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]

The rules say no, you can't do that.

Where is that rule? David Hilbert didn’t seem to have a problem with it.

You said that. I said that's not true, because there are counterexamples - certain things in the anything of any size category don't fit.

That’s like saying a square circle is a counterexample to a round plane figure whose boundary consists of points equidistant from a fixed center point. To be a limitless space just means that there is no limit to what can fit in it. It means that anything that has any kind of size can fit in it with absolutely no exceptions. It’s logically impossible to have a counterexample to that.

How exactly is that done? How did you decide your method is just as valid as mine? That whole chunk of stuff I cropped doesn't mean much if your method isn't valid. I simply can't see how you can decide if it is possible to do something, prior to checking if it is possible. Frankly it sounds like you are suggesting that you can decide X before deciding X.

We simply analyze the nature of what we are studying. You don’t have to actually fail at counting to infinity to know that you can’t count to infinity; we know this through analyzing the nature of things.

Yes, that's what it means to me, a method invalid if it is set up in a way where a 1 to 1 match would be impossible. Your method is set up in such a way where a 1 to 1 match would be impossible; we know this because it is impossible to find a match for 0, therefore it is invalid.

The method doesn’t make 1 to 1 correspondence impossible. If the method made it impossible, then why does it work for every single finite set in existence? If there are different rules for infinite 1 to 1 correspondence than finite 1 to 1 correspondence, then

What is really going on is that this method contradicts what you want the answer to be and, therefore, you want to call it invalid, so you can throw it out. It’s not rational to throw methods out simply because they don’t give you the answer you want.

They mean that if you go in a straight line, you would never hit an edge, nor you would never loop back to a place you've been before, also the distance between any two points in space is increasing.

Calling the universe an actual infinite is not a statement about space travel; that is simply an illustration to point to what it means for the universe to be an actual infinite. You would never reach the end because there is no end; it would stretch on forever, where nothing could exist beyond the universe. Oh, but wait a little and the universe will expand, and you can go to this impossible to exist beyond. It’s logical nonsense.

You said the same kind of thing before. If we can rule a scenario out, then we wouldn't need to appeal to intuition.

I’m not sure how this addresses my point: different kinds of things expanding have different kinds of expectations on how the expansion would look. We would expect to see a preferred direction relative to center in a universe whose objects are expanding within a static “container” of space. But we would expect to see every vantage point appear to be the center in a universe whose “container” of space is itself expanding.

Because it's not rational to assume something is there when there is no evidence either way.

It’s not rational to assume it’s there or not there when there is no evidence either way. But, knowing what dictionaries are, we realize that they are designed to leave implications unsaid and, therefore, any evidence for or against proposed implications must come from somewhere else.

I offered my reasoning before, I can formalize what I said as extra premises:
2.1) For all X, if there are P, then you can start from any P and end at X.
2.2) For all X, if (You can start from any P and end at X) and (you can S and E,) then you can W and E.

Where is your support for 2.2? Why does the ability to start at P, move through X and end at E have anything to say about not starting anywhere, moving through X and ending at E? It’s the same hole in your reasoning that I’ve asked about in every attempt. No more changing terms and phrasings. Stick with only these terms and argument and provide the missing premise(s).

[Bust Nak]

Where is that rule? David Hilbert didn’t seem to have a problem with it.

It can be found in your typical high school math text book, typically stated as "infinity - infinity is undefined." Hilbert didn't have a problem with it, no, he followed it, he only talked about adding infinite guests into his hotel.

That’s like saying a square circle is a counterexample to a round plane figure whose boundary consists of points equidistant from a fixed center point. To be a limitless space just means that there is no limit to what can fit in it. It means that anything that has any kind of size can fit in it with absolutely no exceptions. It’s logically impossible to have a counterexample to that.

But I can prove that some things don't fit. So it's time to discard the idea that limitless space means that there is no limit to what can fit in it.

We simply analyze the nature of what we are studying...

So go ahead, show me how you analyze whether your method is set up in a way where a 1 to 1 match would be impossible.

The method doesn’t make 1 to 1 correspondence impossible. If the method made it impossible, then why does it work for every single finite set in existence?

It doesn't work though, there is never a match for the first member of the second set, finite or infinite, using your method of: "we match the first member of the first set (1) with the second member of the second set (1)...The second member of the first set (2) with the third member of the second set (2), and so on."

What is really going on is that this method contradicts what you want the answer to be and, therefore, you want to call it invalid...

I am not just calling it invalid, it is invalid according to this test for validity: is it set up in a way where a 1 to 1 match would be impossible? Yes, it is.

Calling the universe an actual infinite is not a statement about space travel; that is simply an illustration to point to what it means for the universe to be an actual infinite. You would never reach the end because there is no end; it would stretch on forever, where nothing could exist beyond the universe. Oh, but wait a little and the universe will expand, and you can go to this impossible to exist beyond. It’s logical nonsense.

Not seeing why that is problematic at all, where are you seeing any going to "impossible to exist beyond?" Going beyond the universe is still not a thing when the universe expands. It's not even a thing if the universe is finite, you still can't go beyond the universe.

I’m not sure how this addresses my point: different kinds of things expanding have different kinds of expectations on how the expansion would look. We would expect to see a preferred direction relative to center in a universe whose objects are expanding within a static “container” of space. But we would expect to see every vantage point appear to be the center in a universe whose “container” of space is itself expanding.

Why just appear to be center everywhere, and not there is no center?

It’s not rational to assume it’s there or not there when there is no evidence either way.

But it is rational to not assume it is there. Work from there.

But, knowing what dictionaries are, we realize that they are designed to leave implications unsaid and, therefore, any evidence for or against proposed implications must come from somewhere else.

That it made it next to impossible for you to accept infinite math is a good reason against the implication.

Where is your support for 2.2?

It's just a trivial fact that if you can start at P, through X, to E, then you don't have to start from X to get to E. How is that not completely obvious?

Why does the ability to start at P, move through X and end at E have anything to say about not starting anywhere, moving through X and ending at E?

That's what the proof is for, it tells you exact why the ability to start at P through X to E (along with other premises) mean not starting anywhere. The premises are true, the steps are valid, the conclusion must follow.

[The Tanager]

It can be found in your typical high school math text book, typically stated as "infinity - infinity is undefined." Hilbert didn't have a problem with it, no, he followed it, he only talked about adding infinite guests into his hotel.

When doing a quick google search you get all kinds of different answers (including from mathematical sources) that seem to agree and disagree with you here. So, perhaps it is better to ask why any source would say infinity minus infinity is undefined.

But I can prove that some things don't fit. So it's time to discard the idea that limitless space means that there is no limit to what can fit in it.

If you want to try to prove it, go ahead. All you’ve done so far is assume something not limited in size can’t fit into a “container” that is not limited in what can fit into it.

So go ahead, show me how you analyze whether your method is set up in a way where a 1 to 1 match would be impossible.

Where is the logical contradiction of my method?

It doesn't work though, there is never a match for the first member of the second set, finite or infinite, using your method of: "we match the first member of the first set (1) with the second member of the second set (1)...The second member of the first set (2) with the third member of the second set (2), and so on."

{a, b, c} and {1, 2, 3}

My method says to match ‘a’ with ‘2’, then ‘b’ with ‘3’, then ‘c’ with ‘1’. This matching method works in every single case of finite sets. This method clearly does not make 1 to 1 matching impossible.

Not seeing why that is problematic at all, where are you seeing any going to "impossible to exist beyond?" Going beyond the universe is still not a thing when the universe expands. It's not even a thing if the universe is finite, you still can't go beyond the universe.

Thinking about the universe like a flat number line:

If finite, we have something like [-5, 4, …., 0, …4, 5]. To expand, we must go beyond the -5 or the 5, analogically speaking. So, we get [-6, 5, 4, …, 0, …4, 5]. Okay, let’s transfer that to an actually infinite universe where X is infinity: ['-X'………., -1000, -999, …….., 0, ….. 999, 1000, ………..X]. With the expansion, we would now have ['-X-1', -X……, -1000, ….1000, ….X].

'-X-1' didn’t exist before the infinite universe expanded, it was a point you couldn’t reach, just like you could reach -6 prior to the expansion of the finite universe. But if the universe stretches on forever, how could there be a point that exists that wasn’t included in that stretching on forever.

Why just appear to be center everywhere, and not there is no center?

Whether there is a center is a separate question. We have started with the agreement that, from our vantage point within an expanding universe, it looks like we are in the center. If the universe expanded within the “container” of space, filling it more and more, then the only way our vantage point would look like the center is if it were the center. But that isn’t our universe. Space, the “container,” is part of the universe that is expanding. The container is expanding. Every point within space will look like the rest of the universe is expanding from it as though it is the center and this says nothing about whether we actually are in the center or not or if it makes sense to say there is a center at all.

But it is rational to not assume it is there. Work from there.

How does that help you?

That it made it next to impossible for you to accept infinite math is a good reason against the implication.

Why?

It's just a trivial fact that if you can start at P, through X, to E, then you don't have to start from X to get to E. How is that not completely obvious?

Sure, but that’s not what 2.2 says. “You can W and E” is not equivalent to “you don’t have to start from X to get to E”; it’s equivalent to “without starting at any P you can move through X and get to E”. Starting from P to then move through X and reach E is not support for not starting at any P, then moving through X and reaching E.

That's what the proof is for, it tells you exact why the ability to start at P through X to E (along with other premises) mean not starting anywhere. The premises are true, the steps are valid, the conclusion must follow.

None of your premises support the move I just mentioned above.

[Bust Nak]

When doing a quick google search you get all kinds of different answers (including from mathematical sources) that seem to agree and disagree with you here.

Wait what? What phrase where you searching for?

So, perhaps it is better to ask why any source would say infinity minus infinity is undefined.

Because anything else would lead to contradictions.

If you want to try to prove it, go ahead.

That's what the deductive proof is for.

Where is the logical contradiction of my method?

I don't see one. It's just impossible to get a 1 to 1 match.

{a, b, c} and {1, 2, 3}

My method says to match ‘a’ with ‘2’, then ‘b’ with ‘3’, then ‘c’ with ‘1’. This matching method works in every single case of finite sets. This method clearly does not make 1 to 1 matching impossible.

Sure, but this isn't the method you presented earlier. Matching the first member of the first set (a) with the second member of the second set (2)...The second member of the first set (b) with the third member of the second set (3) and so on would leave 1 unmatched.

Thinking about the universe like a flat number line:

If finite, we have something like [-5, 4, …., 0, …4, 5]. To expand, we must go beyond the -5 or the 5, analogically speaking. So, we get [-6, 5, 4, …, 0, …4, 5]. Okay, let’s transfer that to an actually infinite universe where X is infinity: ['-X'………., -1000, -999, …….., 0, ….. 999, 1000, ………..X].

That's not how infinity works at all. It's just [………., -1000, -999, …….., 0, ….. 999, 1000, ……….] It's not the case that the number line stop at X where X is infinity. Instead, the number line doesn't stop.

Whether there is a center is a separate question. We have started with the agreement that, from our vantage point within an expanding universe, it looks like we are in the center. If the universe expanded within the “container” of space, filling it more and more, then the only way our vantage point would look like the center is if it were the center. But that isn’t our universe. Space, the “container,” is part of the universe that is expanding. The container is expanding. Every point within space will look like the rest of the universe is expanding from it as though it is the center and this says nothing about whether we actually are in the center or not or if it makes sense to say there is a center at all.

That's why we appeal to intuition.

How does that help you?

There is no contradiction without the implication that expansion implies a boundary.

Why?

Because understanding things is good?

Sure, but that’s not what 2.2 says. “You can W and E” is not equivalent to “you don’t have to start from X to get to E”

It literally is that. What difference are you seeing "you can without..." and "you don't have to...?"

[The Tanager]

Wait what? What phrase where you searching for?

I did a couple different phrasings, but all around infinity minus infinity.

Because anything else would lead to contradictions.

Exactly! We get contradictions. When we get contradictions we throw the object out as not making sense. You go along with this here, but at other times when faced with a contradiction, you’ve said to throw out the parts that led to the contradiction to keep the object as making sense. You can’t have it both ways.

That's what the deductive proof is for.

You gave a deductive proof for a limitless thing not fitting in a limitless space? I missed that. Could you repeat it?

Where is the logical contradiction of my method?

I don't see one. It's just impossible to get a 1 to 1 match.

We say things are logically impossible if we note a logical contradiction that would keep it from happening. You don’t see any, so are you holding on to blind faith that there still is one?

Sure, but this isn't the method you presented earlier. Matching the first member of the first set (a) with the second member of the second set (2)...The second member of the first set (b) with the third member of the second set (3) and so on would leave 1 unmatched.

It is the method I presented; you cut off the ending in your latest quotes. We will get to the point where all we have in the second set left to match is the first member. If these sets have 1 to 1 correspondence, then there will be a member in the first set to match it (in finite sets we call it the last member).

So, you agree it works. Yet, when we apply it to infinite sets along with other valid matching methods, we get contradictions. But, unlike above, rather than saying 1 to 1 correspondence and infinity is “undefined” like in subtraction, you say, well, just get rid of the method you used that brought about the contradiction. This isn’t consistent.

That's not how infinity works at all. It's just [………., -1000, -999, …….., 0, ….. 999, 1000, ……….] It's not the case that the number line stop at X where X is infinity. Instead, the number line doesn't stop.

I didn’t say the number line stopped at infinity; it was an analogy to show the whole thing, in this case, stretching in infinity. The point is that what expansion means with finite numbers leads to contradictions when applied to infinity as though it is an amount as well. But, unlike above, rather than saying an infinite universe expanding is “undefined” you say, well, just change what expansion means. Well, why not change what subtraction means to avoid those contradictions? This isn’t consistent.

That's why we appeal to intuition.

The intuition about us not being in the center, right? If so, what does that do here? Every point, those in the center and those not in the center will still look like they are in the center because every vantage point looks like it does from the actual center.

But it is rational to not assume it is there. Work from there.

How does that help you?

There is no contradiction without the implication that expansion implies a boundary.

There is a difference between “don’t assume X is there” and “assume X isn’t there”. “Without the implication” is the latter. If that is what you meant above, then why think that is rational?

That it made it next to impossible for you to accept infinite math is a good reason against the implication.

Why?

Because understanding things is good?

I agree. Why is accepting an aspect of infinite mathematics that results in a contradiction “understanding things”. Yet, you won’t accept the contradictions that result from subtracting infinite math and that is also “understanding things”.

It literally is that. What difference are you seeing "you can without..." and "you don't have to...?"

If you can start at P, move through X and get to E, it’s a trivial fact that “you don’t have to start from X to get to E”. But it’s not a trivial fact that you can get to E without starting at P or X, which is what you need to show. What your previous proof showed was that you can W and E if one starts at P. But what you are trying to show is that you can W and E without starting at P or X. You haven’t shown that.

[Bust Nak]

I did a couple different phrasings, but all around infinity minus infinity.

And some one said infinity minus infinity is defined? As what exactly?

Exactly! We get contradictions. When we get contradictions we throw the object out as not making sense. You go along with this here, but at other times when faced with a contradiction, you’ve said to throw out the parts that led to the contradiction to keep the object as making sense. You can’t have it both ways.

Throwing out "infinity minus infinity" sounds like throwing out the parts that led to contradiction rather than throwing out the object. What both ways?

You gave a deductive proof for a limitless thing not fitting in a limitless space? I missed that. Could you repeat it?

I was referring to this, I've added some extra steps near the end to include stuff we've discussed since I first presented it:

1) there is a 1 to 1 match between integers and decimals. (assumption)
2) if there is a 1 to 1 match between integers and decimals, then all decimals can be ordered into a linear sequence {r1, r2, r3, ...} (premise)
3) all decimals can be ordered into a linear sequence {r1, r2, r3, ...} from (1 and 2)
4) let r0 be a decimal number constructed thus: its first digit is taken from the first digit of r1, its second digit is the second dight of r2 and so on. (define r0)
5) let r0' be a modified version of r0 where each of its digits is shifted up once. For example, 3.69 would be modified to 4.70 using this method (define r0')
6) r0' is not r1, because their first digits are different, it's not r2 because their second digits are different and so on. (from 5)
7) r0' is not in the linear sequence {r1, r2, r3.... } (from 6)
8) contradiction, therefore the assumption is false. (from 7 and 3)
9) there is no 1 to 1 match between integers and decimals. (from 1 and 8)
9.1) there is however a 1 to many match between integers and decimals. (premise)
9.2) if you can match some elements but not all, then you would run out of room (as opposed to have too much room) if you try to match the elements one to one. (premise)
10) you would run out of room if you try to match one decimal to one integer. (from 9, 9.1 and 9.2)

Think of integers as spaces you can place number in, the set of decimals is a limitless thing not fitting into that limitless space.

We say things are logically impossible if we note a logical contradiction that would keep it from happening. You don’t see any, so are you holding on to blind faith that there still is one?

I am not. No idea what you are referring to here. It's impossible to find a 1 to 1 match with these sets {0, 1} and {a, b} with this method: match 0 with a. Is there a contradiction with matching 0 with a? No, you can indeed just match 0 with a and stop there, you just won't have a match with 1 or b. Where do you see blind faith entering the picture with my example here?

It is the method I presented; you cut off the ending in your latest quotes. We will get to the point where all we have in the second set left to match is the first member...

No, we won't. The first member of the second set is always left unmatched. Are you seriously suggesting that "matching the first member of set 1 with the second of set 2 and so forth and then having a member of the first set left over to match the first member of set 1" is the same method as "matching the first member of set 1 with the second of set 2 and so forth?"

If these sets have 1 to 1 correspondence, then there will be a member in the first set to match it (in finite sets we call it the last member).

No with your method there isn't.

I didn’t say the number line stopped at infinity...

Well, that's what you wrote: ['-X'………., -1000, -999, …….., 0, ….. 999, 1000, ………..X]. X and -X are clearly at the ends of the series.

it was an analogy to show the whole thing, in this case, stretching in infinity.

Then the analogy fails, because there isn't an X at the end of infinity.

The point is that what expansion means with finite numbers leads to contradictions when applied to infinity as though it is an amount as well.

So discard the part about what expansion means!

But, unlike above, rather than saying an infinite universe expanding is “undefined” you say, well, just change what expansion means. Well, why not change what subtraction means to avoid those contradictions?

We have. If you stick to the naive meaning of subtraction when doing infinite math, you get contradictions, so we changed it to say it's undefined.

The intuition about us not being in the center, right? If so, what does that do here? Every point, those in the center and those not in the center will still look like they are in the center because every vantage point looks like it does from the actual center.

So we conclude there is no center, what's the sticking point here?

There is a difference between “don’t assume X is there” and “assume X isn’t there”. “Without the implication” is the latter. If that is what you meant above, then why think that is rational?

It's not just the latter. Think atheism; think of the difference between "believe there is no god" and "don't believe there is a god." "Without god" describe both cases.

I agree. Why is accepting an aspect of infinite mathematics that results in a contradiction “understanding things”.

It isn't. Understanding why infinite mathematics doesn't result in any contradiction is "understanding things;" understanding that an apparent contradiction is purely semantic, the result of combining incompatible definitions is "understanding things."

If you can start at P, move through X and get to E, it’s a trivial fact that “you don’t have to start from X to get to E”.

Good, that's what I was going for. You do remember challenging me to prove that you don't have to start from X to get to E, right? Sounds like this much has been resolved? You now accept that 3) does follow from my premises?

But it’s not a trivial fact that you can get to E without starting at P or X, which is what you need to show. What your previous proof showed was that you can W and E if one starts at P.

Well, my proof is supposed to prove this: "From infinity past, with no start to your counting, you can end at 'last Sunday.'" "No start" is the same thing as "without starting at P or X." I have added the extra steps to include the extra premises from my explanation for step 3:

1) for all X: you can start counting from X and end at "last Sunday." (premise)
2) for all X: there are prior members (P) before X. (premise)
2.1) For all X, if there are prior members before X, then you can start from any P and end at X. (premise)
2.2) For all X, if (you can start from any P and end at X) and (you can start counting from X and end at "last Sunday") then without starting from X you can count through X and end at "last Sunday." (premise)
2.3) For all X, you can start from any P and end at X. (from 2 and 2.1)
2.4) For all X, (you can start from any P and end at X) and (you can start counting from X and end at "last Sunday") from (2.3 and 1)
3) for all X: without starting from X you can count through X and end at "last Sunday." (from 2.2 and 2.4)
4) Without starting from any X, you can end at "last Sunday." (from 3)
5) From infinity past, with no start to your counting, you can end at "last Sunday." (from 4)

Sounds to me like you now accept all of my premises, yet you still don't think it does the job. So which steps do you think is invalid?

[The Tanager]

And some one said infinity minus infinity is defined? As what exactly?

That you could get different answers, using Hilbert’s Hotel as an example.

Throwing out "infinity minus infinity" sounds like throwing out the parts that led to contradiction rather than throwing out the object. What both ways?

You are saying we can’t do “infinity minus infinity” because of the contradictory answers. That’s not throwing out the contradictions but agreeing they are there and following that their existence leads to rejecting the ability to do “infinity minus infinity”. You are rejecting subtraction as possible with infinity; you aren’t redefining ‘subtraction.’

You want it both ways because you don’t follow this principle with “infinity expanding”. When contradictions come up you don’t reject expansion as possible with infinity, but instead try to get around the contradictions by redefining ‘expansion’. Be consistent. Either “discard the part about what [subtraction] means” (so we can get every whole number as an answer to infinity minus infinity) or accept that “infinity expanding” doesn’t make sense.

I was referring to this, I've added some extra steps near the end to include stuff we've discussed since I first presented it:

….

This still ignores what I said about “no 1 to 1 match” could mean that (a) one will run out of room or (b) “1 to 1 match” doesn’t make sense between the two sets.

To be a limitless room means that one can never run out of room within which to fit anything that has size. It’s logically impossible, by definition, to have something that doesn’t fit. This is identical to how a square circle cannot exist. Any attempt at a proof, at best, can only fool you into thinking otherwise.

I am not. No idea what you are referring to here. It's impossible to find a 1 to 1 match with these sets {0, 1} and {a, b} with this method: match 0 with a. Is there a contradiction with matching 0 with a? No, you can indeed just match 0 with a and stop there, you just won't have a match with 1 or b.

“Matching ‘0’ with ‘a’” is not a valid method for matching the members of two sets; it’s just matching two points that a set may or may not have. When deciding on valid methods, we don’t have any particular sets or members in mind. You don’t talk about a ‘0’ or an ‘a’ or whatever. You are trying to come up with a way to test any sets that will come up. My method (and the other one you gave for {0, …} and {1, …}) does this.

Where is the logical contradiction of my method?

I don't see one. It's just impossible to get a 1 to 1 match.

Where do you see blind faith entering the picture with my example here?

I addressed that comment to what I’ve quoted here, not the example I just responded to above. You see no logical contradiction, but you are still claiming it is logically impossible. On what basis?

Are you seriously suggesting that "matching the first member of set 1 with the second of set 2 and so forth and then having a member of the first set left over to match the first member of set 1" is the same method as "matching the first member of set 1 with the second of set 2 and so forth?"

No. My method was the former. You probably got confused because, at one point, I used “and so forth” to refer back to my method instead of writing it all out again.

Well, that's what you wrote: ['-X'………., -1000, -999, …….., 0, ….. 999, 1000, ………..X]. X and -X are clearly at the ends of the series.

But you understand the concept of infinity, so I figured you wouldn’t treat that as an “end” and would be able to follow the analogy. The analogy doesn’t consider that as an end.

So discard the part about what expansion means!

The opposite of what you do with “infinity minus infinity”.

So we conclude there is no center, what's the sticking point here?

Why would we conclude that? That every point looks like it would from the actual center, doesn’t say anything about whether there is an actual center point or not.

It's not just the latter. Think atheism; think of the difference between "believe there is no god" and "don't believe there is a god." "Without god" describe both cases.

Then you are describing two different concepts with the same term and then run the risk of equivocating on that term, which would be irrational. The new definition of atheism causes so much unneeded confusion; let’s not repeat that problem here.

If you want “without the implication” to refer to “don’t assume X is there,” then we don’t reach “expansion doesn’t imply a boundary” and, therefore, the possibility of a contradiction still remains. You have to say there isn’t a contradiction (not just that I don’t know if there is one or not) for your conclusion (that an infinite universe can expand) to go through.

If you want “without the implication” to refer to “assume X isn’t there,” then you are begging the question.

Either way, your conclusion doesn’t go through.

It isn't. Understanding why infinite mathematics doesn't result in any contradiction is "understanding things;" understanding that an apparent contradiction is purely semantic, the result of combining incompatible definitions is "understanding things."

If the contradiction I was pointing to was semantic, sure, but it isn’t. You are playing both sides of this with subtraction and expansion.

Well, my proof is supposed to prove this: "From infinity past, with no start to your counting, you can end at 'last Sunday.'" "No start" is the same thing as "without starting at P or X."

1) for all X: you can start counting from X and end at "last Sunday." (premise)
2) for all X: there are prior members (P) before X. (premise)
2.1) For all X, if there are prior members before X, then you can start from any P and end at X. (premise)
2.2) For all X, if (you can start from any P and end at X) and (you can start counting from X and end at "last Sunday") then without starting from X you can count through X and end at "last Sunday." (premise)
2.3) For all X, you can start from any P and end at X. (from 2 and 2.1)
2.4) For all X, (you can start from any P and end at X) and (you can start counting from X and end at "last Sunday") from (2.3 and 1)
3) for all X: without starting from X you can count through X and end at "last Sunday." (from 2.2 and 2.4)
4) Without starting from any X, you can end at "last Sunday." (from 3)
5) From infinity past, with no start to your counting, you can end at "last Sunday." (from 4)

Sounds to me like you now accept all of my premises, yet you still don't think it does the job. So which steps do you think is invalid?

What you are trying to get to is that without starting at P or X, you can move through X and reach E, right?

[Bust Nak]

That you could get different answers, using Hilbert’s Hotel as an example.

Sounds like prelude in explaining why infinity - infinity is undefined.

You are saying we can’t do “infinity minus infinity” because of the contradictory answers. That’s not throwing out the contradictions but agreeing they are there and following that their existence leads to rejecting the ability to do “infinity minus infinity”. You are rejecting subtraction as possible with infinity; you aren’t redefining ‘subtraction.’

You want it both ways because you don’t follow this principle with “infinity expanding”. When contradictions come up you don’t reject expansion as possible with infinity, but instead try to get around the contradictions by redefining ‘expansion’. Be consistent.

Okay. I see what you are getting at now. What's so inconsistent about discarding stuff to get rid of contradictions, even when the stuff I discard isn't the same in the two examples? The point is to get rid of contradictions. Minor point subjection is possible with infinity, just not specifically infinity - infinity.

This still ignores what I said about “no 1 to 1 match” could mean that (a) one will run out of room or (b) “1 to 1 match” doesn’t make sense between the two sets.

I am not ignoring it, that's why I added the extra steps. We know it make sense because matching make sense, so it's just a matter of how many you can match. We can match some but not all, hence running out of room.

To be a limitless room means that one can never run out of room within which to fit anything that has size. It’s logically impossible, by definition, to have something that doesn’t fit. This is identical to how a square circle cannot exist. Any attempt at a proof, at best, can only fool you into thinking otherwise.

You are rejecting a deductive proof because you reject its conclusion, that's not rational. The only rational reason to reject a deductive proof is because it is unsound.

“Matching ‘0’ with ‘a’” is not a valid method for matching the members of two sets; it’s just matching two points that a set may or may not have. When deciding on valid methods, we don’t have any particular sets or members in mind.

Of course we do. The method I offer gives a 1 to 1 match with the sets {0} and {a}, and therefore valid for those two sets, but isn't valid for any other sets. This means the validity of a method cannot be determined in insolation from the sets it's being used on.

I addressed that comment to what I’ve quoted here, not the example I just responded to above. You see no logical contradiction, but you are still claiming it is logically impossible. On what basis?

On the basis that the answer to the question of "is it possible to find a match for 0?" is "no, it is not possible." I suppose in a sense, you could say there is a contradiction in the form of (finding a match for 0) and not (finding a match for 0.)

No. My method was the former. You probably got confused because, at one point, I used “and so forth” to refer back to my method instead of writing it all out again.

Then by simply analyze the nature of what we are studying, without have to actually fail at applying the method to know that there is no last element in an infinite set, we can conclude your method is invalid.

But you understand the concept of infinity, so I figured you wouldn’t treat that as an “end” and would be able to follow the analogy. The analogy doesn’t consider that as an end.

Okay, so where is this "impossible to exist beyond," if I wasn't suppose to treat X as the boundary that marks the "beyond?"

The opposite of what you do with “infinity minus infinity”.

As above, either way, I am discarding things to get rid of contradictions.

Why would we conclude that? That every point looks like it would from the actual center, doesn’t say anything about whether there is an actual center point or not.

Because it is intuitive, bearing in mind what I said about probable being strongly tied together, if not synonymous.

Then you are describing two different concepts with the same term and then run the risk of equivocating on that term, which would be irrational. The new definition of atheism causes so much unneeded confusion; let’s not repeat that problem here.

It should be unambiguous with concept I was referring to after I specified don't assume it's there.

If you want “without the implication” to refer to “don’t assume X is there,” then we don’t reach “expansion doesn’t imply a boundary” and, therefore, the possibility of a contradiction still remains.

That's fine, it's still the case that the contradiction is only there when the implication is there. It doesn't matter if the implication isn't actually there, or just not assumed to be there.

If the contradiction I was pointing to was semantic, sure, but it isn’t. You are playing both sides of this with subtraction and expansion.

Why would that mean the contradiction you were pointing to was not simple semantic, which can be resolved simply by using another definition that doesn't have a built-in implication?

What you are trying to get to is that without starting at P or X, you can move through X and reach E, right?

Close enough. What I was trying to get to is this: without starting at all, you can move through X and reach E.

[The Tanager]

Okay. I see what you are getting at now. What's so inconsistent about discarding stuff to get rid of contradictions, even when the stuff I discard isn't the same in the two examples? The point is to get rid of contradictions. Minor point subjection is possible with infinity, just not specifically infinity - infinity.

The problem is that in one case you redefine a term rather than say it’s illogical or undefined and in the other case you say it’s illogical or undefined rather than redefining the term. Why you do which one seems ad hoc.

9) there is no 1 to 1 match between integers and decimals. (from 1 and 8)
9.1) there is however a 1 to many match between integers and decimals. (premise)
9.2) if you can match some elements but not all, then you would run out of room (as opposed to have too much room) if you try to match the elements one to one. (premise)
10) you would run out of room if you try to match one decimal to one integer. (from 9, 9.1 and 9.2)

This still ignores what I said about “no 1 to 1 match” could mean that (a) one will run out of room or (b) “1 to 1 match” doesn’t make sense between the two sets.

I am not ignoring it, that's why I added the extra steps. We know it make sense because matching make sense, so it's just a matter of how many you can match. We can match some but not all, hence running out of room.[/quote]

I don’t see how the extra steps account for my response. In premise 9.2, we don’t know if we can match some elements but not all because if “no 1 to 1 match” means (b), then we don’t know if the hypothesis of 9.2 is true or false.

To be a limitless room means that one can never run out of room within which to fit anything that has size. It’s logically impossible, by definition, to have something that doesn’t fit. This is identical to how a square circle cannot exist. Any attempt at a proof, at best, can only fool you into thinking otherwise.

You are rejecting a deductive proof because you reject its conclusion, that's not rational. The only rational reason to reject a deductive proof is because it is unsound.

No, I’m rejecting the proof for the reason above. I’m saying that you are wasting your time and that you might as well try to offer a deductive proof for the existence of a square circle.

Of course we do. The method I offer gives a 1 to 1 match with the sets {0} and {a}, and therefore valid for those two sets, but isn't valid for any other sets. This means the validity of a method cannot be determined in insolation from the sets it's being used on.

Methods don’t have actual members. The method you are offering should be phrased as something like: if the set has 1 member, then match that to a member (or the first member or whatever) of the second set and if the second set has remaining members, then there is no 1 to 1 correspondence. The validity of the method has to be determined in isolation from the sets it's being used on so that we won’t just ignore all the methods that fail.

Are you seriously suggesting that "matching the first member of set 1 with the second of set 2 and so forth and then having a member of the first set left over to match the first member of set 1" is the same method as "matching the first member of set 1 with the second of set 2 and so forth?"

Then by simply analyze the nature of what we are studying, without have to actually fail at applying the method to know that there is no last element in an infinite set, we can conclude your method is invalid.

My method doesn’t say anything about a last element. All it says is that there would have to be a member left over to match the first member of set 2 for 1 to 1 correspondence to be true. This is the last member of finite sets, but not having a last member doesn’t get the infinite series off the hook as the method didn’t require it to be a last member.

Okay, so where is this "impossible to exist beyond," if I wasn't suppose to treat X as the boundary that marks the "beyond?"

Nothing can exist beyond infinity. But the concept of expansion means things have reached something that wasn’t previously there.

Because it is intuitive, bearing in mind what I said about probable being strongly tied together, if not synonymous.

No, your comments assumed there was a center and concluded that it would be improbable that a specific point (rather than all other points put together) was at the center. I then added that it is actually just as probable that that specific point was the center versus any other particular point.

If you want “without the implication” to refer to “don’t assume X is there,” then we don’t reach “expansion doesn’t imply a boundary” and, therefore, the possibility of a contradiction still remains.

That's fine, it's still the case that the contradiction is only there when the implication is there. It doesn't matter if the implication isn't actually there, or just not assumed to be there.

It does matter because you are making a further claim based on no contradiction being there when all we would have is that “I don’t know” if a contradiction is there or not.

If the contradiction I was pointing to was semantic, sure, but it isn’t. You are playing both sides of this with subtraction and expansion.

Why would that mean the contradiction you were pointing to was not simple semantic, which can be resolved simply by using another definition that doesn't have a built-in implication?

I didn’t say the contradiction I was pointing to was not semantic because you are playing both sides. The second part was about how you say the proper way to understand “infinity expanding” is to semantically define away the contradiction, but the proper way to understand “infinity minus infinity” isn’t to define away the contradiction.

What you are trying to get to is that without starting at P or X, you can move through X and reach E, right?

Close enough. What I was trying to get to is this: without starting at all, you can move through X and reach E.

Here is the form of your argument:

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 P or X (or it’s equivalent “without starting at all”)
T = count through X

1) For all x: You can S and E
2) For all x: There are P
2.1) For all x: If there are P, then you can B
2.2) For all x: If you can B and S and E, then you can W and T and E
2.3) For all x: You can B
2.4) For all x: You can B and S and E
3) For all x: You can W and T and E
4) You can W and T and E
5) From infinity past with W being true, you can E

Okay, then the problem is still in 2.2. You simply asserted this as a premise, the other premises did not lead you there. I don’t agree with its truth. I don’t see why you think the truth of beginning at any P, moving through X, and ending at E means that without beginning at P or X, you can move through X and end at E.

[Bust Nak]

The problem is that in one case you redefine a term rather than say it’s illogical or undefined and in the other case you say it’s illogical or undefined rather than redefining the term. Why you do which one seems ad hoc.

I am just getting rid of whatever is causing a contradiction. A definition is causing a contradiction, get rid of it. Subtraction lead to a contradiction, get rid of it. Nothing ad hoc about that.

I don’t see how the extra steps account for my response. In premise 9.2, we don’t know if we can match some elements but not all because if “no 1 to 1 match” means (b), then we don’t know if the hypothesis of 9.2 is true or false.

We do know that because we know 1 to 1 match means having the exactly the required amount room, so no 1 to 1 match means not having the right amount of room, plus one to many match we can conclude there isn't enough room.

No, I’m rejecting the proof for the reason above. I’m saying that you are wasting your time and that you might as well try to offer a deductive proof for the existence of a square circle.

If I have one for a square circle, you bet I will be presenting it.

Methods don’t have actual members. The method you are offering should be phrased as something like: if the set has 1 member, then match that to a member (or the first member or whatever) of the second set and if the second set has remaining members, then there is no 1 to 1 correspondence.

What's wrong with naming the specific about which member I match? Why should it be phrased like that? Why can't I phrase my method as "match the first member of the first set with the second then stop" without naming actual members?

My method doesn’t say anything about a last element. All it says is that there would have to be a member left over to match the first member of set 2 for 1 to 1 correspondence to be true.

Same thing, the left over member is the last member. We can also conclude that this is invalid because it gives false positive. This method will say there is no 1 to 1 correspondence with a {0, ...} with itself.

Nothing can exist beyond infinity. But the concept of expansion means things have reached something that wasn’t previously there.

That something that wasn't there previously isn't beyond infinity though, so what's wrong with reaching that something?

No, your comments assumed there was a center and concluded that it would be improbable that a specific point (rather than all other points put together) was at the center. I then added that it is actually just as probable that that specific point was the center versus any other particular point.

So? It's still more less probable that a 6 is rolled on a dice, even when it has an equal chance of being rolled than any other number. That doesn't change anything.

It does matter because you are making a further claim based on no contradiction being there when all we would have is that “I don’t know” if a contradiction is there or not.

Why does that matter? If the implication is there then there is a contradiction, if there isn't then there isn't one. I don't want there to be one, so use the definition without out.

I didn’t say the contradiction I was pointing to was not semantic because you are playing both sides. The second part was about how you say the proper way to understand “infinity expanding” is to semantically define away the contradiction, but the proper way to understand “infinity minus infinity” isn’t to define away the contradiction.

Why doesn't saying infinity minus infinity is undefined, qualify as an example of defining away the contradiction?

Here is the form of your argument:

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 P or X (or it’s equivalent “without starting at all”)
T = count through X

1) For all x: You can S and E
2) For all x: There are P
2.1) For all x: If there are P, then you can B
2.2) For all x: If you can B and S and E, then you can W and T and E
2.3) For all x: You can B
2.4) For all x: You can B and S and E
3) For all x: You can W and T and E
4) You can W and T and E
5) From infinity past with W being true, you can E

Okay, then the problem is still in 2.2.

Try this:
W = without starting at X (no mention of P. It’s not equivalent "without starting at all")

You need two different kinds of without starting. Without starting at all doesn't enter the picture till step 5) From infinity past without starting at all (as opposed to W being true,) you can E