How did Gottlob Frege influence Bertrand Russell’s philosophical work?

Gottlob Frege significantly influenced Bertrand Russell’s work in the development of analytic philosophy and modern logic. Russell admired Frege’s logicist research program, which sought to derive all of mathematics from basic logical laws, and he actively promoted these ideas in his early writings, such as The Principles of Mathematics (1903) and later in Principia Mathematica (1910–13).12

Frege’s influence was foundational in two primary ways:

• Logical Analysis: Russell adopted and expanded upon Frege’s use of quantifiers and predicates to analyze the logical structure of language. In his paper "On Denoting" (1905), Russell applied this framework to solve problems regarding definite descriptions, demonstrating how to treat them as quantificational rather than as singular terms.3
• The Linguistic Turn: Together, Frege and Russell initiated the "linguistic turn," shifting the focus of philosophy toward the analysis of language as a means to resolve metaphysical problems.3

However, their relationship also involved a critical challenge: in 1902, Russell discovered a contradiction in Frege’s system, now known as Russell’s paradox. This discovery exposed a flaw in Frege’s unrestricted comprehension principle, forcing Frege to attempt modifications to his axioms and ultimately impacting the trajectory of his work.452