I'm just playing with some thoughts here:
I have near me a plastic bottle filled with isopropyl alcohol, and a cardboard box filled with paper security envelopes. The contents of each container are in a different phase to one another -- solid and liquid, respectively -- and the cardboard is more porous than the plastic container is. (though, to touch, it has a similar feeling because box has been printed on, and the process makes the outside of the cardboard somehow feel smooth and wax-ish like plastic)
Two measures -- third "things" -- which relate them are both length and volume. Mathematically these are related, of course, but there's certainly a distinction to be had between those ways of relation. The bottle of isopropyl alcohol is 1.66 cigarette packs tall, while the envelope box is 1.2 cigarette packs tall -- and we may ask for some fourth thing to clarify the cigarette pack, such as a ruler, but 'cigarette pack' is good enough for our purposes. Continuing this process it turns out the envolope box is about 1.2 cig-packs cubed, and the bottle is about 1.06 cig-packs cubed. But the appearance and function of the bottle suggests that it is more voluminous than the envelope box. It doesn't fit within my desk drawer as easily as the envelope box does. It also carries liquid, which suggests volume, where envelopes -- while technically having a volume -- certainly do not suggest volume.
Length is a basis of comparison, and volume is calcuable (in limited circumstances) from lengths, but the comparison of length and volume are different between the two objects. What is similar, however, is that 'length' and 'volume' -- both conceptual notions -- are serving as a way to compare two distinct entities. We can further specify these conceptual notions (perhaps you thought that my usage of cig-boxes just wasn't up to the task), but the idea of a "ruler", a third entity functioning as a point of comparison, is only brought in to this process of comparison because we already have a notion of length, and realize that though 'length' is no entity unto itself, it is a notion which allows us to compare entities.
composition -- 'paper', 'plastic' -- and function -- in these two examples, containment -- seem to me to be bases of comparison between entities as well.
I don't know if I'd want to ascribe all that to language use, per se. That seems a bit speculative -- though I could see the ability to pick out entities, naming them (more or less), being ascribed to language use.
We can of course consciously, deliberately construct categories, but we'll just be trying to formalize our intuition, rather than actually describing a literal ubiquitous feature. — Wosret
I think this is a different sort of question from your opening post though, no? Whether we are actually describing a literal ubiquitous feature is different from how we relate, thereby finding sameness, in entities which are different, no?