I've been trying to look into why models / modelling / model theory let us down (I suspect it is because they are being misused) and I got hold of Burrow & Walsh, Philosophy and model theory, Oxford, 2018. Every here and there I find a "juicy" philosophical bit, which sets me off.

The authors won't admit to pushing "internalism", which seems to be about inference yet it is stated that it is free of "semantics".

My own instincts lie in semiotics, phenomenology, and the kind of reasoning (which I have been calling "inference") which I find in Jevons, Thouless, or books cowritten by Fosl.

To my mind "semantics" as a word means the exact opposite to its apparent specialised meaning in "formal logic".

Would I be right in thinking that cross checking "logic" by actual inference is likely to produce fairly reliable results because it is often not too vast in scale to fall greatly foul of Godel's incompleteness theorem?

Do professional "formal logic" practitioners think the general public wouldn't be interested and that a strange notation has to be denoted the sole entry point (and to what we might ask)? Do they think it wouldn't be good to simultaneously paraphrase as they go along, not only to inspire newcomers, but as a cross check for themselves?

I know abstracts are abstract, but they are still kinds of things. When I read string theory books or recursion books, there are lovely pictures of the topology I was always so fond of as an infant (with no-one to help me then), but not in "logic" books, where they would be equally appropriate.

Why do authorities underestimate the intelligence and flair of outsiders and then complain there aren't enough takers for science and maths studies?

(Incidentally I now call "universals" an intermediate level of "object" - of beholding - between "primary" and "secondary objects".)