How did Bertrand Russell’s notation differ from Gottlob Frege’s notation?

Gottlob Frege and Bertrand Russell utilized fundamentally different systems of notation to express logical concepts.

Frege’s notation, introduced in his 1879 work Begriffsschrift, was unique and two-dimensional. This complex, unconventional format was a significant factor in why his work remained little-read during his lifetime. Frege based his notation on mathematical functions, treating predicates as functions rather than using the algebraic methods common to the Boolean tradition.12

In contrast, Bertrand Russell, while a great admirer of Frege’s logicist program, did not adopt Frege’s notation. Instead, in works such as Principia Mathematica, Russell employed a system derived from the work of Giuseppe Peano, Charles Sanders Peirce, and Ernst Schröder. Russell’s notation for relations and functions was closely aligned with the Peirce-Schröder tradition, which was more widely accepted and utilized by other logicians of the era.12

While both men were instrumental in developing modern formal logic, their divergence in notation reflects their differing approaches to the history and practice of symbolic logic.123