Full Idea
A 'propositional function' is generated when one of the terms of the proposition is replaced by a variable, as in 'x is wise' or 'Socrates'.
Gist of Idea
'Propositional functions' are propositions with a variable as subject or predicate
Source
Penelope Maddy (Naturalism in Mathematics [1997], I.1)
Book Reference
Maddy,Penelope: 'Naturalism in Mathematics' [OUP 2000], p.9
A Reaction
This implies that you can only have a propositional function if it is derived from a complete proposition. Note that the variable can be in either subject or in predicate position. It extends Frege's account of a concept as 'x is F'.