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.