[Thoughts on the term “ontology”.]
In philosophy, ontology refers to the subfield aiming to answer the question “Which things exist?”.
Perhaps as a consequence of this, hearing “ontology” makes me think of questions like: What are the primitives or building blocks here? E.g. in a spreadsheet, there would be cells; in a graph there would be vertices and edges etc.
But I think the important things Jacob is talking about show up as answer to the different question of which relations there are between these primitives. E.g. the important thing about a spreadsheet is that each cell is unique identified by a pair of numbers, that you can perform computations/functions on the values of cells; the important thing about a (certain type of) graph is that every edge has exactly one vertex as source and exactly one vertex as target.
Brainstorm for alternative terms: structure, conceptual structure, conceptual apparatus, conceptual scheme, conceptual toolkit, relations, relational constraints, conceptual landscape, …
(The math version of my complaint is that “ontology” makes me think of set theory, whereas I think the important bits are more naturally visible from a category theory point of view.)
[Thoughts on what to do if there is an ontological mismatch between one’s thinking and a tool]
When I saw Jacob present a version of the OP in person, the discussion focused on cases where the correct response is to use a different tool, ideally one that matches the natural ontology of ones thinking. E.g. when using a whiteboard rather than a Google doc to express thoughts most naturally expressed as a mind map.
But I think it’s important that there are other cases where it can actually beneficial to ‘learn how to think in a different ontology’. I think this is quite common in pure maths, but also shows up in more everyday situations: e.g. initially I found it quite counterintuitive to use, say, Emacs org mode or LaTeX, but after I had payed the fixed cost of adapting to the ontologies imposed by them I actually think that it made me more efficient at some tasks.
Similarly, I think it’s useful to be able to translate between different ontologies. To learn this, it can be useful to deliberately expose oneself to ontologies that seem unnatural/bad/cumbersome initially.