Bertrand Russell is such an inspirational figure I hardly know where to begin. Russell was at Trinity College, Cambridge alongside G.H.Hardy FRS (1877-1947) who wrote the wonderful book “A Mathematicians apology” claiming in it that everything he had done was worthless, rather a strange statement. Hardy worked with the great Indian Mathematician S. Ramanujan FRS (1887-1920) (yes the man who knew infinity) and J.E. Littlewood FRS (1885-1977) creating fruitful collaborations. Bertrand (if I may) wrote his Principia masterpiece and named it in the spirit of I.Newton (1643-1727) who also wrote a Principia, this naming was actually quite common with Charles Lylle FRS (1797-1875) the father of Geology similarly writing his masterpiece with the title Principles of Geology (which I have in my office at home).
Bertrand’s work was in logic and included ideas of Kurt Godel (1906-1978) who worked on two of Hilbert’s (1862-1943) famed 23 problems in which the eighth is the legendary Riemann hypothesis and which is still unresolved (as stated on 8th September 2021) today. Godel developed his incompleteness theorem, and it is well known that Kurt took up a job at Princeton’s Institute of advanced study so that he could talk to Einstein and take long walks with him, I would have loved to have been a fly on the wall during these talks, but I recall reading that Kurt stated that he loved hearing Albert’s laugh as it made the whole room shake (awesome).
Returning to Bertrand (who won the Nobel Prize in literature in 1950, what an intellect) developed in 1901 what has become known as Russell’s Paradox and which overturned the life work of Gottlob Frege in a single swoop, however Russell states that Frege acted with incredible integrity and fortitude even though his entire life’s pursuits had been shown to be incomplete, thus:
As I think about acts of integrity and grace, I realise that there is nothing in my knowledge to compare with Frege’s dedication to truth. His entire life’s work was on the verge of completion, much of his work had been ignored to the benefit of men infinitely less capable, his second volume was about to be published, and upon finding that his fundamental assumption was in error, he responded with intellectual pleasure clearly submerging any feelings of personal disappointment. It was almost superhuman and a telling indication of that of which men are capable if their dedication is to creative work and knowledge instead of cruder efforts to dominate and be known. (Quoted in van Heijenoort (1967), 127).
Russell’s so-called Barber problem paradox is a misnomer as it was known to Frege and was not stated by Russell, the paradox can be stated as:
“The barber is the “one who shaves all those, and those only, who do not shave themselves”. The question is, does the barber shave himself?”
Thinking about this one soon realises that there is a circular contradiction.
Well Bertrand gives us more wise words in this quote: “The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.”