First I want to say this article is very well articulated and I for one appreciate it. Secondly no one like to admit a truth about science that comes from the limitations of existing. Math is a regimental discipline that is designed to tell us about the substance of this reality. It cannot ever be used to prove or disprove things that have no substantial existence. This is why a person has to be able to verify and confirm there integers by a physical count. With out that one can use the math symbols and principals. but it will not represent reality.
Both sides of this issue have a problem with this as a fact. Until evidence is truth again it will remain so.
Really nice post.