I think we mostly understand the paper the same way. Still this seems utterly unremarkable to me, but maybe I am still just missing the important point. If you

I think we mostly understand the paper the same way. Still this seems utterly unremarkable to me, but maybe I am still just missing the important point. If you want to come up with a language to talk about the world, a logical system in this case, you make choices. You decide if you want to be first order or higher order, whether you want temporal facts, what you allow your variables to range over, which inference rules to use, and what predicates you allow. Or whatever else. If you only want to talk about physical things, you may be able to get away with existential qualification. If you also want to deal with concepts like Santa Claus you probably have to be more sophisticated because now »exists« is an overloaded term in your domain and throwing the same existential qualifiers in front of everything won't yield results that can be meaningfully translated to statements about the world. In the end you have the world, you have a model of the world in your logic, and you have some kind of mapping between the world and your model, most likely even on a meta level. Not only do objects in your logic have to be related to objects in the world, but the very structure of your logic, its inference rules, the allowed constructs, and so on, have to map to some of the structure of how the world works. So as I said, it should come at no surprise that differences in logic have to be equated with differences in the world you are modelling, but the real significance of that, if any, is still beyond me.