My original comment was about your inappropriate use of the word "quantitative." It was not about being for or against gold standard, although I did subsequently made some comments about that.
You have now gone completely away from the original point, and yet confound the problem with statement such as these:
the statement quoted is far from mathematically precise.
Actually, it is; I am surprised that you, apparently familiar with notions of order and cardinality, would make a statement to the contrary. The author may or may not have sufficiently supported his claim, but the claim's formulation is mathematically precise.
I've attracted your attention to what I thought was your misuse of standard terminology. You've reflected on that and apparently disagree. I think we can leave things at that.
It is quite clear that you dislike the article, but not at all clear why. Once one reason you offer is shot down, you move to another. I have no time for games of the type "chase the moving target." Sorry.
I have probably done as much work in set theory, number theory, mathematical logic, and mathematical economics as anyone on this board. The use of “quantitative” was entirely appropriate, but it is pointless to continue a discussion with someone who thinks that the now much discussed sentence constitutes a useful claim, mathematically or otherwise, or that the author’s brief, undisciplined romp through 800 years of history is to be taken with the same seriousness as Friedman’s and Swartz’s work on economic history.