Meditation on « Russell's silence »

Saunders Mac Lane (1909-2005) was an American mathematician who, together with Samuel Eilenberg, founded category theory.


Mac Lane had an interesting anecdote in his autobiography:


"Early in my work at Harvard, I had a confrontation with Bertrand Russell. At the time, he was visiting the United States and one of the social science departments at Harvard. The mathematics colloquium invited him to give an address on foundations, which he did: the audience that came was so large that the colloquium had to move from its regular room to a larger room normally used by physicists.


Russell proceeded to give an enthusiastic lecture, which, roughly speaking, described the state of mathematical logic as it was in 1920. At the end of his talk, the chairman asked for questions. Being a little disappointed that he hadn抰 covered any recent results, I asked Russell how he related all this to Hilbert's recent work on first order logic and to Kurt Goel's spectacular results with his incompleteness theorem. There was a long silence. Finally, the chairman said, perhaps someone else has a question". Fortunately, someone did.


I never met Russell again. As an undergraduate at Yale I was mightily impressed by Principia Mathematica Russell had been my hero. By 1938, I realized that new ideas about logic were even more impressive. In retrospect, I felt guilty about my question should have known that Russell would not have been able to answer. In doing so, I was too impatient to realize that he had appropriately decided to shift his early interest from logic to other subjects had not kept up with current results in logic because he had been busy working on other things. However, it is a fact that the splendid background development in Principia made Godel theorem possible. »


There have been various speculations about "Russell's silence", including, for example, Mac Lean's explanation that « he had appropriately decided to shift his early interest from logic to other subjects had not kept up with current results in logic because he had been busy working on other things ».


However, from Alasdair Urquhart's compilation of "Russell's response to Godel's theorem" [2] [3], we can see that Russell was always concerned with Godel's theorem, and he expressed his confusion and doubts frankly at various times, describing Godel's theorem as a "paradox" (1945), a "puzzle" (1950), a "difficulty" (1965), etc.


I prefer to look at "Russell's silence" from another angle: faced with Gödel's theorem on the "altar", Russell chose to remain persistently silent in front of a packed audience in the room, thus putting himself in an awkward situation, rather than say something against his heart.


 

Reference :

[1] Saunders Mac Lane: A Mathematical Autobiography. https://www.amazon.com/Saunders-Mac-Lane-Mathematical-Autobiography/dp/1568811500

[2] Alasdair Urquhart, Russell and Gödel. https://www.academia.edu/27310325/Russell_and_G%C3%B6del

[3] Meditation on « Russell’s response to Godel’s theorem », https://revisiter-godel-article.blogspot.com/2022/11/meditation-on-russells-response-to.html

Comments

Post a Comment

Popular posts from this blog

Workshop on revisiting Gödel's Incompleteness Theorems (25th WCP, August 1-8, 2024, Rome, Italy)

  General abstract  Journey to the Edge of Reason - The Life of Kurt Gödel by Stephen Budiansky in 2021 (Norton & Company) presents « The first major biography written for a general audience of the logician and mathematician whose Incompleteness Theorems helped launch a modern scientific revolution. Nearly a hundred years after its publication, Kurt Gödel ’ s famous proof that every mathematical system must contain propositions that are true—yet never provable—continues to unsettle mathematics, philosophy, and computer science. » This is no exaggeration, so what is there in Gödel's incompleteness theorem that unsettles people until now? Taking a closer look, we find that there is a malaise implicit in Gödel's proof: Gödel claimed to have argued that a paradoxical proposition such as « saying of itself that it is unprovable" is an "undecidable proposition" in a formal system, and thus concluded the incompleteness of the formal system. We can't help...
Read more

Meditation on « Russell’s response to Godel’s theorem »

Alasdair Urquhart's article «  Russell and Gödel »   is very helpful for a comprehensive understanding of Russell's views of Gödel's theorem, where Chapitre 3 is « Russell’s response to Godel’s theorem ». Russell was very careful in his responses to Gödel's theorem, as presented in this article ([1] p.10-14), and Russell never made a simple right or wrong judgement about Gödel's theorem, but was honest in expressing his confusion and doubts : in a 1945 article, Russell described Gödel's theorem as paradox; in a 1950 article, Russell described Gödel's theorem as puzzle; in a 1963 letter to Leon Henkin, Russell expresses his puzzles about Gödel's theorem; and in a 1965 commentary, Russell said that Gödel presented a new difficulty, … Russell's attitude was consistent. In 1965 Russell was invited by Schilpp to write the following commentary on Gödel's work ([1] p.10-14) : Not long after the appearance of Principia Mathematica, G¨odel propounded a ne...
Read more