# Bertrand Russell

Philosophy is a weird subject. Many of us have had to learn some of it in high school, but we quickly dismissed it as we move forward in life, only to rediscover it as soon as we hit some midlife crisis along the way. Or, at least, that was the experience of this author. Yet philosophy is the only real bridge uniting all sciences, and as such deserves a much brighter spot on it. In particular, the road that led us to the computer was primarily built by philosophers, and in particular, by Bertrand Russell, whose 1959 interview is the subject of this month’s Vidéothèque article.

To say that Bertrand Russell is a towering figure in the history of philosophy and mathematics is a gross understatement. As said previously in this magazine,

The name of Kurt Gödel often appears in the pages of this magazine, and with reason. After all, the thought process that led to modern computing has Gödel as a major milestone and can be clumsily summarized as follows: Cantor ⇒ Hilbert ⇒ Russell ⇒ Gödel ⇒ Church ⇒ Turing ⇒ Von Neumann.

Russell is the incarnation of the inflection point between 19th century mathematics and the 20th century computer you are using to read these lines. He thought about and asked the right questions at the right times. Let us consider three contributions directly related to our daily work as dwellers with code and programming.

First, Russell’s famous paradox led to the proposal of a type theory, arguably at the origin of most type systems we use today. Alonzo Church references Russell’s paper “Mathematical Logic as Based on the Theory of Types” as prior work in “A Formulation of the Simple Theory of Types”. Leslie Lamport and Lawrence Paulson explained it decades later:

As programmers know, an unduly restrictive type system can make it hard to write perfectly reasonable expressions. Whitehead and Russell realized that a type discipline has to be ﬂexible. The proof of a theorem like x ∈ {x } must not depend on the type of x. They invented (in 1910!) the concept we now call polymorphism, which they called typical ambiguity.

Second, Russell’s search for a coherent set of rules for all mathematics, as described in his and Whitehead’s Principia Mathematica, led directly to Gödel stating his incompleteness theorems, themselves at the very origin of the science of computation. The influence of Russell’s work on Gödel’s was highlighted by Alasdair Urquhart in the December 2016 edition of The Bulletin of Symbolic Logic:

In spite of the highly critical remarks quoted above, Gödel’s work shows the strong imprint of Principia from his work on completeness to the results on the continuum hypothesis.

Third, Russell anticipated Lambda calculus 30 years before Alonzo Church, and even the “lambda” notation is said to have evolved from Russell’s and Whitehead’s Principia, following typesetting difficulties, as explained by Kevin C. Klement, professor at the Philosophy Department of the University of Massachusetts, in 2010, quoting a 1984 book by Henk Barendregt.

To sum up: in 1903, after he had done a close study of Frege’s logic and inspired by Frege’s

Wertverlaüfenotation, Russell hit upon a sort of logical system of functional abstraction operating very much like modern Lambda Calculi.

Beyond his contributions to logic and mathematics, Russell was also a passionate fighter for peace and nuclear disarmament, most notably using his celebrity to contact directly Nikita Khrushchev and John F. Kennedy in the most complicated moments of the Cold War, or joining forces with Albert Einstein, Jean-Paul Sartre, or Simone de Beauvoir in successive calls for peace. His writing begat the bestseller philosophy book of the 20th century, and brought him a Nobel Prize in Literature, among other accolades. Oh, and did I mention that he was the doctoral advisor to Ludwig Wittgenstein?

But as I stated at the origin of this article, philosophy is a weird subject, and it is always somewhat shrouded (at least in the mind of the uninitiated) in mystery, elitism, and pretentiousness. And unfortunately, many use philosophy as a weapon to “separate the grain from the chaff” among members of society, instead of advocating for its core principle: that of bringing knowledge and society together through thinking. Fittingly enough, citing the names of Schopenhauer, Luc Ferry, Spinoza, Alain Badiou, Confucius, Hannah Arendt, or Marcus Aurelius into a conversation is a sure way to lose 90% of your audience in a few seconds.

We do not want to lose our audience here; we want to enlighten them, the same way this author was enlightened by learning about, if not always directly reading, the works of the aforementioned personalities. In particular, philosophy and mathematics have a strong bond, and thinking about thinking becomes, with a little practice and awareness, a healthy exercise for any thinking mind. This is akin to figuring out the right algorithm for your application, a fundamental skill at work. Besides, surprisingly enough, both exercises are deeply intertwined and connected in mysterious ways.

Thinking minds abound in the software field. Here is this author wishing for all of those software workers reading this article to dive into the subject of philosophy with open arms and minds. You will all emerge a stronger person, able if not to justify, at least to understand the choices you make in everyday life, and in particular, your professional one, generating empathy for you, and then for others.

But where to start? Well, thankfully many works by Bertrand Russell are now available in the public domain, so here go some suggestions. On the Project Gutenberg there are quite a few, including “Mysticism and Logic and Other Essays”, “An Essay on the Foundations of Geometry”, and “The Analysis of Mind”. On Standard Ebooks, “The Problems of Philosophy” is “an introductory book for a beginner in philosophical studies.” All excellent starting points, even if somewhat demanding in terms of concentration. A notepad next to your book is highly recommended.

We are about to finish this article, but we have not even talked about this month’s Vidéothèque video. Actually, we have already talked about this short video in our edition about Mathematics a few months ago, but it is worth repeating the core of this interview here, in an edition about perspectives:

In this world, which is getting more and more closely interconnected, we have to learn to tolerate each other. We have to learn to put up with the fact, that some people say things that we don’t like. We can only live together in that way. And if we are to live together and not to die together, we must learn a kind of charity and a kind of tolerance, which is absolutely vital to the continuation of human life on this planet.

Cover snapshot by the author.