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]

Lets go there, don't you want to listen to mathematicians when thinking about quantity, counting and calculations? What reason is there to reject these assumption when it works out just fine mathematically?

It’s not that I’m not wanting to listen to mathematicians, it’s that I’m not sure you are correctly portraying what mathematicians are saying. Philosophers of math will disagree on these kinds of things, just like any area of knowledge.

Does the label "number" matter, if we agree on the features that infinity has?

No, the label doesn’t matter if we are talking about the same concept. We don’t seem to agree on the features that infinity has, though.

How do you tell the difference between the two? Is there an actual difference beyond semantics?

Yes, there is a difference between being a number and not being a number. Is “cat” a number? No, but if it were, then you could somehow do arithmetic with it.

Why this and not "in arithmetic, any number minus itself is 0 except for infinity. Well, can’t we just redefine that rule without the last clause? Not simply on the assumption that infinity isn't a number. We need to prove infinity isn't a number, not just assume it isn't and then redefine everything on the basis of that assumption?

Why this and not "there’s just different rules for finite math and infinite math. That there is something different between finite and infinite despite both being numbers?"

You don’t form original definitions with all logically possible exceptions. You form a definition and then, if needed, redefine it to better fit reality. If we follow your method, then we’ve got to put every other single concept in the exception category and then disprove them all.

Is it different though? That "adding one more star" is the same as adding one more in 5+1. Same as "add one more" in there is an infinite number of stars, adding one more star and there would still be infinite number of stars.

“Adding one more star” to a finite number of stars that has no limit to what it could be [we both agree on this aspect being true of ‘infinity’] is different from adding one more to five actual stars known to exist. In the former, we have one more actual star and still the same “no limit” what how many there could be…the limit isn’t one bigger. In the latter, we have one more actual star.

First of all, do you now accept that according to current scientific thought, the universe is an actual infinite (as opposed finite in size but no limit as to how big it can get?) There is no conflict between not having a boundary and expanding, infinity + 1 is still infinity.

No, I don’t accept that according to current scientific thought, the universe is actually infinite. I’m not convinced the site’s explanation you gave either (1) is current scientific thought (as if there is agreement among scientists anyway) or (2) technically precise. Surely, current scientific thought isn’t okay with logical contradictions of something with no boundary expanding being that previous boundary that isn’t a boundary.

Okay, there might be, but what reason do you have for thinking there has to be one? Remember, your original contention was that "given an actually infinite universe" might be an incoherent statement like a married bachelor.

For the various reasons we’ve been talking about.

Right, but you accept there is no true definition as such? You said definitions should be based on truth, not popularity; but it's just a matter of convention, agreed upon for the sake of communication.

I do think there is an objective truth about the concept we call ‘infinity’ and, therefore, a true definition does exist.

I can work with that. Going back to your earlier point, you said if one was able to move from left to right most end then one should be able to move from right to left most end. No, the left most end does not exist, so you shouldn't be able to. It's still the case that direction matters, it's still the case that traversal is not reversible.

You are still misunderstanding my points because you keep using the more narrow sense of ‘end’ as “an endpoint.” If you think an infinite set with no end-point on one side cannot be traversed by its very definition, then an A-theory infinite past cannot be traversed and, thus, you would be agreeing with me that we can’t get to the present moment with an A-theory infinite past.

While we are here, I thought we agreed to exclude the present moment and focus only on the past? We are traversing the infinite past to Monday the 17th of Jan 2022, or just call it "Monday." I don't want to revisit the red herring of whether present moment treated as if it is a member of the infinite past or not.

Perhaps I had a typo? because I didn’t mean to exclude the present moment. This whole discussion is about traversing an infinite past so we can reach the present moment. The separation of the present moment out is absolutely not a red herring, but vital to the whole conversation.

No, there isn't. I asked you this before, where are you getting this infinite step/gap idea from? There is no such gap in an infinite past, therefore false analogy.

By the very definitions of the concepts. Step 1 is traversing the infinite past…i.e., the infinite “step/gap” prior to the present moment (step 2).

Why would it be logically impossible though, why would it be akin to a square circle? I kept asking you why, and that's what lead you to the "if there is an infinite gap then..." conditional statement. Well, what if there isn't? Then it wouldn't be akin to a square circle.

Correct…if there isn’t an infinite gap/step, then it wouldn’t be akin. But, by definition, there is that infinite gap/step, so the conditional statement is fulfilled.

No it isn't. An ceaseless series can have either zero or one end. It would only be logically impossible to get to the point of easing in an ceaseless series with zero ends. Why would it be impossible for those ceaseless series one end?

You are still equivocating on “end” here. I’m talking about how the series of past events would stretch on forever, whatever direction you want to think about it in. One cannot, by definition, get to where there is nothing left to do in the series. Thus, the series is ceaseless, whether you have a “zero or one end.”

[Bust Nak]

It’s not that I’m not wanting to listen to mathematicians, it’s that I’m not sure you are correctly portraying what mathematicians are saying. Philosophers of math will disagree on these kinds of things, just like any area of knowledge.

Well, the following is very well defined: cardinality is the size of a set, and transfinite cardinal numbers are the sizes of infinite sets. I think most mathematician accept that. Do you think I am not portraying them correctly when I say infinite sets are a thing in math and they have a size?

No, the label doesn’t matter if we are talking about the same concept. We don’t seem to agree on the features that infinity has, though.

Right, so going back to my last point, do you accept that "infinity is a number except you can't count to it" and "infinity is not a number because you can't count to it" is not worth debating about, given that the reason is the same? Last I checked the reason you gave for infinity not being a number, works as reason for "infinite is a number except..."

Yes, there is a difference between being a number and not being a number. Is “cat” a number? No, but if it were, then you could somehow do arithmetic with it.

And how would you do arithmetic with it, what is that "somehow?" Point being that math does not just leave it as "somehow" but tell you exactly how (and how not to,) because it makes sense to treat infinity that way, the math works and you can draw useful real life conclusion using infinity that way.

You don’t form original definitions with all logically possible exceptions. You form a definition and then, if needed, redefine it to better fit reality.

Okay, the let my change my argument to: it's been redefine to better fit reality, don't undefined it back just to exclude infinity as a number.

“Adding one more star” to a finite number of stars that has no limit to what it could be [we both agree on this aspect being true of ‘infinity’] is different from adding one more to five actual stars known to exist. In the former, we have one more actual star and still the same “no limit” what how many there could be…the limit isn’t one bigger. In the latter, we have one more actual star.

So the results aren't the same, but why would that make the "adding one more star" bit different? Surely the "adding one more star" bit is the arithmetic.

No, I don’t accept that according to current scientific thought, the universe is actually infinite. I’m not convinced the site’s explanation you gave either (1) is current scientific thought (as if there is agreement among scientists anyway) or (2) technically precise. Surely, current scientific thought isn’t okay with logical contradictions of something with no boundary expanding being that previous boundary that isn’t a boundary.

Okay, even if you don't accept that it is the consensus. You can clearly see that scientists are seriously considering an actual infinite universe, same can be said for much of history, with philosophers dealing with whether the universe was eternal or not. That should still be enough to show that it cannot be discarded as a trivial logical contradiction. As for the supposed contradiction, why are you associating expansion with a boundary in the first place?

For the various reasons we’ve been talking about.

All of which, by my count, has been addressed, is being addressed. Just to double check, anything missing from this list of reasons? The conversation has gone on for some time.
Infinite sets can't be unmeasurable and measurable.
The size of infinite sets can't be a matter of quantity and not be a specific quantity.
If a series can be traverse in one direction then it can be from the other direction.
Infinite gap.

I do think there is an objective truth about the concept we call ‘infinity’ and, therefore, a true definition does exist.

We can't talk about the concept we call "infinity" until we have a definition of what infinity is. Any objective truth about the concept, flows from the definition. Consider this example, ancient Semites were not incorrect for classifying bats as "birds," they just have a different definition for birds than we do, even if objectively bats are closer to rodents than to birds biologically.

You are still misunderstanding my points because you keep using the more narrow sense of ‘end’ as “an endpoint.”

I have no idea what you mean by the wider sense of "end." You spoke of ceaseless, that's still an appeal to endpoints - lacking an endpoint in a particular direction makes a series ceaseless. So what if I am use "end" in a different way that you are using? My argument for the importance of direction still holds, I could have use the term "cap" or "finale" or "terminal," my argument does not rely on precise semantics.

If you think an infinite set with no end-point on one side cannot be traversed by its very definition, then an A-theory infinite past cannot be traversed and, thus, you would be agreeing with me that we can’t get to the present moment with an A-theory infinite past.

I've made it very clear that I don't think that, an infinite series with no end-point on one side can be traversed in one direction.

Perhaps I had a typo? because I didn’t mean to exclude the present moment. This whole discussion is about traversing an infinite past so we can reach the present moment. The separation of the present moment out is absolutely not a red herring, but vital to the whole conversation.

While traversing an infinite past so we can reach the present moment is vital to the whole conversation, whether present moment should be counted as part of the past or not is irrelevant. It is a red herring because of this trivial argument:

1) we can traverse an infinite past to reach Monday the 17th.
2) we can traverse a finite gap between Monday the 17th and the present moment, to reach the present moment.
3) therefore we can traverse an infinite past to reach the present moment.

Presumably, you accept that the argument is valid, and accept premise 2. All that needs discussing is premise 1. As long as you can reach "Monday" you can reach the present, regardless of whether the present moment is a member of the past or not. You voiced your agreement a few weeks ago.

By the very definitions of the concepts. Step 1 is traversing the infinite past…i.e., the infinite “step/gap” prior to the present moment (step 2).

You are just repeating the same falsehood. Traversing the infinite past does not involve any sort of infinite "gap." One infinite "step" is fine as long as it is countable and in the right direction.

Correct…if there isn’t an infinite gap/step, then it wouldn’t be akin. But by definition, there is that infinite gap/step, so the conditional statement is fulfilled

But nothing, there is no such thing as an infinite gap in an infinite past. I don't know what exactly are the definitions you are appealing to here, but even the stuff you said about the amount of members in an infinite set not ending by definition makes no mention of gaps.

You are still equivocating on “end” here. I’m talking about how the series of past events would stretch on forever, whatever direction you want to think about it in. One cannot, by definition, get to where there is nothing left to do in the series. Thus, the series is ceaseless, whether you have a “zero or one end.”

Okay, so now the argument become whether an infinite past fits the definition of "ceaseless" or not. It does not because there is no infinite gap to stop one from getting to the point where there is nothing left to do in the series.

[The Tanager]

Well, the following is very well defined: cardinality is the size of a set, and transfinite cardinal numbers are the sizes of infinite sets. I think most mathematician accept that. Do you think I am not portraying them correctly when I say infinite sets are a thing in math and they have a size?

I think mathematicians, especially drawing on Cantor, have made infinite sets axiomatic and, from there, are speaking about conceptual truths of what infinite math would be like but haven’t established that these pick out truths about reality.

Right, so going back to my last point, do you accept that "infinity is a number except you can't count to it" and "infinity is not a number because you can't count to it" is not worth debating about, given that the reason is the same? Last I checked the reason you gave for infinity not being a number, works as reason for "infinite is a number except..."

It’s not worth debating as long as later equivocations do not happen with those terms.

Okay, the let my change my argument to: it's been redefine to better fit reality, don't undefined it back just to exclude infinity as a number.

Yes, but definitions and re-definitions need to have support for doing so. The support will be different for a definition of Frodo Baggins made up by Tolkien versus discovering a truth about reality, such as mathematics, what a "cat" is, etc.

“Adding one more star” to a finite number of stars that has no limit to what it could be [we both agree on this aspect being true of ‘infinity’] is different from adding one more to five actual stars known to exist. In the former, we have one more actual star and still the same “no limit” what how many there could be…the limit isn’t one bigger. In the latter, we have one more actual star.

So the results aren't the same, but why would that make the "adding one more star" bit different? Surely the "adding one more star" bit is the arithmetic.

The difference is that you are talking about adding one more star to an infinity of actually existing stars.

Okay, even if you don't accept that it is the consensus. You can clearly see that scientists are seriously considering an actual infinite universe, same can be said for much of history, with philosophers dealing with whether the universe was eternal or not. That should still be enough to show that it cannot be discarded as a trivial logical contradiction.

I’m not trivially discarding it. I’ve spent many words supporting my claims. That shows I’m taking it seriously.

As for the supposed contradiction, why are you associating expansion with a boundary in the first place?

When you expand something from 5 feet to 6 feet, you’ve crossed a “boundary” that the thing had not previously crossed (in this case, 5 feet). An expansion logically requires moving past a previous boundary since it was smaller than it is now.

All of which, by my count, has been addressed, is being addressed. Just to double check, anything missing from this list of reasons? The conversation has gone on for some time.
Infinite sets can't be unmeasurable and measurable.
The size of infinite sets can't be a matter of quantity and not be a specific quantity.
If a series can be traverse in one direction then it can be from the other direction.
Infinite gap.

That’s probably a good summation. I don’t have the time to check back on all of the wordings and see if I’d add something else.

We can't talk about the concept we call "infinity" until we have a definition of what infinity is. Any objective truth about the concept, flows from the definition. Consider this example, ancient Semites were not incorrect for classifying bats as "birds," they just have a different definition for birds than we do, even if objectively bats are closer to rodents than to birds biologically.

I agree. As of right now, we have “infinity” as a boundary concept and “infinity” as a numerical concept. I’m convinced the former is relevant to the reality of our discussion. I’m not convinced the second concept is.

I have no idea what you mean by the wider sense of "end." You spoke of ceaseless, that's still an appeal to endpoints - lacking an endpoint in a particular direction makes a series ceaseless. So what if I am use "end" in a different way that you are using? My argument for the importance of direction still holds, I could have use the term "cap" or "finale" or "terminal," my argument does not rely on precise semantics.

I’m not talking about the terms but the concepts picked out by them. Take [1, 2, 3, 4, 5] and [...1, 2, 3, 4, 5,...]. Both of these have ends/sides (in my sense), while only the former has endpoints.

I've made it very clear that I don't think that, an infinite series with no end-point on one side can be traversed in one direction.

For an entire set to be traversed, every member would have been “reached”. That means the “end” of both “sides” of the set would have to be “reached”. If you only think endpoints are things that can be reached, then the set isn’t fully traversed.

While traversing an infinite past so we can reach the present moment is vital to the whole conversation, whether present moment should be counted as part of the past or not is irrelevant. It is a red herring because of this trivial argument:

1) we can traverse an infinite past to reach Monday the 17th.
2) we can traverse a finite gap between Monday the 17th and the present moment, to reach the present moment.
3) therefore we can traverse an infinite past to reach the present moment.

Presumably, you accept that the argument is valid, and accept premise 2. All that needs discussing is premise 1. As long as you can reach "Monday" you can reach the present, regardless of whether the present moment is a member of the past or not. You voiced your agreement a few weeks ago.

All you’ve done is re-termed the “present” to "Monday the 17th" as that which is preceded by an "infinite past". The same reasoning still applies. Using “the present” instead of a specific date is an attempt to avoid confusion since we are talking about an infinite "past"; thus using only the general terms "past" and "present". It doesn’t matter what actual date we are talking about with an infinite past.

But nothing, there is no such thing as an infinite gap in an infinite past. I don't know what exactly are the definitions you are appealing to here, but even the stuff you said about the amount of members in an infinite set not ending by definition makes no mention of gaps.

The “definitions” in the sense of what we've said about these concepts; I haven't, and am not interested in trying to, formalize it in a succinct dictionary entry definition at the moment. If an infinite past precedes the present moment (or Monday the 17th or whatever date you want to talk about), then there is an infinite gap/step and then the present/last Monday/etc.

[Bust Nak]

I think mathematicians, especially drawing on Cantor, have made infinite sets axiomatic and, from there, are speaking about conceptual truths of what infinite math would be like but haven’t established that these pick out truths about reality.

That doesn't really answer my question, I did not ask if they have established infinite math reflect truths about reality or not; I ask you if I was misrepresenting them when I said infinite sets have a size in math.

Yes, but definitions and re-definitions need to have support for doing so. The support will be different for a definition of Frodo Baggins made up by Tolkien versus discovering a truth about reality, such as mathematics, what a "cat" is, etc.

The math works isn't good enough support for you?

The difference is that you are talking about adding one more star to an infinity of actually existing stars.

As opposed to adding one more star to a finite amount of actually existing stars? What is the difference other than one more star to 5 stars is 6 stars, while one more start to infinite stars is infinite stars?

I’m not trivially discarding it. I’ve spent many words supporting my claims. That shows I’m taking it seriously.

Measurable vs immeasurable, quantity but not a specific quantity sound like a trivial contradiction to me.

When you expand something from 5 feet to 6 feet, you’ve crossed a “boundary” that the thing had not previously crossed (in this case, 5 feet). An expansion logically requires moving past a previous boundary since it was smaller than it is now.

The gap between point A and point B was 5 feet, now it's 6 feet, space has expanded and yet does not refer to boundary at all.

I agree. As of right now, we have “infinity” as a boundary concept and “infinity” as a numerical concept. I’m convinced the former is relevant to the reality of our discussion. I’m not convinced the second concept is.

If you are going to dismiss actual infinity as a concept, then why are you even entertaining the idea of an infinite past?

I’m not talking about the terms but the concepts picked out by them. Take [1, 2, 3, 4, 5] and [...1, 2, 3, 4, 5,...]. Both of these have ends/sides (in my sense), while only the former has endpoints.

I can work with that, you stated that if one could traverse an infinite past moving from past end to present end then it should be traversable from the present end to past end. Traverse mean reaching the endpoint, there is only one endpoint at the present end, so it is not the case that traversing is reversible.

For an entire set to be traversed, every member would have been “reached”. That means the “end” of both “sides” of the set would have to be “reached”. If you only think endpoints are things that can be reached, then the set isn’t fully traversed.

If you can reach the endpoints from the other end then why wouldn't every member be reached too? You think traversing the infinite past would involve some sort of skipping over of elements?

All you’ve done is re-termed the “present” to "Monday the 17th" as that which is preceded by an "infinite past". The same reasoning still applies. Using “the present” instead of a specific date is an attempt to avoid confusion since we are talking about an infinite "past"; thus using only the general terms "past" and "present". It doesn’t matter what actual date we are talking about with an infinite past.

The actual date doesn't matter, but are you suggesting that Monday isn't part of the infinite past?

The “definitions” in the sense of what we've said about these concepts; I haven't, and am not interested in trying to, formalize it in a succinct dictionary entry definition at the moment. If an infinite past precedes the present moment (or Monday the 17th or whatever date you want to talk about), then there is an infinite gap/step and then the present/last Monday/etc.

Why? That is a non-sequitur. How are you getting from the premise "an infinite past precedes the present moment" to your conclusion that "there is an infinite gap?" Are gaps and steps the same thing to you?

[The Tanager]

That doesn't really answer my question, I did not ask if they have established infinite math reflect truths about reality or not; I ask you if I was misrepresenting them when I said infinite sets have a size in math.

We are talking about infinite sets in reality, not just as concepts in math. Your argument treats those concepts as truths about reality. So, yes, I think you are misunderstanding what mathematicians are saying in relation to what we are talking about.

The math works isn't good enough support for you?

When we are talking about things existing in reality rather than mathematical concepts, yes.

As opposed to adding one more star to a finite amount of actually existing stars? What is the difference other than one more star to 5 stars is 6 stars, while one more start to infinite stars is infinite stars?

The difference is you have not established that infinity is a number in that way. What you are doing is akin to saying that adding 1 more star to a cat of stars gives us a cat of stars.

Measurable vs immeasurable, quantity but not a specific quantity sound like a trivial contradiction to me.

It doesn’t to me for the reasons I’ve given.

The gap between point A and point B was 5 feet, now it's 6 feet, space has expanded and yet does not refer to boundary at all.

Just because you don’t refer to it doesn’t mean it isn’t there. The gap temporarily was bounded, had a boundary at 5 feet, which it was not larger than. By the very nature of what it means to expand, the gap has crossed that previous “boundary” and it is now bounded at 6 feet. It could expand further.

If you are going to dismiss actual infinity as a concept, then why are you even entertaining the idea of an infinite past?

What do you mean by "dismiss"? If you mean it in the sense of "treat as unworthy of serious consideration," then I’m not dismissing it as a concept. I’m analyzing it and then seeing that it doesn’t make sense and, therefore, concluding that such a thing doesn’t exist in reality. To do that, I must first entertain the idea.

I can work with that, you stated that if one could traverse an infinite past moving from past end to present end then it should be traversable from the present end to past end. Traverse mean reaching the endpoint, there is only one endpoint at the present end, so it is not the case that traversing is reversible.

If you can move through every element in a set (what I mean by ‘traverse’), why does it matter which order you do it in? You can go right to left, left to right, or skip around. You either can move through every element or you cannot. In this way, traversing means reaching both sides of the set. When a set doesn’t end on one side (whatever direction or path one took to try to get there) it cannot be traversed, by definition. The A-theory infinite past cannot be traversed, by definition, and, thus, the present could never be reached.

The actual date doesn't matter, but are you suggesting that Monday isn't part of the infinite past?

Any Monday prior to March 4, 2022, of course, is part of the infinite past to us. The point is that picking a date in the past doesn't change anything. Yes, you can note a finite distance between one moment in the past and the present. But you've still got to worry about the infinite amount of events prior to that Monday now. How could you reach that day if the past was infinite prior to it? The exact same issues come up. All you've done is trick yourself into thinking you've shown this present moment can be reached, when you've kicked the actual problem, in the first place, back as though that solves anything.

Why? That is a non-sequitur. How are you getting from the premise "an infinite past precedes the present moment" to your conclusion that "there is an infinite gap?" Are gaps and steps the same thing to you?

For this part of our conversation, they are terms denoting the same concept. In A-theory, you have to move through, step across, traverse the gap that is the past before you can reach the present moment. If that step/gap is infinite, how can you traverse it?

[Bust Nak]

We are talking about infinite sets in reality, not just as concepts in math. Your argument treats those concepts as truths about reality. So, yes, I think you are misunderstanding what mathematicians are saying in relation to what we are talking about.

You have the wrong end of the stick, I am presenting concepts in math as support that infinity isn't contradictory - i.e. merely possible, coherent concepts to talk about. Look at the title of this thread - it makes a claim about impossibility, I am addressing that claim, saying it is possible, as opposed to it is the case in reality. I asked you to join this thread because you've made similar claim about it being impossible, there is a huge difference between possibility and actuality.

When we are talking about things existing in reality rather than mathematical concepts, yes.

How about when we are talking about things that could potentially exist in reality?

The difference is you have not established that infinity is a number in that way. What you are doing is akin to saying that adding 1 more star to a cat of stars gives us a cat of stars.

The adding part is still the same though even in your example.

It doesn’t to me for the reasons I’ve given.

The one reason is it doesn't make sense to you.

Just because you don’t refer to it doesn’t mean it isn’t there. The gap temporarily was bounded, had a boundary at 5 feet, which it was not larger than. By the very nature of what it means to expand, the gap has crossed that previous “boundary” and it is now bounded at 6 feet. It could expand further.

Well, there you go, there is a boundary (the temporary one that expanded from 5 to 6,) yet no boundary (of how big a snapshot of the whole thing is,) nor boundary (of how big the gap can potentially be,) no contradictions here, just a single word used for three different concepts.

What do you mean by "dismiss"? If you mean it in the sense of "treat as unworthy of serious consideration," then I’m not dismissing it as a concept. I’m analyzing it and then seeing that it doesn’t make sense and, therefore, concluding that such a thing doesn’t exist in reality. To do that, I must first entertain the idea.

But your analysing begin with traversing an actual infinity is impossible "by definition." How seriously can you possibility be when considering traversing a set that cannot be traverse by definition?

If you can move through every element in a set (what I mean by ‘traverse’), why does it matter which order you do it in? You can go right to left, left to right, or skip around. You either can move through every element or you cannot. In this way, traversing means reaching both sides of the set. When a set doesn’t end on one side (whatever direction or path one took to try to get there) it cannot be traversed, by definition.

Why not? I tried to pin you down on a definition before, and you just told me it's part of the concept. I told you why the order matters, it is because of the endpoints. If you are disregarding the matter of endpoints, then why would you even suggest that a set cannot be traversed in the first place? The answer to "can you count to infinity" becomes a simple "yes," if you don't care about endpoints, because of the fact that you can count from zero to every single integer, AKA moving through every element in a set.

Any Monday prior to March 4, 2022, of course, is part of the infinite past to us. The point is that picking a date in the past doesn't change anything. Yes, you can note a finite distance between one moment in the past and the present. But you've still got to worry about the infinite amount of events prior to that Monday now.

That's right, but earlier you made an objection on whether the present moment was part of the infinite past of not, the whole point of picking a date was to address that one objection. Whether you can reach Monday or not, is the exact same debate as whether you can reach the present moment or not. I wouldn't have went on this tangent had you not complained that I was treating the present moment as a member of the infinite past.

How could you reach that day if the past was infinite prior to it?

By iterating through each and every single one of those infinite days, one day at a time.

All you've done is trick yourself into thinking you've shown this present moment can be reached, when you've kicked the actual problem, in the first place, back as though that solves anything.

There is no trick, recall if you will, I stated that all that needs discussing is premise 1: "we can traverse an infinite past to reach Monday the 17th."

For this part of our conversation, they are terms denoting the same concept. In A-theory, you have to move through, step across, traverse the gap that is the past before you can reach the present moment. If that step/gap is infinite, how can you traverse it?

See above.

[The Tanager]

You have the wrong end of the stick, I am presenting concepts in math as support that infinity isn't contradictory - i.e. merely possible, coherent concepts to talk about. Look at the title of this thread - it makes a claim about impossibility, I am addressing that claim, saying it is possible, as opposed to it is the case in reality. I asked you to join this thread because you've made similar claim about it being impossible, there is a huge difference between possibility and actuality.

We aren’t talking about the impossibility of an actual infinite as a mathematical concept, though. We are talking about the impossibility of an actual infinite of past events in reality, given the A-theory of time. That context changes things.

I’m not arguing that an actual infinite is inherently an incoherent mathematical concept. It isn’t, by definition, given it’s axiomatic nature within infinite mathematics. The question is whether infinite mathematics has anything to do with the reality of an A-theory infinite past. That is what I’m arguing is seemingly contradictory.

The adding part is still the same though even in your example.

The adding part is only the same if it’s not a category mistake. You need to establish that adding is something that can be done in this situation.

It doesn’t to me for the reasons I’ve given

The one reason is it doesn't make sense to you.

No, I’ve explained why it doesn’t make sense to me.

Well, there you go, there is a boundary (the temporary one that expanded from 5 to 6,) yet no boundary (of how big a snapshot of the whole thing is,) nor boundary (of how big the gap can potentially be,) no contradictions here, just a single word used for three different concepts.

If I’m understanding you correctly, when talking about expanding from 5 to 6, I meant it in the whole snapshot kind of way.

But your analysing begin with traversing an actual infinity is impossible "by definition." How seriously can you possibility be when considering traversing a set that cannot be traverse by definition?

‘Married bachelor’ is impossible because of what ‘married’ and ‘bachelor’ mean. Until you analyze what the terms mean, you wouldn’t know it is incoherent to put them together. It’s the same here. I’ve been listening to and working with you on analyzing the various terms involved that go into finding out if “traversing an actual infinity” is possible or not. That’s as serious as one can take it.

Why not? I tried to pin you down on a definition before, and you just told me it's part of the concept. I told you why the order matters, it is because of the endpoints. If you are disregarding the matter of endpoints, then why would you even suggest that a set cannot be traversed in the first place? The answer to "can you count to infinity" becomes a simple "yes," if you don't care about endpoints, because of the fact that you can count from zero to every single integer, AKA moving through every element in a set.

Traversing something means you end the process of movement through it; you have traversed it and now you can be onto something else. If the set never ends, how can you end that process? It’s clearly illogical. It’s simply part of the concept of what it means to end and not end. You can’t have a non-ending thing end. Just like you can’t have a married unmarried person.

Even if the set ends on one side, it still doesn’t end on the other. It doesn’t matter what order one moves in, one part of the set is unending or ongoing. An unending/ongoing thing cannot end by very clear definition. I’m just working with the words here.

As to counting to infinity, you have to first show that infinity is an integer. You haven’t established that.

That's right, but earlier you made an objection on whether the present moment was part of the infinite past of not, the whole point of picking a date was to address that one objection. Whether you can reach Monday or not, is the exact same debate as whether you can reach the present moment or not. I wouldn't have went on this tangent had you not complained that I was treating the present moment as a member of the infinite past.

Yes, but in moving from ‘present’ to ‘last Monday’ you now have an infinite past prior to ‘last Monday’ to deal with. ‘Last Monday’ now can’t be treated as part of that infinite past even though it’s part of the infinite past in relation to today. You are right back to the same problem you tried to get away from.

By iterating through each and every single one of those infinite days, one day at a time.

That’s like saying “I can make a square circle” by just adding corners to the circle.

[Bust Nak]

We aren’t talking about the impossibility of an actual infinite as a mathematical concept, though. We are talking about the impossibility of an actual infinite of past events in reality, given the A-theory of time. That context changes things.

I’m not arguing that an actual infinite is inherently an incoherent mathematical concept. It isn’t, by definition, given it’s axiomatic nature within infinite mathematics. The question is whether infinite mathematics has anything to do with the reality of an A-theory infinite past. That is what I’m arguing is seemingly contradictory.

What things do the context changes? What argument do you have against the possibility A-theory infinite past, that doesn't also apply to the mathematical concept? Point being, if an argument that applies to the mathematical concept, fails to prove the mathematical concept impossible, then it doesn't work in proving the infinite past impossible. Last I checked, traversing an infinite past is exactly the same conceptually as the mathematical counting down through every single integer to zero (or count up through negative integers to zero.)

The adding part is only the same if it’s not a category mistake. You need to establish that adding is something that can be done in this situation.

It could be done because it is done in math.

No, I’ve explained why it doesn’t make sense to me.

You've pointed out some features, but why are they problematic, other than not making sense to you?

If I’m understanding you correctly, when talking about expanding from 5 to 6, I meant it in the whole snapshot kind of way.

How can it be the whole snapshot when then context is an infinite universe?

‘Married bachelor’ is impossible because of what ‘married’ and ‘bachelor’ mean. Until you analyze what the terms mean, you wouldn’t know it is incoherent to put them together. It’s the same here. I’ve been listening to and working with you on analyzing the various terms involved that go into finding out if “traversing an actual infinity” is possible or not. That’s as serious as one can take it.

So tell me what "infinite" and "traverse" mean in general, even if you don't want to be tried down to a definition, that makes it incoherent to put them together. More importantly what makes these meanings, "the real meaning" so to speak.

Traversing something means you end the process of movement through it;

How can you possibly reference "end the process" at the same time as dismissing the importance of the presence of an endpoint? Earlier you complained that I was using the narrow sense of "end," but you are doing the same thing, here you are taking about ending the process, as in the directional, finish, complete, or terminate; as opposed to the wider meaning that is agnostic on direction, include the meaning related to a beginning.

you have traversed it and now you can be onto something else. If the set never ends, how can you end that process? It’s clearly illogical. It’s simply part of the concept of what it means to end and not end. You can’t have a non-ending thing end. Just like you can’t have a married unmarried person.

You can't, but that's moot, because the process in question - the A theory infinite past does end, in the same sense of "end" in "ending a process."

Even if the set ends on one side, it still doesn’t end on the other. It doesn’t matter what order one moves in, one part of the set is unending or ongoing. An unending/ongoing thing cannot end by very clear definition. I’m just working with the words here.

It clearly does matter because it ends in one direction but not in the other, whether it is an "unending/ongoing thing" or not depends solely on whether there is an endpoint in the direction one moves in. You are conflating the two meanings of "end." "Unending/ongoing" appeals to the directional meaning of end, where as "it still doesn't end" appeals tot he non-directional meaning of end.

As to counting to infinity, you have to first show that infinity is an integer. You haven’t established that.

Why does that matter when I can count to it, given the assumption that the presence of an endpoint doesn't matter? At worse that just open up the scenario of counting to a non-integer. But this part is now moot too, I only brought up counting to infinity because previously you said moving through every element in a set was what you mean by "traverse;" this latest post added "end the process" into the requirement.

Yes, but in moving from ‘present’ to ‘last Monday’ you now have an infinite past prior to ‘last Monday’ to deal with. ‘Last Monday’ now can’t be treated as part of that infinite past even though it’s part of the infinite past in relation to today. You are right back to the same problem you tried to get away from.

Remind me, why is it a problem in the first place, the question has always been whether an infinite past can be traversed or not, why is whether a particular item an element in that set or not relevant in answering that question?

That’s like saying “I can make a square circle” by just adding corners to the circle.

Is it like that though, why would the presence of an endpoint or lack there of, changes how traversing work?

[The Tanager]

I didn't directly respond to every quote, but I feel I responded to every critique. If you feel I missed something, please bring it back and clarify how I haven't seemed to address it.

What things do the context changes? What argument do you have against the possibility A-theory infinite past, that doesn't also apply to the mathematical concept? Point being, if an argument that applies to the mathematical concept, fails to prove the mathematical concept impossible, then it doesn't work in proving the infinite past impossible. Last I checked, traversing an infinite past is exactly the same conceptually as the mathematical counting down through every single integer to zero (or count up through negative integers to zero.)

I’ll try again. There is a difference between saying:

(1) let’s assume an actual infinite is a number and see what applying mathematical equations spits out. Yeah, I have no problem with that.

(2) prove an actual infinite is a number that can be applied to things in reality, so that what the math spits out means something real. That’s the problem here. You seem to be arguing that (2) is good to go because mathematicians do (1). I disagree.

You've pointed out some features, but why are they problematic, other than not making sense to you?

I’ve explained why in numerous posts. You’ve responded to those, which shows it has been more than me simply saying “it just doesn’t make sense to me.” If you have specific posts that you don’t get or that you think clearly say “they are problematic because they don’t make sense to me” then quote those and I’ll clarify.

How can it be the whole snapshot when then context is an infinite universe?

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

So tell me what "infinite" and "traverse" mean in general, even if you don't want to be tried down to a definition, that makes it incoherent to put them together. More importantly what makes these meanings, "the real meaning" so to speak.

‘(Actual) infinite’ would mean a currently existing amount that is limitless or endless. Something that is endless cannot be completed, it will just keep going (in one or more directions). ‘Traverse’ means to travel through. As I’m using it, it denotes not just an act of traveling within, but of having traveled throughout the entire set, i.e., completed the journey. This is the “real meaning” because of the nature of A-theory time, where we must travel through the entire set (the “past”) to get to the present. But how can an endless (i.e., something that can’t ever be completed) amount be completed? It can’t be, by definition.

You can't, but that's moot, because the process in question - the A theory infinite past does end, in the same sense of "end" in "ending a process."

No. If the A-theory infinite past does not end, in the same sense of “end” in my “ending a process,” then the present can logically never be reached. The past HAS to end in order to reach the present because of the nature of A-theory.

As to counting to infinity, you have to first show that infinity is an integer. You haven’t established that.

Why does that matter when I can count to it, given the assumption that the presence of an endpoint doesn't matter? At worse that just open up the scenario of counting to a non-integer. But this part is now moot too, I only brought up counting to infinity because previously you said moving through every element in a set was what you mean by "traverse;" this latest post added "end the process" into the requirement.

Stop saying I’m adding things into the requirement. I’m not. You assume I mean X, build a critique off of that assumption and then I clarify that I don’t mean X.

In the analogy of counting, integers are the only things that can be counted. To say you can count to a non-integer would have to include things like being able to count to cat and my front tooth. That’s nonsense. The assumption that the presence of an endpoint doesn’t matter doesn’t change this.

Remind me, why is it a problem in the first place, the question has always been whether an infinite past can be traversed or not, why is whether a particular item an element in that set or not relevant in answering that question?

The problem is whether one can move through the entire infinite past (with no startpoint) to reach the present moment. You pulled ‘Last Monday’ out, made that a startpoint, and then showed you can move from that startpoint to the endpoint of the present. Okay, but the problem is moving through the entire infinite past with no startpoint to reach the present.

[Bust Nak]

I’ll try again. There is a difference between saying:

(1) let’s assume an actual infinite is a number and see what applying mathematical equations spits out. Yeah, I have no problem with that.

(2) prove an actual infinite is a number that can be applied to things in reality, so that what the math spits out means something real. That’s the problem here. You seem to be arguing that (2) is good to go because mathematicians do (1). I disagree.

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.

I’ve explained why in numerous posts. You’ve responded to those, which shows it has been more than me simply saying “it just doesn’t make sense to me.” If you have specific posts that you don’t get or that you think clearly say “they are problematic because they don’t make sense to me” then quote those and I’ll clarify.

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.

Is the infinite you are talking about not a “whole”?

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.

‘(Actual) infinite’ would mean a currently existing amount that is limitless or endless. Something that is endless cannot be completed, it will just keep going (in one or more directions).

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.

‘Traverse’ means to travel through. As I’m using it, it denotes not just an act of traveling within, but of having traveled throughout the entire set, i.e., completed the journey. This is the “real meaning” because of the nature of A-theory time, where we must travel through the entire set (the “past”) to get to the present.

That's fine, that's how I use the term traverse.

No. If the A-theory infinite past does not end, in the same sense of “end” in my “ending a process,” then the present can logically never be reached. The past HAS to end in order to reach the present because of the nature of A-theory.

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.

Stop saying I’m adding things into the requirement. I’m not. You assume I mean X, build a critique off of that assumption and then I clarify that I don’t mean X.

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.

In the analogy of counting, integers are the only things that can be counted. To say you can count to a non-integer would have to include things like being able to count to cat and my front tooth. That’s nonsense. The assumption that the presence of an endpoint doesn’t matter doesn’t change this.

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.

The problem is whether one can move through the entire infinite past (with no startpoint) to reach the present moment. You pulled ‘Last Monday’ out, made that a startpoint, and then showed you can move from that startpoint to the endpoint of the present. Okay, but the problem is moving through the entire infinite past with no startpoint to reach the present.

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?