 Quantifying over functions of r-type \((\tau)/n\) of order \(k\) in a definition of a new function yields a function of r-type \((\tau)/n+1\), and so a function of order one higher, \(k+1\). Two kinds of functions, then, can be of the second order: (1) functions of first-order functions of individuals, of r-type \(((\iota)/1)/1\), and (2) functions of r-type \((\iota)/2\), such as our example “\(\hat{x}\) has all the qualities that great generals have”. This latter will be a function true of individuals such as Napoleon, but of a higher order than simple functions such as “\(\hat{x}\) is brave”, which are of r-type \((\iota)/1\).