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6,813,320 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 : 6,813,320
Genre: Education
Date of upload: Sep 8, 2022 ^^
Rating : 4.771 (6,398/105,229 LTDR)
RYD date created : 2024-05-18T14:26:41.481822Z
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YouTube Comments - 18,876 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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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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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!
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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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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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As more of a physicist than a mathematician I have always held that there are no exceptions to a rule. If an exception is encountered then the 'rule' is not a rule and the 'rule' requires modification such that the exception no longer exists under the modified rule. Set theory rule #11 is at fault. Think of it spatially - set A has a boundary as it 'contains', and the set that 'contains' set A has a second boundary around Set A and is spatially different from Set A - therefore a set cannot contain itself.
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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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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 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.
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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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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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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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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, âdonât worry, you wonât need to remember thatâ 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!
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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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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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The root issue is self-referencing, as noted by Douglas Hofstadter in his famous book "GĂśdel, Escher, Bach": any language that allows objects to make reference to themselves will contain a form of Russell's Paradox.
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About 20 years ago I wrote a book about this (and other) paradoxes called 101 Philosophy Problems. It's really not complicated. See the tale of the Barber - given sole responsibility to shave everyone in the village EXCEPT those who normally shave themselves - but who will shave the Barber? However, Jeffrey is right that SOLUTIONS to it create new problems about how we both talk and think about the world. People - philosophers! - even say things like "such a barber cannot exist⌠Put another, way, the cures are worse than the disease. The problem for Frege and also Russell (as he mentions) is that it shows the limits of maths and logic. The more intriguing problem is that it shows the limits of how we think.
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Thank you for this. What got me here is my quest to understand Robert S. Hartman's formal axiology. Glad I found your channel.
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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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