Full Idea
By 1879 Frege had discovered an algorithm, a mechanical proof procedure, that embraces what is today standard 'second order logic'.
Gist of Idea
In 1879 Frege developed second order logic
Source
report of Gottlob Frege (Begriffsschrift [1879]) by Hilary Putnam - Reason, Truth and History Ch.5
Book Reference
Putnam,Hilary: 'Reason, Truth and History' [CUP 1998], p.124
A Reaction
Note that Frege did more than introduce quantifiers, and the logic of predicates.