Full Idea
Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought.
Gist of Idea
Boole applied normal algebra to logic, aiming at an algebra of thought
Source
report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3
Book Reference
Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.51
A Reaction
The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one.