Russell's Paradox - a simple explanation of a profound problem

Published 2022-09-08
This is a video lecture explaining Russell's Paradox. At the very heart of logic and mathematics, there is a paradox that has yet to be resolved. It was discovered by the mathematician and philosopher, Bertrand Russell, in 1901. In this talk, Professor Jeffrey Kaplan teaches you the basics of set theory (a foundational branch of mathematics dating back to the 1870s) in 20 minutes. Then he explains Russell’s Paradox, which is quite a thrilling thing if you are learning it for the first time. Finally, Kaplan argues that the paradox goes even deeper than Russell himself realized.

Also, I should mention Georg Cantor, Gotlob Frege, Logicism, and Zermelo–Fraenkel set theory in this description for keyword search reasons.

All Comments (21)
  • Viktoria
    My teacher told me that "all rules have exceptions" and I told her that that meant that there are rules that don't have exceptions. Because if "all rules have exceptions" is a rule then it must have an exception that contradicts it.
  • Vean
    I love the style in which you present your podcasts. You have personality, you connect, you hold our interest ❤
  • Nour Art
    I could sit through a 5 hours math class of this guy, he somehow made a math subject entertaining.
  • Pablo Ucan
    I can't help thinking that on some perverse level Russel was pleased with himself that his ideas had the power to literally blow someones mind.
  • muddledmess
    As someone who is much more linguistic in my thinking than mathematical, this was a great explanation.
  • RayPalmer
    As a History teacher I must say that all set theory you explained starts to make more sense when you talked about the linguistic! Really interesting!
  • Never thought I could have such an enjoyable time watching a 30 min video on advanced mathematical theory. I chuckled and even laughed multiple times. Well done sir
  • Vean
    Jeffrey, you are a born teacher, thank you for explaining this ❤
  • Treezy DCM
    I truly enjoyed your explanation, it is just down to earth and graspable. Thank you! The way I see it is like this: life is full of contradictions that don't always have an explanation, or also life is paradoxical and we have to accept it. Russell just grasped this via Set Theory :P
  • Loved your summary, normally it takes much longer to develop all these topics. Amazing work Jeffrey
  • Alyaster
    Loved this. Highly entertaining and instructive. Top marks.
  • lighthouse
    You are extremely smart and well spoken, thanks for explaining this concept so thoroughly!!
  • JessicaOverthinks
    Honestly, there's a lot beyond my understanding. So it was weirdly reassuring to hear about the genius guy whose brain just straight-up blue screened because of this paradox.
  • This was really good. You're going to be a star.

    I've been studying logic and set theory intermittently for 6 years. Wish this video was around when I started.
  • Antonio Concilio
    Well done! A fantastic video, and an excellent explanation.
  • Casey MrChiller
    From what I have found this paradox has been resolved by the Zermelo-Fraenkel set theory. If a given set z and predicate n exists the subset is {x belongs to z: n(x)} instead of the set {x: n(x)}. This means only subsets can be constructed and that there does not exist a set containing all sets. Interesting stuff! Great video.
  • Michael Long
    Interesting discussion which reminds me of 1959 when I was in 7th grade in Junior H.S. (oops, got to be culturally correct - Middle School). In Math class the first book we worked out of was called 'Sets and Sentences' - an introduction to Set theory for 12 year olds. Thank goodness we weren't introduced to Russell's Paradox that year.
  • Awesome video! your explanation is right on the spot. - Also "predicate" means pre= Anterior/prior, Dicate= made/Known, on the same context "Contradiction" is Contra=opposite/denial, diction= said/mentioned. and they both open the door to "Conditionality", which in on itself is conditional. - :)
  • thestatusjoe
    Great video. I think it perfectly illustrates the fundamental flaws inherent to viewing language as a logical system. Even Wittgenstein, once considered the greatest champion of linguistic logic, decided later in his life to abandon that path. Language is not and never will be logical, because the purpose of language is not description but communication. All language is at its core more concerned with forming connections and being useful than with being accurate to reality
  • DarkSorc7
    Absolutely mind bending. Loved it.