Actual infinities.

[RoadRunner79]

---

While it sounds good, I think that there are problems with the infinite number of points between any two points (crossing an infinite number while traversing between those two points).
Mostly I would ask, how a point is being defined in this example, and how one point  is differentiated from another?  Usually an example is given, where the distance is divided over and over again (potentially infinite) however to me, it seems that the math always gives you a finite number (no matter how long you persist in this). 

It seems that the definition of the point, must be left undefined in which case; I ask what is it describing at all?  It cannot be defined as anything related to physical distance or volume.  For such would lead to a contradiction.  If I have two positions 1 meter apart then there is a finite length.  If the point is defining anything in relation to the distance, then it cannot be both infinite and finite in the same sense at the same time.   I can describe the distance as 1 meter or 1000 mm because they are defined and have a relation to one another; as well, I can go even smaller in my definition, however I always have a finite number for the distance.

As to arguments which are claimed to Dr. Craig, which then requires an actual infinite.  This would need to be more specific to answer.   Do the arguments require an actual singularity, or are they just surrounding what is commonly called the Big Bang Singularity?  If they do not require a singularity, then it is not inconsistent.  There may be some arguments effected, but it is difficult to tell, without being more specific.  It has occurred to me (within the last year), that the infinite when talking about a singularity comes from dividing by zero.  Some say, and I tend to agree, that this is better described as undefined, rather than infinite.  And the question comes about, if you can have something physical, that can be described as truly inhabiting zero space/volume?  Even with an astronomically small number (for volume), then it becomes finite again. 

I think the following describes my position on this fairly well, And I think that the word "infinite" is often used as shorthand for either very small or very large.
http://www.physlink.com/education/askexperts/ae251.cfm

---

If the Universe is expanding, as WLC says that he believes in, what, exactly, is it expanding into?

We had touched on this a little while ago. I believe that when I turned the same reasoning against an infinite universe, that you then said it was a nonsense question.

P.S.  We can talk about this later, if you want, but Cantor proved that there is an actual infinite between two finite points on the real number line:

https://www.khanacademy.org/math/math-fo...infinities

An actual infinite of what (numbers you can make up)? I don't disagree here. However I think that the trick here, is that points is really left undefined. As soon as you define what is in between, you have a finite number of them. Either that or the what really has nothing to do with anything physical or describing the movement, and so it would be in error to make that comparison. I don't think that anyone is arguing against infinity as a abstract or concept. It appears that a lot of this works on loose and shifting definitions.