(October 10, 2018 at 1:17 pm)SteveII Wrote:(October 10, 2018 at 12:59 pm)polymath257 Wrote: I'm really wondering what you are expecting here. This is recognized generally by most cosmologists. For infinite space, it is supported by the zero curvature of space (although not proven).
Since most science articles are interested in the observational aspects, we don't see *proof* that there are infinitely many objects. But again, that is a different issue than whether it is a logical impossibility. After Cantor, it is generally recognized to not be a logical issue, but an observational one.
Take any article in cosmology and see if it allows for infinite space. Essentially every one does. Take any article that discusses something prior to the Big Bang and see if it allows for infinite time. Essentially every article of that type does.
if you really want a list from arxiv.org, I can supply one.
You misunderstand. I don't want a science article. I want to see an article that argues that an actual infinity of concrete objects can logically exists. Your entire argument rests on this. You are making metaphysical (not scientific) claims and therefore you need metaphysical reasoning to support your metaphysical claims.
The logical possibility is demonstrated by the consistency of the math. That is *all* that is required to show that the concept is consistent.
Metaphysics is usually simply re-arranging preconceptions. It is flawed from the beginning. The *only* relevant questions are whether the concept of infinity is logically inconsistent (it isn't) and whether observation supports some actual infinity. I agree that we have no *positive proof* of an infinite space, for example, but the current evidence certainly allows for that possibility. But that isn't the issue. The issue is whether an actual infinity is *logically* contradictory. And the math shows that it isn't.
That we are talking about 'concrete' objects is irrelevant to the logical possibility. All that is required is an infinite extent of space (certainly a logical possibility) and concrete objects scattered in that infinite space.