Actual Infinity in Reality?

[SteveII]

I don't think the B Theory of time solves the underlying problem of having a series of cause/effect relationships. It seems to me that even if all points of time are equally real, they are still ordered by a structure we call cause/effect--a tangible series of objects we can use in thought experiments. [NOTE: I say this to start because there are some here who deny even this].

Like I keep saying, cause/effect relationships are only meaningful to talk about in a certain context (from a temporal perspective). When we're discussing the fundamental nature of reality, especially if we're assuming B-theory of time (and/or eternalism), you have to be willing to accept that it may be logically possible that causality is just an illusion. If there is no time flow, then there is not really change or motion happening. And no causality. Which possibly leaves us with simply an eternal 4D (or higher) static structure of which every time moment is a part of. I'm just saying.

Do you really believe that? It seems to me you are looking for a theory that gets you a past infinite rather than looking for theories that relate better to reality. 

For example, you. Do you imagine that the thing that makes you you endures from moment to moment? How does human consciousness work with "causality being an illusion"

Perhaps a variation of Hilbert's Hotel:

We can conceive of a possible world (much like the one you are proposing) with a beginningless series of discrete successive events of equal duration leading up to the present (real or perceived present). 

[ ...en, ... e5, e4, e3, e2, e1, e0]

We can conceive of another possible world with exactly the same events in the same order, but in between each of those events, another event occurs.

[ ...en, En, ... e5, E5, e4, E4, e3, E3, e2, E2, e1,E1, e0]

In this series, an infinite number of additional events have been added to an already infinite series of events. Are there more events? No. Infinity + infinity = infinity. We can also do the subtraction example from Hilbert, and imagine all the events prior to e3 could have been left out of the chain. 

[e3, e2, e1, e0]

In this series, we have subtracted an infinite number of events from an infinite number of events. Infinity - Infinity = 4.  Alternately, every other event could have been left out:

[ ...en, ... e4, e2, e0]

In this series, we have left out an infinite number of events from an infinite number of events. Infinity - Infinity = Infinity. 

This is not just "counter-intuitive". Actual infinities of real objects leads to absurdities (metaphysical impossibilities). Therefore an actual infinite is not logically possible. 

[Example language from a paper from Wes Morrison - http://spot.colorado.edu/~morristo/EndlessFuture.pdf]

I already addressed this earlier, Steve. Go back a few pages to find my post where I show how inf - inf is indeterminate. You are doing subtractions with different instances of infinite sets. There's no contradiction here.

In the first case of subtraction, you took out everything up until e4 (including e4), so of course you will end up with just 4 events.

In the second case, you took out an infinite set from another infinite set in a way where an infinite set remains (by taking out one event for every two events we go through).

In the addition case, you seem to be missing some important assumptions here, so I'm not going to comment on that until I get a clearer picture of what you mean by "discrete" and such.

An you keep failing to understand that the point of Hilbert's Hotel (or the reformulated example) is to show that infinite set theory and how you can use them in theoretical mathematics does not translate into the world of real objects. Don't keep asserting that because mathematicians can do it paper--therefore reality. No one has shown how that is possible yet. You have failed to produce a single reference in this thread and the last that shows the mathematicians believe there can be an infinite amount of an actual thing. You can not get to an actual infinite by adding one thing after another. In the real world, that's what you have to do--add things one after another. You can't just jump to the end and declare that one actually exists because we can write it down on paper and talk about potential infinities in theory. 

Don't give me equations with the word 'infinity' in them. That is not proof or even a good indication that one can exists. Give me examples of something or show where smart people talk about how they can exist and I will reconsider. Until then, all you are doing is asserting a claim with nothing to back it up.

[polymath257]

First, the singularity is NOT an event: it is a failure of the coordinate system to describe a situation. In this case, if you use standard general relativity, it describes a limit of infinite curvature.

I clearly did not say the singularity was an event. There was a change. Something started everything. 

Yes, it actually is part of the theory that the *previous* spacetimes already exist.

Note how you had to say *previous* when I said they have to all exist already--past and present. BECAUSE if all of them do not exist at once (in other words they exist sequentially as the theory clearly states), you have a very big problem of a past infinite. We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!? You keep asserting that how it is. Explain why we could ever logically get to our current universe.  

You are assuming that if time is infinite, there is an infinite gap between two events. That is false. There is no 'infinite wait' because the process is always ongoing with an infinite amount *already* having happened at any point. If you pick any point in the sequences, the time to now is finite.

---

Like I keep saying, cause/effect relationships are only meaningful to talk about in a certain context (from a temporal perspective). When we're discussing the fundamental nature of reality, especially if we're assuming B-theory of time (and/or eternalism), you have to be willing to accept that it may be logically possible that causality is just an illusion. If there is no time flow, then there is not really change or motion happening. And no causality. Which possibly leaves us with simply an eternal 4D (or higher) static structure of which every time moment is a part of. I'm just saying.

Do you really believe that? It seems to me you are looking for a theory that gets you a past infinite rather than looking for theories that relate better to reality. 

For example, you. Do you imagine that the thing that makes you you endures from moment to moment? How does human consciousness work with "causality being an illusion"

I already addressed this earlier, Steve. Go back a few pages to find my post where I show how inf - inf is indeterminate. You are doing subtractions with different instances of infinite sets. There's no contradiction here.

In the first case of subtraction, you took out everything up until e4 (including e4), so of course you will end up with just 4 events.

In the second case, you took out an infinite set from another infinite set in a way where an infinite set remains (by taking out one event for every two events we go through).

In the addition case, you seem to be missing some important assumptions here, so I'm not going to comment on that until I get a clearer picture of what you mean by "discrete" and such.

An you keep failing to understand that the point of Hilbert's Hotel (or the reformulated example) is to show that infinite set theory and how you can use them in theoretical mathematics does not translate into the world of real objects. Don't keep asserting that because mathematicians can do it paper--therefore reality. No one has shown how that is possible yet. You have failed to produce a single reference in this thread and the last that shows the mathematicians believe there can be an infinite amount of an actual thing. You can not get to an actual infinite by adding one thing after another. In the real world, that's what you have to do--add things one after another. You can't just jump to the end and declare that one actually exists because we can write it down on paper and talk about potential infinities in theory. 

Don't give me equations with the word 'infinity' in them. That is not proof or even a good indication that one can exists. Give me examples of something or show where smart people talk about how they can exist and I will reconsider. Until then, all you are doing is asserting a claim with nothing to back it up.

No, that is NOT the reasoning. The reasoning is that it works mathematically, so *there is no contradiction*. You are the one claiming a contradiction, but have yet to actually show one.

You keep claiming there has to be some sort of 'infinite wait' in the case of an infinite regress, but that is simply false: there is still only a finite amount of time between any two events.

[Jehanne]

Professor Wes Morriston has some excellent papers on this subject:

http://spot.colorado.edu/~morristo/selected-papers.html

(Oh, sorry for the duplicate link, sort of.)

[GrandizerII]

Like I keep saying, cause/effect relationships are only meaningful to talk about in a certain context (from a temporal perspective). When we're discussing the fundamental nature of reality, especially if we're assuming B-theory of time (and/or eternalism), you have to be willing to accept that it may be logically possible that causality is just an illusion. If there is no time flow, then there is not really change or motion happening. And no causality. Which possibly leaves us with simply an eternal 4D (or higher) static structure of which every time moment is a part of. I'm just saying.

Do you really believe that? It seems to me you are looking for a theory that gets you a past infinite rather than looking for theories that relate better to reality.

Unlike your favored theory of time, the B-theory of time is supported by modern science (Einsteinian relativity and all). So perhaps you should make an attempt to discard theories that don't better relate to reality and adhere to ones that do. So why aren't you doing that? Could it be because you need God to exist?

For example, you. Do you imagine that the thing that makes you you endures from moment to moment? How does human consciousness work with "causality being an illusion"

I am a perdurantist, meaning that I am the sum of all time instances of me (in this local universe, in case of a multiverse). This is a logical implication of eternalism.

Human consciousness perceives causality from our temporal perspective. It's not an illusion in the sense that it isn't perceived. Rather, it is an illusion in the sense that fundamentally, causality is not a feature of the underlying reality.

An you keep failing to understand that the point of Hilbert's Hotel (or the reformulated example) is to show that infinite set theory and how you can use them in theoretical mathematics does not translate into the world of real objects. Don't keep asserting that because mathematicians can do it paper--therefore reality. No one has shown how that is possible yet. You have failed to produce a single reference in this thread and the last that shows the mathematicians believe there can be an infinite amount of an actual thing.

I never said that mathematical possibility automatically translates to actual possibility. What I did do is challenge you to provide that logical/metaphysical/physical constraint that would prevent an actual infinity from existing in reality. You have yet to do so. So until you do, it is fair to say that an actual infinity in reality seems logically possible.

You can not get to an actual infinite by adding one thing after another. In the real world, that's what you have to do--add things one after another. You can't just jump to the end and declare that one actually exists because we can write it down on paper and talk about potential infinities in theory.

First of all, under the B-theory of time, there is no potential infinity, the only type of infinity is an actual infinity. If I were a vastly more superior entity than I actually am (almost godlike), and the universe was infinite in spacetime, there would be infinite time moments which cover every instance of me counting every positive integer ever. But because I am only human, I can only live for so long, and so I will not ever be able to count every single element in an infinite set of positive integers.

And second, one need not have to count things for things to start existing.

Don't give me equations with the word 'infinity' in them. That is not proof or even a good indication that one can exists. Give me examples of something or show where smart people talk about how they can exist and I will reconsider. Until then, all you are doing is asserting a claim with nothing to back it up.

The premise is that an actual infinity is an infinity (say, an infinite set of things) in which all its elements exist already. And using analogies like the Hilbert's Hotel, and the other one you used in this thread, we saw that such a premise would imply counter-intuitive outcomes, but not logical contradictions. If we assume actual infinity in reality, then we notice there is no logical contradiction that arises from doing so. Therefore, in the absence of counter logic/evidence, an actual infinity in reality is logically possible. This is a sufficiently conclusive argument in response to the objection that an actual infinity is not logically possible. Nothing more on my part needs to be argued.

[SteveII]

I clearly did not say the singularity was an event. There was a change. Something started everything. 


Note how you had to say *previous* when I said they have to all exist already--past and present. BECAUSE if all of them do not exist at once (in other words they exist sequentially as the theory clearly states), you have a very big problem of a past infinite. We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!? You keep asserting that how it is. Explain why we could ever logically get to our current universe.  

You are assuming that if time is infinite, there is an infinite gap between two events. That is false. There is no 'infinite wait' because the process is always ongoing with an infinite amount *already* having happened at any point. If you pick any point in the sequences, the time to now is finite.

I assume and implied no such 'infinite gaps'. I said: "We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!? You keep asserting that how it is."

Ironically, you just asserted that is it possible again without addressing the point: how do we get an infinite number of universes sparked/spawned/whatever before ours? There would still need to be an infinite more that need to happen first. You seem to think that if math can use infinities in equations, then this is not a logical problem--it is! A very big one. 

---

Do you really believe that? It seems to me you are looking for a theory that gets you a past infinite rather than looking for theories that relate better to reality. 

For example, you. Do you imagine that the thing that makes you you endures from moment to moment? How does human consciousness work with "causality being an illusion"


An you keep failing to understand that the point of Hilbert's Hotel (or the reformulated example) is to show that infinite set theory and how you can use them in theoretical mathematics does not translate into the world of real objects. Don't keep asserting that because mathematicians can do it paper--therefore reality. No one has shown how that is possible yet. You have failed to produce a single reference in this thread and the last that shows the mathematicians believe there can be an infinite amount of an actual thing. You can not get to an actual infinite by adding one thing after another. In the real world, that's what you have to do--add things one after another. You can't just jump to the end and declare that one actually exists because we can write it down on paper and talk about potential infinities in theory. 

Don't give me equations with the word 'infinity' in them. That is not proof or even a good indication that one can exists. Give me examples of something or show where smart people talk about how they can exist and I will reconsider. Until then, all you are doing is asserting a claim with nothing to back it up.

No, that is NOT the reasoning. The reasoning is that it works mathematically, so *there is no contradiction*. You are the one claiming a contradiction, but have yet to actually show one.

You keep claiming there has to be some sort of 'infinite wait' in the case of an infinite regress, but that is simply false: there is still only a finite amount of time between any two events.

Again, I proposed no infinite wait. Only the logic that an infinite number of universes still must come before ours can occur (because any multiverse model is one of a series of contingent universes). I am not claiming a contradiction, I am claiming it is metaphysically impossible. Overcome this objection or you have lost the argument.

[polymath257]

You are assuming that if time is infinite, there is an infinite gap between two events. That is false. There is no 'infinite wait' because the process is always ongoing with an infinite amount *already* having happened at any point. If you pick any point in the sequences, the time to now is finite.

I assume and implied no such 'infinite gaps'. I said: "We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!? You keep asserting that how it is."

Ironically, you just asserted that is it possible again without addressing the point: how do we get an infinite number of universes sparked/spawned/whatever before ours? There would still need to be an infinite more that need to happen first. You seem to think that if math can use infinities in equations, then this is not a logical problem--it is! A very big one. 

---

No, that is NOT the reasoning. The reasoning is that it works mathematically, so *there is no contradiction*. You are the one claiming a contradiction, but have yet to actually show one.

You keep claiming there has to be some sort of 'infinite wait' in the case of an infinite regress, but that is simply false: there is still only a finite amount of time between any two events.

Again, I proposed no infinite wait. Only the logic that an infinite number of universes still must come before ours can occur (because any multiverse model is one of a series of contingent universes). I am not claiming a contradiction, I am claiming it is metaphysically impossible. Overcome this objection or you have lost the argument.

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.

And yes, you made a claim that an infinite wait would be required when you said that we would still be waiting for an infinite number of universes to spark. No, we would NOT be waiting. An infinite number *would already have happened*, so we only have to wait a finite number from any point to get to the present. You seem to not grasp the idea of an infinite regress: *there is no start*, so at any point you set down, an infinite number of events have *already& happened.

So, where, precisely, is the impossibility? What is the argument that this cannot be the case? Other than a silly 'we wouldn't be here', which shows a deep misunderstanding, you have given nothing.

[pocaracas]

Ironically, you just asserted that is it possible again without addressing the point: how do we get an infinite number of universes sparked/spawned/whatever before ours? There would still need to be an infinite more that need to happen first. You seem to think that if math can use infinities in equations, then this is not a logical problem--it is! A very big one. 

You are aware that each of those Universes would be pretty much like our own, right?



Personally, I think better in terms of an infinite space-time framework, with each 4-dimensional point (possibly limited by the 4D Planck length) having a certain, albeit extremely low, probability of spawning a Universe.

[LadyForCamus]

Steve, I think you are confusing logic with intuition here. Just because the concept feels strange and contradictory to imagine doesn’t mean that it’s illogical. The math is the logic. As we were discussing before, many theories in physics begin as theoretical, mathmatical models before scientists conduct real world experiments to test them against reality. The mathematical model is exactly what demonstrates that the theory is...theoretically, logically possible. Whether or not it comports with our physical reality is another story, but neither Grand nor Poly are asserting that it does. They’re simply showing you it’s a mathematically sound theory, and therefore, there is no logical contradiction. You keep saying it’s not logical, but you haven’t pointed out any failure in the logic. All you’re doing is saying, ‘I just don’t see how his could ever be.’ That’s simply an argument from personal incredulity.

[SteveII]

Do you really believe that? It seems to me you are looking for a theory that gets you a past infinite rather than looking for theories that relate better to reality.

Unlike your favored theory of time, the B-theory of time is supported by modern science (Einsteinian relativity and all). So perhaps you should make an attempt to discard theories that don't better relate to reality and adhere to ones that do. So why aren't you doing that? Could it be because you need God to exist?

There are many people that do think the B theory of time is correct (physicist, cosmologists, philosophers) . General nor Special Relativity do not entail the B theory of time--it only implies that such a theory my be correct. BUT, more importantly, your belief there is no causal connections is NOT a part of the B Theory of time. If you think it is, it should be easy to post a link from a nice concise article on the subject. 

For example, you. Do you imagine that the thing that makes you you endures from moment to moment? How does human consciousness work with "causality being an illusion"

I am a perdurantist, meaning that I am the sum of all time instances of me (in this local universe, in case of a multiverse). This is a logical implication of eternalism.

That does not answer the question. Yes or no--are you the same person you were in 2010 or will be in 2020? If not, you have temporal parts that are causally connected in a specific direction--from earlier than to later than. 

Human consciousness perceives causality from our temporal perspective. It's not an illusion in the sense that it isn't perceived. Rather, it is an illusion in the sense that fundamentally, causality is not a feature of the underlying reality.

Again, you have not shown that to be part of the theory. Can you explain why science is almost entirely focused on causation if it is an illusion.  It seem the claim that it is an illusion is driven by something else rather than science. 

An you keep failing to understand that the point of Hilbert's Hotel (or the reformulated example) is to show that infinite set theory and how you can use them in theoretical mathematics does not translate into the world of real objects. Don't keep asserting that because mathematicians can do it paper--therefore reality. No one has shown how that is possible yet. You have failed to produce a single reference in this thread and the last that shows the mathematicians believe there can be an infinite amount of an actual thing.

I never said that mathematical possibility automatically translates to actual possibility. What I did do is challenge you to provide that logical/metaphysical/physical constraint that would prevent an actual infinity from existing in reality. You have yet to do so. So until you do, it is fair to say that an actual infinity in reality seems logically possible.

How many times have I asked this: " We could not have gotten to our current universe without an infinite amounts of universes already being created. We would still be waiting for an infinite amount of universe to be sparked before ours could be sparked--which will never happen, because there still needs to be an infinite more that need to come first. Why can't you address this!?"

You think you have the answer to this by claiming that causation is an illusion (or some people think it is an illusion). However, you have failed to back this counter-claim up. Show us why against all reason/intuition/experience/science that causation is an illusion. Until you do, simply the fact that such a theory exists does not undercut my argument. 

You can not get to an actual infinite by adding one thing after another. In the real world, that's what you have to do--add things one after another. You can't just jump to the end and declare that one actually exists because we can write it down on paper and talk about potential infinities in theory.

First of all, under the B-theory of time, there is no potential infinity, the only type of infinity is an actual infinity. If I were a vastly more superior entity than I actually am (almost godlike), and the universe was infinite in spacetime, there would be infinite time moments which cover every instance of me counting every positive integer ever. But because I am only human, I can only live for so long, and so I will not ever be able to count every single element in an infinite set of positive integers.

NOT SO. The B theory of time does not entail an actual infinite. The standard big bang models all have our spacetime manifold with a definite beginning. Anything with a beginning is by definition not an actual infinite. 

And second, one need not have to count things for things to start existing.

If something were to "start existing" it most certainly can be counted. 

Don't give me equations with the word 'infinity' in them. That is not proof or even a good indication that one can exists. Give me examples of something or show where smart people talk about how they can exist and I will reconsider. Until then, all you are doing is asserting a claim with nothing to back it up.

The premise is that an actual infinity is an infinity (say, an infinite set of things) in which all its elements exist already. And using analogies like the Hilbert's Hotel, and the other one you used in this thread, we saw that such a premise would imply counter-intuitive outcomes, but not logical contradictions. If we assume actual infinity in reality, then we notice there is no logical contradiction that arises from doing so. Therefore, in the absence of counter logic/evidence, an actual infinity in reality is logically possible. This is a sufficiently conclusive argument in response to the objection that an actual infinity is not logically possible. Nothing more on my part needs to be argued.

One man's "counter-intuitive outcomes" is another man's absurdities. Notice the word I marked above - assume. If you assume an actual infinite, you are question begging. 

Again, you think you have answered my objection with your "illusory causation" theory. You have not shown you theory to have any merit.

[LadyForCamus]

Everything about quantum mechanics is counter-intuitive; that doesn’t make QM absurd or illogical, lol.