Introduction: Frege and Russell (01:18)

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The work on which Frege and Russell each began concerned mainly mathematics and logic, but its implications have dominated subsequent English-speaking philosophy. This program will avoid mathematical technicality but examine these implications.

Backgrounds of Frege and Russell (02:12)

Magee discusses Frege's and Russell's lives and works. Frege's work was unknown until Russell drew attention to it.

Frege's Goal (00:55)

Frege found mathematics insufficiently precise; even Euclid made assumptions he did not make explicit. He developed a more rigorous notation.

Frege's Approach (01:49)

Frege sought to ground arithmetic in pure logic by defining mathematical concepts in logical terms or showing it as deducible from logical premises.

Logic as Objective (01:51)

Before Frege, laws of logic were regarded as laws of thought. Frege held that the validity of a proof could not depend on our psychology, attacking Husserl and German idealism and developing a theory of meaning.

Sense and Reference (03:13)

Frege introduced the distinction between sense and reference. A.J. Ayer explains the distinction.

Philosophy Moves Toward Logic (01:08)

The theory of knowledge was long the dominant concern of philosophy. Anglo-American philosophy has shifted its focus to logic and questions about meaning; Frege has been influential.

Dummett Exaggerates on Frege (01:27)

Ayer disputes Dummett's claim that Frege revolutionized philosophy by dethroning the theory of knowledge; the study of meaning dates to Socrates and encompasses its own theory of knowledge.

Russell Finds Contradiction in Frege (02:32)

Russell did work Frege had already done before discovering him. Russell exposed a fatal deficiency in Frege's system. Frege thought his life's work had been demolished.

Frege Ignored (01:25)

Prior to Russell's discovery of Frege, his ideas were ignored in England because he wrote in German, and in Germany because Germans were committed to a psychological view of logic.

Revival of Logic (01:45)

The science of logic had been static since Aristotle but exploded as a result of Russell's and Frege's work. The effect has been to subdue logic to mathematics, whereas the reverse was Russell's and Frege's goal.

Russell Moves to Philosophy (03:26)

Apart from the theory of description, there is little connection between Russell's logic and his work in general philosophy. Rather, Russell simply follows in the British empiricist tradition in philosophy.

Russell's Interest in Justification (01:28)

Connecting Russell's logic his philosophy is his interest in justification; his empiricism sought to justify science in terms of sense data. When learning geometry at twelve, he agreed only provisionally to accept axioms.

Russell's Empiricism (03:22)

During most of his life, Russell believed in the existence of a physical world merely as the best explanation for sensory experiences. During one period, he believed every scientific statement could be reduced to sensory experience.

Justification, Metaphysics and Science (02:17)

Russell's effort to insure that our beliefs related to evidence sweeps aside metaphysics. Russell sought justification for science and found that it required assumptions taken on faith.

Russell's Influence (01:56)

In logic, Russell was influential, but when it came to applying logic to philosophy, it was his contemporaries like Whitehead who influenced him. Other thinkers swayed him toward and away from idealism.

Russell and Analytic Philosophy (01:29)

Russell persuaded subsequent philosophers that since science is sovereign, all philosophy could do is elucidate and analyze. Believing philosophical problems had solutions, he opposed purely linguistic philosophy.

Russell's Influence on Ayer (02:19)

Ayer traces to Russell's direct influence his own view that a philosopher should start with sense data, his Humean rejection of causal necessity, his rejection of metaphysics, and his belief that philosophical questions have answers.

Russell's Status Post-WWII (02:53)

After WWII, Russell was downgraded due to an upgrading of Moore, the philosopher of common sense, Ayer says. Magee counters that many major names of the time were influenced by Russell.

Frege Revival (02:30)

Ayers discusses the works and thinkers who led the Frege revival but doesn't know what caused it and doesn't think it had lasting importance.

Russell's Value (00:50)

Ayers believes Russell's influence will last; his answers will require consideration, and his conception of philosophy as consisting of clarification, analysis and justification of important beliefs is correct. His clear prose is valuable.

Credits: Frege, Russell, and Modern Logic (00:45)

Credits: Frege, Russell, and Modern Logic