Actual Infinity in Reality?

[RoadRunner79]

This is certainly an interesting conversation. In the interest to advance it further, I offer the following observations about some of the discussion so far.

It seems to be repeated often, that many cosmologist do not have  an issue with an actual infinity or an infinite universe.  However, whether this notion is popular or not, what matters is the reason behind their opinions.  From what I understand, I do not believe that they are referring to some expertise in their field, nor to some understanding or observation of the universe, which is little known to the lay person.  Even if granted for the sake of argument, In my opinion; I doubt that it is even possible to measure something as being infinite.  About the most that we gather from science is a nearly flat curvature of the universe, which could be consistent with, but does not necessarily require an infinite universe.

The question has been asked, if the universe is not infinite, then what is space expanding into.  I think that this is a good question, and I do not know the answer.   But it seems that it poses more of an issue if space is already and entirely completed infinite.  The question still remains, and I don't see why an answer for one, would not work in the other.  Accept that with an infinite, you already have the universe being limitless.

It is argued, that math has axioms, that deal with infinite sets.  Ok.... I don't see where anything which has been presented deals with the topic of an actual vs a potential infinite.  I also do not believe that the extrapolations or concept of infinity count as an actual or completed infinite.  Not in the sense of the philosophical objections.   Perhaps it fits the definition of a completed set, but I don't think that this is meeting the philosophical objections.

I do agree, and would say that I am more aware of the arguments that infinity isn't a number, and therefore shouldn't be treated like a number.  Thanks to those who brought this to attention.    Infinity means endless or without limit.  I think it's also very easy, as I catch myself and others who would say it is not a number, can easily slip back into that bad pattern of thought.

For Zeno's paradox,  it was offered that calculus is the answer, and that a infinite small amount of time, and an infinitely small distance can be covered.  I don't buy it.   It doesn't matter if you have a lot of time, or infinitely small amounts of time, or however much time.  If you follow that procedure of infinitely dividing in half the remainder, you will never reach the destination.  It's not a matter of time.   This may also be demonstrating the issue above of using infinity as a number.  Also, you cannot have an infinite number of small distances in a finite distance, nor an infinite amount of time, in a finite time.  This is a contradiction.  Zeno in his paradox, was arguing that there was no motion.  And we can easily observe that his conclusion is false.  Not only can I set out to and reach a distance of 10 ft.  I may very well pass it.  Who are you going to believe "Zeno... or you lying eyes?"  There is nothing wrong with Zeno's math, the simplest answer is that there is a problem with his underlying assumptions.  

If I'm understanding correctly, I don't think that anyone is making an argument for an actual infinity, only that it is possible.  And if scientist are not saying much about from their field about actual infinities, then I don't see why the are being brought up.   Mathematicians have assumptions about infinities, but are not working towards demonstrating an actual infinity, but assuming that at least an abstract set of infinite numbers exist.  Which is how the system is set up to begin with, and you can always add, and carry over the remainder (potentially endlessly).  But there isn't a set of numbers floating out there in the either.  Even our finite minds cannot hold a endless amount of numbers.  It can only try to grasp the concept.  And this is where I think that the contradiction lies.  In an infinite number of things is complete and an actual infinite is to say that it exists in it's entirety.  However it's endless you can always add one more, that wasn't there before.  If you cannot add one more, then it is not infinite.

But these are only two tools to truth.  Philosophers have had objections to infinity for a long time.  They have paradoxes.  And I believe contradictions.  Something can not be infinite and finite at the same time.  It cannot be endless and have an end.  It cannot be completed and incomplete a moment later.  And even if you are not convinced that these are contradictions (infinity can be a difficult thing to grasp and you or I may be in error)  There are still the paradoxes or absurdities.  No matter how you slice it, it seems that there is a lot more reason to doubt an actual infinity and I see no reasons to believe for it.