Good note. Your examples suggest thinking of 'property' as a sort of discontinuous indicator function on the subsets. I'm thinking about the interdependence between the function values or across subsets, regardless of continuity, in the context of universal computation. How to localize or define intelligence? Take the example of IQ, as a platonic ideal for measuring intelligence, vs all possible groups you could make with those people. Hard to define intelligence https://news.ycombinator.com/item?id=39977664