Frege and Russell: The Birth of Analytic Philosophy

Logic as the Foundation of Knowledge

At the end of the 19th century, the German mathematician Gottlob Frege (1848–1925) created what became analytic philosophy—not intentionally, but in the search for the foundations of arithmetic. His question: what is the number “2”? Not “what is 2+2”—but what does “two” actually mean. It was necessary to answer this question precisely, without appealing to intuition.

Frege invented modern symbolic logic—a language in which logical relations can be written with mathematical rigor. His “Begriffsschrift” (Concept Script, 1879) was a turning point: for the first time, logic received a notation comparable in precision to algebraic notation.

Sense and Reference: The Two Dimensions of Meaning

Frege made a fundamental distinction that became the basis of semantics. “The morning star” and “the evening star” are the same celestial body (Venus). They have the same referent (Bedeutung—what they refer to). But they differ in sense (Sinn—the mode of presentation). “The morning star = the evening star” is not a tautology, but an informative discovery, because the two senses are different.

This distinction has enormous consequences. It explains why “2+2=4” and “the square of the hypotenuse equals the sum of the squares of the legs” are both true, but the first is trivial, while the second is a discovery. It also explains why statements about non-existent objects (“the present king of France is bald”) create logical problems.

Bertrand Russell and Logical Atomism

Bertrand Russell (1872–1970) read Frege and continued his program. Together with Whitehead, he wrote “Principia Mathematica” (1910–1913)—a grand three-volume work reducing mathematics to logic. Simultaneously, Russell developed the philosophy of language.

Russell discovered that Frege regarded numbers as “concepts”—objects of the logical world. This led to paradoxes (the famous “Russell’s paradox”: the set of all sets that do not contain themselves as a member). Russell showed that the intuitive concepts of mathematics require stricter logical analysis.

His “theory of descriptions” solves the problem of the “present king of France”: such expressions are not names, but “descriptions,” abbreviations for complex propositions. “The present king of France is bald” means: “There exists one and only one present king of France, and he is bald”—which, in the absence of a king, is false, not meaningless.

Logical Positivism: The Vienna Circle

In the 1920s and 1930s, a circle of philosophers and scientists formed in Vienna, inspired by Russell and the early Wittgenstein: Moritz Schlick, Rudolf Carnap, Otto Neurath. Their program—logical positivism or neopositivism.

The verification principle: a statement is meaningful only if it is either analytically true (by definition) or empirically verifiable. The statements of metaphysics (“The Absolute is spiritual,” “Free will exists”), religion, and traditional ethics do not pass this test—they are, literally, meaningless.

This is a radical position, which was soon challenged. The verification principle itself is not verifiable—it is not an empirical statement. But the discussion about the limits of meaningfulness and the nature of scientific knowledge turned out to be exceptionally productive.

Question for reflection: Can most of your business and life beliefs be tested as rigorously as Russell tested logical assertions? What would happen if we applied the verification principle to corporate strategies?