Bertrand Russell: A relentless logician

This transcript comes from an interview on a British television network in the 1960s, with the great philosopher Bertrand Russell, who passed away 55 years ago last month. Despite his strong views on the distinctions between science and philosophy, throughout his long and remarkable life—during which he witnessed the decay and downfall of an old world—he never missed an opportunity to connect the two.

Bertrand Russell was born in Wales, Great Britain, as the third son of a liberal aristocratic family. His parents held the titles of Viscount and Viscountess Amberley and championed progressive causes for their time, such as support for birth control and women’s suffrage. Russell had little opportunity to know them: his mother died of diphtheria when he was two, and his father died of pneumonia two years later.

He was then sent to live with his grandparents, who were considered quite old even in terms of that era. There he came to know his grandfather, John Russell, a former prime minister of Britain.

Bertrand later recounted that his grandfather had once met Napoleon Bonaparte during his exile on the island of Elba in 1814—an event that occurred roughly 140 years before this interview took place (!). His grandfather died when Bertrand was six, and his grandmother thereafter became the dominant figure in his life.

Despite his parents' request that he be raised as an agnostic—one who holds that belief or disbelief in God is unwarranted since His existence cannot be proven either way—his grandmother, a devout Presbyterian, refused to follow their wishes in his upbringing. However, she was also remarkably progressive in her views.

Russell barely had a chance to know his parents: his mother died of diphtheria when he was about two years old, and his father died of pneumonia two years later.

Russell’s youth and adolescence was marked by loneliness, and on many occasions, he contemplated ending his own life. It was an old book, Euclid’s “Elements”, that profoundly reshaped his worldview. This 13-volume work, which formed the foundation of scientific education for over 1,500 years, came into his hands when he was just 11 years old.

From that moment and for nearly three decades, mathematics became the central pursuit of Russell's life. At the same time, his deep engagement with Christian dogmas led him to two profound philosophical conclusions—both reached before he turned 18: first, that free will is an illusion; and second, that there is no life after death. Around this period, he also embraced atheism, drawing him closer to the beliefs of his late parents.

In 1890 Russell began his studies at Trinity college at Cambridge, the prestigious institution that had once been home to Issac Newton and later also Niels Bohr.

One of the faculty members was the philosopher and mathematician Alfred North Whitehead, who not only cultivated Russell’s mathematical abilities but also led him into the depths of logic, as we will soon explore. The rest of the decade was marked by a series of romantic entanglements, including his first marriage to Alice, which soon fell apart and ended in separation.

At the turn of the 20th century, Bertrand Russell was working on his essay “The Foundations of Mathematics”, in which he sought to demonstrate that mathematics and logic are fundamentally the same. In 1901, while immersed in work on his book, he was troubled by a thought that could be illustrated through a figurative short tale – a story he called The Barber Paradox.

In a remote village, there was only one barber who followed a strict rule: he shaved everyone who did not shave themselves but never shaved anyone who did. This leads to a paradoxical question: Is the barber allowed to shave himself?

On one hand, if the barber shaves himself, then according to the rule, he is not allowed to do so—creating a contradiction. On the other hand, if the barber does not shave himself, then according to the rule, he must shave himself—again leading to a contradiction. This seemingly silly story can be formulated in a more formal manner, which was precisely what Bertrand Russell did.

He presented this paradox to his German colleague Gottlob Frege – a logician, philosopher, and mathematician who advocated logicism, the view that all of mathematics could be reduced to logic. Russell argued that the paradox contradicted one of the axioms in one of Frege’s volumes. To Frege’s great embarrassment, he was forced to abandon the completion of his next volume and acknowledge that he had no satisfactory resolution to Russell’s paradox.

This paradox was the driving force behind Russell's magnum opus, his most significant work, to which he devoted nearly a decade of his life alongside his mentor and old friend Whitehead. Their work focused on the foundations of mathematics, mathematical logic and the ambitious attempt to establish a firm connection between the two.

Their guiding principles were twofold: (1) Every mathematical truth can be translated into a logical truth. (2) Every mathematical proof can be reformulated as a logical proof. These were bold claims that did not escape the scrutiny of their critics.

While Frege defined a mathematical set based on its members, which led to the paradox, Russell circumvented this issue by defining a set according to a rule that determines its members. His and Whitehead’s essay Principia Mathematica, named in reference to Newton’s legendary work, promoted the development of an entirely new field of mathematics: Axiomatic Set Theory.

The main contributors to the formation of the new field were Ernst Zermelo and Abraham Fraenkel. Fraenkel later immigrated to Israel, where he became rector of the Hebrew University of Jerusalem (HUJI). Axiomatic set theory is widely regarded as the most effective resolution to Russell’s paradox, preceded by a theory developed by Russell himself, known as type theory.

In 1905 Russell published a major philosophical essay. Titled, “On Denoting”, it became one of the most important works in the history of analytic philosophy, a field pioneered by Frege, Russell, and others. This discipline seeks to analyze language, words, and the way they relate through logical means. It is difficult to separate Russell’s work in this area from his mathematical work, as both belong to the same intellectual continuum—one centered on the attempt to ground everyday life in logical foundations.

By the early 1910s, Russell had already been elected a Fellow of the Royal Society, and following the publication of the first edition of Principia Mathematica, the purely mathematical chapter of his career had largely come to a close.

He took up a teaching position at Cambridge University and began speaking publicly on contemporary issues. By the middle of the decade, World War I had broken out, and his pacifist views put him at odds with his employers. As a result, Russell was dismissed from his position and even imprisoned for violating the Defence of the Realm Act, which prohibited such expressions of dissent.

In 1920, Russell traveled to the newly established Soviet Union, where he met Lenin. He was among the first Western intellectuals to express discomfort with the direction in which the rising superpower was heading. This decade also brought significant personal changes for Russell. He entered his second marriage, to Dora, and the couple spent a year in China.

During this time, their children, John and Kate, were born. Together, they founded Beacon Hill, an experimental school that operated from 1927 to 1943, promoting progressive educational ideas. During this period, Russell also made several unsuccessful attempts to run for Parliament.

By the early 1930s, Russell had divorced Dora and married for a third time, to Patricia, with whom he had a son, Conrad—who would later become a founding member of Britain’s Liberal Democratic Party. In 1940, Russell moved to the United States, where he was appointed a professor of philosophy in New York.

However, his appointment was met with public protests, and the opposition was so strong that his position was ultimately revoked. During World War II, Russell adopted a more pragmatic stance, particularly in response to the growing threat to world peace posed by Nazi Germany, describing war as "the least bad option".

As the war drew to a close, Russell returned to Britain, where he gained increasing public influence among scientists and intellectuals. In 1946 he published another highly influential work, “History of Western Philosophy”, which traced the history of philosophical thought from the days of Socrates to the works of Russell himself.

Thus he became one of the only mathematicians to have ever been awarded the Nobel Prize, which is not awarded for achievement in mathematics. This made him one of the few mathematicians ever to receive a Nobel Prize, as the award is not granted for contributions to mathematics.

In his later years—after marrying for the fourth time, to Edith, who was many years his junior—Russell’s reputation as a staunch anti-war and anti-religion philosopher became firmly established.

During the 1950s, he introduced a thought experiment known as Russell’s Teapot, arguing that in matters concerning the existence of a higher power, the burden of proof lies with the believer, not the skeptic. His argument, which carries a noticeable tone of ridicule toward religion, was as follows:

“If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is an intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense.

If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.”

This manifesto marked the closing of a chapter Einstein had opened with another letter he had written in 1939 with Leo Szilard, which contributed to the establishment of the Manhattan Project. Perhaps in doing so, Einstein sought to atone for the consequences of that earlier letter.

In 1961, for the second time in his life, Russell was imprisoned—this time for a week—after organizing a hunger strike against the Vietnam War. He later established a public tribunal that accused the United States of committing war crimes.

Though he was the first to be awarded The Jerusalem Prize for the Freedom of the Individual in Society in 1963, Russel did not spare the young State of Israel from criticism. In January 1970 just two days before his death at the age of 97, he issued a strong condemnation of Israel’s military actions in its conflict with Egypt, making it his last political statement.

True to his agnostic convictions, he requested to be cremated, and his ashes were scattered. Russell’s ideas continue to resonate, as do the many questions philosophy seeks to answer—though, at times, the ball ends up at the scientists’ court.

Russell’s ideas continue to resonate, as do the many questions philosophy seeks to answer—though, at times, those questions find their way into the realm of science.