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

Bertrand Russell's set theory paradox on the foundations of mathematics, axiomatic set theory and the laws of logic. A celebration of Gottlob Frege.

Thank you to Professor Joel David Hamkins for your help with this video.

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*Sources*

*Music*

[upandatom]

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

[joescott]

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

[johnathancorgan]

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.

[blackpenredpen]

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

[robertferraro]

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

[garyhughes]

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.

[post]

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

[DanHoke]

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.

[davidsapir]

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.

[VexLimenOfficial]

"So Baldrick, if I have some beans and add one more bean, what does that make?"

"A very small casserole m'lord."

[xacharon]

Great video, but my favorite moment is when you said "Tifa is a dog" and she looks at you as if saying "Wait?? I'm a DOG???"

[hvhvgitaar]

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 😂

[malfunction]

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 :)

[vamsikrishnan]

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

[chrisrichards]

Just discovered this channel and spent most of the day just watching a bunch of your videos. Seriously some of the best and most accessible, entertaining science content I've ever come across.

[usvalve]

In the UK, we use the Brexit method to solve the Barber Paradox: the barber keeps saying he's going to shave himself, but he never does :-)

[robertmontgomery]

Brilliant. There’s nothing else like this. I’ve been struggling with this for too long to mention and this graphic presentation is the clearest I’ve encountered.

[rotflmaopmpqxyz]

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

[denniskeefe]

What a wonderful comment about Frege by Russel! Frege, one who put the search of truth above all other matters. You know, as an older retired person, who used to be in the get-ahead-game -- though not particullary dedicated to that -- it is heartwarming to thnk that you can dedicate your last years to Fregel's ideals, and not be penalized for it.

[hunterterrell]

"my nose will now grow" said pinnochio