[sebastiennight]

The first question is weird. Many subsets of X can have property Y without X having it, wouldn't you say?

"If the desert is not covered in palm trees, how can a subset of it be covered in palm trees?"

"If the neural network is not activating, how can a node of the network be activating?"

[downboots]

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