Actual Infinity in Reality?

[Whateverist]

The essence of goddidit reasoning at its most basic.

[Jehanne]

Here's, from what I can tell, the Quantum Eternity Theorem that Sean Carroll referenced in his debate with WLC.  It's from David Griffith's book on Quantum Mechanics:

[polymath257]

What is the world does it mean to be a metaphysical impossibility except that there is an internal contradiction? Where is the impossibility of having infinitely many precursors? YOu have pointed to none or given a reason to think such is impossible.

Your very sentence "Where is the impossibility of having infinitely many precursors?" contains the metaphysical impossibility. It's that simple. You will never get to the present because there are always and infinite amount of precursors that still need to happen to get to the present.

No, that is NOT the case. We aren't waiting for an infinite number to happen. At any point, there is only a finite wait to any other point.  So, for example, between 100 years in the past and now is only a wait of 100 years, not an infinite amount of time. And, at both now and 100 years ago *an infinite amount of time had already passed*. There isn't an infinite amount to still occur to get to the present.

The precursors *have already happened*.

You have *yet* to show what the impossibility is.

---

I have no idea where you are getting these infinite gaps I supposedly am proposing. Your theory has events every moment in time going back. I am talking about the same scenario. I am not talking about a start to such a sequence either for your scenario. The fact that you have no start is the problem that creates the metaphysical impossibility. You cannot have a sequence of events ending today because there will always have to have happened a infinite amount of sequences before you get today. You will never get to today. Ever. I don't know how to say it any clearer.  

What is the metaphysical problem with having no start? Specifically?

Yes, precisely, there has already been an infinite number of events at any point in time. So?

[SteveII]

Your very sentence "Where is the impossibility of having infinitely many precursors?" contains the metaphysical impossibility. It's that simple. You will never get to the present because there are always and infinite amount of precursors that still need to happen to get to the present. 


I have no idea where you are getting these infinite gaps I supposedly am proposing. Your theory has events every moment in time going back. I am talking about the same scenario. I am not talking about a start to such a sequence either for your scenario. The fact that you have no start is the problem that creates the metaphysical impossibility. You cannot have a sequence of events ending today because there will always have to have happened a infinite amount of sequences before you get today. You will never get to today. Ever. I don't know how to say it any clearer.  

Notice how Grnadizer gets this. However, he is trying to solve it by saying there are no sequences that have to happen because there is no such thing as cause/effect. So he is not arguing for an actual infinity of events. He says there are just no events.

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Then this should be easy to show me shouldn't it! Abstract uncountable potentially infinite sets are useful on paper. Show me in mathematics where an infinite set has no beginning. Only that would be an actual infinite in mathematics. If you can only find sets with a beginning, all you are talking about is potential infinite sets. Apples and oranges. 

They do not translate to the real world. You three are hiding behind this leap. I challenge any of you to find a paper that describes how an actual infinite is possible.

Okay, I think I finally understand your objection here.  You’re saying that time-flow is what’s throwing a wrench into translating an actual infinite from math to reality.  I get what you mean, but I am no physicist so I’ll let Grand and Poly continue on.  However I will say, as Grand has said, I don’t see how an actual infinity wouldn’t be logically possible if we assume B theory of time is correct.  Directionality of time wouldn’t be an issue in that case, if my understanding of the theory is correct.

First, I don't think the B Theory of Time is correct. But leaving that aside for now, the B Theory of Time holds that all past, present and future time slices are all real simultaneously in a four dimensional spacetime manifold. Our current universe's physical laws govern this manifold so this manifold is only as old as the universe. There is nothing in the theory that claims a past infinite. 

The past infinite claim is derived from either a cosmology model, just accepting it as a brute fact (no explanation that could be forthcoming), or just asserting it must be so. The eternal universe models are not the most popular models because they lack components or plug values. The data that keeps coming in suggests a Big Bang-type model. 

Grand seems to see the problem of a past infinite series of cause/effects is metaphysically impossible--that's why he is claiming there is no such thing as a cause/effect so there are not an infinite amount of events/relationships to trigger the logic. 

But even if he believes there are not causes/effects in our spacetime manifold, a Big Bang-type model indicates a beginning of our spacetime manifold--a "prior to" if you will. If spacetime manifolds can begin, then even if we guess at a multiverse theory, we have established cosmic cause/effect -or to say it another way, was contingent upon the previous state. We can run these states back into infinity and we get the same problem--if there was an infinite amount of events (prior states) in the past, we would never get through them all to get to the event that spawned our universe.

Even if you say "well, then there is a larger B Theory-type spacetime manifold which contains all this", you still have clear "prior to" and "after than" states (cause/effect) that trigger the impossibility of traversing an infinite amount of events to get to our special little slice of infinity--our universe. Because--remember, there is nothing about the B theory of time that implies a past infinite--so simply declaring such a manifold does not get around the problem.

[SteveII]

Your very sentence "Where is the impossibility of having infinitely many precursors?" contains the metaphysical impossibility. It's that simple. You will never get to the present because there are always and infinite amount of precursors that still need to happen to get to the present.

No, that is NOT the case. We aren't waiting for an infinite number to happen. At any point, there is only a finite wait to any other point.  So, for example, between 100 years in the past and now is only a wait of 100 years, not an infinite amount of time. And, at both now and 100 years ago *an infinite amount of time had already passed*. There isn't an infinite amount to still occur to get to the present.

The precursors *have already happened*.

You have *yet* to show what the impossibility is.

---

I have no idea where you are getting these infinite gaps I supposedly am proposing. Your theory has events every moment in time going back. I am talking about the same scenario. I am not talking about a start to such a sequence either for your scenario. The fact that you have no start is the problem that creates the metaphysical impossibility. You cannot have a sequence of events ending today because there will always have to have happened a infinite amount of sequences before you get today. You will never get to today. Ever. I don't know how to say it any clearer.  

What is the metaphysical problem with having no start? Specifically?

Yes, precisely, there has already been an infinite number of events at any point in time. So?

There could not have been that many events already (because events are things that can be counted backwards one before the other and by definition, you can't get to infinity by successive addition). Even if you still can't wrap your head around the standard definitions of infinity, doesn't the fact that there still has to be an infinite amount more events that have to happen before "any point in time" give you pause? By the very definition of infinity, you cannot traverse it to get to the events of today. There will always and forever be more events that must happen first!

You can't simply treat infinity as one thing that you can throw into a sentence because mathematicians use it in set theory. You are talking about an infinite series of events. These events have substance and are real things. You make a claim when you say there are an infinite series of events and you have to tell us how, against all logic, that is even possible. 

Doesn't it seem odd to you that you can't find an article to explain this for you? 

Unless you have something new, this is the last time I am going to say the same thing. 20 times is my limit.

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Steve,

In the peer-reviewed scientific literature, there are eternal models of cosmology.  Do you believe that Roger Penrose considers his CCC model of cosmology to be a "logical impossibility"?  And, why are these scientific papers getting published if they are so flawed?  Now, if time must be finite, as you claim, then is space also finite?

P.S.  Are all sets that are "potential infinite" the same cardinality?  Or, are some bigger than others?

How do I know if Penrose even believes his theory to be the best one? Even if he got the math right, that does not imply in the least that an actual infinity exists. 

Do you think that every scientific paper that gets published is true or that even the authors think it is true?

Are you asking if space is an actual infinite of distance or substance, then no. If you are asking is space a potential infinite of distance or substance -- that seems possible. 

It seem to me that different potential infinities can accumulate more quickly so there should be some mathematical differentiation for that, but at the end of the day, there is no upper limit so it does not make sense when talking about real objects--and that is the topic of this thread and what I intend to discuss.

[Jehanne]

Steve,

If space is, as you claim, something that is finite, how is the Universe expanding? If it is expanding, then how is its volume increasing?

[SteveII]

Steve,

If space is, as you claim, something that is finite, how is the Unierse expanding?  If it is expanding, then how is its volume increasing?

It seems that the fabric of space is expanding--like a loaf of raisin bread being cooked. Raisins are the galaxies and the space between them expands while it is being baked. Raisins move in the dough even as the dough is expanding. Everything is getting further apart but not from a center. 

Expanding means the volume is increasing so I don't understand your last sentence.

[polymath257]

No, that is NOT the case. We aren't waiting for an infinite number to happen. At any point, there is only a finite wait to any other point.  So, for example, between 100 years in the past and now is only a wait of 100 years, not an infinite amount of time. And, at both now and 100 years ago *an infinite amount of time had already passed*. There isn't an infinite amount to still occur to get to the present.

The precursors *have already happened*.

You have *yet* to show what the impossibility is.

---

What is the metaphysical problem with having no start? Specifically?

Yes, precisely, there has already been an infinite number of events at any point in time. So?

There could not have been that many events already (because events are things that can be counted backwards one before the other and by definition, you can't get to infinity by successive addition). Even if you still can't wrap your head around the standard definitions of infinity, doesn't the fact that there still has to be an infinite amount more events that have to happen before "any point in time" give you pause? By the very definition of infinity, you cannot traverse it to get to the events of today. There will always and forever be more events that must happen first!

You can't simply treat infinity as one thing that you can throw into a sentence because mathematicians use it in set theory. You are talking about an infinite series of events. These events have substance and are real things. You make a claim when you say there are an infinite series of events and you have to tell us how, against all logic, that is even possible. 

Doesn't it seem odd to you that you can't find an article to explain this for you? 

Unless you have something new, this is the last time I am going to say the same thing. 20 times is my limit.

---

Steve,

In the peer-reviewed scientific literature, there are eternal models of cosmology.  Do you believe that Roger Penrose considers his CCC model of cosmology to be a "logical impossibility"?  And, why are these scientific papers getting published if they are so flawed?  Now, if time must be finite, as you claim, then is space also finite?

P.S.  Are all sets that are "potential infinite" the same cardinality?  Or, are some bigger than others?

How do I know if Penrose even believes his theory to be the best one? Even if he got the math right, that does not imply in the least that an actual infinity exists. 

Do you think that every scientific paper that gets published is true or that even the authors think it is true?

Are you asking if space is an actual infinite of distance or substance, then no. If you are asking is space a potential infinite of distance or substance -- that seems possible. 

It seem to me that different potential infinities can accumulate more quickly so there should be some mathematical differentiation for that, but at the end of the day, there is no upper limit so it does not make sense when talking about real objects--and that is the topic of this thread and what I intend to discuss.

Why are you counting *backwards*? Time moves forward! Nobody is counting backwards from today to the infinite past.

I'm not sure what you mean by there having to be an infinite number of *more* events before any particular moment of time. Where is the 'more'?

So, what we do *NOT* have is a situation

start----infinite time----now.

Instead, we have the situation for any point in the past,

infinite time----point in the past---finite time---now.

At no point in this progression is there an infinite amount of *more* time to traverse. The amount of time between any two events is always finite. And the amount of time in the past of any event is infinite.

I really don't see where there is a problem here. No infinite traversal is required in a finite time. And an infinite traversal in an infinite time is not a problem.

Again, you fail to explicit state what the problem is. Nobody is claiming an infinite amount of any substance in a finite region. But an infinite amount of space or an infinite amount of time (neither of which is a substance) have no issues that I can see. And an infinite amount of substance throughout an infinite space is also no problem that I can see. And nothing you have said leads me to think differently on that.

And what does it even mean to be a potential infinity of space? isn;t that *exactly* the same as there being an actual infinity of space? if you can always go further (potential infinity), doesn't that mean that all of space is an actual infinity?

[Jehanne]

Steve,

If space is, as you claim, something that is finite, how is the Universe expanding?  If it is expanding, then how is its volume increasing?

It seems that the fabric of space is expanding--like a loaf of raisin bread being cooked. Raisins are the galaxies and the space between them expands while it is being baked. Raisins move in the dough even as the dough is expanding. Everything is getting further apart but not from a center. 

Expanding means the volume is increasing so I don't understand your last sentence.

Professional astronomers don't have a problem with space being an actual infinite:

The long explanation is below. However, if you just want a short answer, I'll say this: if the universe is infinitely big, then the answer is simply that it isn't expanding into anything; instead, what is happening is that every region of the universe, every distance between every pair of galaxies, is being "stretched", but the overall size of the universe was infinitely big to begin with and continues to remain infinitely big as time goes on, so the universe's size doesn't change, and therefore it doesn't expand into anything. If, on the other hand, the universe has a finite size, then it may be legitimate to claim that there is something "outside of the universe" that the universe is expanding into. However, because we are, by definition, stuck within the space that makes up our universe and have no way to observe anything outside of it, this ceases to be a question that can be answered scientifically. So the answer in that case is that we really don't know what, if anything, the universe is expanding into.

What is the universe expanding into? (Intermediate)

I just wanted your perspective on this question.

[polymath257]

Steve,

If space is, as you claim, something that is finite, how is the Unierse expanding?  If it is expanding, then how is its volume increasing?

It seems that the fabric of space is expanding--like a loaf of raisin bread being cooked. Raisins are the galaxies and the space between them expands while it is being baked. Raisins move in the dough even as the dough is expanding. Everything is getting further apart but not from a center. 

Expanding means the volume is increasing so I don't understand your last sentence.

And in a flat spacetime, which is what seems to be the case, space is infinite in extent.

And yes, it is the case that expansion can happen with finite space. You are correct here.