is my attempt at showing how.
A potentially infinite number of numbers.
Why potentially, we are not talking about iterative process here?
Why do you think that?
Because there is nothing stopping me from adding infinitely many 1's together.
What is the sum of (1+1+1+1+...)?
Infinity. A summary of the reasoning to my answer: It's either a finite integer or infinity, we can rule out finite, so we are left with infinity; actual vs potential is only applicable when it comes to iterative process and this isn't an iterative process.
But the previous steps in your logic are all dependent upon starting at a particular number. You haven’t shown the reasoning that allows you to move from that to getting the same results by not starting at a particular number.
That's what the series Z stuff was suppose to be, the reasoning that allows me to move from starting at a particular number to not starting at a particular number.

Online
User avatar
JoeyKnothead
Under Probation
Posts: 17636
Joined: Fri Jun 06, 2008 10:59 am
Location: Here
Has thanked: 610 times
Been thanked: 453 times

Re: God Must Exist: Infinite Regression is Impossible

Post #455

Post by JoeyKnothead »

We_Are_VENOM wrote: Mon Sep 27, 2021 10:28 pm
JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am While not holding your "uncaused cause" to the same criteria.
And why isn't my uncaused cause held to the same criteria? See OP.
As I said, you merely push the question of origins back a step, then declare it immune to the question of origins.

We only ever observe thought to be a product of the physical, so now we've got another question regarding an entity that can create at will.

Where's the energy to drive that thought? Another question, but one we can apply to the universe. If your "uncaused cause" has the energy to create, why can't the universe? After all, we only observe energy within the universe, and never observe it outside the universe.
JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am We observe the universe exists. We can therefore conclude it might well be its own "uncaused" entity.
I already gave reasons as to why the universe cannot be uncaused.
And they fail without a means of confirmation.

In my hypothesis, we observe the universe to exist, so it could well be its own "uncaused cause". I at least have a universe to point to. You have ether.
JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am We don't need to, have no need to, add the extra god step into the equation.
Not only do we need to, we did.
You should at least give your co-writer a credit.

Your uncaused cause suffers from multiple problems - no means to confirm, and special pleading among em.
JoeyKnothead wrote: Mon Sep 27, 2021 8:55 am Your inability to see the failures in your OP, and further argumentations based thereupon, are reflected in your inability to understand opposing arguments.
We observe the universe to exist. That fact alone 'allows' us to consider the universe its own "uncaused cause".
LOL. So, let me see if I have this correct..
1. The universe exists.
2. Therefore, the universe is its own "uncaused cause".
Text book example of a non sequitur.
No more sequiturish than "god did it".

I'm merely pointing out that if your "cause", which you haven't shown to exist can be "uncaused", then the universe, which we observe, might well be "uncaused" as well.
And I will just leave it there, respectfully. See ya around, Joey :handshake:
You too friend, it's fun going back and forth with ya. Stay safe.
Some say it came from Memphis down in Tennessee
Or it drifted in from Georgia about 1953
Just as long as it's greasy, as long as it's fast
As long as it's pumpin' honey, it's gonna last

It's the hillbilly rock, beat it with a drum
Playin' them guitars like shootin' from a gun
Keepin' up the rhythm, steady as a clock
Doin' a little thing called the hillbilly rock
- Marty Stuart

User avatar
The Tanager
Prodigy
Posts: 3054
Joined: Wed May 06, 2015 11:08 am
Has thanked: 11 times
Been thanked: 41 times

Re: God Must Exist: Infinite Regression is Impossible

Post #456

Post by The Tanager »

Bust Nak wrote: Tue Sep 28, 2021 12:47 pmRight, and I am saying it's you job to show that it doesn't apply here.

And I don’t understand why it should be. You are either making the claim that it applies to all cases (and therefore have the burden of showing it does) or admitting that it doesn’t apply to all cases (and agreeing with me). If the latter, then you still need to show that it applies in the specific case you want it to apply in.
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmBecause the limit to quantity must also be a quantity.

Why?
Bust Nak wrote: Tue Sep 28, 2021 12:47 pm
What do you mean “the height that isn’t a thing”?

Infinite height.

How would that be a height that isn’t a thing?
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmOkay, in that sense your concept about what kinds of things height can be applied to is more complicated than mine, due to the extra clause of finite vs infinite.

I’m not saying there is such a thing as an infinite height (as a quantity), though.
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmHere is a source about infinity in general, https://www.britannica.com/science/infinity-mathematics
Here is one about limits, https://www.intmath.com/differentiation ... iation.php
Here is one about lines meeting at infinity, https://www.britannica.com/science/projective-geometry

I don’t see the support in those pages. Walk me through why you think it is support for what you’ve been claiming..
Bust Nak wrote: Tue Sep 28, 2021 12:47 pm
If the infinite past is like the number line, then the present moment is outside of and after the number line. So, you’d have to complete the number line before the present moment could occur. If you complete the number line (the infinite past) have you completed a finite or infinite amount of events?

An infinite amount of events.

If it was a finite amount of events, how many events would we have passed through before reaching this present moment? A finite number, right? If it is an infinite amount of events, then we would pass through an infinite number before reaching this present moment. Why is this not “reaching” infinity?
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmThat's right, still not sure what you are getting at, series Z was not presented as a series that fits the model (1, 2, 3, ... X). Recall if you will, one of my earlier claim, (1, 2, 3, ... X) and (1, 2, 3, …) are different concepts, the point was one implies the other. Building series Z is my attempt at showing how.

And I still think it an unsound way to do so. Using the infinite instantiations of a particular model is just extra work that is unhelpful.
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmWhy potentially, we are not talking about iterative process here?

Didn’t you want me to count how many numbers there are? Let’s see (4, 5, 6). That’s three but let’s keep going (7, 8, 9, 10), now we are up to 7. I’ll keep going and whenever you stop me, I’ll have a finite answer of what I’m up to. No matter if I had eternity for this process. This is what potential infinite is.
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmBecause there is nothing stopping me from adding infinitely many 1's together.

That doesn’t explain why it is possible to reach an (actual) infinite quantity by doing so.
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmInfinity. A summary of the reasoning to my answer: It's either a finite integer or infinity, we can rule out finite, so we are left with infinity; actual vs potential is only applicable when it comes to iterative process and this isn't an iterative process.

You seem to be needing it to be an integer that is either finite or infinite. I don’t see why that is the case, though. I don’t think there is an actual integer as a sum. You need to show that it is.
Bust Nak wrote: Tue Sep 28, 2021 12:47 pmThat's what the series Z stuff was suppose to be, the reasoning that allows me to move from starting at a particular number to not starting at a particular number.

What true premise allows you to make that move? I don’t think you have one. I've responded as to why the ones you've given don't get you there.

Bust Nak
Savant
Posts: 9217
Joined: Mon Feb 27, 2012 6:03 am
Location: Planet Earth
Has thanked: 73 times
Been thanked: 82 times

Re: God Must Exist: Infinite Regression is Impossible

Post #457

Post by Bust Nak »

The Tanager wrote: Tue Sep 28, 2021 9:15 pm And I don’t understand why it should be. You are either making the claim that it applies to all cases (and therefore have the burden of showing it does) or admitting that it doesn’t apply to all cases (and agreeing with me). If the latter, then you still need to show that it applies in the specific case you want it to apply in.
And I've done that by pointing out that it's a general rule.
Why?
Because that's how it's defined in math. And more generally, the speed limit is a speed, the weight limit is a weight, a spatial limit is a place.
How would that be a height that isn’t a thing?
You tell me, you suggested that it might not be.
I’m not saying there is such a thing as an infinite height (as a quantity), though.
Yes? Which mean you need an extra clause that exclude infinite height (as a quantity), where as I don't.
I don’t see the support in those pages. Walk me through why you think it is support for what you’ve been claiming.
Re: infinity as a quantity "Mathematical infinities occur, for instance, as the number of points on a continuous line or as the size of the endless sequence of counting numbers: 1, 2, 3,…. "
Re: limits as a quantity "In the study of calculus, we are interested in what happens to the value of a function as the independent variable gets very close to a particular value."
Re: defining infinity for where line meets "Desargues who first introduced a single point at infinity to represent the projected intersection of parallel lines. Furthermore, he collected all the points along the horizon in one line at infinity."
If it was a finite amount of events, how many events would we have passed through before reaching this present moment? A finite number, right?
Of course.
If it is an infinite amount of events, then we would pass through an infinite number before reaching this present moment. Why is this not “reaching” infinity?
As I keep repeating, because none of those infinitely many events are an infinity away from the present, there is a finite gap between them and the present moment.
And I still think it an unsound way to do so. Using the infinite instantiations of a particular model is just extra work that is unhelpful.
But earlier you seemed to have accepted that series Z is equivalent to (1, 2, 3, ...), and now you are saying it's unsound? Did I misunderstand you?
Didn’t you want me to count how many numbers there are?
No, I want you to tell me how many numbers there are.
That doesn’t explain why it is possible to reach an (actual) infinite quantity by doing so.
Hold on, earlier you suggested that (1 + 1 + 1 + ...) was impossible; here you seemed to have let my counter-argument slide without addressing it. Also I've affirmed that reaching infinity is impossible, don't expect explanations for the possibility for reaching infinity from me.
You seem to be needing it to be an integer that is either finite or infinite. I don’t see why that is the case, though. I don’t think there is an actual integer as a sum. You need to show that it is.
Why? I need it to be a quantity, we both agree it's not an actual integer. An actual integer would trivially be finite.
What true premise allows you to make that move? I don’t think you have one. I've responded as to why the ones you've given don't get you there.
This one: series Z is equivalent to (1, 2, 3, ...).

User avatar
The Tanager
Prodigy
Posts: 3054
Joined: Wed May 06, 2015 11:08 am
Has thanked: 11 times
Been thanked: 41 times

Re: God Must Exist: Infinite Regression is Impossible

Post #458

Post by The Tanager »

Bust Nak wrote: Wed Sep 29, 2021 7:42 am
And I don’t understand why it should be. You are either making the claim that it applies to all cases (and therefore have the burden of showing it does) or admitting that it doesn’t apply to all cases (and agreeing with me). If the latter, then you still need to show that it applies in the specific case you want it to apply in.

And I've done that by pointing out that it's a general rule.

Done what? Both of the options I mentioned above would mean you have the burden to show it applies in the specific case of quantity, rather than me having the burden to show it doesn’t apply. Even so, I’ve still shared why I don’t think it applies in the specific case of quantity, using the counterexample of an infinite square, but we are still discussing that example.
Bust Nak wrote: Wed Sep 29, 2021 7:42 amBecause that's how it's defined in math. And more generally, the speed limit is a speed, the weight limit is a weight, a spatial limit is a place.

I don’t think it is just defined that way in math. It seems to me that mathematics has an idea of ‘infinity’ that treats it as a boundary, the very idea of no number is as large as infinity, rather than a number itself. It also has an idea of ‘infinity’ as a number, although I’m not sure it argues for that as a reality rather than just showing what would be true if such a thing existed.
Bust Nak wrote: Wed Sep 29, 2021 7:42 am
How would that be a height that isn’t a thing?

You tell me, you suggested that it might not be.

That wording (“height that isn’t a thing”) was yours and it is a bit confusing. I suggested that the concept of an infinite height (in your sense of that term) might be a logical contradiction because of the very natures of what it means to have height and to be unlimited. Is that what “height that isn’t a thing” means?
Bust Nak wrote: Wed Sep 29, 2021 7:42 amRe: infinity as a quantity "Mathematical infinities occur, for instance, as the number of points on a continuous line or as the size of the endless sequence of counting numbers: 1, 2, 3,…. "

I have no problem saying the sequence has an infinite size or an infinite number of points. By that one could mean they are giving the actual quantity or an idea meant to convey that the points continue on forever, not providing us with a particular or determinate quantity. Infinity stands in for that truth.
Bust Nak wrote: Wed Sep 29, 2021 7:42 amRe: limits as a quantity "In the study of calculus, we are interested in what happens to the value of a function as the independent variable gets very close to a particular value."

The page goes into limits as x approaches infinity, but I don’t see where it addresses our question.
Bust Nak wrote: Wed Sep 29, 2021 7:42 amRe: defining infinity for where line meets "Desargues who first introduced a single point at infinity to represent the projected intersection of parallel lines. Furthermore, he collected all the points along the horizon in one line at infinity."

Parallel lines, by mathematical definition, never meet. They can look like they meet but the ‘projected intersection’ can’t be an actual intersection, by definition.
Bust Nak wrote: Wed Sep 29, 2021 7:42 amAs I keep repeating, because none of those infinitely many events are an infinity away from the present, there is a finite gap between them and the present moment.

We aren’t talking about the gap between each individual element of one set and the element outside of that set. We are talking about moving through the whole first set and then reaching the element in addition to that set. There being a finite gap there is irrelevant; you’ve still had to move through the entire infinite set before reaching that finite gap

If we’ve moved through every single event in the infinite set, how many events have we moved through? A finite amount or an infinite amount? An infinite amount. Thus, we would have “reached” infinity in having completed that set.
Bust Nak wrote: Wed Sep 29, 2021 7:42 amNo, I want you to tell me how many numbers there are.

How are those different things? We come up with “how many” by various ways of counting.
Bust Nak wrote: Wed Sep 29, 2021 7:42 amHold on, earlier you suggested that (1 + 1 + 1 + ...) was impossible; here you seemed to have let my counter-argument slide without addressing it. Also I've affirmed that reaching infinity is impossible, don't expect explanations for the possibility for reaching infinity from me.

I think I’ve misunderstood you previously (and/or perhaps still). Are you saying (1+1+1+...) and (1, 2, 3, …) are both ways to represent counting and that, therefore, both are impossible? Or something else?
Bust Nak wrote: Wed Sep 29, 2021 7:42 amWhy? I need it to be a quantity, we both agree it's not an actual integer. An actual integer would trivially be finite.

I thought you were saying that. So, you are saying an integer plus an integer plus an integer, etc. gives us a quantity that is not an integer. Help me understand what it means to be a quantity that is not an integer in this way.
Bust Nak wrote: Wed Sep 29, 2021 7:42 amBut earlier you seemed to have accepted that series Z is equivalent to (1, 2, 3, ...), and now you are saying it's unsound? Did I misunderstand you?

The series (!, @, #, $, %, ^, &, …) is also equivalent. That doesn’t mean it logically supports the truth of (1, 2, 3, …). They are both built off the same principle. They are instances of the same model.

The way I think one gets from (1, 2, 3, …, X) to (1, 2, 3, …) involves some premise about there being infinite instances. Infinite meaning ‘unending’. We go from series that both begin and end with a number to a series that begins but doesn’t end through a premise(s) that takes the ending away. I don’t think the model you start with matters. I think the model (X, …, 3, 2, 1) will also get you to (1, 2, 3 ,...) in the same way.

That principle can’t get you from (X, …, 3, 2, 1) to (... 3, 2, 1) because it takes the end away, not the beginning and, here, you need the beginning taken away through a new premise.

Bust Nak
Savant
Posts: 9217
Joined: Mon Feb 27, 2012 6:03 am
Location: Planet Earth
Has thanked: 73 times
Been thanked: 82 times

Re: God Must Exist: Infinite Regression is Impossible

Post #459

Post by Bust Nak »

The Tanager wrote: Thu Sep 30, 2021 2:16 pm Done what? Both of the options I mentioned above would mean you have the burden to show it applies in the specific case of quantity...
Why doesn't showing it applies in general fulfil that burden?
Even so, I’ve still shared why I don’t think it applies in the specific case of quantity, using the counterexample of an infinite square, but we are still discussing that example.
How does casting doubt on the concept of an infinite square help support that infinity isn't a quantity?
I don’t think it is just defined that way in math. It seems to me that mathematics has an idea of ‘infinity’ that treats it as a boundary, the very idea of no number is as large as infinity, rather than a number itself...
Yes, but that that boundary is a quantity. Pointing out that it is treated as a boundary doesn't mean it's not treated as a quantity.
That wording (“height that isn’t a thing”) was yours and it is a bit confusing. I suggested that the concept of an infinite height (in your sense of that term) might be a logical contradiction because of the very natures of what it means to have height and to be unlimited. Is that what “height that isn’t a thing” means?
Yes.
I have no problem saying the sequence has an infinite size or an infinite number of points. By that one could mean they are giving the actual quantity or an idea meant to convey that the points continue on forever, not providing us with a particular or determinate quantity. Infinity stands in for that truth.
But some how you have a problem taking the trivial step of acknowledge that size and number of things fits exactly the definition of quantity. Why not merge the two? It represent a quantity that is larger than any other.
The page goes into limits as x approaches infinity, but I don’t see where it addresses our question.
It says the limit is a value, and the relevant definition of value goes along the lines of "a magnitude, quantity, or number."
Parallel lines, by mathematical definition, never meet. They can look like they meet but the ‘projected intersection’ can’t be an actual intersection, by definition.
That's one definition of parallel lines. By another, all lines meet at one point. As long as you don't mix the definitions up, there is no equivocation.
We aren’t talking about the gap between each individual element of one set and the element outside of that set. We are talking about moving through the whole first set and then reaching the element in addition to that set. There being a finite gap there is irrelevant...
Not so, while we are indeed talking about moving through the whole first set, but that involves moving through each of those individual element, which brings the gap between each elements into the picture, making it relevant. I was referring to the finite gaps between each of the elements in the entire infinite set. Not the one between the last element of the set and the one outside of the set.
If we’ve moved through every single event in the infinite set, how many events have we moved through? A finite amount or an infinite amount? An infinite amount. Thus, we would have “reached” infinity in having completed that set.
Still doesn't follow. Moving through every single event in the infinite set does not involve such a thing as reaching infinity.
How are those different things? We come up with “how many” by various ways of counting.
Okay, then let me rephrase that by asking if you can tell me how many there are, without using iterative ways of counting, but with other ways of counting. This is the kind of things I have in mind, there were 10 apples in a bag, 2 has been taken out. I can tell you there are 8 apples in the bag by subtraction, without pointing to each apple in turn in the bag going, 1, 2, 3 ... 8; pointing to each one in turn is an iterative way of counting.
I think I’ve misunderstood you previously (and/or perhaps still). Are you saying (1+1+1+...) and (1, 2, 3, …) are both ways to represent counting and that, therefore, both are impossible? Or something else?
I am saying to be consistent, one has to hold that either both are possible or both are impossible, since are both ways to represent counting, or as I would rather point it, invoke the same concept of infinity.
I thought you were saying that. So, you are saying an integer plus an integer plus an integer, etc. gives us a quantity that is not an integer. Help me understand what it means to be a quantity that is not an integer in this way.
First, infinity needs to be a quantity for the concept of "larger than a quantity" to be a coherent concept. Next, infinity is a quantity that is larger than any integer; "larger than any" implies that infinity cannot be an integer, as something cannot be larger than itself.
The series (!, @, #, $, %, ^, &, …) is also equivalent. That doesn’t mean it logically supports the truth of (1, 2, 3, …). They are both built off the same principle. They are instances of the same model.
Equivalent is stronger connection than mere instances of the same model. If A and (B is equivalent to A), then B. Surely that counts as one logically supports the other?
The way I think one gets from (1, 2, 3, …, X) to (1, 2, 3, …) involves some premise about there being infinite instances. Infinite meaning ‘unending’. We go from series that both begin and end with a number to a series that begins but doesn’t end through a premise(s) that takes the ending away. I don’t think the model you start with matters. I think the model (X, …, 3, 2, 1) will also get you to (1, 2, 3 ,...) in the same way.

That principle can’t get you from (X, …, 3, 2, 1) to (... 3, 2, 1) because it takes the end away, not the beginning and, here, you need the beginning taken away through a new premise.
Same request as before, can you tell me explicitly what principles it is that can take me from (1, 2, 3, …, X) to (1, 2, 3, …) and I will produce this new premise to get from (X, …, 3, 2, 1) to (... 3, 2, 1) using the same wording.

In the mean time, I will try something like this: I can gets from (X, …, 3, 2, 1) to (..., 3, 2, 1) involves some premise about there being infinite instances. Infinite meaning ‘unbeginning’. We go from series that both begin and end with a number to a series that ends but doesn’t begin through a premise(s) that takes the beginning away.

User avatar
The Tanager
Prodigy
Posts: 3054
Joined: Wed May 06, 2015 11:08 am
Has thanked: 11 times
Been thanked: 41 times

Re: God Must Exist: Infinite Regression is Impossible

Post #460

Post by The Tanager »

Bust Nak wrote: Fri Oct 01, 2021 7:58 amWhy doesn't showing it applies in general fulfil that burden?

If your claim is that it always applies, then showing that it sometimes applies does not fill the burden. If your claim is that it applies most but not all of the time, then you have the burden of showing it applies in the specific case under consideration, that that case is one of the ‘most’ and not the other.
Bust Nak wrote: Fri Oct 01, 2021 7:58 amHow does casting doubt on the concept of an infinite square help support that infinity isn't a quantity?

I think we are talking past each other with ‘quantity’. I have no problem saying a quantity is infinite, with the concepts I have of those terms. But you talked about infinity being a quantity in the same way the 5 is. To me 5 is a number in a way that speaks of being a determinate number, which infinity cannot be, by definition. So, I think we need to clear this up.
Bust Nak wrote: Fri Oct 01, 2021 7:58 amThat's one definition of parallel lines. By another, all lines meet at one point. As long as you don't mix the definitions up, there is no equivocation.

How can they meet (A) and not meet (non-A) in the same sense at the same time? There has to be an equivocation somewhere or that is a contradiction. That they meet in projective geometry cannot the same as meeting in the plane.
Bust Nak wrote: Fri Oct 01, 2021 7:58 amNot so, while we are indeed talking about moving through the whole first set, but that involves moving through each of those individual element, which brings the gap between each elements into the picture, making it relevant. I was referring to the finite gaps between each of the elements in the entire infinite set. Not the one between the last element of the set and the one outside of the set.

The present is outside of the entire infinite set, so the gaps between elements within the set is irrelevant.
Bust Nak wrote: Fri Oct 01, 2021 7:58 amStill doesn't follow. Moving through every single event in the infinite set does not involve such a thing as reaching infinity.

If you move through 5 events you will have reached the quantity of 5. If through 2000 events, then you’ve reached the quantity of 2000. Why is it different when moving through an infinite number of events?
Bust Nak wrote: Fri Oct 01, 2021 7:58 amOkay, then let me rephrase that by asking if you can tell me how many there are, without using iterative ways of counting, but with other ways of counting. This is the kind of things I have in mind, there were 10 apples in a bag, 2 has been taken out. I can tell you there are 8 apples in the bag by subtraction, without pointing to each apple in turn in the bag going, 1, 2, 3 ... 8; pointing to each one in turn is an iterative way of counting.

Sure. How does that change anything? My answer is still that there are a potentially infinite amount of numbers. I didn’t literally count anything out to give you that answer. It’s just about applying logic.
Bust Nak wrote: Fri Oct 01, 2021 7:58 amI am saying to be consistent, one has to hold that either both are possible or both are impossible, since are both ways to represent counting, or as I would rather point it, invoke the same concept of infinity.

Then, I misunderstood what you meant by those. Yes, both are possible.
Bust Nak wrote: Fri Oct 01, 2021 7:58 amSame request as before, can you tell me explicitly what principles it is that can take me from (1, 2, 3, …, X) to (1, 2, 3, …) and I will produce this new premise to get from (X, …, 3, 2, 1) to (... 3, 2, 1) using the same wording

In the mean time, I will try something like this: I can gets from (X, …, 3, 2, 1) to (..., 3, 2, 1) involves some premise about there being infinite instances. Infinite meaning ‘unbeginning’. We go from series that both begin and end with a number to a series that ends but doesn’t begin through a premise(s) that takes the beginning away.

It is, of course, your responsibility to present the principles to support your view. (1, 2, 3, …, X) means we can start at a particular number and count to another particular number. (1, 2, 3, …) is an attempt to say that the above process never has to end; you can keep counting finite numbers/quantities forever. In both, there must be a starting number or none of the other numbers, much less the last number, could ever be counted.

I don’t see how you can use the same principles (however they are formulated) when trying to claim that there actually isn’t a start to the counting process at all, yet we have reached the middle of the counting process. That is the big difference. That must be supported in the case of moving from (X, ..., 3, 2, 1) to (..., 3, 2, 1), which isn't a part of moving from (1, 2, 3, ..., X) to (1, 2, 3, ...).

Post Reply