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]

That's wasn't all you claimed, you said you have abandoned the premise that a wall can be infinite. So why can't it?

No, I’ve abandoned it in the sense that I see no reason to use a wall being infinite as support for other claims. I’ve abandoned it in the sense that I see no reason to think a wall can be infinite. Your claims rest on a wall being infinite. So, why can it?

So question away. What's seems wrong to you, other than expanding implies boundary to you?

That’s it. Your response is simply “just take the implication away”. That’s like telling me to take the square circle implications away. You can’t do it. Your response is that we have a deductive proof that shows why we can’t do that. That kind of deductive proof is easy to reject; simply reject one of the definitional statements. I offered (or at least gestured towards it, I can’t remember) a deductive proof for expanding implying a boundary, but also said it would be easy to reject because you could just reject the definitional statements that build it up.

The fact remains that you have given no attempt to positively explain expansion without boundary. You give examples assuming such a thing. And you try to negatively explain it.

I did though. Repeated here for your convenience: the wall is now longer, expanded, but since there was never a boundary in the first place, no boundary was crossed; infinite means there is no boundary; and that's what making a brick longer means, the whole wall becomes longer. You can't say I haven't even tried. I asked you which part needs further explanation, but all I am getting back is, you don't understand how those concepts can be combined.

Yes, I can say you still haven’t tried. This explanation assumes there was never a boundary, it doesn’t explain how the initial wall can exist without a boundary. Defining something into existence (“the infinite means there is no boundary”) is not an explanation of how it makes sense; it’s an assumption.

It is simpler when characteristic X is not having characteristic Y.

So, a man without hair causing X is a simpler explanation than a man with hair?

"It's not there" is simpler than "it is there, we just can't detect it."

Given the way the universe is expanding there is no way we could detect it (at least without being able to reach the end of the universe perhaps). “It’s not there” is just as much an assumption from ignorance as “it’s there” would be. They are equal in simplicity.

Your words were "because those are contradictions..." You have your own burden to fulfill.

Sure, but my meaning is my own, not what you read into my phrase. I think it’s clear from the wider context of our conversation that I’m saying I doubt it’s a contradiction. You can retreat to semantics or address clarifications when they come and move the discussion forward.

It does not take the form of A and not A, therefore it's not a contradiction.

Yes, it does. It matches in all points and then spits out results that are A and non-A.

That's not what I asked you though. I asked if you accepted this premise: If you can start from any prior member and end at X and then start counting from X and end at last Sunday, then you can, without starting at X, count through X and end at last Sunday. Do you agree with that?

Yes.

As I keep telling you, that's what the proof is for. A sound proof leads to true conclusion. If you accept the premises, and can't find an invalid step, then you are forced to accept that without starting at P or X, you can end at last Sunday. So once again, do you agree with the premise in question?

With the clarifications perhaps my earlier response will become clearer. The problem then comes with:

4.2) not (exist X where cannot W and T and E).

There is a circumstance of all X’s where you cannot W and T and E, namely, one where you don’t B (i.e., you don’t start from P). You claimed premise 3 supports 4.2, but it doesn’t. Premise 3 states that for all circumstances of X, you CAN W and T and E. It doesn’t say you always will. What circumstances will you always W and T and E? Well, look at 2.2. It will be those circumstances that you can B and S and E.

At the top of the last paragraph I offered a circumstance for X where you don’t B. Premise 2.2 only tells us that we will W and T and E when you B. Thus, there is a counter-example to premise 4.2. This means that premise 5 doesn’t follow.

[Bust Nak]

No, I’ve abandoned it in the sense that I see no reason to use a wall being infinite as support for other claims. I’ve abandoned it in the sense that I see no reason to think a wall can be infinite. Your claims rest on a wall being infinite. So, why can it?

Because there is nothing stopping it form being infinite.

That’s it. Your response is simply “just take the implication away”. That’s like telling me to take the square circle implications away.

It's not like that because square circles are literal contradictions - we have a deductive proof that shows why we can’t have square circles. Reject one of the definitional statements amounts to accepting that they are a contradiction by definition.

I offered (or at least gestured towards it, I can’t remember) a deductive proof for expanding implying a boundary, but also said it would be easy to reject because you could just reject the definitional statements that build it up.

But what you are calling the "definitional statement," isn't definitional. The definition of expand does not mention boundary. Having that as a premise in an argument for showing expanding implies a boundary is a question begging fallacy.

Yes, I can say you still haven’t tried. This explanation assumes there was never a boundary...

Not an assumption. Unlike the expand implies boundary" claim, this is definitional: it's literally how infinity is defined.

it doesn’t explain how the initial wall can exist without a boundary. Defining something into existence (“the infinite means there is no boundary”) is not an explanation of how it makes sense; it’s an assumption.

But you said the individual concepts made sense to you, you just don't see how they can be combined. I was tasked with explaining how the two concepts can be combined. So now you are saying infinity in isolation doesn't make sense to you, even without bringing expanding into the picture? That doesn't seem to gel with what you said above re: "that's it."

So, a man without hair causing X is a simpler explanation than a man with hair?

Is hair a factor in the cause? If so, yes, it is simpler.

Given the way the universe is expanding there is no way we could detect it (at least without being able to reach the end of the universe perhaps). “It’s not there” is just as much an assumption from ignorance as “it’s there” would be. They are equal in simplicity.

No it is not. One less entity is simpler. This is fundamental.

Sure, but my meaning is my own, not what you read into my phrase. I think it’s clear from the wider context of our conversation that I’m saying I doubt it’s a contradiction. You can retreat to semantics or address clarifications when they come and move the discussion forward.

It's not a simple doubt when you say things like "Yes, it does. It matches in all points and then spits out results that are A and non-A." Go on, prove it.

With the clarifications perhaps my earlier response will become clearer. The problem then comes with:

4.2) not (exist X where cannot W and T and E).

There is a circumstance of all X’s where you cannot W and T and E, namely, one where you don’t B (i.e., you don’t start from P).

Just so I don't have to keep referring to older pages:

S = start counting from X
E = end at last Sunday
P = prior members before X
B = start from any P and end at X
W = without starting at X (no mention of P. It’s not equivalent "without starting at all")
T = count through X
I = without starting at all

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

4.2) is a deductive step, there can be no circumstance where you cannot W and T and E, not even the one you named, if the logic from 3 to 4.2 is valid and premise 3 true. Which of these (or both) are you disputing exactly?

You claimed premise 3 supports 4.2, but it doesn’t. Premise 3 states that for all circumstances of X, you CAN W and T and E. It doesn’t say you always will.

I am not just claiming 3 supports 4.2, I am claiming they are logically equivalent. I don't need premise 3 to say "you always will," I need it to say "you CAN;" which it does, so what's exactly is the problem here?

What circumstances will you always W and T and E? Well, look at 2.2. It will be those circumstances that you can B and S and E.

Ignoring "always will" vs "can" for now. Why is this bit even an issue? "Those circumstances that you can B and S and E" covers all circumstances, there are no circumstances where that isn't true.

At the top of the last paragraph I offered a circumstance for X where you don’t B. Premise 2.2 only tells us that we will W and T and E when you B.

Read it again, 2.2 says "If you can B and can S and E, then you can W and T and E." You can B, even if you don't B. It doesn't say anything about "will."

I asked if you agree 2.2 and you told me yes, now looks like you were agreeing to something other than what I asked you after all. One more try, read it carefully before answering: If you can start from any prior member and end at X and then start counting from X and end at last Sunday, then you can, without starting at X, count through X and end at last Sunday. Nothing about "always will," just what is possible. Do you agree with that?

[The Tanager]

But what you are calling the "definitional statement," isn't definitional. The definition of expand does not mention boundary. Having that as a premise in an argument for showing expanding implies a boundary is a question begging fallacy.

I think you might have misunderstood what I was saying about your request for a deductive proof. It’s easy to offer those without actually solving anything. You can make an if-then deductive proof for anything, that the opponent will just turn around and reject the if-statement.

So, where are we at? Does expansion imply a boundary? The definition doesn’t help us here, by definition of what a definition is, as I’ve said (the bit about implications logically not being stated). I see no reason to accept your belief that no mention of boundary/no boundary should make ‘no implication” the default. It's not simpler because the question isn't being addresssed at all, so there can't be a simpler answer. That leaves both of us with a burden for our view.

So, let's keep exploring. Do you think only things that can be quantified can expand? Or can non-quantifiable things also expand?

I did though. Repeated here for your convenience: the wall is now longer, expanded, but since there was never a boundary in the first place, no boundary was crossed; infinite means there is no boundary; and that's what making a brick longer means, the whole wall becomes longer. You can't say I haven't even tried. I asked you which part needs further explanation, but all I am getting back is, you don't understand how those concepts can be combined.

Yes, I can say you still haven’t tried. This explanation assumes there was never a boundary, it doesn’t explain how the initial wall can exist without a boundary. Defining something into existence (“the infinite means there is no boundary”) is not an explanation of how it makes sense; it’s an assumption.

Not an assumption. Unlike the expand implies boundary" claim, this is definitional: it's literally how infinity is defined.

The assumption here is that there could be an (actual) infinite wall to begin with. This assumes that infinity is a quantity/amount that can be applied to a wall. You’ve got to show that infinity is a quantity/amount for your explanation to work. Yes, you are defining infinity as a quantity/amount, but you need to show that this makes sense to do. Yes, mathematicians define it as such, but those that do, say this is what it would be like if it’s a quantity; they don’t offer arguments for it being a quantity.

But you said the individual concepts made sense to you, you just don't see how they can be combined. I was tasked with explaining how the two concepts can be combined. So now you are saying infinity in isolation doesn't make sense to you, even without bringing expanding into the picture? That doesn't seem to gel with what you said above re: "that's it."

All along I’ve been questioning whether (actual) infinity makes sense.

Is hair a factor in the cause? If so, yes, it is simpler.

So, how is “no center” or “center” a factor in the cause (and cause of what, exactly)?

No it is not. One less entity is simpler. This is fundamental.

How is the center an entity?

It's not a simple doubt when you say things like "Yes, it does. It matches in all points and then spits out results that are A and non-A." Go on, prove it.

Prove that it matches in all points and then spits out results that are A and non-A?

Scenario 1
Amount of guests: infinity
Number of rooms: infinity
Method of guests to room: 1 guest for every room

Okay, how many empty rooms do we have? Spit out the result: zero

Scenario 2
Amount of guests: infinity
Number of rooms: infinity
Method of guests to room: 1 guest for every room

Okay, how many empty rooms do we have? Spit out the result: one

In scenario 1 we have zero (let’s call that A). In scenario 2 we have one. One is not-zero or not-A. This looks like a contradiction to me. You are saying it’s not. For it not to be, I’ve got to be putting the scenarios together wrongly. I’m open to being wrong, so please show me how it’s not a contradiction.

S = start counting from X
E = end at last Sunday
P = prior members before X
B = start from any P and end at X
W = without starting at X (no mention of P. It’s not equivalent "without starting at all")
T = count through X
I = without starting at all

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

I am not just claiming 3 supports 4.2, I am claiming they are logically equivalent. I don't need premise 3 to say "you always will," I need it to say "you CAN;" which it does, so what's exactly is the problem here?

Do you see premise 3 to be claiming that for all X’s you can W and T and E or to be claiming that for all circumstances all X’s find themselves in you can W and T and E?

[Bust Nak]

I see no reason to accept your belief that no mention of boundary/no boundary should make ‘no implication” the default.

That it would lead to all sorts of craziness if that wasn't the default, is a good reason to accept it. Without this rule, you can literally tag on any old implication you feel like attaching. Why stop at expansion implies boundary? Why not just tag on the implication of impossible to the definition of infinity and be done with it? You need a reason to have an implication.

It's not simpler because the question isn't being addresssed at all...

What question are you referring to here exactly?

Do you think only things that can be quantified can expand? Or can non-quantifiable things also expand?

I can't think of any non-quantifiable things expanding.

The assumption here is that there could be an (actual) infinite wall to begin with. This assumes that infinity is a quantity/amount that can be applied to a wall.

These are fine assumptions to make. What's wrong with these assumptions? You have to make these assumptions to begin to make sense of them.

You’ve got to show that infinity is a quantity/amount for your explanation to work. Yes, you are defining infinity as a quantity/amount, but you need to show that this makes sense to do. Yes, mathematicians define it as such, but those that do, say this is what it would be like if it’s a quantity; they don’t offer arguments for it being a quantity.

Well, that's not what they say. Why not just take their word for it that it IS a quantity?

All along I’ve been questioning whether (actual) infinity makes sense.

Yeah, but when I asked you what doesn't make sense, you said you couldn't see how something infinite can expand, that doesn't sound like you thought it was problematic on its own. That's why the conversation took the path that it did, I was explaining how the two concepts can combine.

So, how is “no center” or “center” a factor in the cause (and cause of what, exactly)?

Don't understand what you are asking here. What cause? My point was simple. Don't assuming something is there, unless there is evidence for it, the default is it's not there.

How is the center an entity?

It is a thing with a distinct existence, apart form the entity it is part of.

Prove that it matches in all points and then spits out results that are A and non-A?

Try the following format, this is the kind of thing I was asking for:
1) If X is a circle then all points are equidistant from its the centre. (premise)
2) If X is a square then not all points are equidistant from its the centre. (premise)
3) X is both a circle and a square. (assumption)
4) all points are equidistant from its the centre. (from 1 and 3)
5) not all points are equidistant from its the centre. (from 2 and 3)
6) all points are equidistant from its the centre and not all points are equidistant from its the centre (from 4 and 5)

Scenario 1
Amount of guests: infinity
Number of rooms: infinity
Method of guests to room: 1 guest for every room

Okay, how many empty rooms do we have? Spit out the result: zero

Scenario 2
Amount of guests: infinity
Number of rooms: infinity
Method of guests to room: 1 guest for every room

Okay, how many empty rooms do we have? Spit out the result: one

In scenario 1 we have zero (let’s call that A). In scenario 2 we have one. One is not-zero or not-A. This looks like a contradiction to me. You are saying it’s not. For it not to be, I’ve got to be putting the scenarios together wrongly. I’m open to being wrong, so please show me how it’s not a contradiction.

Same response as before, you failed to take into account of the guests moving around from scenario 1 to 2.

S = start counting from X
E = end at last Sunday
P = prior members before X
B = start from any P and end at X
W = without starting at X (no mention of P. It’s not equivalent "without starting at all")
T = count through X
I = without starting at all

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

I am not just claiming 3 supports 4.2, I am claiming they are logically equivalent. I don't need premise 3 to say "you always will," I need it to say "you CAN;" which it does, so what's exactly is the problem here?

Do you see premise 3 to be claiming that for all X’s you can W and T and E or to be claiming that for all circumstances all X’s find themselves in you can W and T and E?

I still don't see the difference between these two claims. All cats are mammal. Is there any circumstances where a cat can find itself where it is not a mammal? What if the cat is dead, well it's a deal mammal. What if the cat is actually a carrot, then it wouldn't be a mammal but a vegetable. Would that count a "circumstance?"

There are no conditional clause attached to for all X’s you can W and T and E; therefore for all circumstances all X’s find themselves in you can W and T and E.

[The Tanager]

That it would lead to all sorts of craziness if that wasn't the default, is a good reason to accept it. Without this rule, you can literally tag on any old implication you feel like attaching. Why stop at expansion implies boundary? Why not just tag on the implication of impossible to the definition of infinity and be done with it? You need a reason to have an implication.

I’m not just tagging on any old implication. I’m working off of what we already know about all non-infinite measurements. Measuring something seems to denote a boundary. Object X goes such and such a distance, not lesser and not farther. Yet when something gets bigger it goes farther than it was, farther than the previous measurement. But you want to say just leave those implications aside; it is getting bigger, but not going farther.

It's not simpler because the question isn't being addresssed at all…

What question are you referring to here exactly?

The definition is not addressing the question of whether boundary or no-boundary is the implication. Since it isn’t addressed by the definition, the default is not a no-boundary implication; it’s “I don’t know if there is a boundary implication or not”. Both ‘no-boundary’ and ‘yes-boundary’ bring in equal added elements to the situation, so they are equal in simplicity.

I can't think of any non-quantifiable things expanding.

Me neither. So, at best, the definition path above has taken us to a tie on the issue. But we agree that a thing must be a quantity in order to expand. You are trying to prove actual infinity is a quantity. You have continually assumed it because mathematicians treat it as such. I’ve countered that even in doing so that they admit they have simply assumed it is a quantity.

Well, that's not what they say. Why not just take their word for it that it IS a quantity?

If they say it is a quantity without just assuming it is a quantity, then give the proof they offer. There isn’t any because it’s simply assumed to be a quantity and then they work out what all would follow. But your burden here is to show it is a quantity.

These are fine assumptions to make. What's wrong with these assumptions? You have to make these assumptions to begin to make sense of them.

You are trying to make sense of an infinite wall expanding. It can’t expand if you can’t have an infinite wall to begin with. You’ve assumed that an infinite wall could exist in order to speak about it expanding. That’s not a fine assumption; it’s begging the question.

Don't understand what you are asking here. What cause? My point was simple. Don't assuming something is there, unless there is evidence for it, the default is it's not there.

No, the default is “I don’t know if there is a center or not”. Center or no-center are both one assumption added to one’s explanation of everything.

It is a thing with a distinct existence, apart form the entity it is part of.

Why do you think it’s a distinct entity and not just a distinct conceptual part of the entity?

Same response as before, you failed to take into account of the guests moving around from scenario 1 to 2.

That’s not a part of the scenarios, but how we move from one scenario to the next.

I still don't see the difference between these two claims. All cats are mammal. Is there any circumstances where a cat can find itself where it is not a mammal? What if the cat is dead, well it's a deal mammal. What if the cat is actually a carrot, then it wouldn't be a mammal but a vegetable. Would that count a "circumstance?"

There are no conditional clause attached to for all X’s you can W and T and E; therefore for all circumstances all X’s find themselves in you can W and T and E.

Here are two different circumstances a single X can find itself in:

Circumstance 1 - {P, …, X, …, 99, 100}
Circumstance 2 - {..., P, …, X, …, 99, 100}

Let’s say X = 1 and apply that to your proof:

S = start counting from X
E = end at last Sunday
P = prior members before X
B = start from any P and end at X
W = without starting at X (no mention of P. It’s not equivalent "without starting at all")
T = count through X
I = without starting at all

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

To say “for all X (i.e., for all values X could have), you can W and T and E” is different than to say “for all X (i.e., every circumstance all values of X could find themselves in), you can W and T and E”.

If you are only talking about all values X could have, then I agree with the truth of premise 3. The problem is that this wouldn’t be addressing the question I’ve asked of you.

If you are talking about all circumstances, then I don’t agree with the truth of premise 3. That’s because premise 2.2 narrows the circumstances that one is looking at. Circumstance 2 does not fit the if-statement here because you aren’t starting from P and, therefore, not B (and S and E). So, it’s not demonstrated that “for all X (i.e., every circumstance all values of X could find themselves in), you can W and T and E”. Or to note the same problem when we get to premise 4.2, the X in circumstance 2 is a possible counter example, because it has not been demonstrated that the X in this circumstance can, without starting at X and explicitly without starting at P, allow one to count through X and end at last Sunday.

[Bust Nak]

I’m not just tagging on any old implication. I’m working off of what we already know about all non-infinite measurements. Measuring something seems to denote a boundary. Object X goes such and such a distance, not lesser and not farther. Yet when something gets bigger it goes farther than it was, farther than the previous measurement. But you want to say just leave those implications aside; it is getting bigger, but not going farther.

Sounds like you agree with me that you need a reason to have an implication. As for your reason, why do you think something that applies to the finite, also applies to the infinite? As an argument, I've already objected to it as hasty generalization.

The definition is not addressing the question of whether boundary or no-boundary is the implication. Since it isn’t addressed by the definition, the default is not a no-boundary implication; it’s “I don’t know if there is a boundary implication or not”. Both ‘no-boundary’ and ‘yes-boundary’ bring in equal added elements to the situation, so they are equal in simplicity.

I don't really get what you mean about not addressing the question.

As for the "I don't know" being the default, let me adjust my statement to take that into account. Before anything is known, the default is I don't know one way or the other; after we have investigated and have discovered no evidence of something, the new default is that something doesn't exist.

Me neither. So, at best, the definition path above has taken us to a tie on the issue. But we agree that a thing must be a quantity in order to expand. You are trying to prove actual infinity is a quantity. You have continually assumed it because mathematicians treat it as such. I’ve countered that even in doing so that they admit they have simply assumed it is a quantity.

Well you are simply wrong. They have not assumed such a thing, they have defined it as such.

If they say it is a quantity without just assuming it is a quantity, then give the proof they offer...

I have presented multiple mathematical definitions that prove that it's defined as such.

You are trying to make sense of an infinite wall expanding. It can’t expand if you can’t have an infinite wall to begin with. You’ve assumed that an infinite wall could exist in order to speak about it expanding. That’s not a fine assumption; it’s begging the question.

How?! I really don't get the way you think. You can't even begin to entertain a concept if you don't start with the assumption that it's possible. How are you suppose to be able to preform any sort of analysis beyond comprehending what the individual words say, if you don't assume it is possible?

No, the default is “I don’t know if there is a center or not”. Center or no-center are both one assumption added to one’s explanation of everything.

You have not taken the lack of evidence into account.

Why do you think it’s a distinct entity and not just a distinct conceptual part of the entity?

Not seeing much distinction. Either or both, just a matter of perspective. One entity with an extra part is still less simple than one entity without.

That’s not a part of the scenarios, but how we move from one scenario to the next.

Okay, don't see how that changes anything, it explains why there is a difference between the scenarios.

Here are two different circumstances a single X can find itself in:

Circumstance 1 - {P, …, X, …, 99, 100}
Circumstance 2 - {..., P, …, X, …, 99, 100}

Let’s say X = 1 and apply that to your proof:

S = start counting from X
E = end at last Sunday
P = prior members before X
B = start from any P and end at X
W = without starting at X (no mention of P. It’s not equivalent "without starting at all")
T = count through X
I = without starting at all

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

To say “for all X (i.e., for all values X could have), you can W and T and E” is different than to say “for all X (i.e., every circumstance all values of X could find themselves in), you can W and T and E”.

Is it? That statement is true for both circumstances you mentioned, so it still sounds like the same thing to me.

If you are talking about all circumstances, then I don’t agree with the truth of premise 3.

It's not a premise, it follows deductively from prior steps, so there no need to say you don't agree with this when the actual objection you have seems to be with 2.2...

That’s because premise 2.2 narrows the circumstances that one is looking at. Circumstance 2 does not fit the if-statement here because you aren’t starting from P and, therefore, not B (and S and E)...

I have no idea what you mean here. 2.2 is true for Circumstance 2: for all X including ones that is in the sequence {..., P, …, X, …, 99, 100}, if you can B and S and E, then you can W and T and E. What's problem did you spot here?

[The Tanager]

Sounds like you agree with me that you need a reason to have an implication. As for your reason, why do you think something that applies to the finite, also applies to the infinite? As an argument, I've already objected to it as hasty generalization.

No, I’m saying what applies to quantities should be consistent, unless shown otherwise. You are saying there is such a thing as an infinite quantity. Okay, it should be consistent with what happens to other quantities, unless evidence points otherwise. Your response is to just assume it’s different unless I can rule that out. As an argument, I’ve already objected to that as shifting the burden.

I don't really get what you mean about not addressing the question.

The definition doesn’t address the question of whether expansion definitely implies a boundary or definitely doesn’t imply a boundary.

As for the "I don't know" being the default, let me adjust my statement to take that into account. Before anything is known, the default is I don't know one way or the other; after we have investigated and have discovered no evidence of something, the new default is that something doesn't exist.

This is shifting the burden. You’ve said here that since your opponent’s position hasn’t been supported, your position is therefore the default. Yet, you haven’t supported your position, which using this logic, would mean your opponent’s position should be the new default, as well. No, "I don't know" is still the default.

Well you are simply wrong. They have not assumed such a thing, they have defined it as such.

Defining it as such, with no positive evidence for doing so, is assuming such a thing.

If they say it is a quantity without just assuming it is a quantity, then give the proof they offer…

I have presented multiple mathematical definitions that prove that it's defined as such.

Okay, but present the proof that it should be defined as such a reality.

How?! I really don't get the way you think. You can't even begin to entertain a concept if you don't start with the assumption that it's possible. How are you suppose to be able to preform any sort of analysis beyond comprehending what the individual words say, if you don't assume it is possible?

What do you think?:

1) If the sides of an object get longer, then the whole object has expanded
2) A square circle is a thing with sides
3) The sides in a square circle can become longer
4) Therefore, a square circle can expand

No, the default is “I don’t know if there is a center or not”. Center or no-center are both one assumption added to one’s explanation of everything.

You have not taken the lack of evidence into account.

There is a lack of evidence for both positions.

Not seeing much distinction. Either or both, just a matter of perspective. One entity with an extra part is still less simple than one entity without.

It’s not like a physical part; it’s a naming convention of an abstract concept. A phone has a sim card and you can move that part around in the phone’s design and it’s still the sim card. Whatever part of space would be the “center,” if you move it to another location, it would no longer be the center. The center isn’t a thing like that.

Okay, don't see how that changes anything, it explains why there is a difference between the scenarios.

No, it explains that it’s a different scenario. A different scenario with all the same inputs, but a different result.

Is it? That statement is true for both circumstances you mentioned, so it still sounds like the same thing to me.

It’s true that Lily, my cat, is black and my car is black, but that doesn’t make them the same thing.

It's not a premise, it follows deductively from prior steps, so there no need to say you don't agree with this when the actual objection you have seems to be with 2.2…

I didn’t spell it all out. The key premise is 3 and I’m rejecting that. I’m rejecting that because premise 2.2 narrows down the circumstances where one can W and T and E. At that point, 2.3 becomes false “for all x (i.e., every circumstance all values of X could find themselves in). This means that 2.4 is also false. This means that 3 is false.

[Bust Nak]

No, I’m saying what applies to quantities should be consistent, unless shown otherwise.

That's what I've been doing. I gave you all sorts of reasons why things that applies to the finite does not apply to the infinite. Instead of discarding this notion of "quantities should be consistent," you reject what can be shown deductively.

The definition doesn’t address the question of whether expansion definitely implies a boundary or definitely doesn’t imply a boundary.

Therefore you shouldn't assume it implies a boundary; given it it conflict with other definitions, you should accept that it does not imply a boundary. Why is that so contentious?

This is shifting the burden. You’ve said here that since your opponent’s position hasn’t been supported, your position is therefore the default. Yet, you haven’t supported your position...

That's what the "after investigation, we have no evidence" is supposed to be - support for my position.

Defining it as such, with no positive evidence for doing so, is assuming such a thing.

No, it is not. You don't need to assume anything, except maybe shared basic English vocabulary, to create a definition.

Okay, but present the proof that it should be defined as such a reality.

It should be defined as such because mathematicians are the authority of defining mathematical constructs.

What do you think?:

1) If the sides of an object get longer, then the whole object has expanded
2) A square circle is a thing with sides
3) The sides in a square circle can become longer
4) Therefore, a square circle can expand

I entertained the notion and concluded that the argument is valid but not sound. To do that I started with the presumption the stuff mentioned are all possible.

There is a lack of evidence for both positions.

So you go for the position that is simpler.

It’s not like a physical part; it’s a naming convention of an abstract concept. A phone has a sim card and you can move that part around in the phone’s design and it’s still the sim card. Whatever part of space would be the “center,” if you move it to another location, it would no longer be the center. The center isn’t a thing like that.

The phone still have a center though, regardless of where the sim card slot is. You still don't assume there is one, without evidence. You still go with the assumption that there isn't one, if you did a good faith searched for evidence and found none. Not seeing what your point is.

No, it explains that it’s a different scenario. A different scenario with all the same inputs, but a different result.

Ah huh, so some how a different scenario with all the same inputs giving a different result, is contradictory to you?

It’s true that Lily, my cat, is black and my car is black, but that doesn’t make them the same thing.

That's not a good analogy. If my cat is onyx and my car is black, then they are the same color, despite the different wording. In other words "onyx" and "black" is the same thing.

I didn’t spell it all out. The key premise is 3 and I’m rejecting that. I’m rejecting that because premise 2.2 narrows down the circumstances where one can W and T and E. At that point, 2.3 becomes false “for all x (i.e., every circumstance all values of X could find themselves in). This means that 2.4 is also false. This means that 3 is false.

How? I still have no idea what you are talking about. How does 2.2 narrow down the circumstances when it is true for all circumstances: including ones that is in the sequence {..., P, …, X, …, 99, 100}?

[The Tanager]

That's what I've been doing. I gave you all sorts of reasons why things that applies to the finite does not apply to the infinite.

You did not give all sorts of reasons. You’ve said what? Mathematicians define it as such. Yet that reason isn’t even accurate because they openly admit it is axiomatic, that it’s an assumption, not something they have proven.

Therefore you shouldn't assume it implies a boundary; given it it conflict with other definitions, you should accept that it does not imply a boundary. Why is that so contentious?

Because that is completely ad hoc. You are begging the question in order to avoid logical contradictions, not because of any positive support.

That's what the "after investigation, we have no evidence" is supposed to be - support for my position.

So, after investigation, we have no evidence that God doesn’t exist, therefore theism is supported? That is the equivalent of what you are doing here. I could say the same thing. After investigation, we have no evidence there is no center. Therefore, I’ve supported my position; it’s the default unelss you prove otherwise. This isn’t rational.

It should be defined as such because mathematicians are the authority of defining mathematical constructs.

But mathematicians say it is assumed, not proven. If they offer proof rather than mere assumption, then bring that to the discussion.

What do you think?:

1) If the sides of an object get longer, then the whole object has expanded
2) A square circle is a thing with sides
3) The sides in a square circle can become longer
4) Therefore, a square circle can expand

I entertained the notion and concluded that the argument is valid but not sound. To do that I started with the presumption the stuff mentioned are all possible.

Why is it unsound?

There is a lack of evidence for both positions.

So you go for the position that is simpler.

Which doesn’t help here because they are equally simple. “There is a center” is one additional claim. “There is no center” is one additional claim. You are fooling yourself by saying “there is no center” is not a claim being added to the explanation, when it clearly is. You are fooling yourself by equating the zero center with it being zero additional claims.

The phone still have a center though, regardless of where the sim card slot is. You still don't assume there is one, without evidence. You still go with the assumption that there isn't one, if you did a good faith searched for evidence and found none. Not seeing what your point is.

My point was that the “center” of a phone isn’t a part of the phone that can be called a separate entity from other parts of the phone; it’s just a naming convention of a specific location relative to the whole object. So, it’s not like “center of the phone” or “center of the universe” is an additional entity to those objects making it a more complex object than if it had no center.

Ah huh, so some how a different scenario with all the same inputs giving a different result, is contradictory to you?

Yes, for the reasons I’ve already shared.

How? I still have no idea what you are talking about. How does 2.2 narrow down the circumstances when it is true for all circumstances: including ones that is in the sequence {..., P, …, X, …, 99, 100}?

Actually the problem is in premise 2.1. It is not true that in the above sequence, if there is a P, that you can B. The sequence above is defined in a way that you can’t B because it’s illogical to create a sequence where you don’t B and then say you can B in that same sequence. If you B’d in that sequence, then you’ve created a different sequence.

[Bust Nak]

You did not give all sorts of reasons. You’ve said what? Mathematicians define it as such. Yet that reason isn’t even accurate because they openly admit it is axiomatic, that it’s an assumption, not something they have proven.

I also mentioned that contradictions that would result if you treat infinity the same as finite, as well as incompatibility with popular thesis re: infinite universe.

Because that is completely ad hoc. You are begging the question in order to avoid logical contradictions, not because of any positive support.

It's not ad hoc though, avoiding logical contradiction is something that you should be doing in all things.

So, after investigation, we have no evidence that God doesn’t exist, therefore theism is supported?

No, when there is no evidence for something one way or the other after investigation, you go with it does not exist.

But mathematicians say it is assumed...

No, they have said no such thing. Why is the concept of definition so contentious? I defined IZZXY as "a square circle." I don't have to assume square circles is a coherent concept to do that, do I?

Why is it unsound?

Premise 2 is not true.

Which doesn’t help here because they are equally simple. “There is a center” is one additional claim. “There is no center” is one additional claim.

Yes, both are additional claims but "there is no center" is the simpler claim then "there is a center."

My point was that the “center” of a phone isn’t a part of the phone that can be called a separate entity from other parts of the phone; it’s just a naming convention of a specific location relative to the whole object.

Why isn't a specific location relative to the whole object, a separate entity from other parts of the phone? It's not the top of the phone, so it's separate from that. It's not the bottom of the phone, so it's separate from that.

Yes, for the reasons I’ve already shared.

And the explanation why two different scenarios gave different results doesn't cause you to reconsider?

Actually the problem is in premise 2.1. It is not true that in the above sequence, if there is a P, that you can B. The sequence above is defined in a way that you can’t B because it’s illogical to create a sequence where you don’t B and then say you can B in that same sequence. If you B’d in that sequence, then you’ve created a different sequence.

So you are telling me, you cannot count from 1 to 5 in this sequence {1, 2, 3, 4, 5, 6}? The only thing you can do in this sequence is count from 1 to 6 and that's it?

So would you accept something like, if you can count from 1 to 5 in this sequence {1, 2, 3, 4, 5} and you can count from 5 to 6 in this sequence, then you can count from 1 to 6 through 5 in this sequence {1, 2, 3, 4, 5, 6}? It would serve the same purpose as the premise if you can count from 1 to 5 and from 5 to 6 in this sequence {1, 2, 3, 4, 5, 6} then you can count from 1 to 6 through 5.