Russell's Paradox - A Ripple in the Foundations of Mathematics

What is a number? (no using the word number)

What I learned from this is if you get a letter from Bertrand Russell, don't read it.

I enjoyed this video so much. The animation and the explanation are so good!

I'm three years late to the party, but I really enjoyed this video and wanted to offer an answer to the important question you asked, "What Is A Number?" The most perfect definition of what a number is that I've ever come across was over 25 years ago when I first read a book called "Mister God This Is Anna." Anna was a truly remarkable 5 year old girl who asked the same question and shared her incredible answer. Anna knew that 1 planet and 1 ant were in no way equal, but wanted to find how and why the number 1 made them equally countable as "1" mathematically. She discovered her answer through a light and shadow experiment. She had an adult set up an overhead projector so a blank square of light shined on a wall. She then placed an apple on the overhead projector screen which made a 2D shadow of the apple on the wall. She then taped a piece of paper on the wall, traced the outline of the apple's shadow and cut it with scissors. She then placed the paper cutout of the apple's shadow in front of the projector holding it at a 90 degree angle, which created the 1D shadow of a line on the wall. She put another piece of paper on the wall, traced the line and cut it out. Then she took the paper cutout of the line and held it over the projector at a 90 degree angle...and was left with a zero dimensional dot on the wall. Then she pointed in excitement and said. "That's what a number is!" No matter what the size, weight or shape of the object was that she conducted this experiment with, she was always left with the exact same dot. She then realized that if there was a projector and a wall big enough, her experiment would get the same dot putting a planet in front of it as an ant. And so Anna concluded that in our three dimensional universe, a number is light's shadow of a shadow of a shadow. I've never found a more beautiful or perfect definition that doesn't use the word "number" and is fully supported by experiment with completely repeatable results.

The clarity you bring to these difficult to articulate and comprehend topics is exceptional.

This was fantastic. Please don't worry about being overly-nuanced or complex--there is already plenty of dumbed-down content available elsewhere, and you have a skill at presenting complex concepts in a straightforward, understandable manner. Thanks.

The barber was pulling his hair out trying to solve this problem, which ironically did solve the problem.

This is the best and clearest explanation of Russell's paradox that I've ever heard/seen. Thank you so much. I think I actually get it now :)

nice video, but OMG i feel so bad for frege. imagine being so determined that you would solve all of math and then your years of hard work is just crushed. i understand math is like that because theres paradoxes and all, but i feel like me and lots of other people can relate to the poor man mentally

Consider a sets of all sets that have never been considered. Oh wait, they’re all gone now, never mind.

Not only did Russell live a long life (he died aged 97), make huge contributions to logic and win the Nobel Prize for Literature. He also wrote A History of Western Philosophy, a book which remains the standard text for anyone interested in the subject. In short, Bertrand Russell was a truly remarkable guy. This was a great video. Thx for sharing.

The barber is a woman....................................

omg i've seen videos on this paradox so often but this is the first time i actually got it!! Thank you sm🙏🏼

This is brilliant. I was trained as a physicist and last night - over a bottle of wine - tried to explain the Russel paradox to my baffled adolescent daughters 😃. I now sent them this link 😂

"So Baldrick, if I have some beans and add one more bean, what does that make?" "A very small casserole m'lord."

That was absolutely beautiful! Explained at a level that even I could understand, and with great animation. Yes, it did bring me out in a chuckle with the sets within sets. Proves what a mess we all are! 🤭

Quick point: There isn't actually any paradox with Frege's theory of concepts and extensions at all (as it was presented in this video at least); that idea is used in ZFC set theory all the time (every well-defined property φ induces a class of sets satisfying φ). The reason this isn't a contradiction is that there is no notion of a class containing another class - so you can't have a class of classes that do not contain themself. The contradiction seems to just be in the way he defined "set". If you swap it for the modern idea of a set, then you get a perfectly good model for set theory.

Gottlob Frege: * makes a definition of number* Bertrand Russell : I'm about to end this man's whole career

This was great. I have heard Russell's Paradox before and my response was usually, "Ok, but so what?" What you did here was put a seemingly uninteresting paradox into both the historical and mathematical context to help me see why this paradox is so important and interesting. Thank you.

Upstanding presentation.., I found it very insightful w/thought provoking explanations and great animation!