I remember a mention somewhere of this kind of approach to inverse foundations for set theory, but lost track of the reference. IIRC, the approach didnt have pr

I remember a mention somewhere of this kind of approach to inverse foundations for set theory, but lost track of the reference. IIRC, the approach didnt have problem with empty set, but would allow the existence as a default until some obstruction. So, 'large sets' (nowadays called proper classes) would exist.