consisting of persons, then (1) says that any two persons who are physically indiscernible are mentally indiscernible, and (2) says that any person who has a mental property has some physical property such that any person with that physical property has that mental property.

Some points of clarification: first, the definitions above involve quantification over properties and hence higher-order logic. Second, in (1), expressions of the form capture the concept of sharing all properties, or