 The exclamation mark “!” following a variable for a function and preceding the argument, as in “\(f\bang \hat{x}\)”, “\(\phi \bang x\)”, “\(\phi\bang \hat{x}\)”, indicates that the function is predicative, that is, of the lowest order which can apply to its arguments. In Church’s notation, this means that predicative functions are all of the first level, with types of the form \((\ldots)/1\). As a result, predicative functions will be of order one more than the highest order of any of their arguments. This analysis is based on quotations like the following, in the Introduction to PM: 