Full Idea
Three systems of semantics for second-order languages: 'standard semantics' (variables cover all relations and functions), 'Henkin semantics' (relations and functions are a subclass) and 'first-order semantics' (many-sorted domains for variable-types).
Gist of Idea
Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics?
Source
Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
Book Reference
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.-13
A Reaction
[my summary]