Yes, the bolded is exactly correct. The person who claims the universe has always existed is claiming that this moment now is the end point of an infinitely long series of (non-infinitessimal) points.
I've been puzzling over these passages for a few days. I'm not sure I understand the work they're doing for your view. Perhaps there's something here I'm just not grasping. I'd appreciate you explaining these points a different way.
I’d like to re-frame this discussion as a conversation about lines and infinity, because that is where I perceive our disagreement (or misunderstanding). It could be a time-line or a line of yarn or a line on a graph or a line of cocaine. What the line
is doesn’t particularly matter in order for us to talk about something being infinite. I think the implications of time on this discussion are causing confusion due to complexity.
So because of its simplicity, I’d like to talk about this in terms of a Cartesian plane instead of time. I think we can make our arguments in that context without losing anything we need.
Here is the real crux of my argument: there is no such thing as an ‘infinite line’. There is only an infinite set of points. The mathematical description of a line
is an infinite set of points, but I don’t think that’s a good definition of a line and it actually creates a logical impossibility, so I’m going to discard it for a new one that I think captures everything important about a line without the problems:
A line is the distance between two defined points.
On a two-dimensional Cartesian plane, a line’s two points are represented by two coordinates: (x,y) (x,y). If I provide actual values for x and y, we have a line.
Absent real values, (x,y)(x,y) as expressed is not actually a line. Rather, (x,y)(x,y) indicates the
form the line will take on a Cartesian plane. If we were using Euclidean space for this discussion, the form of a line would be (x,y,z)(x,y,z). All the same, (x,y,z)(x,y,z) is not, itself, a line. It is a formula for a line.
Now, if I only define values for one point, (3,7)(x,y) we still don’t have a line. We have a point. No line can be created until both points are
defined. That does not make the existence of a line impossible; it simply means my line, as I’ve started it, is incomplete.
Let’s redirect momentarily to infinity.
An infinite set has no defined (or definable) beginning or end. Because of this quality of infinity, it cannot be used to define a line. In other words, (3,7)(∞,∞) is the same as (3,7)(x,y). To say “the end of an infinity” is the equivalent of of saying “a non-point point” or “point B”. Where is point B? Nowhere. Where is (∞,∞)? Nowhere. It isn’t real.
Infinite sets are also comprised of finite units or points. If we were simply charting points on a graph, we could go (1,1)(1,2,)(1,3)(1,4): ...and on forever in either direction. We could also draw a line between any two of those points. We could also select an individual point anywhere in the infinite set.
That last feature of an infinite set is important: an individual point in an infinite set exists,
but its location in relation to the infinite set cannot be described. Why? Because we cannot create a line between it and “the end of infinity”.
Does that make an infinite set impossible? No! It simply means our way of locating a point in relationship to a set of points—drawing a line to that set’s conclusion—is not a tool we can use to locate a point in relationship to
the entire infinite set. You can locate its relationship to another point in the set, which allows you to draw a line, but our inability to locate a point’s position relative to an entire set doesn’t make the point’s existence impossible.
And that, to be punny, is the point.
(cont.)
