Actual Infinity in Reality?

[GrandizerII]

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.

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.

Ok, so about the addition case, I'm assuming that there are gaps in between the initial moments into which you can insert the extra moments. So correct me if that's not the case.

Either way, again, you have to keep in mind that just because you have derived the equation inf + inf, doesn't mean that you are adding two instances of the same infinite set to get a totality which is equal to that same infinite set.

In such a case, you have the original infinite set + an additional infinite set to get a newly updated infinite set.

This is a loose analogy, but it's like almost saying that finity + finity (in the form of 3 + 4) = finity (7), rather than 3 + 3 = 3. So there's no contradiction. Infinity is just a confusing concept to those who don't take the time to understand what it's really referring to. And it's counter-intuitive for most (if not all) of us, no question.