Higher-order

Higher-order functions are functions that can treat functions (function as language construct) like any other value, e.g. they can accept functions as arguments and return functions.

Higher-order logics

• quantifying over individuals

• quantifying over sets of individuals

• quantifying over sets of predicates

n-order logics, ZOL » FOL » SOL » HOL

• Zeroth-order logics, n = 0

• First-order logics, n = 1

• Second-order logics, n = 2

• Higher-order logics, n > 2

FOL,SOL are not higher-order logics.

To achieve higher-order you need to start have variables that range over "higher" concepts.

Orders: a theoretic language with variables that range over objects is a higher-order language (right?)