1001Philosophers

Bertrand Russell vs Gottlob Frege

Frege and Russell are the two founders of modern logic and of the analytic tradition. Russell discovered the contradiction in Frege's Grundgesetze that bears his name, and the resulting correspondence is one of the most important episodes in the history of logic.

At a glance

Bertrand RussellGottlob Frege
Dates1872 – 19701848 – 1925
NationalityBritishGerman
EraContemporaryModern
Movements Analytic Philosophy Analytic Philosophy
Profile Bertrand Russell → Gottlob Frege →

Where they agree

Both held that logic is the foundation of mathematics, both held that the analysis of language must distinguish sharply between sense and reference, and both treated the logical analysis of language as the proper method of philosophy. Frege's theoretical apparatus shaped Russell's decisively.

Where they disagree

Frege held that arithmetic could be reduced to logic via his system of basic laws, and that classes (extensions of concepts) are the entities that ground number-theoretic discourse. Russell's paradox — the class of all classes that are not members of themselves — showed Frege's system to be inconsistent, a discovery Frege accepted with characteristic rigor. Russell's response was the theory of types, which restricts the formation of classes to avoid the paradox; Frege ultimately abandoned the logicist program. They also disagreed sharply on the analysis of definite descriptions, with Russell's On Denoting rejecting Frege's account of names without bearers.

Representative quotes

Bertrand Russell

  • “The whole problem with the world is that fools and fanatics are always so certain of themselves, but wiser people so full of doubts.”

    The fundamental cause of the trouble is that in the modern world the stupid are cocksure while the intelligent are full of doubt.

  • “The good life is one inspired by love and guided by knowledge.”

    What I Believe, 1925

  • “To fear love is to fear life, and those who fear life are already three parts dead.”

    Marriage and Morals, 1929

Gottlob Frege

  • “Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.”

    Attributed to Frege in: A. A. B. Aspeitia (2000), Mathematics as grammar: 'Grammar' in Wittgenstein's philosophy of mathematics during the Middle Period , Indiana University, p. 25

  • “If the task of philosophy is to break the domination of words over the human mind [...], then my concept notation, being developed for these purposes, can be a useful instrument for philosophers [...] I believe the cause of logic has been advanced already by the invention of this concept notation.”

    Begriffsschrift (1879) Preface to the Begriffsschrift

  • “Begriffsschrift (1879) Preface to the Begriffsschrift”

    If the task of philosophy is to break the domination of words over the human mind [...], then my concept notation, being developed for these purposes, can be a useful instrument for philosophers [...] I believe the cause of logic has been advanced already by the invention of this concept notation.

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