1001Philosophers

Gottlob Frege vs Bertrand Russell vs Ludwig Wittgenstein

Frege, Russell, and Wittgenstein are the three founders of analytic philosophy. Russell discovered the contradiction in Frege's Grundgesetze that bears his name, and Wittgenstein was Russell's student at Cambridge before the First World War. The three together established modern logic and the philosophical method of logical analysis.

Key differences at a glance

Gottlob FregeBertrand RussellLudwig Wittgenstein
Aim of logical analysis Reduce mathematics to logic via classes.Disclose the ultimate constituents of reality.Dissolve philosophical problems by clarifying their linguistic form.
Theory of meaning Sense and reference; logicist semantics.Logical atomism: simple particulars and universals compose reality.Later: meaning is use within forms of life.
Status of philosophy Foundational science of logic and mathematics.Theoretical inquiry into what there is.Therapeutic dissolution of confusions arising from language.
After Russell's paradox Logicist program ultimately abandoned.Theory of types preserves the project.Tractatus reframes the project as the showing of logical form.

Biographical facts

Gottlob FregeBertrand RussellLudwig Wittgenstein
Dates 1848 – 19251872 – 19701889 – 1951
Nationality GermanBritishAustrian
Era ModernContemporaryContemporary
Profile Gottlob Frege →Bertrand Russell →Ludwig Wittgenstein →

Where they agree

All three held that the analysis of language and the foundations of logic is a central problem of philosophy, all three treated mathematics and modern logic as essential tools of philosophical inquiry, and all three rejected the appeals to intuition and to historical authority that had dominated nineteenth-century philosophy.

Where they disagree

The disagreements concern what logical analysis ultimately delivers. Frege held that logic is the foundation of mathematics and that arithmetic could be reduced to logic via classes (extensions of concepts) — a project Russell's paradox showed to be inconsistent. Russell held that logical analysis discloses the ultimate constituents of reality (logical atomism) and developed the theory of types to avoid the paradox. Wittgenstein, in the Tractatus, agreed in form but reached a more austere conclusion: most traditional philosophy attempts to say what can only be shown, and many philosophical problems dissolve once their linguistic form is properly understood. The later Wittgenstein went further still, abandoning the picture theory of meaning altogether for meaning as use within forms of life.

Representative quotes

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.

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

Ludwig Wittgenstein

  • “The world is everything that is the case.”

    Original German: Die Welt ist alles, was der Fall ist .

  • “Whereof one cannot speak, thereof one must be silent.”

    Wovon man nicht sprechen kann, darüber muss man schweigen.

  • “The limits of my language mean the limits of my world.”

    Variant translations: | The limits of my language stand for the limits of my world. | The limits of my language are the limits of my mind. All I know is what I have words for. | Original German: Die Grenzen meiner Sprache bedeuten die Grenzen meiner Welt.

Pairwise comparisons

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