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]

Disagree all you like, but do you have an argument against an actual infinite, that isn't also an attack on the mathematical concept? I don't need infinite to be a number, just that it is a coherent concept.

No, you need ‘infinite’ to be a coherent concept as a number rather than as just a boundary idea. That’s where our disagreement lies.

I don't remember what specific post, but I am remember something along the lines of how can infinity be measurable and not measurable, and how can a quantity not be a specific quantity. I think these qualify as they are problematic because they don't make sense.

Any one concept as being both measurable and immeasurable (in the same context, sense, etc.) is a clear logical contradiction. It's a textbook example of the law of (non-)contradiction. As to the quantity that isn’t a specific quantity, what I said (or at least tried to say), was that I don’t understand the concept you are trying to get across by using that phrasing. That doesn’t mean it’s a contradiction; I just can’t tell if it is until I understand the terms. I told you what it sounded like to me and you have seemed to say "I don't mean that" but haven't said what you do mean; you've just kept the unexplained phrasing as though it is a logical concept.

Is the infinite you are talking about not a “whole”? Maybe you have a specific notion of “snapshot” that I don’t?

I was when speaking about infinity, but specifically, when speaking of expanding from 5 to 6. I am not because 6 is clearly not infinite.

You are wanting ‘infinite,’ here, to be a measure of the same type as 6, though. The “whole” universe has a current size (‘infinite’) and it is expanding. It’s going from ‘infinite’ to something larger than ‘infinite’. I’m reminded of my kids and when I’ll say something like I love you an infinity amount and then them responding that they love me ‘infinity plus one’. But if ‘infinite’ is unbounded, how can you go beyond a boundary to increase its size? It doesn’t make logical sense, having understood the meanings of the terms.

Is the "cannot be completed" bit integral to the concept, or a conclusion drawn from the concept? I ask because I've been arguing that endless does not imply cannot be completed. If it just part of the definition, then the question becomes, is an A-theory infinite past as example of an "actual infinite" as described here.

I think there is some miscommunication here. The A-theory infinite past does end, in the same sense of "end" in "ending a process," i.e. an endpoint as opposed to a startpoint. The past has to end, it ends at the present moment. I agree with what you stated here, so I am not sure how that is supposed to counter what I said.

Again, you are using “end” in a more narrow sense than I am in even talking about “ending a process.” An infinite series, by definition, cannot be finished/completed/entirely moved through because it just keeps going forever, whichever direction you want to think about it going off in forever (one or both “sides”).

When you then equate this idea of “finish” with the chronological idea of “end,” then you run into an unintended semantic trick that is causing you to misunderstand the issue we are talking about. It’s an equivocation that makes it seem logical for an infinite series to end, as long as that end comes on the back end rather than the front end.

So, I think “cannot be completed” is integral to the concept itself, not a conclusion drawn from it. The conclusion is that A-theory and ‘infinite past’ are logically contradictory because you must be able to finish/complete/entirely move through every element of something that cannot be finished/completed/entirely moved through.

What am I supposed to call it, if not addition when the clarification has something that wasn't there in the original thing that I was critiquing? You said by "traverse" you meant move through every element in a set, without mention reaching the endpoint. I had a reason for thinking the missing bit was not a mere oversight because at the time I was (I still am) making a huge deal about reaching the endpoint.

That’s you adding “reaching the endpoint,” not me. You added something not there, I am clarifying that it was not there; I’m subtracting what you’ve added to my definition. That you want to make a huge deal about something missing from what I said and me correcting your addition of it to what I said is hardly me adding things into the requirement. You added it, with no good reason that I can see, for doing so.

Indeed, that was the point when I was still under the impression that by "traverse" you meant only move through every element in a set, without also having to reach the end.

Not reach the endpoint(s), but “end the process” or finish/complete/entirely move through every point. You can’t reach the endpoint of something that doesn’t have an endpoint. Endpoint in the sense of either the front end or the back end, not just the back end. An infinite past has no “front end,” thus that “side” of the process never ends, all of the elements on that “side”, they go on forever, the whole process is never reached, completed, finished, ended.

I agree with all of that, but I just don't see how that answers my question. How is any of that relevant as to whether Last Monday or the present is a member of the set "infinite past" or not?

The present is what we are trying to reach. It must follow an infinite past. Thus, it cannot be a part of the infinite past. It is simpler to keep “Last Monday” as part of the infinite past since it is prior to the present. At this point we have two groups: (a) “infinite past” and (z) present. The question is whether one can reach (z) from (a) given A-theory.

But, if you want to take “Last Monday” out, then you have now created three groups: (a) “infinite past”, (x) “Last Monday” until right before the present moment, and (z) present. You then show that one can reach (z) from (x). Okay, but we were talking about reaching (z) from (a), which is a different kind of thing than (x) is.

(a) is a series that has no startpoint but has an endpoint
(x) is a series that has a startpoint and an endpoint

[Bust Nak]

No, you need ‘infinite’ to be a coherent concept as a number rather than as just a boundary idea. That’s where our disagreement lies.

I need counting to the final number in an ordered infinite set of integers to be a coherent concept, I do not need infinity to be a number (in the same sense 5 is a number) for that. I don't need that because as I said right from the get go, infinity is not a number in the same sense as the number 5: one can count to 5, but one cannot count to infinity.

As for "a number but not in the same sense 5 is a number," that much is trivial, as the phrase is intentionally vague. I can just arbitrary remove whatever feature you find problematic, even to the point of triviality, until you accept it is coherent.

Any one concept as being both measurable and immeasurable (in the same context, sense, etc.) is a clear logical contradiction. It's a textbook example of the law of (non-)contradiction.

That's the point, infinity is both measurable and immeasurable, but in different context or sense. There is a easy way out of the supposed contradiction, yet it remained a sticking point for you. That's why I accused you of dismissing it with the reason of it doesn't make sense to you.

As to the quantity that isn’t a specific quantity, what I said (or at least tried to say), was that I don’t understand the concept you are trying to get across by using that phrasing.

I am trying say that "how many stars are there?" remains a incoherent question regardless of whether the universe is finite or actually infinite. I am also saying that it is a different question to "is there a limit to the number of stars in the universe?" I am struggling to explain it because it just make trivial intuitive sense to me. I might be able to explain it better if you ask more questions.

You are wanting ‘infinite,’ here, to be a measure of the same type as 6, though. The “whole” universe has a current size (‘infinite’) and it is expanding. It’s going from ‘infinite’ to something larger than ‘infinite’. I’m reminded of my kids and when I’ll say something like I love you an infinity amount and then them responding that they love me ‘infinity plus one’. But if ‘infinite’ is unbounded, how can you go beyond a boundary to increase its size? It doesn’t make logical sense, having understood the meanings of the terms.

I don't think you do understand the meanings of the terms, the bit I bolded in particular, while 5 to 6 is getting bigger, infinity plus one is not bigger than infinity. As I said before, there are at least 3 concepts of boundary in play here. Current size (or snapshot as I called it,) the temporary one from 5 to 6, and of how big something can potentially be. There is no conflict in going beyond a boundary to increase its size (the temporary sense) of something that is unbounded (snapshot and potential sense.) The concept involve both going beyond and not going beyond the boundary, but in difference context or sense.

Again, you are using “end” in a more narrow sense than I am in even talking about “ending a process.” An infinite series, by definition, cannot be finished/completed/entirely moved through because it just keeps going forever, whichever direction you want to think about it going off in forever (one or both “sides”).

When you then equate this idea of “finish” with the chronological idea of “end,” then you run into an unintended semantic trick that is causing you to misunderstand the issue we are talking about. It’s an equivocation that makes it seem logical for an infinite series to end, as long as that end comes on the back end rather than the front end.

Okay, that is very confusing, what does "ending a process," "finishing a process," "completing a process," and "moving through the entire process" even mean, if not: going through every step of the process in order iteratively, until there are no further steps to perform (reaching just the back end, as you called it?)

So, I think “cannot be completed” is integral to the concept itself, not a conclusion drawn from it. The conclusion is that A-theory and ‘infinite past’ are logically contradictory because you must be able to finish/complete/entirely move through every element of something that cannot be finished/completed/entirely moved through.

Given the premise that "completion" is a distinct concept to "reaching just the back end," I am not completing the process by reaching just the present moment from an infinite past, so there goes your supposed contradiction with completing something that cannot be completed. There is no problem with not completing something that cannot be completed, is there?

That’s you adding “reaching the endpoint,” not me. You added something not there, I am clarifying that it was not there; I’m subtracting what you’ve added to my definition. That you want to make a huge deal about something missing from what I said and me correcting your addition of it to what I said is hardly me adding things into the requirement. You added it, with no good reason that I can see, for doing so.

Okay, you added "ending that process," I was operating under the impression that it is synonymous with "reaching the endpoint (just the back end.)" There is a good reason to equate those two, Google says ending (verb): come or bring to a final point... sounds like the reaching just back end to me.

Not reach the endpoint(s), but “end the process” or finish/complete/entirely move through every point. You can’t reach the endpoint of something that doesn’t have an endpoint. Endpoint in the sense of either the front end or the back end, not just the back end. An infinite past has no “front end,” thus that “side” of the process never ends, all of the elements on that “side”, they go on forever, the whole process is never reached, completed, finished, ended.

That sounds contradictory, you have equated ending/finishing/completing with moving through every point, they cannot possible be the same concept since you can move entirely through every point of an infinite sequence that doesn't end/finish/be completed.

The present is what we are trying to reach. It must follow an infinite past. Thus, it cannot be a part of the infinite past. It is simpler to keep “Last Monday” as part of the infinite past since it is prior to the present. At this point we have two groups: (a) “infinite past” and (z) present. The question is whether one can reach (z) from (a) given A-theory.

But, if you want to take “Last Monday” out, then you have now created three groups: (a) “infinite past”, (x) “Last Monday” until right before the present moment, and (z) present. You then show that one can reach (z) from (x). Okay, but we were talking about reaching (z) from (a), which is a different kind of thing than (x) is.

(a) is a series that has no startpoint but has an endpoint
(x) is a series that has a startpoint and an endpoint

I still don't see why it matters whether Last Monday/present moment is a member of the infinite past or not. As far as I can tell, it doesn't matter since reaching (z) from (a) is the exact same thing as reaching (z), via (x), from (a).

Why does it matter if you group (...3, 2, 1, 0) into one set {... 3, 2, 1, 0} or two sets {... 3, 2, 1}, {0}?

[The Tanager]

I need counting to the final number in an ordered infinite set of integers to be a coherent concept, I do not need infinity to be a number (in the same sense 5 is a number) for that. I don't need that because as I said right from the get go, infinity is not a number in the same sense as the number 5: one can count to 5, but one cannot count to infinity.

Here is a set: {q, w, e, r, t, y}. If one moved from one element to the next, left to right, analogically, what would you say this set is like counting to?

As for "a number but not in the same sense 5 is a number," that much is trivial, as the phrase is intentionally vague. I can just arbitrary remove whatever feature you find problematic, even to the point of triviality, until you accept it is coherent.

Sure, I could vaguely agree that at some trivial point I would be able to agree with your phrase. The question then becomes if it means anything to our discussion here. I have no idea if it does. For that, you are going to have to be less vague, laying out (at least) all the features of what you think it means to be a ‘number’.

That's the point, infinity is both measurable and immeasurable, but in different context or sense. There is a easy way out of the supposed contradiction, yet it remained a sticking point for you. That's why I accused you of dismissing it with the reason of it doesn't make sense to you.

What are the different contexts and senses? Not a vague, undefined difference, but the actual difference.

I am trying say that "how many stars are there?" remains a incoherent question regardless of whether the universe is finite or actually infinite. I am also saying that it is a different question to "is there a limit to the number of stars in the universe?" I am struggling to explain it because it just make trivial intuitive sense to me. I might be able to explain it better if you ask more questions.

I certainly think those are two different questions, but how is “how many stars are there?” an incoherent question, especially in a finite universe. Of course there is a coherent answer to that question, even if we don’t know it.

I don't think you do understand the meanings of the terms, the bit I bolded in particular, while 5 to 6 is getting bigger, infinity plus one is not bigger than infinity. As I said before, there are at least 3 concepts of boundary in play here. Current size (or snapshot as I called it,) the temporary one from 5 to 6, and of how big something can potentially be. There is no conflict in going beyond a boundary to increase its size (the temporary sense) of something that is unbounded (snapshot and potential sense.) The concept involve both going beyond and not going beyond the boundary, but in difference context or sense.

The point is that if an actually infinite “whole” is expanding, then, by the definition of what it means to expand, it would have to be getting bigger. Yet, something that is actually infinite can’t get bigger. Thus, the contradiction.

I don’t see the distinction you are making in your first and second senses of ‘boundary’ above. The temporary boundary is a move from one ‘snapshot’ to a new ‘snapshot’. The ‘snapshot’ itself doesn’t seem to be a ‘boundary’ concept. It could have reached a temporary boundary or have reached its true boundary.

Okay, that is very confusing, what does "ending a process," "finishing a process," "completing a process," and "moving through the entire process" even mean, if not: going through every step of the process in order iteratively, until there are no further steps to perform (reaching just the back end, as you called it?)

The concept is stripped of its relationship to chronology. It’s only about every member in the series being reached/counted. This could involve moving forwards, backwards, zigzag, whatever. This way, we don’t allow the semantics of order to confuse the issue.

Given the premise that "completion" is a distinct concept to "reaching just the back end," I am not completing the process by reaching just the present moment from an infinite past, so there goes your supposed contradiction with completing something that cannot be completed. There is no problem with not completing something that cannot be completed, is there?

You are “completing the process” of moving through the infinite past in order to reach the present moment. You must move through the entire infinite past before undergoing the present moment.

Okay, you added "ending that process," I was operating under the impression that it is synonymous with "reaching the endpoint (just the back end.)" There is a good reason to equate those two, Google says ending (verb): come or bring to a final point... sounds like the reaching just back end to me.

Even if the communication is wholly my fault, it’s still not me adding to the requirement, right?

That sounds contradictory, you have equated ending/finishing/completing with moving through every point, they cannot possible be the same concept since you can move entirely through every point of an infinite sequence that doesn't end/finish/be completed.

That sounds like begging the question. The question is whether you can move through every point of an infinite sequence. Your defense here is to simply assume it can be done. On the other hand, it seems to me that the definition of an infinite sequence is that the sequence just goes on forever. That’s what the “...” stands for.

I still don't see why it matters whether Last Monday/present moment is a member of the infinite past or not. As far as I can tell, it doesn't matter since reaching (z) from (a) is the exact same thing as reaching (z), via (x), from (a).

Why does it matter if you group (...3, 2, 1, 0) into one set {... 3, 2, 1, 0} or two sets {... 3, 2, 1}, {0}?

You’re right in that one doesn’t have to break the groups up; it just may help some people avoid mistakes in their logic. If I said it was required, then I was wrong.

Your logic has been that if you can get from 1 to 0, then you should be able to get from (...) to (1) to (0). That doesn’t logically follow. Reaching (z) from (a) is the exact same thing as reaching (z), via (x) from (a). That doesn’t mean one can do it. All you’ve shown, by pulling (x) out, is that we can reach (z) from (x), not that we can reach (z) from (a).

[Bust Nak]

Here is a set: {q, w, e, r, t, y}. If one moved from one element to the next, left to right, analogically, what would you say this set is like counting to?

This is like counting from 1 to 6. (Or any six consecutive numbers, forward or backwards.)

Sure, I could vaguely agree that at some trivial point I would be able to agree with your phrase. The question then becomes if it means anything to our discussion here. I have no idea if it does. For that, you are going to have to be less vague, laying out (at least) all the features of what you think it means to be a ‘number’.

Lets start with these four features: mathematically construct, represent a quantity, can be use as limits, can be operated on with certain arithmetic functions (e.g. +1.) Having said that, I'd actually rather we sidestep this part of our conversation and focus on the main point, which was whether counting to the final number in an ordered infinite set of integers is a coherent mathematical concept. I still think I don't require infinity to be a number for that discussion.

What are the different contexts and senses? Not a vague, undefined difference, but the actual difference.

You can measure an actual infinite universe in the sense of measuring the distance between two points within the universe, but cannot measure it from edge to edge.

I certainly think those are two different questions, but how is “how many stars are there?” an incoherent question, especially in a finite universe. Of course there is a coherent answer to that question, even if we don’t know it.

Sorry, that was a typo, I meant to say coherent. I was trying to say there is a coherent answer to the question in an infinite universe, and that answer is "infinite, that's how many stars there are." In contrast, "infinite, that is to say there is no limit as to how many stars there could be" is the answer to another question.

The point is that if an actually infinite “whole” is expanding, then, by the definition of what it means to expand, it would have to be getting bigger. Yet, something that is actually infinite can’t get bigger. Thus, the contradiction.

Then don't call it expanding as a whole, how about we use the phrase "expanding everywhere" instead?

I don’t see the distinction you are making in your first and second senses of ‘boundary’ above. The temporary boundary is a move from one ‘snapshot’ to a new ‘snapshot’. The ‘snapshot’ itself doesn’t seem to be a ‘boundary’ concept. It could have reached a temporary boundary or have reached its true boundary.

A snapshot of 5 and 6, is a different snapshot to the one of the universe as a whole.

The concept is stripped of its relationship to chronology. It’s only about every member in the series being reached/counted. This could involve moving forwards, backwards, zigzag, whatever. This way, we don’t allow the semantics of order to confuse the issue.

Forwards, backwards, zigzag, whatever are still orders. I am going to mash my keyboard for a bit to illustrate my point: "ksgf aab jsfbkjassjbvafwdjbavdjnb" the sequence begins with k, then s, followed by g... ending with b. Okay, so the same key appears multiple times, and many keys don't appear at all, so it isn't a great analogy of the passage of time, but lets set that aside for now. Arbitrary as it is, what do you call "first k, then s, followed by g... ending with b" if not the "order" of that sequence? I am willing to adjust my word usage to match what you say here.

You are “completing the process” of moving through the infinite past in order to reach the present moment. You must move through the entire infinite past before undergoing the present moment.

That's kind of the point. Your definition/concept of infinity is confused, at least the way I am reading you. First you say merely being endless in any direction means it cannot be completed. Here you are seemingly saying something different, that moving through the entire sequence before reaching the present moment count as completing. What is reaching the present moment, if not reaching the narrowly defined, chronological idea of "end?" Doesn't that mean "completing" must take into account the narrowly defined chronological idea of "end" rather than the wider any direction idea of "end?"

Even if the communication is wholly my fault, it’s still not me adding to the requirement, right?

Doesn't really matter. Lets move on.

That sounds like begging the question. The question is whether you can move through every point of an infinite sequence. Your defense here is to simply assume it can be done.

That much is not an assumption but a triviality. Consider counting up from 0, you won't ever reach the back end, because there is no back end. Yet there is no number you can't move through, that is to say, you can move through every number. This is why counting through every point can't be the same concept as ending the process. You need two concepts, move through every point, and reaching the back end, combined to make "ending the process."

Perhaps more to the point, I am not on the defence here. I purposely reached out to those who would go as far as to present objections against an infinite past, so I can have the easy job of picking things apart. (I stated this a while ago. I don't quite remember how that went.) Either way, what you see as simply assuming that it is possible is actually just rejecting the assumption that it is impossible. It's question begging to presume it can't be done, as part of an argument (or in the case above, integral part of a definition) against its possibility. The position I would defend is this: there are no sound argument against infinite regression, therefore it is possible.

I actually tried and had a go with an argument for infinite past appears some 6 months ago, which went along the lines of counting from ... to 0 is possible because you can construct a set of all sequences that take the from of {X ... 0}, and such a set would having endless members. I don't remember how that part of our conversation ended either.

On the other hand, it seems to me that the definition of an infinite sequence is that the sequence just goes on forever. That’s what the “...” stands for.

That part is fine, but "goes on forever" is not the same thing as cannot move through every point of an infinite sequence and then reaching just back end.

Your logic has been that if you can get from 1 to 0, then you should be able to get from (...) to (1) to (0).

No, that's not it. My logic here, is that if you can get from (...) to 1 and from 1 to 0, then you should be able to get from (...) to 1 to 0. My logic for getting from (...) to 1 is above.

[The Tanager]

Lets start with these four features: mathematically construct, represent a quantity, can be use as limits, can be operated on with certain arithmetic functions (e.g. +1.) Having said that, I'd actually rather we sidestep this part of our conversation and focus on the main point, which was whether counting to the final number in an ordered infinite set of integers is a coherent mathematical concept. I still think I don't require infinity to be a number for that discussion.

Okay. How would you define “mathematical”?

You can measure an actual infinite universe in the sense of measuring the distance between two points within the universe, but cannot measure it from edge to edge.

Two thoughts here:

1. That sounds like the same sense of “measure” to me. We can measure from point to point because both of those exist. We can’t measure from edge to edge because at least one of those “edges” doesn’t exist.

2. How is measuring the distance between two points within the universe measuring an actual infinite universe? That’s like measuring the window in a house and saying we’ve measured the house. We haven’t measured the house, but a part of the house. You haven’t measured the infinite universe but a finite part of the universe.

Sorry, that was a typo, I meant to say coherent. I was trying to say there is a coherent answer to the question in an infinite universe, and that answer is "infinite, that's how many stars there are." In contrast, "infinite, that is to say there is no limit as to how many stars there could be" is the answer to another question.

I agree those are different questions. I’m waiting to see how the first is a coherent answer, though. As of now it seems like a category mistake of saying “no boundary, that’s how many stars there are”. “No boundary” isn’t a “how many there currently are”.

The point is that if an actually infinite “whole” is expanding, then, by the definition of what it means to expand, it would have to be getting bigger. Yet, something that is actually infinite can’t get bigger. Thus, the contradiction.

Then don't call it expanding as a whole, how about we use the phrase "expanding everywhere" instead?

I don’t see how that helps. We are still talking about an object expanding, getting bigger.

A snapshot of 5 and 6, is a different snapshot to the one of the universe as a whole.

I’m not sure I’m following. There is a snapshot of the whole ‘X’ at 5 and then a different snapshot of the whole ‘X’ at 6. The infinite universe as a whole is also an ‘X’ that is bigger at one snapshot than the other one.

Forwards, backwards, zigzag, whatever are still orders. I am going to mash my keyboard for a bit to illustrate my point: "ksgf aab jsfbkjassjbvafwdjbavdjnb" the sequence begins with k, then s, followed by g... ending with b. Okay, so the same key appears multiple times, and many keys don't appear at all, so it isn't a great analogy of the passage of time, but lets set that aside for now. Arbitrary as it is, what do you call "first k, then s, followed by g... ending with b" if not the "order" of that sequence? I am willing to adjust my word usage to match what you say here.

Yes, those are all orders. What I’m saying is that the same truths (as far as ‘completing the process’ or going through every point) remain the same for all orders. Yes, the order one went through every point changes, but that the sequence can be completed or not does not change.

That's kind of the point. Your definition/concept of infinity is confused, at least the way I am reading you. First you say merely being endless in any direction means it cannot be completed. Here you are seemingly saying something different, that moving through the entire sequence before reaching the present moment count as completing. What is reaching the present moment, if not reaching the narrowly defined, chronological idea of "end?" Doesn't that mean "completing" must take into account the narrowly defined chronological idea of "end" rather than the wider any direction idea of "end?"

No. The whole series cannot be completed because, being infinite, the series contains an unending number of members one has to move through (whatever the direction of movement). Yet, on A-theory, you have to complete or move through the past in order to get to the present. Thus, the contradiction between an A-theory infinite past.

Yes, A-theory has a narrow use of the chronological “end” but this doesn’t change the application of the above principle because that principle is true regardless of direction.

That much is not an assumption but a triviality. Consider counting up from 0, you won't ever reach the back end, because there is no back end. Yet there is no number you can't move through, that is to say, you can move through every number. This is why counting through every point can't be the same concept as ending the process. You need two concepts, move through every point, and reaching the back end, combined to make "ending the process."

You can’t move through every number in the sense that there will always be more members to move through. Thus, you can’t ever complete the series. This is true whether there is only a front end, only a back end, or neither end.

Perhaps more to the point, I am not on the defence here. I purposely reached out to those who would go as far as to present objections against an infinite past, so I can have the easy job of picking things apart. (I stated this a while ago. I don't quite remember how that went.) Either way, what you see as simply assuming that it is possible is actually just rejecting the assumption that it is impossible. It's question begging to presume it can't be done, as part of an argument (or in the case above, integral part of a definition) against its possibility. The position I would defend is this: there are no sound argument against infinite regression, therefore it is possible.

Your picking apart, itself, becomes open to being picked apart. Once that happens, you are put on the defense and have a burden to bear. I’ve given arguments as to why I see an A-theory infinite past as impossible. You’ve critiqued those. You bear the burden of those critiques. If they fail, then they aren’t valid critiques and the original argument remains sound.

I actually tried and had a go with an argument for infinite past appears some 6 months ago, which went along the lines of counting from ... to 0 is possible because you can construct a set of all sequences that take the from of {X ... 0}, and such a set would having endless members. I don't remember how that part of our conversation ended either.

I didn’t think your argument was sound. I forget how we transitioned from that, too.

That part is fine, but "goes on forever" is not the same thing as cannot move through every point of an infinite sequence and then reaching just back end.

Why isn’t it the same? It goes on forever in one direction. Stripped of thought about order, the members of the series clearly “go on forever”.

No, that's not it. My logic here, is that if you can get from (...) to 1 and from 1 to 0, then you should be able to get from (...) to 1 to 0. My logic for getting from (...) to 1 is above.

Yes, you are correct. I was shortcutting it but could have said it clearer. My reasons against that logic are above.

[Bust Nak]

Okay. How would you define “mathematical”?

Just use the standard dictionary definitions. Mathematical, relating to mathematics. Mathematics, science of number, quantity, and space, either as abstract concepts ( pure mathematics ), or as applied to other disciplines such as physics and engineering.

Two thoughts here:

1. That sounds like the same sense of “measure” to me. We can measure from point to point because both of those exist. We can’t measure from edge to edge because at least one of those “edges” doesn’t exist.

2. How is measuring the distance between two points within the universe measuring an actual infinite universe? That’s like measuring the window in a house and saying we’ve measured the house. We haven’t measured the house, but a part of the house. You haven’t measured the infinite universe but a finite part of the universe.

Both of these are fine. Points that exist and edges that doesn't, part of something and the whole thing, in both cases we are talking about measuring in a different context. Nothing contradictory about can measure and cannot measure then, is there?

I agree those are different questions. I’m waiting to see how the first is a coherent answer, though. As of now it seems like a category mistake of saying “no boundary, that’s how many stars there are”. “No boundary” isn’t a “how many there currently are”.

That's the idea I was trying to get across, "no boundary" isn't a "how many there currently are" therefore "infinity" isn't saying "no boundary."

I don’t see how that helps. We are still talking about an object expanding, getting bigger.

Are we? It was infinity before the plus one, it is still infinity after the plus one. Doesn't sound like getting bigger to me.

I’m not sure I’m following. There is a snapshot of the whole ‘X’ at 5 and then a different snapshot of the whole ‘X’ at 6. The infinite universe as a whole is also an ‘X’ that is bigger at one snapshot than the other one.

Think of your house analogy above. The expansion from 5 to 6, is referring to the window. The universe as a whole is the whole house. The snapshot of the window, is a different snapshot than one of the whole house.

Yes, those are all orders. What I’m saying is that the same truths (as far as ‘completing the process’ or going through every point) remain the same for all orders. Yes, the order one went through every point changes, but that the sequence can be completed or not does not change... The whole series cannot be completed because, being infinite, the series contains an unending number of members one has to move through (whatever the direction of movement). Yet, on A-theory, you have to complete or move through the past in order to get to the present...

Same challenge as the one in a previous post, why is moving through the past in order and then getting to the present, considered of "completing the process" when it is still the case that there is an unending number of members one has to move through in the direction of movement, i.e. chronologically? (More below...)

You can’t move through every number in the sense that there will always be more members to move through.

Okay, but you can move through every number in this sense:

1) If you can count from an integer N, to N+1, then you can move through N. (defining move through)
2) You can count from 0 to 1. (premise)
3) You can move through 0. (from 1 and 2, base case)
4) If you can count from N to N+1, then you can count from N+1 to N+2. (premise)
5) If you can move through N, you can move through N + 1. (from 1 and 4, inductive step)
6) You can move through every number. (from 3 and 5, proof by mathematic induction)

So to carry on from above. When you say an infinite series "cannot be completed," and one has to "complete the process" by moving through the past in order to get to the present, you are talking about two different sense of completing. I am not completing in the sense you are talking about, since there is still an unending number of members one has to move through chronologically. But I am completing the process by moving through every member in the sense outlined in my proof, and then reaching the chronological back end. Therefore there is no contradiction with completing a process that cannot be completed.

Your picking apart, itself, becomes open to being picked apart. Once that happens, you are put on the defense and have a burden to bear. I’ve given arguments as to why I see an A-theory infinite past as impossible. You’ve critiqued those. You bear the burden of those critiques. If they fail, then they aren’t valid critiques and the original argument remains sound.

Yep, that's fine. The point is still this though: I was not just assuming infinite past is possible, I am rejecting your assumption that it is impossible. Think of that point as a follow up critique of your critique of I was just assuming. This seems like a moot point now though, since I think I am making headway in attacking the impossible to complete the incompletable claim itself.

I didn’t think your argument was sound. I forget how we transitioned from that, too.

That's okay, I'd rather focus on just picking apart arguments against its possibility.

Why isn’t it the same? It goes on forever in one direction. Stripped of thought about order, the members of the series clearly “go on forever”.

So don't strip the thought about order, that's a different sense of completing the process that does not go on forever, but ends at the back end, the narrower sense of end. Two senses of completing the process, no contradiction.

[The Tanager]

Just use the standard dictionary definitions. Mathematical, relating to mathematics. Mathematics, science of number, quantity, and space, either as abstract concepts ( pure mathematics ), or as applied to other disciplines such as physics and engineering.

Okay, so you are using ‘infinite’ as a space (since you said it’s not a number and the standard dictionary definition of quantity is “the amount or number…”, right? If so, then what does it mean to be an ordered (spatially?) infinite set of integers?

Both of these are fine. Points that exist and edges that doesn't, part of something and the whole thing, in both cases we are talking about measuring in a different context. Nothing contradictory about can measure and cannot measure then, is there?

We are talking about being able to measure the whole of an infinite universe, not about measuring the whole versus measuring a part. What are the two senses of ‘measure’ you are talking about in measuring the whole of an infinite universe? I’m saying the whole of an infinite universe can’t be measurable and immeasurable.

That's the idea I was trying to get across, "no boundary" isn't a "how many there currently are" therefore "infinity" isn't saying "no boundary."

Okay, but what is it saying instead? A number makes sense of that question, but you say infinity isn’t a number. So, what other kinds of things make sense of that question that ‘infinity’ might be that kind of thing?

Are we? It was infinity before the plus one, it is still infinity after the plus one. Doesn't sound like getting bigger to me.

So, you agree with me that the article you brought up logically contradicts itself! Something that is actually infinite isn’t expanding. So, which one do you believe science supports: that the universe is finite and expanding or infinite and not expanding?

Think of your house analogy above. The expansion from 5 to 6, is referring to the window. The universe as a whole is the whole house. The snapshot of the window, is a different snapshot than one of the whole house.

The article you brought up is talking about the whole house. It said that the universe is actually infinite and expanding. It wasn’t just talking about a “window”.

Okay, but you can move through every number in this sense:

1) If you can count from an integer N, to N+1, then you can move through N. (defining move through)
2) You can count from 0 to 1. (premise)
3) You can move through 0. (from 1 and 2, base case)
4) If you can count from N to N+1, then you can count from N+1 to N+2. (premise)
5) If you can move through N, you can move through N + 1. (from 1 and 4, inductive step)
6) You can move through every number. (from 3 and 5, proof by mathematic induction)

So to carry on from above. When you say an infinite series "cannot be completed," and one has to "complete the process" by moving through the past in order to get to the present, you are talking about two different sense of completing. I am not completing in the sense you are talking about, since there is still an unending number of members one has to move through chronologically. But I am completing the process by moving through every member in the sense outlined in my proof, and then reaching the chronological back end. Therefore there is no contradiction with completing a process that cannot be completed.

Your job isn’t done, yet. You are talking about individual numbers. You’ve got to start talking about mathematical series. How do you get to the premise that “You can move through every number in every mathematical series? Or, at the least, an infinite mathematical series.

So don't strip the thought about order, that's a different sense of completing the process that does not go on forever, but ends at the back end, the narrower sense of end. Two senses of completing the process, no contradiction.

Yes, those are two senses. Realize, however, that we were asking a question, using one sense of ‘completing the process’ and that, in answer, you changed the meaning of the term to try to get around that answer. That’s the equivocation fallacy. You realize you are making this change but then still seem to think you are answering the same question, the same sense, when you are not.

[Bust Nak]

Okay, so you are using ‘infinite’ as a space (since you said it’s not a number and the standard dictionary definition of quantity is “the amount or number…”, right?

No, I am using infinite as a quantity, aka an amount, or size.

We are talking about being able to measure the whole of an infinite universe, not about measuring the whole versus measuring a part. What are the two senses of ‘measure’ you are talking about in measuring the whole of an infinite universe? I’m saying the whole of an infinite universe can’t be measurable and immeasurable.

The whole of an infinite universe can’t be measurable in the edge to edge sense; the whole of an infinite universe can be measurable in the every part of it sense.

Okay, but what is it saying instead? A number makes sense of that question, but you say infinity isn’t a number. So, what other kinds of things make sense of that question that ‘infinity’ might be that kind of thing?

Quantity.

So, you agree with me that the article you brought up logically contradicts itself! Something that is actually infinite isn’t expanding. So, which one do you believe science supports: that the universe is finite and expanding or infinite and not expanding?

Neither, the universe is infinite and expanding, in the sense that it is expanding everywhere.

The article you brought up is talking about the whole house. It said that the universe is actually infinite and expanding. It wasn’t just talking about a “window”.

What if the house is made of nothing but windows? Think green house.

Alternatively, what if I can measure not just the windows, but also the bricks?

Your job isn’t done, yet. You are talking about individual numbers. You’ve got to start talking about mathematical series. How do you get to the premise that “You can move through every number in every mathematical series?

That's not my claim though. My claim is you can move through every number in some infinite mathematical series, namely those that have a 1:1 mapping to natural numbers.

Yes, those are two senses. Realize, however, that we were asking a question, using one sense of ‘completing the process’ and that, in answer, you changed the meaning of the term to try to get around that answer. That’s the equivocation fallacy. You realize you are making this change but then still seem to think you are answering the same question, the same sense, when you are not.

I don't know what you are talking about. You said it's impossible to complete a process that is impossible to complete. I am just pointing out that there are two sense of completing the process, so it's not a contradiction to complete a process that is impossible to complete in light of these two senses. I don't see any questions here. Suffice to say that if you asked me whether a process can be completed in the sense that is impossible to complete, I would say no.

[The Tanager]

No, I am using infinite as a quantity, aka an amount, or size.

What is the difference between a number and an amount/size?

The whole of an infinite universe can’t be measurable in the edge to edge sense; the whole of an infinite universe can be measurable in the every part of it sense.

You can measure (1) the whole of something or (2) part(s) of something. The “edge to edge” sense is (1). Your second sense above is (2). Our discussion involves (1).

Are we? It was infinity before the plus one, it is still infinity after the plus one. Doesn't sound like getting bigger to me.

So, you agree with me that the article you brought up logically contradicts itself! Something that is actually infinite isn’t expanding. So, which one do you believe science supports: that the universe is finite and expanding or infinite and not expanding?

Neither, the universe is infinite and expanding, in the sense that it is expanding everywhere.

So, it’s not expanding, but it’s expanding everywhere? How does the addition of “everywhere” change anything?

What if the house is made of nothing but windows? Think green house.

Alternatively, what if I can measure not just the windows, but also the bricks?

If the “whole” is a series of windows, then we’re talking about the sum of all windows, rather than just one window. If all the windows in your greenhouse expand in size, then the greenhouse is also expanding in size. Changing the terms doesn’t change anything. Break up the parts all you want. If all of the parts are expanding in size, then the whole is expanding in size.

Your job isn’t done, yet. You are talking about individual numbers. You’ve got to start talking about mathematical series. How do you get to the premise that “You can move through every number in every mathematical series? Or, at the least, an infinite mathematical series.

That's not my claim though. My claim is you can move through every number in some infinite mathematical series, namely those that have a 1:1 mapping to natural numbers.

In looking at this again, you did start to talk about series, so I apologize for my error there. As for your claim, yes, I’m asking you to prove that claim. Your argument doesn’t get you there. It talks about moving through every number in every finite mathematical series. Your argument covers that when we are starting at one integer and count to another integer that we can move through every integer in that series. That is not the infinite series analogical to an A-theory infinite past. What are your next steps to get rid of the “starting at one integer” part?

I don't know what you are talking about. You said it's impossible to complete a process that is impossible to complete. I am just pointing out that there are two sense of completing the process, so it's not a contradiction to complete a process that is impossible to complete in light of these two senses. I don't see any questions here. Suffice to say that if you asked me whether a process can be completed in the sense that is impossible to complete, I would say no.

But why does the second sense have anything to do with what I’m saying? I’ll grant you two senses. I’m saying I’m talking about sense (1). In sense (1), by definition, an infinite series is a process that can’t be completed. An A-theory past requires the series of past events to be completed in sense (1). Therefore, an A-theory infinite past requires a series that can’t be completed (sense 1) to be completed (sense 1). To respond that an A-theory infinite past can be completed in sense 2 is irrelevant.

[William]

[Replying to The Tanager in post #559]

So, it’s not expanding, but it’s expanding everywhere? How does the addition of “everywhere” change anything?

Is 'everywhere' that which it is expanding into? In order for something physical to expand, it requires the space in which to expand into.

It has its own space-time which is expanding eternally into another space which is 'everywhere'.