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

I asked my girlfriend if we could have sets and she told me no because I didn't contain myself.

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.

Unlike many of your commenters, I don't have anything pithy to say about your presentation. I had never heard of Russell's Paradox or anyone else's Paradox. All I can do is tell you how much I appreciate how you described it. I did have to go back and review a couple of sections near the end, but I got it! You are passionate about sharing your knowledge with everyone who cares to learn. Even, and perhaps especially, people incarcerated in prisons. You are a gifted teacher, so thank you for sharing your knowledge with ALL of us.

At my age (77), I am not going to wade through 18,643 comments to check if someone else has made the same comment as I am making here! I apologise in advance, however, if that is, in fact, the case. When I first came across Russell's Paradox, more than 50 years ago, I explained it to myself as follows: if A is a set, then A is not the same thing as {A}, the set containing A. A set, in short, cannot be a member of itself, and the Paradox arises because the erroneous assumption is being made that a set can be a member of itself - your Rule 11. On the few occasions in the last 50 years when I have thought about this again, I have come to the same conclusion. I concur with the other comments about the quality of your presentation. Well done!

I really didn’t expect LeBron James to be so crucial to the fundamentals of set theory. What a legend.

I started reading Russel’s “the limits of the human mind” and I found out mine lasted one paragraph.

I've tried watching this twice now and I realise that I am a member of the set of people who don't care enough about Russell's Paradox to watch to the end.

As a child I spent weeks writing "S, P, AO, Agent" and whatever else, under words for a language class (this was in a different country so abbreviations may not carry over) - its been 2 decades since, and today is the first time I have seen it used to explain something. It saved me 60, or maybe 90 seconds. Time well spent!

I speak German and understand the letter Russell wrote to his colleague. the level of confidence he put into his writing that his recipient will just understand him amazes me.

Thank you for the brilliantly clear, insightful and extensive exposition of Russell's Paradox! Thank you too for not mentioning the dull, trite and deeply unhelpful 'Barber' analogy along the way either!

As someone who has never been good at math and gets anxious at basic addition and multiplication, thank you. You explained everything in a way that was quick, easy to understand and actually giving me a time frame on how long it will take you to explain something and giving the sort of cliff notes was really awesome. Literally every time you said, “don’t worry, you won’t need to remember that” I felt relief. And I actually learned something without feeling fucking dumb as bricks lol came for the philosophy, stayed for your awesome way of educating!

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

For a 57 year old man who cannot even recite his times tables (my head just doesn't do maths), I'm stunned I actually followed that, I really did!! That speaks volumes about this guys ability to convey information. I applaud you Sir, especially for the ability to hold my attention for the entire video. I quite enjoyed that!! I've no idea what use it is to me personally, but it was fascinating!

I have no interest in mathematics and no advanced training in mathematics, but i can follow the concepts --and more to the point - I love listening to characters who love what they do, and Jeff, you are a fascinating character. And that is a compliment.

Thank you for this. What got me here is my quest to understand Robert S. Hartman's formal axiology. Glad I found your channel.

I think my favourite example of this is "this sentence is a lie". It's the example that helped me to grasp the paradox.

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.

The root issue is self-referencing, as noted by Douglas Hofstadter in his famous book "Gödel, Escher, Bach": any language that allows objects to make reference to themselves will contain a form of Russell's Paradox.

I took a set theory class about a year ago, and this was beyond interesting. I was immediately asking about infinite sets the first day. Something seemed wonky. I get it based on real life, set is basically perception and allocations within it, and how things apply to singular vs multiples. Here's a goofy idea, would an empty set be able to equate to potential energy? It's a set with no content, but holds "reservation", it has potential

Your, sir, are the best best teacher i have ever seen in my life.