Here is another in the recent spate of mathematics posts. I take up now, as I did in my last post, some material that I had originally drafted for the first post in this series.
Whenever it has been designated for its own post, material can grow, as has the material of this post in the drafting. Large parts of this post are taken up with

the notion (due to Collingwood) of criteriological sciences, logic being one of them;

Gödel’s logical theorems of completeness and incompleteness.