Bertrand Russell: The Teapot Crackpot

Bertrand Arthur William Russell, 3rd Earl of Russell, born in 1872, was a renowned mathematician and philosopher. Russell’s work spanned many different fields, from the foundations of logic to the inner workings of society. Russell published more than 70 books and countless essays spanning all of his interests, culminating in Russell winning the 1950 Nobel Prize in Literature (1). Throughout his life, Russell participated in many social movements, including but not limited to supporting women’s right to vote, pacifism and freedom of religious thought. Russell remained involved in both philosophical and activist work until he died at the age of 97, in 1970. (1).

1 Early Life and Career

Bertrand Russell was born May 18, 1872 in the village of Trelleck within the Monmouthshire county of Wales, United Kingdom. His parents, John and Katharine Louisa Russell, were considered radicals at the time for their support of birth control and promotion of atheism. The Russell family was an institution of aristocracy, with John Russell’s official title being Lord Amberley and Bertrand Russell’s grandfather, Earl, having been called upon by Queen Victoria to serve as Prime Minister in the 1840s and 60s (5).

In 1876 Russell’s mother and sister Rachel both died of diphtheria. Russell’s father then died of bronchitis two years later in 1876, leaving Russell and his brother Frank in the care of their paternal grandparents. Russell grew up lonely during his years living with this grandparents, often contem- plating committing suicide (5). He stated later in life that the only reason he did not take his own life was his passion to learn more about mathematics. When Russell came of age he went to Trinity College to study mathematics and philosophy, quickly gaining praise and prestige, then moving on to complete his studies at Cambridge (5). While formally a mathematician, Russell’s first published work outside of university was a study of social politics. In 1896 Russell published German Social Democracy, a study of the German governmental system. This was not Russell’s last piece writing on politics, a subject he continued to study throughout his life. His next major work, at Trinity, was An Essay on the Foundations of Geometry, which explored the fundamental mathematical concepts in a non-Euclidean space (1).

2 The World Wars

As with many who were alive during the first half of the 20th century, Russell was greatly influenced by both World War I and World War II. Russell was at Trinity College during World War I, and was a staunch pacifist (5). During World War I Russell took an anti-war stance, actively promoting pacifism and arguing against the war. His actions let to his dismissal from Trinity college an imprisonment under the Defence of the Realm Act 1914. Russel was convicted and imprisoned again in 1918 for publicly speaking out against Britain asking the United States to join the war effort. After the war ended in November in 1918 Russell was reinstated to his former position at Trinity College, though he would resign not long after (5).

Decades later during World War II, Russell took the (very unpopular) stance that Great Britain should not show hostility towards Nazi Germany. Russell believed that if German forces where to try to invade the island mainland of Great Britain, people should welcome them with kindness and compassion. He believed that the best course of action was to have the leaders of Britain and Germany meet and discuss matters to negotiate peace over tea (5). A very solution. As the war continued and the war crimes committed by the Nazis became more apparent and well known, Russell came to change his views towards that of war being the ”lesser of two evils.” He recognised that if Hitler was to conquer all of Europe, it would be the end of democracy and freedom and the victory of fascism. While Russell was a firm pacifist, he came to the conclusion that under extreme circumstances war could be the only solution to maintain peace and freedom (? ).

3 Mathematics

Russell’s most well known work in the field of mathematics is his Principles of Mathematics. Russell wrote his Principles of Mathematics with the help of fellow mathematician Alfred North Whitehead. Principles of Mathematics (often abbreviated as PM ) was written in three volumes, published in 1910, 1912 and 1913 (? ). Russel stated that PM had three primary goals: to fully explore the extent of mathematical logic, to write mathematical proofs and propositions using a single and understandable symbolic set, and to find solutions to mathematical paradoxes and contradictions (? ). While PM was a very instrumental text at the time and is important to remember in mathematical history, it is rarely used or studied today. A primary reason for this it that, despite its goal of making an using a non-complex symbol set for proofs, is quite complex and difficult to understand. One such example of PM ’s complexity and long-windedness is the section of hundreds of pages of mathematical text leading to a proof of the validity of 1 + 1 = 2 (4).

Another of Russell’s major contributions to mathematics is his famous paradox. Russell first discovered the paradox existed in 1901, but never published it. Russell’s paradox relates to the field of näıive set theory (4). It states that a set of all sets that are not members of themselves looks to be a member of itself, but is in fact not. To put this in simpler terms, some sets, such as a set of all baseball cards, is a set that does not contain themselves. A set such as a set of all things that are not baseball cards is a member of itself because it is not a baseball card.

In Russell’s paradox, the set of all sets that are not members of themselves is known as ”R.” If R contains itself, that means it is within its own set, and by definition not a member of itself, hence the paradox (4). Like- wise, if R is not a member of its own set, then it does not contain itself and, by definition, is a member of itself.

Russell’s paradox can be written symbolically as: Let R = {x|x /∈ x}, then R ∈ R ⇐⇒ R /∈ R (1)

More modern and formal presentations of Russell’s paradox in Definite Naive Set Theory write it using the common unrestricted comprehension axiom schema:

∀x∃y(x ∈ y ⇐⇒ ϕ(x)) (2)

This means that for any formula, ϕ, with the input variable of x, through instantiation we have:

ϕ(x) ∈ ϕ(x) ⇐⇒ ϕ(x) /∈ ϕ(x) (3)

showing an innate contradiction (4).

One of Russell’s most impactful legacies in mathematics outside of the writing of PM and his other works is his influence in Kurt Gödel’s Incom- pleteness Theorem. Gödel was an Austrian mathematician born in 1906 who emigrated to the United States during World War II, and had a profound effect on the philosophy behind scientific thinking (6). In his old age he began to believe that everyone but his wife wanted to poison him, causing him to only eat food his wife prepared for him. Once she passed away, Gödel starved himself to death rather than eat food cooked by someone else. Gödel’s Incompleteness Theorem has to do with the bounds of what is and is not provable using standard logic (6).

Theorem 1 ”Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F.” (6)

4 Philosophy

While known greatly for his work in mathematics, Russell also wrote on almost all philosophical topics. He is considered by some to be the father of modern analytic philosophy (4). Analytic philosophy is a method of tackling philosophical issues and problems analysing the fundamental components of the topic. It generally has an emphasis on precise logic. On the topic of ethics, Russell was a self described utilitarian, meaning he judged the moral value of an action or idea based on how useful it is to society as a whole, rather than based on the intent (4).

One of Russell’s most famous thought experiments is that of Russell’s teapot. Russell’s Teapot posits that there is a teapot orbiting the Sun somewhere between Earth and Mars. The teapot would be too small to see with a telescope (or at least telescopes that were present at the time), which means that it would be impossible to prove its existence. However, it is also impossible to categorically prove that the teapot does not exist. Obviously, there is no teapot orbiting the Sun, but the argument can be made and cannot be disproved. Russell used this analogy to demonstrate that, when in a philosophical discussion, the burden of proof lies on the party making the affirmative statement (4).

Russell first presented his teapot analogy in 1952, in an article titled ”Is There a God?” He thought that the existence of a god of any kind was about as likely as a teapot revolving around the Sun. While Russell originally presented the teapot in the context of religion, it has often been related to scientific proof since its inception (4). In this context when a scientist has a theory, say a physicist about the origins of the universe, he or she must not only present the claim, but also present reason and evidence for why the claim is true. However, someone who is refuting the claim only needs to show a flaw in reason or why the evidence may be misleading, without providing any concrete proof of their own. Some scientists and philosophers, such as Paul Chamberlain, disagree with this idea, saying that anyone making a claim of any kind needs to back that claim up with sufficient evidence (4).

5 Society

While much of Russell’s work focused on mathematics and philosophy, he was never afraid to venture into the realm of social activism to speak out against what he saw as wrong with society. Russell, like many other thinkers of his time, pushed for what was described as a ”scientific society.” A ”sci- entific society” is one where the goal of the group is to collectively advance scientifically, while also abolishing war and any other form of violent conflict (4). Russell advocated for a single, overarching, powerful government body to act over the entire world. He believed that this type of leadership would be able to maintain peace and prosperity, while also limiting population growth (4). Some of Russell’s opinions are similar to those of noted philosopher Thomas Hobbes, who believed that the only way to make a cooperative Society with was an all-powerful”leviathan” government. However, Russell did have more faith in the virtues of humanity than Hobbes, who believed that people were naturally violent and selfish creatures that must be forced to work together rather than kill each other over food.

6 Religion

Russel’s father, John Russell, was a staunch atheist and encouraged the same mentality in his son. This is most evident when they asked the noted philosopher John Stuart Mill to be Russell’s secular godfather (5). Mill was a public agnostic and well-known skeptic, who often questioned the tenants of Britain’s most popular religion of the time, Christianity. However, Mill died in 1873, a year after Russell was born. While Mill never influenced religious Russell’s views directly, his writings had a great influence on Russell’s life (5).

Russell lived his life as an agnostic, believing religion was nothing more than myth and superstition (4). He claimed that, despite the positive effects of religion, it largely served to hurt people and society. Russell believed religion obfuscated science and analytical thought, replacing reason with dependency on an authority system (4).

7 Death and Legacy

Russell died at the age of 97 on February 2nd, 1970. He is remembered as one of the most influential mathematicians and philosophers of the early 20th century (5). He is celebrated for his works and contributions to logical-mathematical and analytical philosophy, while also pushing for social progress and freedom. Russell and his work are remembered today in the form of the Bertrand Russell Archives and the Bertrand Russell Research Centre, both located at McMaster University in Canada (5).

References

1. ”About Bertrand Russell.” About Bertrand Russell – The Bertrand Russell Society users.drew.edu/ jlenz/brs-about-br.html.
2. Bertrand Russell, ”The Study of Mathematics,” The New Quarterly 1 (Nov 1907) Repr. Philosophical Essays, Longmans, Green, and Co., 1910; Mysticism and Logic and Other Essays, London, Longsmans, Green and Co., 1918, pp. 58-73.
3. Bertrand Russell – Nobel Lecture. NobelPrize.org. Nobel Media AB. Sun. 17 Nov 2019.
4. Irvine, Andrew David., and Deutsch, Harry. ”Russell’s Paradox.” Stanford Encyclopedia of Philosophy 2016. Print.
5. Monk, Ray. ”Bertrand Russell.” Encyclopedia Britannica, Encyclopedia Britannica, Inc., 1 Nov. 2019, https://www.britannica.com/biography/Bertrand-Russell
6. Raatikainen, Panu. ”Gödel’s Incompleteness Theorems.” Stanford Encyclopedia of Philosophy 2015. Print.
7. Image: Bertrand Russell. Wikipedia.https://en.wikipedia.org/wiki/BertrandRussell