God Must Exist: Infinite Regression is Impossible

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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!!

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Re: God Must Exist: Infinite Regression is Impossible

Post #881

Post by Bust Nak »

The Tanager wrote: Wed Mar 15, 2023 11:01 am If you agree (you said "Okay"), why waste our time clarifying your misunderstanding of my words or my lack of clarity?
Because you never got round to affirming that infinity is indeed a quantity.
Show that an infinite quantity is an actual quantity.
I refer you back to my various points, re: consistency with cosmology and mathematics, as well as my counter-points against your objections.
No, it keeps us from equivocating on numeric value and simplicity of a theory.
Lets try an analogy: if I say to you, the weight of two bags of marbles is equal because there are 5 marbles in each bag, then I am implying the weight of each marble is the same, am I not? If the marbles weight differently from each other, then just knowing there are an equal number of marbles is not enough information to make the determination that the bags are equal weight. Now do you see why I think you are implying all assumptions weights the same, when you say two scenarios are equal weight because each there is 1 assumption in each?
How is calculus outside math (which is part of what is in your logical circle)?
You can use it to calculate a variety of real life stuff, demonstrating external consistency.
And I’ve shared what I think your latest flaw is (#859). Your premise 2.1) is false. The premise should read: 2.1’) For all x: If there are P in circumstances of this type {..., X}, then you can B in circumstances of this type {P, …, X}.
You can B in circumstances of this type {P, …, X}, but you can also B in circumstances of this type {…, X}. If you cannot B in circumstances of this type {…, X}, then there must be a lowest P where you can B below which you can no longer B. There is no lowest P, therefore 2.1 holds as stated.
You offered a proof (let’s call this P). I critiqued (let’s call that C1) premise 2.1. If true, then P is unsound. You critiqued (let’s call this C2) your C1. If true, C1 disappears and P is not shown to be unsound. I critiqued (let’s call this C3) your C2. If true, C2 disappears, leaving C1 intact and, thus, P being unsound. Your latest critique (let’s call this C4) was to say that’s what the proof is for. Thus, C4 is identical to P. Okay, so C1 is calling P into question and your support against that is C4/P. So, P is true because P is true. Circular reasoning.
That's not what's happening though. I offered a proof (let’s call this P). You critiqued (let’s call that C1) premise 2.1. If true, then P is unsound. I critiqued (let’s call this C2) your C1. If true, C1 disappears and P is not shown to be unsound. You critiqued (let’s call this C3) a lack of support for the conclusion of P. Well, that's what P is for, supporting the conclusion of P, that's my C4. C3 is invalidated by the very existence of P, nothing circular about that.
You can reach 2 in some circumstances without starting at X. That’s all you’ve shown. Now take me the next step to: You can reach 2 without starting at all.
Nothing has changed, just instantiate e with a 2, that's how you can reach 2 without starting at all:

2.2) For all x: If you can B for circumstances {..., X} and S and E for circumstances {X, …, 2}, then you can W and T and E for circumstances {..., X, …, 2} (premise)
2.3) For all x: You can B for circumstances {..., X} (from 2 and 2.1)
2.4) For all x: You can B for circumstances {..., X} and S and E for circumstances {X, …, 2} (from 1 and 2.3)
3) For all x: You can W and T and E for circumstances {..., X, …, 2} (from 2.2 and 2.4)
4.1) If not (can I and E for circumstances {..., X, …, 2}) then there exist X where cannot W and T and E for circumstances {..., X, …, 2} (premise)
4.2) not (exist X where cannot W and T and E for circumstances {..., X, …, 2}) (from 3)
4.3) Not not (can I and E for circumstances {..., X, …, 2}) (from 4.1 and 4.2)
5) You can I and E for circumstances {..., X, …, 2}

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Re: God Must Exist: Infinite Regression is Impossible

Post #882

Post by The Tanager »

Bust Nak wrote: Thu Mar 16, 2023 8:28 pmBecause you never got round to affirming that infinity is indeed a quantity.
I have affirmed it is defined that way, by mere assumption, in order to see what would result via the mathematical equations. Your case requires you to support it beyond assumption.
Bust Nak wrote: Thu Mar 16, 2023 8:28 pmI refer you back to my various points, re: consistency with cosmology and mathematics, as well as my counter-points against your objections.
And I refer you back to my responses to how that doesn’t show an infinite quantity is an actual quantity in real life.
Bust Nak wrote: Thu Mar 16, 2023 8:28 pmLets try an analogy: if I say to you, the weight of two bags of marbles is equal because there are 5 marbles in each bag, then I am implying the weight of each marble is the same, am I not? If the marbles weight differently from each other, then just knowing there are an equal number of marbles is not enough information to make the determination that the bags are equal weight. Now do you see why I think you are implying all assumptions weights the same, when you say two scenarios are equal weight because each there is 1 assumption in each?
I can understand that. I don’t see how it helps you here, though. The effect we are explaining isn’t a quantitative question.
Bust Nak wrote: Thu Mar 16, 2023 8:28 pmYou can use it to calculate a variety of real life stuff, demonstrating external consistency.
Yes, the math works in ways that help us in reality. This was already covered in the circle you were thinking in.
Bust Nak wrote: Thu Mar 16, 2023 8:28 pmYou can B in circumstances of this type {P, …, X}, but you can also B in circumstances of this type {…, X}. If you cannot B in circumstances of this type {…, X}, then there must be a lowest P where you can B below which you can no longer B. There is no lowest P, therefore 2.1 holds as stated.
There cannot be a lowest P in any of these circumstances because of the nature of infinite series. Above we are separating infinite series into two mutually exclusive categories, to where this truth is still true. You are then saying that another truth in one of these categories gives us a truth about the other kind of category that contradicts the truth that holds in all infinite series. The truth about one category has nothing to do with the truth of another category.
Bust Nak wrote: Thu Mar 16, 2023 8:28 pmThat's not what's happening though. I offered a proof (let’s call this P). You critiqued (let’s call that C1) premise 2.1. If true, then P is unsound. I critiqued (let’s call this C2) your C1. If true, C1 disappears and P is not shown to be unsound. You critiqued (let’s call this C3) a lack of support for the conclusion of P. Well, that's what P is for, supporting the conclusion of P, that's my C4. C3 is invalidated by the very existence of P, nothing circular about that.
If C1 is a critique of a premise in P, then how can P's conclusion be what rebuts C1? The conclusion can't be reached if C1 isn't done away with. Your way to do away with it is to assume P has no viable critique and the conclusion therefore follows.

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Re: God Must Exist: Infinite Regression is Impossible

Post #883

Post by Bust Nak »

The Tanager wrote: Fri Mar 17, 2023 6:37 pm I have affirmed it is defined that way, by mere assumption, in order to see what would result via the mathematical equations. Your case requires you to support it beyond assumption.
That's that mere assumption claim again. It's defined as such, no assumption involved. I start with the assumption that the definition is coherent, but that's not the same as assuming it is a quantity.
And I refer you back to my responses to how that doesn’t show an infinite quantity is an actual quantity in real life.
All of which have been addressed.
I can understand that. I don’t see how it helps you here, though. The effect we are explaining isn’t a quantitative question.
Okay, so you accept that some assumptions can be more simple then other assumptions. So back to my point, "yes something" is less simple than "no something."
Yes, the math works in ways that help us in reality. This was already covered in the circle you were thinking in.
So reality count as inside the math circle? Then what's wrong with just staying in that circle?
There cannot be a lowest P in any of these circumstances because of the nature of infinite series.
Which means it must be possible able to pick any X less than 2, out of an infinitely many of options you can pick from, and not start at the X you have chosen and count up to 2. Why is this such a sticking point?
Above we are separating infinite series into two mutually exclusive categories, to where this truth is still true. You are then saying that another truth in one of these categories gives us a truth about the other kind of category that contradicts the truth that holds in all infinite series. The truth about one category has nothing to do with the truth of another category.
What categories are those? Frankly I never quite got what your objection is supposed to be, I just kept changing the wording to included whatever new criteria you can up with, without understanding your underlying point.
If C1 is a critique of a premise in P, then how can P's conclusion be what rebuts C1?
It can't? I don't know what you are thinking here, C2 is what is supposed to rebut C1.
The conclusion can't be reached if C1 isn't done away with. Your way to do away with it is to assume P has no viable critique and the conclusion therefore follows.
Well yeah, in the example, P has no viable critique, but C1 is addressed by C2, C3 is addressed by the mere existence of P.

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Re: God Must Exist: Infinite Regression is Impossible

Post #884

Post by The Tanager »

Bust Nak wrote: Sun Mar 19, 2023 7:54 amThat's that mere assumption claim again. It's defined as such, no assumption involved. I start with the assumption that the definition is coherent, but that's not the same as assuming it is a quantity.
Looks the same to me. If you’ve nothing new to add, then we’ve each had our say there.
Bust Nak wrote: Sun Mar 19, 2023 7:54 am
And I refer you back to my responses to how that doesn’t show an infinite quantity is an actual quantity in real life.
All of which have been addressed.
I think inadequately so; you think adequately so. If you’ve nothing new to add, then we’ve each had our say there.
Bust Nak wrote: Sun Mar 19, 2023 7:54 amOkay, so you accept that some assumptions can be more simple then other assumptions. So back to my point, "yes something" is less simple than "no something."
Some doesn’t mean all or even this particular one. Why this particular one? I’ve shared why I think this particular one doesn’t. If you’ve nothing new to add, then we’ve each had our say there.
Bust Nak wrote: Sun Mar 19, 2023 7:54 amSo reality count as inside the math circle? Then what's wrong with just staying in that circle?
No, that calculus helps us in reality counts as the “the math works out” part of the circle.
Bust Nak wrote: Sun Mar 19, 2023 7:54 amWhich means it must be possible able to pick any X less than 2, out of an infinitely many of options you can pick from, and not start at the X you have chosen and count up to 2. Why is this such a sticking point?
Not starting at X isn’t the problem; it’s the not starting at P part.
Bust Nak wrote: Sun Mar 19, 2023 7:54 amWhat categories are those? Frankly I never quite got what your objection is supposed to be, I just kept changing the wording to included whatever new criteria you can up with, without understanding your underlying point.
Beginningless infinite series {..., X} and series that have a beginning {P, …, X}.
Bust Nak wrote: Sun Mar 19, 2023 7:54 amWell yeah, in the example, P has no viable critique, but C1 is addressed by C2, C3 is addressed by the mere existence of P.
No, C3 knocked C2 out, leaving only P and C1.

How does P address C3? C3 was that there logically can’t be a lowest P in an actually infinite series, by its very definition, and that my view doesn’t contradict this truth. What premise in P proves otherwise?

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Re: God Must Exist: Infinite Regression is Impossible

Post #885

Post by brunumb »

I have not been following this thread but you guys seem to be having an infinitely great time with it. This clip from one of my favorite scientists caught my eye and I thought it might be an interesting diversion. Enjoy, or not.

George Orwell:: “The further a society drifts from the truth, the more it will hate those who speak it.”
Voltaire: "Those who can make you believe absurdities can make you commit atrocities."
Gender ideology is anti-science, anti truth.

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Re: God Must Exist: Infinite Regression is Impossible

Post #886

Post by Bust Nak »

The Tanager wrote: Sun Mar 19, 2023 10:00 pm Looks the same to me. If you’ve nothing new to add, then we’ve each had our say there.
They cannot be the same thing, just look at the example you kept using: Square circles are both squares and circles, yet incoherent. If you can accept one yet reject the other, they can't be the same thing.
I think inadequately so; you think adequately so. If you’ve nothing new to add, then we’ve each had our say there.
You say that, yet in every instance of this, I was the one having the last word and you saying you have nothing new to add.
Some doesn’t mean all or even this particular one. Why this particular one?
Because all does mean all. "No something" is always simpler than "yes something."
No, that calculus helps us in reality counts as the “the math works out” part of the circle.
So what more do you need to accept that infinity is actually a quantity other than "the math works out?"
Not starting at X isn’t the problem; it’s the not starting at P part.
That's what the whole proof is for. Not starting at X is just a step to get to that conclusion. You are fixated on that step expecting it to do something that it's not required to do. The not starting comes later.
Beginningless infinite series {..., X} and series that have a beginning {P, …, X}.
I figured it was something like that, but I was confused because you said splitting infinite series into two category and {P, …, X} isn't a category of infinite series.
No, C3 knocked C2 out, leaving only P and C1.
That's the original scenario you presented, did you spot the bit I modified to make my scenario?
How does P address C3? C3 was that there logically can’t be a lowest P in an actually infinite series, by its very definition, and that my view doesn’t contradict this truth. What premise in P proves otherwise?
C3 was that there is no rational support leading to the conclusion that it is possible to not start at all. P is the rational support leading to the conclusion that it is possible to not start at all.

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Re: God Must Exist: Infinite Regression is Impossible

Post #887

Post by The Tanager »

Bust Nak wrote: Mon Mar 20, 2023 7:40 amThey cannot be the same thing, just look at the example you kept using: Square circles are both squares and circles, yet incoherent. If you can accept one yet reject the other, they can't be the same thing.
It’s the incoherence that appears from analyzing the accepted definition that leads to the rejection of it being something in reality. Just like the incoherence that appears from analyzing the accepted definition that leads to the rejection of infinity being a quantity.
Bust Nak wrote: Mon Mar 20, 2023 7:40 amYou say that, yet in every instance of this, I was the one having the last word and you saying you have nothing new to add.
If repeating what you’ve already said counts as having the last word, then sure.
Bust Nak wrote: Mon Mar 20, 2023 7:40 amBecause all does mean all. "No something" is always simpler than "yes something."
That’s a claim. Support why one assumption with a numerical value of 0 is always simpler than one assumption with a numerical value greater than 0.
Bust Nak wrote: Mon Mar 20, 2023 7:40 amSo what more do you need to accept that infinity is actually a quantity other than "the math works out?"
That such a thing exists in reality.
Bust Nak wrote: Mon Mar 20, 2023 7:40 am
Not starting at X isn’t the problem; it’s the not starting at P part.
That's what the whole proof is for. Not starting at X is just a step to get to that conclusion. You are fixated on that step expecting it to do something that it's not required to do. The not starting comes later.
And that’s where the proof fails for the reasons I’ve been sharing. The proof doesn’t rationally get to the not starting step.
Bust Nak wrote: Mon Mar 20, 2023 7:40 am
No, C3 knocked C2 out, leaving only P and C1.
That's the original scenario you presented, did you spot the bit I modified to make my scenario?
My scenario followed what the actual argument has been, so why modify it? C2 doesn’t adequately address C1 and P says nothing against C3.
Bust Nak wrote: Mon Mar 20, 2023 7:40 amC3 was that there is no rational support leading to the conclusion that it is possible to not start at all. P is the rational support leading to the conclusion that it is possible to not start at all.
That was not C3. C3 was that there can’t logically be a lowest P in an actually infinite series by its very definition and that what I claimed in C1 did not contradict that.

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Re: God Must Exist: Infinite Regression is Impossible

Post #888

Post by Bust Nak »

First of all, sorry for the long break, I am now back.
The Tanager wrote: Tue Mar 21, 2023 2:58 pm It’s the incoherence that appears from analyzing the accepted definition that leads to the rejection of it being something in reality.
I don't see how that changes what I said, did you assume a square circle is both a square and a circle, did you assume it is coherent?
If repeating what you’ve already said counts as having the last word, then sure.
Yeah, that happens when the response doesn't change what has already been said. See below for an example for such as exchange.
That’s a claim. Support why one assumption with a numerical value of 0 is always simpler than one assumption with a numerical value greater than 0.
This is something I've already said: Because greater then 0 does multiply the number of entities beyond necessity, when 0 entity would suffice.
That such a thing exists in reality.
Why do you need that when all I am claiming is the mere logical possibility of it existing, that it can exist?
And that’s where the proof fails for the reasons I’ve been sharing. The proof doesn’t rationally get to the not starting step.
But all the other reasons have been addressed, the "proof doesn’t rationally get to the not starting step" cannot stand by itself as a reason, because as I keep saying, the proof itself is how to rationally get to the not starting step.
My scenario followed what the actual argument has been, so why modify it?
I changed it exactly because it does not actually followed what the actual argument has been.
That was not C3. C3 was that there can’t logically be a lowest P in an actually infinite series by its very definition and that what I claimed in C1 did not contradict that.
Okay, then that was address with my C4, you critiqued (let’s call this C5) a lack of support for the conclusion of P. Well, that's what P is for, supporting the conclusion of P, that's my C6. C4 is invalidated by the very existence of P, nothing circular about that. Adding extra C's doesn't change the structure of whole picture.

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Re: God Must Exist: Infinite Regression is Impossible

Post #889

Post by The Tanager »

Bust Nak wrote: Tue Apr 18, 2023 6:08 amFirst of all, sorry for the long break, I am now back.
No worries. I hope it was an enjoyable break for you.
Bust Nak wrote: Tue Apr 18, 2023 6:08 amI don't see how that changes what I said, did you assume a square circle is both a square and a circle, did you assume it is coherent?
You have to assume a square circle isn’t incoherent or you’d be begging the question. Then when you analyze an accepted definition and it shows itself to be incoherent, you reject it as being something that could exist in reality. It’s the same way with actual infinites.
Bust Nak wrote: Tue Apr 18, 2023 6:08 amThis is something I've already said: Because greater then 0 does multiply the number of entities beyond necessity, when 0 entity would suffice.
Yes, but I’m asking for support for why simplicity is about the number of entities versus the number of explanatory assumptions made.
Bust Nak wrote: Tue Apr 18, 2023 6:08 amWhy do you need that when all I am claiming is the mere logical possibility of it existing, that it can exist?
You are claiming that it can exist in reality, right?
Bust Nak wrote: Tue Apr 18, 2023 6:08 amOkay, then that was address with my C4, you critiqued (let’s call this C5) a lack of support for the conclusion of P. Well, that's what P is for, supporting the conclusion of P, that's my C6. C4 is invalidated by the very existence of P, nothing circular about that. Adding extra C's doesn't change the structure of whole picture.
I think you are misunderstanding the flow of this. Let’s sketch them all out:

You: P - your proof

Me: C1 - premise 2.1 is faulty because of blah, blah, blah

You: C2 - But for 2.1 to be faulty for the reason you said, this would mean there has to be a lowest P

Me: C3 - There can’t logically be a lowest P in an actually infinite series by definition and C1 does not contradict that

You: C4 - P shows that C3 is false

Me: C5 - P doesn't show us that there has to be a lowest P in an actually infinite series or that C1 contradicts that

Is your C6 really that P's conclusion is that there has to be a lowest P in an actually infinite series or that C1 contradicts that?

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Re: God Must Exist: Infinite Regression is Impossible

Post #890

Post by Bust Nak »

The Tanager wrote: Tue Apr 18, 2023 11:35 am No worries. I hope it was an enjoyable break for you.
Thanks.
You have to assume a square circle isn’t incoherent or you’d be begging the question. Then when you analyze an accepted definition and it shows itself to be incoherent, you reject it as being something that could exist in reality. It’s the same way with actual infinites.
Okay, so why did say I was begging the question when I said that it was a fine to begin with the assumption that infinity (or an infinite wall) isn't incoherent? Also I still want to know if you assumed a square circle is both a square and a circle?
Yes, but I’m asking for support for why simplicity is about the number of entities versus the number of explanatory assumptions made.
It's both, the number of assumptions alone isn't enough to determine which scenario is simpler, we also need to check the relative simplicity of the assumptions themselves. And in this particular case, checking number of assumptions doesn't help at all, because that both scenario makes one assumption: "There is one" vs "there is none."
You are claiming that it can exist in reality, right?
Correct, as opposed to it does exist in reality.
I think you are misunderstanding the flow of this. Let’s sketch them all out:

You: P - your proof

Me: C1 - premise 2.1 is faulty because of blah, blah, blah

You: C2 - But for 2.1 to be faulty for the reason you said, this would mean there has to be a lowest P

Me: C3 - There can’t logically be a lowest P in an actually infinite series by definition and C1 does not contradict that

You: C4 - P shows that C3 is false

Me: C5 - P doesn't show us that there has to be a lowest P in an actually infinite series or that C1 contradicts that

Is your C6 really that P's conclusion is that there has to be a lowest P in an actually infinite series or that C1 contradicts that?
That's not how I remembered it, try this:

C1 - premise 2.1 is faulty because of blah, blah, blah

C2 - But for 2.1 to be faulty for the reason you said, this would mean there has to be a lowest P

C3 - There can’t logically be a lowest P in an actually infinite series by definition and C1 does not contradict that

C4 - That there can't logically be a lowest P is exactly the point, this means 2.1 can't be faulty for the reason you said.

C5 - that we can count to 2 by starting at any P doesn't imply we can count to 2 without starting at all

C6 - that's what the proof is for, to bridge the gap between "we can count to 2 by starting at any P" and "we can count to 2 without starting at all."

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