I didn't downvote you, however both your objections were rather besides the point. One doesn't deal with the issue of Newtonian mechanics, and whether they were indeed as obviously flawed from the beginning -- it feels a bit like explaining the paradox of Achilles reaching the turtle by saying we're living in an integer universe. That may be true, but it feels a rather weak dodging-the-issue explanation.
As for the second answer, it doesn't really state where the calculations in the presentation of the paradox are wrong or are missing something. It just says that they are, so it's a non-solution.
As for the second answer, it doesn't really state where the calculations in the presentation of the paradox are wrong or are missing something. It just says that they are, so it's a non-solution.
Maybe this is because I was a physics student, but to me the missing pieces implied by the second answer are so obvious as to make it not worth my time to type them and yours to read them. Apparently I was mistaken, so here they are.
By the principle of superposition, we can break down a N-body problem into (N choose 2) 2-body problems. Consider the mass M and th...
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.