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6,681,690 Views ⢠Sep 8, 2022 ⢠Click to toggle off description
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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 Russellâs 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 ZermeloâFraenkel set theory in this description for keyword search reasons.
Views : 6,681,690
Genre: Education
Date of upload: Sep 8, 2022 ^^
Rating : 4.772 (6,271/103,608 LTDR)
RYD date created : 2024-04-25T12:10:08.156539Z
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YouTube Comments - 18,643 Comments
Top Comments of this video!! :3
I asked my girlfriend if we could have sets and she told me no because I didn't contain myself.
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This guy mastered writing on a window to a level i've never seen before
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On the predicate paradox: The main issue you seem to be grappling with on this is functionally comparable to the old, simpler paradox: "This sentence is false." If it's false, it's true; if it's true, it's false. So which could it be?
The most descriptively accurate answer I can think of is that it is neither, because it has no constant referential point upon which to base its definition. What can the sentence even proffer within it as "false"? What truth is it trying to debunk? None, because no such truth was extrapolated. Its only point of reference is itself, but it ipso facto eliminates that point by labeling it false, thus leaving it a useless self-contradictory abstraction, vacuous of point, logic, sense or reason.
And keep in mind that for definitions literary or otherwise, constant referential points are not to be underestimated in their essentiality. Without them, the means to describe them become variable and generalized to the point of uselessness. Consider, for example, the set that contains all sets, [X]. Okay- does that set include itself, [X] + [X+1]? Does it include that set, as well, [X] + [X + 1] + [X+2]? You'd have to keep on reiterating the addition of the set within itself ad infinitum, but doing so leaves you with an infinitely escalating value - and if your set contains an infinite value, can you really say you have a definition for it, considering the whole point of these sets was as a means to define whole numbers and now you have to find a single whole number for a sigma function?
This doesn't mean that math is broken, it only means that generalized categorizations give naive (heh) interpretations of mathematics that don't hold up without much greater scrutiny. If Zeno can be wrong about his ideas on motion being an illusion and Euclid can be wrong on his ideas of geometry, so can some professors be wrong about their ideas on sets. Nobody ever said this math stuff was easy, unless they did, in which case they can file under [set x: x contains all people who are shameless liars.]
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I started reading Russelâs âthe limits of the human mindâ and I found out mine lasted one paragraph.
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I really didnât expect LeBron James to be so crucial to the fundamentals of set theory. What a legend.
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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.
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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.
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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.
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I think my favourite example of this is "this sentence is a lie". It's the example that helped me to grasp the paradox.
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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!
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I was sent to Roman Catholic schools. One of the high points was at 'Junior High' school at about age 13 when a teacher (who in retrospect was probably an atheist, although he concealed it well), looked at the class and said: 'God can do everything, right? God is ominpotent.' We had all been programmed that this was the case, so we all said 'Yes, sir.' Then his voice got much quieter and asked us:
'If God can do everything, can he create a rock so heavy that he can't lift it?'
There was silence. Total silence. While the foundations of all the simplistic dogma that we had been taught were blown out of the water by elementary logic that even thirty 13-year olds could grasp.
Thank you, Joe, if you ever see this.
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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.
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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!
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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
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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!
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This reminds me of the "failure paradox" as well.
In a nutshell; if one sets out with the goal to fail, then they can only succeed. Because if they fail then they succeeded at failing which invalidates the failure, but if they fail at failing then they succeeded at failing which is still a success.
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Whoever talks about Russellâs library catalogue paradox automatically gets my subscription!!
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I also just want to appreciate, for a moment, the skill and practice involved in you writing that stuff backwards.
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By the way, the question of whether "is not true of itself" is true of itself is equivalent to whether "this statement is false" is true, which is perhaps the most well-known paradox ever.
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@nyc-exile
1 year ago
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.
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