De Bruijn's observation about typed sets being "close to their interpretations" versus ZF's coding tricks resonates deeply. I was part of that cohort - learned set theory by age 8 in 1971.
I'm working on spatial data organization where the same principle applies - forcing multi-dimensional relationships into rigid 2D grids creates the same kind of nonsense that x∈x creates in untyped set theory. The DOM becomes the type system: dragging tags to spatial zones determines valid operations polymorphically. The same tag exhibits different typed behaviors based on where you drop it.
De Bruijn wants types defined first, then populated. I do the opposite: dump data in, let semantic clustering reveal natural types, then let spatial manipulation expose different facets. The system is hereditarily finite - cards, tags, and workspaces are finite all the way down - which is sufficient for essentially all real-world productivity use cases.
Launching in the next few weeks. Might write a longer piece on practical typed set theory in productivity tools after that.
multicardz: "Drag. Drop. Discover."
Thanks for the food for thought