I often wish I could use the terms "transitive" "equivalence relation" "partition" and "subset", and have people understand their technical meanings.

From the linked article:

It is certainly worth considering the possibility that there is no global element in the Universal Sheaf of Theories.

This sounds like a blatant map/territory confusion. Maybe we haven't found a single theory that applies to all domains. That is, we may have to use multiple inconsistent maps, at least for now. But the territory doesn't refer to our maps to figure out what to do. The territory just does its thing.

Pardon the self-promotion, but the point that post makes is similar to the structure of understanding I outlined here. The sheaf model of knowledge is what I call a Level 2 understanding, and the level that scientists can't yet achieve for General Relativity and Quantum Mechanics.

Ordinary people go through life having different theories about love, religion, politics, when you kick a table it hurts your foot, and so on, and don’t seem to worry a bit about whether the restriction maps are compatible ...

That's what I call a Level 1 understanding.

I probably could have created a better hierarchy if I had been familiar with the sheaf concept -- sounds like an ideal ontology for an AI to have since it faciliates regeneration of knowledge (Level 3) and consilience (Level 2).

I like the idea, but he seems to be using some nonstandard terminology - IIRC, restriction maps still have to be compatible in a presheaf, no?

Edit: Or maybe he's just using "compatible" to mean "can be glued together".