WHY IS FIRST ORDER LOGIC “FIRST ORDER”?

FOL is called “predicate logic”, since its atomic formulae consist of applications of predicate/relation symbols to terms. Why is it also called “first order”? Because its variables range only over individual elements from the interpretation domain. In other words, if A ∈ WFF_FOL then ∃xA ∈ WFF_FOL only when x is an individual variable x ∈ ν…