TO BE DONE
Frege (1879) was the first to devise a general notation of quantification, using auxiliary variables in the modern fashion. So important was this step that we might indeed look upon Frege, rather than Boole, as the founder of modern logic. The present notation, easier to print than Frege's, is from Whitehead and Russell. The pronominal character of the variable was clear to Peano (Formulaire, 1897, p. 26; 1901, p. 2); but it is only with the advent of combinatory logic, founded by Schonfinkel and developed by Curry, that the role of the variable as an index of cross-reference has received full analysis. The analysis consists in showing how variables can be eliminated in favor of a few constant terms designating functions of functions (or relations of relations). See Schonfinkel; also Curry's "Grundlagen," "Apparent Variables," and "Functionality," Rosser's U Mathematical Logic", and my "Reinterpretation" (which cites further papers by Curry).