Well, for starters we live in an integer universe, so there is a leftmost point.
Even beyond that, though, the third law suggests that for every force pulling mass leftward, you have a force pulling mass rightward- and so the center of mass should not move as the collection collapses.
[edit]In case basic physics is not obvious to you, an explanation of what the second line means can be found here.
[EDIT] What I am trying to say is that the problem is that an infinity is not taken as a limit, and thus the approach to the problem is confused.
I am curious why this received downvotes. Is it because people expected me to rot13 my answer?
We've discussed Edward Nelson's beliefs and work before. Now, he claims to have a proof of a contradiction in Peano Arithmetic; which if correct is not that specific to PA but imports itself into much weaker systems. I'm skeptical of the proof but haven't had the time to look at it in detail. There seem to be two possible weakpoints in his approach. His approach is to construct a system Q_0^* which looks almost but not quite a fragment of PA and then show that PA both proves this system's consistency and proves its inconsistency.
First, he may be mis-applying the Hilbert-Ackermann theorem-when it applies is highly technical and can be subtle. I don't know enough to comment on that in detail. The second issue is that in trying to show that he can use finitary methods to show there's a contradiction in Q_0^* he may have proven something closer to Q_0^* being omega-inconsistent. Right now, I'm extremely skeptical of this result.
If anyone is going to find an actual contradiction in PA or ZFC it would probably be Nelson. There some clearly interesting material here such as using a formalization of the surprise examiation/unexpected hanging to get a new proof of of Godel's Second Incompleteness Theorem. The exact conditions which this version of Godel's theorem applies may be different from the conditions under which the standard theorem can be proven.