I'll give you an example of an ontology in a different field (linguistics) and maybe it will help.
This is WordNet, an ontology of the English language. If you type "book" and keep clicking "S:" and then "direct hypernym", you will learn that book's place in the hierarchy is as follows:
... > object > whole/unit > artifact > creation > product > work > publication > book
So if I had to understand one of the LessWrong (-adjacent?) posts mentioning an "ontology", I would forget about philosophy and just think of a giant tree of words. Because I like concrete examples.
Now let's go and look at one of those posts.
https://arbital.com/p/ontology_identification/#h-5c-2.1 , "Ontology identification problem":
Consider chimpanzees. One way of viewing questions like "Is a chimpanzee truly a person?" - meaning, not, "How do we arbitrarily define the syllables per-son?" but "Should we care a lot about chimpanzees?" - is that they're about how to apply the 'person' category in our desires to things that are neither typical people nor typical nonpeople. We can see this as arising from something like an ontological shift: we're used to valuing cognitive systems that are made from whole human minds, but it turns out that minds are made of parts, and then we have the question of how to value things that are made from some of the person-parts but not all of them.
My "tree of words" understanding: we classify things into "human minds" or "not human minds", but now that we know more about possible minds, we don't want to use this classification anymore. Boom, we have more concepts now and the borders don't even match. We have a different ontology.
From the same post:
In this sense the problem we face with chimpanzees is exactly analogous to the question a diamond maximizer would face after discovering nuclear physics and asking itself whether a carbon-14 atom counted as 'carbon' for purposes of caring about diamonds.
My understanding: You learned more about carbon and now you have new concepts in your ontology: carbon-12 and carbon-14. You want to know if a "diamond" should be "any carbon" or should be refined to "only carbon-12".
Let's take a few more posts:
The standard answer is that we say “you lose” - we explain how we’ll be able to exploit them (e.g. via dutch books). Even when abstract “irrationality” is not compelling, “losing” often is. Again, that’s particularly true under ontology improvement. Suppose an agent says “well, I just won’t take bets from Dutch bookies”. But then, once they’ve improved their ontology enough to see that all decisions under uncertainty are a type of bet, they can’t do that - or at least they need to be much unreasonable to do so.
My understanding: You thought only [particular things] were bets so you said "I won't take bets". I convinced you that all decisions are bets. This is a change in ontology. Maybe you want to reevaluate your statement about bets now.
Ontology identification is the problem of mapping between an AI’s model of the world and a human’s model, in order to translate human goals (defined in terms of the human’s model) into usable goals (defined in terms of the AI’s model).
My understanding: AI and humans have different sets of categories. AI can't understand what you want it to do if your categories are different. Like, maybe you have "creative work" in your ontology, and this subcategory belongs to the category of "creations by human-like minds". You tell the AI that you want to maximize the number of creative works and it starts planting trees. "Tree is not a creative work" is not an objective fact about a tree; it's a property of your ontology; sorry. (Trees are pretty cool.)