How did George Boole and Charles Sanders Peirce contribute to mathematical logic?

George Boole and Charles Sanders Peirce were pivotal figures in the development of modern symbolic logic.

George Boole
In 1847, Boole published The Mathematical Analysis of Logic, arguing that logic should be allied with mathematics rather than philosophy. He established the algebra of logic, now known as Boolean algebra, by demonstrating an analogy between algebraic symbols and logical forms. His work, particularly An Investigation into the Laws of Thought (1854), provided a method for drawing logical conclusions from premises, which today serves as the foundation for digital computer circuits and information theory.12

Charles Sanders Peirce
Peirce refined and expanded Boole’s system, moving away from its strictly equational style to focus on the logic of relations. His contributions include:34
* Quantification: He introduced notation resembling modern quantifiers, which were later adopted by others and became standard.34
* Relational Logic: He developed techniques for handling relations, exploring the formal properties of logical inclusion.34
* Logical Representation: He created iconic systems such as existential graphs to represent the structure of thought.34

While Boole founded the algebraic tradition, Peirce’s extensions and notation significantly influenced the evolution of symbolic logic into the 20th century.34