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].

I don't see how you get that this is a problem unless you assume that any series must have a first member.  In that case, you would be assuming what you need to prove.  If time is infinite, like the idea of spatial infinity, then the 4-space manifold that is time+space simply has no boundary in either direction, temporally.  I don't see how the idea that there is a cause/effect relationship between every successive part of that manifold undermines the possibility of it being infinite.

That is the question: does a series of events need a first member? Since this thread is on infinity and not something like the PSR, I will continue to limit it to just the infinity question. I brought up cause/effect because some deny there is as a way to avoid the question. I wanted to make sure we were not talking past each other. 

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.

I don't see that Hilbert's hotel demonstrates that an actual infinity is a metaphysical impossibility.  What metaphysical truth is it contradicting?  You seem to be arguing on the surface here, claiming that it is a metaphysical impossibility without showing any actual metaphysics.  It seems to me that you've simply argued in a circle.  Your metaphysics doesn't admit of an actual infinity, so to you an actual infinity is impossible (metaphysically).  In doing so you seem to have simply assumed what you need to demonstrate.  I don't offhand see how Hilbert's hotel advances your argument any.  To me, it's just a distraction.  The hotel produces results that seem absurd.  It's not clear that Hilbert's hotel demonstrates impossibilities.  You need to show the latter, not the former. 

Possible worlds semantics helps us identify metaphysical possibilities/impossibilities. I set up four such thought experiments above. We clearly have contradictions that arise when comparing these possible worlds. But the real problem is that your position is that all of them are true despite the obvious contradictions. You have not shown why we should accept the contradictions other than to wonder if that's just the way it is. It seems to me that you have some burden of proof to shoulder if you are proposing ignoring obvious contradictions. 

If anything, Hilbert's hotel demonstrates that our understanding of the meaning of reference is undermined by an actual infinity, and that seems true. We can't form a sensible relationship between referents and the things they reference under operations involving infinity. Is that a metaphysical problem, I don't think so. 

Why isn't that question begging? The proposition is that an actual infinity does not exist. To dismiss thought experiments on the basis they don't work with actual infinities needs a little more support.

You need to go further than simply recounting Hilbert's hotel to show that any essential metaphysical assumption has been violated.  When you do, I think you'll find that you've simply assumed your conclusion.

It seems to me you are accepting an actual infinity as a brute fact. Can accepting a brute fact really be considered "logical". 

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

Thanks.  I'll look at this in more detail at a later date.  According to Morriston, "It is controversial, of course, whether there is genuine absurdity in either case."  I don't see that you've eliminated the controversy so much as arbitrarily championed one side of it.

The other side seems to be to claim there are no absurdities. Hard to pick that argument apart when you just showed there is.