For people who haven't encountered it yet, this problem is the famous "Russell's Paradox"[1], which can be stated as
Consider the set R, consisting of all sets S such that S is not an element of S.
Ie in set builder notation
R = {S : S ∉ S}
and then the paradox comes from the followup question. Is R an element of R? Because of course if it is in R, then it is an element of itself so it should not be. And if it's not in R, then it is not an element of itself, so it should be. This is a logical paradox along the same lines as the famous "The barber in this town shaves all men who do not shave themselves. Does he shave himself?"
In modern axiomatic set theory, Russell's paradox is avoided these days by the "axiom of regularity"[2] which prevents a set builder like "the set of all sets who are not members of themselves", so what I wrote above would not be accepted as a valid set builder for this reason by most people.
Russell proposed instead Type theory which got revived when computer science got going.
I'm not familiar with this one but is it misstated here? The barber doesn't only shave men who don't shave themselves. If he doesn't shave himself then he shaves himself and therefore can shave himself without contradiction. If he shaves himself he can shave himself without contradiction. Either way he shaves himself.
(Or maybe I'm just bad at logic)
> The barb in this town shaves all men who do not shave themselves. Does the barber shave themself?
This is a wonderful interview with him that gives a great sense of what he was all about:
• A Conversation with Bertrand Russell (1952) https://youtu.be/xL_sMXfzzyA
While young his grandfather told Bertrand about meeting Napoleon. Late in life Bertrand watched the moon landing on TV.
Obviously that two experiences that span more than one life time, but they are very far apart.
https://www.openculture.com/2022/05/philosopher-bertrand-rus...
> Jan 6/1962 Re nuclear disarmament and world government. BR is not inclined to agree or disagree with Mosley's views, but he does think that Mosley is "rather optimistic" in his expectations. BR provides criticism of his main two objections. (A polite letter.)
> Jan 11/1962 Mosley wants to lunch privately with BR about their differences.
These are basically all the letters exchanged with Mosley:
https://bracers.mcmaster.ca/bracers-basic-search?search_api_...
The letter written by Russell was preceded by a letter from Mosley (maybe trying to bait BR) on "the root differences between us" in December 1961 to which BR replied with two letters before Mosley tried to invite BR for a private lunch which prompted the letter of note response. I think this makes perfect sense, he initially engaged intellectually, but when invited to associate privately he strongly refuses.
The only letters that Russell personally wrote to Oswald were sent in January 1961.
I can't find a copy of the letter this is in response to which would provide more context. I believe it was an invitation of some sort.
Bertrand Russel was a prominent logician and philosopher, more or less invented types to solve a problem he was having with set theory.
https://en.wikipedia.org/wiki/Bertrand_Russell
Sir Oswald Mosley founded the British Union of Fascists.
https://en.wikipedia.org/wiki/Oswald_Mosley