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.
Hi! I'm Jade. Subscribe to Up and Atom for physics, math and computer science videos!
SUBSCRIBE TO UP AND ATOM / upandatom
Visit the Up and Atom Store
store.nebula.app/collections/...
Follow me @upndatom
Up and Atom on Instagram: / upndatom
Up and Atom on Twitter: upndatom?lang=en
A big thank you to my AMAZING PATRONS!
Purple Penguin, Pierre-Yves Gatouillat, Ofer Mustigman, Daeil Kim, Harsh Tank, Alan McNea, Daniel Tan-Holmes, Simon Mackenzie, Lynn Shackelford, Richard Farrer, Adam Thornton, Dag-Erling Smørgrav, Chris Flynn, Andrew Pann, Anne Tan, Joe Court, Bob Wolford, Matt G, Bookmobile, Robert Maxon, Timur Kiyui, Ayan Doss, Broos Nemanic, John Satchell, John Shioli, Sung-Ho Lee, Todd Loreman, Susan Jones, Marc Watkins, Atila Pires dos Santos, Adam J, Roger Johnson, Hervé Dago, Tim Sorbera, Michael McCloskey, Philip Freeman, Bogdan Morosanu, khAnubis, Jareth Arnold, Simon Barker, Shawn Patrick James Kirby, Simon Tobar, Dennis Haupt, Ammaar Esmailjee, Renato Pereira, Simon Dargaville, Noah McCann and Magesh.
If you'd like to consider supporting Up and Atom, head over to my Patreon page :)
/ upandatom
For a one time donation, head over to my PayPal :)
www.paypal.me/upandatomshows
Other Videos You Might Like
Lagrangian Mechanics - A beautiful way to look at the world
• Lagrangian Mechanics -...
Complex Numbers - Rotating The Number Line
• Imaginary Numbers Are ...
Cantor's Infinity Paradox | Set Theory
• Cantor's Infinity Para...
Sources
plato.stanford.edu/entries/ru...
plato.stanford.edu/entries/fr...
plato.stanford.edu/entries/fr...
• Video
• Video
Music
www.epidemicsound.com/

[@upandatom]

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

[@essam352]

Up and Atom The existence of an element. whether it exists or not or repeated

[@mohamedbelgoumri6729]

An object that characterizes (represents) an equivalence class of sets that are in a one to one correspondence Note: cheated, I already did some set theory

[@ARBB1]

A element that represents position on a particular manifold, such as the space of real numbers.

[@autumndidact6148]

I'll bite: The quality of a category that describes the observed occurrence of discrete instances within that category. "Instances" is kind of number related, but strictly speaking the concept only requires understanding of the idea of individual things existing, distinct from others. It's enabled by counting, but it doesn't depend on it.

[@saarangsahasrabudhe8634]

You want to know what a number is? Here you go: kzbin.info/www/bejne/i566npmKqZmJeLM It's the first of a 8-part series of 4-min videos. Next video has a tag (G1). Here are all the videos: kzbin.info/door/RUATK39-y_dSwmN59_-aNQvideos

[@joescott]

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

[@DampeS8N]

Honestly, if you get a letter from Bertrand Russell today, bring that shizz right to James Randi and get yourself a million bucks.

[@michaelsommers2356]

@@DampeS8N There's nothing supernatural in that. They call it 'snail mail' for a reason.

[@NowanIlfideme]

Joe, letter from Bertrand Russell: can you go fetch my teapot, please? (Read as: maybe make a video about interesting thought experiments?)

[@devvynully]

Russell: Dear Joe, I wholeheartedly enjoy your channel and would not change anything.... Except this small thing that will ruin your confidence for eternity. Joe: Wanna collab?

[@Blox117]

but it could have money inside!

[@post1305]

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

[@golfgod1017]

until it grew back

[@post1305]

@@golfgod1017 when the hair grew back, the problem also came back. So, he found himself once more pulling his hair out again trying to solve it.

[@golfgod1017]

@@post1305 unless he learned from the experience and chose a different approach.

[@post1305]

@@golfgod1017 There is no evidence to suggest that happened.

[@golfgod1017]

@@post1305 or you just didn't see the evidence

[@davidsapir3764]

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.

[@muzukashiinamae]

Underrated

[@carlosraventosprieto2065]

Thanks for this!

[@davidsapir3764]

@@carlosraventosprieto2065 You're most welcome!

[@ananyagupta1409]

Bravo!!

[@daithi1966]

Dammit! I just waisted 5 minutes of my life because I read really slow.

[@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 😂

[@Blankpaper_openbook]

yeah i try to explain too ,but most of them have no idea what am i talking

[@jeffbguarino]

You just put the barber into a superposition with himself. You do this by putting him in an isolation box as in Schrodinger's box and you use an electron gun pointed at a spin detector. The detector will reveal if the electron is spin up or spin down. Tell the barber to shave himself if the spin is up and not to shave himself if the spin is down. Then start the gun up and close the box. Inside the box the Barber will be in a state of having shaved himself and not having shaved himself at the same time. You can also solve Russell's paradox using this method and any self referral paradox. You have to use the real world which is quantum mechanics and stop living in Newtons Classical world. Let's face it zero and infinity can't exist. Mathematicians completely ignore the uncertainty principle when they do their thought process to develop math. You can't create math that is impossible. That is what they have done. For Russell's paradox just create two sets R1 is the set of all sets that don't contain themselves and include R1 in the set. R2 is the set of all sets that don't contain themselves and exclude R2 from the set. Put these two sets in writing on two papers in a box and have a random quantum event burn one of the papers. Close the box and inside the box will be a superposition of R1 and R2. The superimposed set is labelled R3 and it contains itself and doesn't contain itself at the same time.

[@johnathancorgan3994]

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.

[@xway2]

I second this message. This is why this channel is great.

[@ivkost]

I on the contrary think that this video did not explain anything substantial or get into sufficient detail. The talk was mostly about history, and introducing various concepts. For me it only managed to define two paradoxes.

[@romwil]

Ivko Stanilov agreed- I absolutely enjoyed the video but was waiting to jump into the abstractions and into the weeds a bit after the intro warning. Hope for a part two going deeper!

[@harrypehkonen]

Brilliant point! I think if the delivery was simplified, a different audience would be attracted. But I'm grateful that these videos were made in a way that appeals to me.

[@Amateur0Visionary]

Well said, sir. I completely agree.

[@blackpenredpen]

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

[@xcalibur6482]

WoW! , youre here... yay!

[@darthvader-oz2om]

Hey dude!!!

[@dakshdheer1681]

You chad LEGEND

[@ccole1255]

@@dakshdheer1681 whaaaaa?

[@seanleith5312]

super cool dude? what the hell!

[@robertferraro236]

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

[@CHOCOLATIONZ]

Frege: here's the neat systematic set theory I made. Russell: *I'm about to end this man's whole career*

[@colinjava8447]

And hospitalize him

[@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???"

[@alex0589]

xacharon insulted that we assumed she couldnt smell cause she’s old. She’s a dog, not a smoker, dammit!

[@Inertia888]

@@alex0589 old people lose the acuity of their senses as they become old, even when they really, really take care of them selves... I think it's just how genetics works, man. i suppose we are probably eventually going to figure out how to prolong this, but i doubt out doggie friend has been genetically modified.

[@AnkhAnanku]

This does bring up a shortcoming of building things out of simple logic: given “dogs have a good sense of smell,” if Tifa does not have a good sense of smell then “Tifa is not a dog” is a logical conclusion, but we can all see she a good gurl

[@archprep131]

xacharon ohhhhhh shit

[@VexLimenOfficial]

"So Baldrick, if I have some beans and add one more bean, what does that make?" "A very small casserole m'lord."

[@jason-paulwells6696]

"Three beans and that one."

[@robertmontgomery6256]

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.

[@malfunction5448]

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 :)

[@EM-qr4kz]

Yeah..

[@rotflmaopmpqxyz]

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

[@Hailfire08]

They haven't been considered, just the set now no longer contains itself :)

[@brianjoelbasualdo7436]

I see the joke you did there

[@talhabedir3812]

so underrated lol

[@muhaimin244]

Nice one. I think paradoxes should be hunted and taken as gateways toward unpacking primitives and axioms.

[@ZucchiZ]

@@muhaimin244 lookup Vsauce

[@vamsikrishnan9714]

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

[@Arigator2]

Foundation is not the right word. These sciences existed for thousands of years before their 'foundations' were even known to exist.

[@fredrikekholm3718]

@@Arigator2 It doesn't matter if the word came before the sciences, it can still be considered a foundation. Just as foundations for houses were foundations long before the name "foundation" was invented. This is actually the case with most things. Think of it as "common source" or "common basis".

[@fahmiyassin2517]

lol

[@PhilBagels]

@@Arigator2 Right, And the same thing is true for mathematics. Science, and math can begin anywhere you like. Whatever you happen to discover, observe, experiment with first. And then it can grow from there in any direction. I think a problem arises when we try to put knowledge into a "tree" format. We make an unfounded assumption that there is a "base" or "foundation" or "root" of the tree, and the rest of science/math grows upward from that. Logic does not have to be at the very "bottom" of the math "tree". Arithmetic works correctly and consistently anyway. We can start with that, and then explore "upwards" or "downwards" as far as we like.

[@Arigator2]

@@fredrikekholm3718 - No, it's not a foundation because they aren't actually built on them. Math and science existed for thousands of years before someone decided to try to come up with a 'foundation'. Math is not based on the definition of a number.

[@kayleym8947]

nice video, but OMG i feel so bad for frege. imagine being so determined that you would solve all of math and then your years of hard work is just crushed. i understand math is like that because theres paradoxes and all, but i feel like me and lots of other people can relate to the poor man mentally

[@xletix69]

omg i've seen videos on this paradox so often but this is the first time i actually got it!! Thank you sm🙏🏼

[@garyhughes1664]

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.

[@bensadowyj1974]

It's a great book (so far), working my through it currently.

[@jonathansturm4163]

Bertrand Russell’s provocative _History of Western Philosophy_ is an entertaining account of his biases. Frederick Copleston’s _A History of Philosophy_ is still the place to start for anyone interested in following man’s speculations about himself and his world.

[@bensadowyj1974]

@@jonathansturm4163 I will check it out

[@anonymike8280]

Yeah, the dude was bomb!

[@spinZ186]

Dumbass alert, Russell’s text is fascinating but nowhere close to standard. Very subjective

[@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.

[@saxonalexander3888]

Thank you

[@lucashuerga1368]

I mean the paradox is another way of saying that an axiom cannot prove itself. That happens in logic therefore in math. If you want to go more in depth you can check out the incompleteness theorem of goedel.

[@yuridesideri7144]

Thank you very much for this video, it was just what I've been looking for in weeks!

[@pedrobernardo5887]

Yep, there we go. New channel that I must watch every single video. Great content Mrs. Jade!

[@sourisvoleur4854]

I love how Immanuel Kant "soon came along" after Aristotle. I once had to teach a Phil 101 course, and our textbook jumped from Aristotle to (I think) Descartes. In the final exam one of my students wrote, "Descartes was a student of Plato, but you'd never know it from the things he wrote."

[@anymaths]

mathematics students

[@hetrodoxlysonov-wh9oo]

mmanuel Kant was a real pissant Who was very rarely stable Heidegger, Heidegger was a boozy beggar Who could think you under the table David Hume could out-consume Wilhelm Freidrich Hegel And Wittgenstein was a beery swine Who was just as schloshed as Schlegel There's nothing Nietzsche couldn't teach ya 'bout the raising of the wrist Socrates, himself, was permanently pissed John Stuart Mill, of his own free will On half a pint of shandy was particularly ill Plato, they say, could stick it away Half a crate of whiskey every day Aristotle, Aristotle was a bugger for the bottle Hobbes was fond of his dram And Rene Descartes was a drunken fart "I drink, therefore I am."

[@captainzork6109]

Is that because the middle ages philosophy only had to do with religion and Plato and Aristotle's Organon, until renaissance humanism came along?

[@sourisvoleur4854]

@@captainzork6109 Not exactly. Even the so-called "churchmen" looked at what we would call philosophical questions about epistemology and ontology and the philosophy of language. There were also philosophers in the Caliphate that I know very little about. More modern thinkers have created theories that people nowadays take more seriously than the medieval ideas, so the medieval philosophers tend to get overlooked and forgotten. It is, however, a deep vein, and I think philosophy is as much about the thought processes as about the end result. Journey vs. destination.

[@captainzork6109]

@@sourisvoleur4854 I'm a psychology graduate, and although my Master is in Theory and History of Psychology, it has only been since a year or so I've started learning philosophy and history more generally. But thus far it seems like their epistemological questions have been very broad: What is the world, and how can we know of it? And, as Nietzsche pointed out, even until Schopenhauer the hinterwelt had always been part of the most prominent thinker's philosophies. That is to say, scholars in the past put so much emphasis on some 'more perfect world', getting lost in a convoluted mythos of heaven and hell, that they failed to make any sense of the here and now. As far as Francis Bacon was concerned, those scholars were all just armchair scientists, who come to the wildest conclusions based on singular experiments Except, of course, when it came to practical things, such as geometry and algebra, which presumably was also helpful for engineering This is all to say: People's worldview used to be wild and stupid, and we are much more sensible nowadays But despite the sources I've come across, I can't help but wonder if it's really all that true there really weren't any unsung heroes from those middle ages. After all, the ancient Greeks had people like Ptolemy, Socrates, Plato, Aristotle, and Galen, and though they believed in the gods, they still came to great thoughts and discoveries I wish there'd be such nice examples of the medieval times, who were influential, but were just overlooked by those in the 14-15th century, who called themselves renaissance humanists

[@RussellSubedi]

I'm Russell and I approve this paradox.

[@sumeshrajurkar5922]

If you're Russell you cannot approve your own paradox, if you approve your paradox you're not Russell. :-)

[@RussellSubedi]

@@sumeshrajurkar5922 First of all, I'm not going to publish something that I don't approve of. Secondly, I'm the other Russell.

[@derylpetersonnnnnnnnn]

@@sumeshrajurkar5922 IT WAS A JOKE YOU ABSOLUTE DUMBASS. HOW DID YOU NOT GET THAT?

[@russellnavin7882]

Plus one.

[@RussellSubedi]

@@derylpetersonnnnnnnnn Yes, how dare he reply to a joke! Please be more mean to him.

[@gardnep]

You are an extraordinary communicator of a difficult subject, well done!!

[@stevesomers7366]

Jade, you have a gift in presenting complex concepts. The only thing more fascinating is you!

[@hunterterrell9930]

"my nose will now grow" said pinnochio

[@zfloyd1627]

Pinnochio's nose would disappear.

[@nene_san]

Ah...I see

[@fahmiyassin2517]

lol

[@argumengenichyperloquaciou4115]

In this case, isn't Pinnochio making a promise and not lying? Pinnochio's nose doesn't grow when he breaks a promise.

[@priteshsoni3891]

@@argumengenichyperloquaciou4115 Let us put it in this way, "My nose is growing now"

[@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 :-)

[@yaff1851]

usvalve If you can only define what you don’t want but not what the heck you do want instead, that’s what you end up with. Just like in mathematics: it’s much easier to debunk than to confirm something.

[@anshulbhardwaj4038]

he can Vax himself and shave others 😂😂

[@pigeonlove]

Please don't refer to the Europeans as armpit hair, they are sensitive about that

[@j3ffn4v4rr0]

You mean, it's much easier to bunk than to debunk? I'd say that's true... @@yaff1851

[@Sunastar4D]

Barberxit... Barbrexit... Barbarella?

[@scottsabey2114]

Upstanding presentation.., I found it very insightful w/thought provoking explanations and great animation!

[@Briaaanz]

Bertrand Russell has been one of my heroes since I first heard about mathematical philosophy

[@pimpom1345]

It was actually first discovered by German mathematicians before him, but he was the first to publish it.

[@denniskeefe1979]

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.

[@jameshoffman552]

5:05 ‘Another philosopher, Immanuel Kant, soon came along’ Soon, as in 2000 years!

[@fukpoeslaw3613]

hey, like jesus!

[@joeyd1734]

relative to the history of people, 2000 years is soon. relative to how long this problem has been around, probably not so soon.

[@stonerdave]

Soon is a relative term

[@tirr1]

Hello, I have to say I discover your channel today. I’ve been watching some of your videos and I really really like it keep going and this is amazing!

[@mober55]

Thank you for doing these videos. I really enjoy these.

[@chrisrichards7063]

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.

[@sean..L]

Wow, Russell literally broke Frege with that meta-set question. Physically and mentally.

[@DavidLindes]

Did he really have a breakdown? I looked around briefly to find something about this, and the closest I found was this quote from him: "Hardly anything more unfortunate can befall a scientific writer than to have one of the foundations of his edifice shaken after the work is finished. This was the position I was placed in by a letter of Mr. Bertrand Russell, just when the printing of this volume was nearing its completion." -- seems level-headed, if emotionally charged, to me. Curious about whether this was just hyperbole for storytelling purposes (which I'm mostly fine with, though it kinda undermines the "I guess he hadn't heard?" line, to me), or if there's more to the story than what I managed to find (in an admittedly not-extensive search).

[@Krmpfpks]

@@DavidLindes The german wikipedia article about Frege is covering his breakdown, but attributes to it to the death of his wife in 1904, two years after Russels letter.

[@DavidLindes]

Krmpfpks: ah, cool. Danke!

[@SedatKPunkt]

Does it also work in order to make a robot (or AI) crash? :D

[@maniacalbarbarian]

I'm definitely not a math person but I believe you hit upon a key component which could have saved thid logician his methodology. She describes concepts and the extensions which derive from them, but the paradox revolves around a superset which in and of itself is not exactly a set, therefore could not be included within itself as a set since it is a superset. Further I believe the paradox is embedded within the definition that these sets can innately even be included together. How can a concept extended to things which are not themselves be comprehensively extrapolated into a group? That super set would essentially be a collection of all things. To put it simply, if one set was a list of all people who were not you, and the other set was a list of people who were not me, then your list would include me and my list would include you, therefore our super list would include everyone, therefore there is no rational way to innately and properly categorize a super list of every individual that is not an individual, that is without merging the definitions of the sets themselves, as in a list of people who were neither you nor me. Anyways I also think that Plato seem to have a proper by excluding numbers into their own realm. I'll probably get raked over coals for this because I don't know it very well at all, but I would presume that this paradox came prior to the concept of imaginary numbers, and somehow I innately think that quantum physics and it's possible underlying foundations have undermined numbers directly being able to describe reality directly and rather reverting to statistics to become a catch-all for all of the inconsistencies, hence the revolutionary qubit, which is now somehow at the foundation of both physics and mathematics subverting what appeared to be logic with something new entirely, where in our super set of individuals who were not individuals might include a matrix of possibilities [ just you, just me, you & me, everybody, nobody, & every interative factorial between nobody & everybody, even duplicates through infinity given the 'probability' of there being a finite limit of particle configurations in and infinite expansive universe beyond our observable one ] Simultaneously! ~ B) Yea Logic !

[@innertubez]

Thanks for this really superbly explained and illustrated video. I have no idea how to define a number; but I think it has to encompass the concept you described whereby different numbers can apply depending on context (one pair of shoes vs two shoes). The context can go all the way up to everything: One universe vs however many points in space; even one multiverse vs however many universes it contains. All the way down to one proton vs three quarks. As I see it, for there to be any numbers other than 1 or 0, there has to be some mechanism of differentiation or segmentation. Consider an infinite, completely empty space. Number would have no meaning as far as I can tell. Even if one proposes an imaginary grid or coordinate system, one is imposing differentiation or segmentation onto that empty space. I sometimes have pondered that I think we can generate our whole number system from just the digit 1 and a set of operations (which I think may implicitly assume the existence of differentiation or segmentation): 1 - 1 = 0, 1 + 1 = 2, 1 + 1 + 1 = 3, .... So I suspect the essence of numbers somehow has to do with 1 (unity/emptiness/etc) and ways of breaking up that unity. Anyway, I will stop my rambling now lol.

[@frankmccann29]

Thank you so much for the material and reminding me you can do anything with functional notation. Great video. Intersecting multi dimensional sets.

[@magnusjonsson7303]

13:23 "Apparently he didn´t know about the breakdown." 😂😂😂 I think this says something about us all; happiness lies in not trying to belong to the set of all sets because this action alone just excludes ourselves 😉.

[@aznkingdom12345]

I'm so glad Up and Atom is a channel on youtube. Keep up the good work. I can't wait to binge on all your videos.

[@hugmyster]

That was absolutely beautiful! Explained at a level that even I could understand, and with great animation. Yes, it did bring me out in a chuckle with the sets within sets. Proves what a mess we all are! 🤭

[@ifechukwuejiofor8479]

Wow. This is an excellent video. The visuals are great and the explanations excellent. Before now, I had found it difficult to fully grasp Russell's paradox. But, while watching this video, I found myself understanding the concept while laughing. Well done!

[@sclarkaz]

And then Gödel wrote a letter to Russel.

[@GrantDexter]

I was going to say: Why are people still looking for a foundation post-Godel?

[@sclarkaz]

@@GrantDexter Exactly. Every meta-system that could provide a foundation is itself subject to incompleteness, infinite regress.

[@franciscofernandez8183]

@@GrantDexter Because they are no longer looking for a complete coherent foundational framework. They are just looking for a list coherent list of axioms that lines up with what we commonly picture as a set. Not complete, just coherent and with the least possible amount of vagueness.

[@crackedcandy7958]

Then Schrödinger asked him if the barber was observed, since he obviously was both shaved and unshaved

[@mikekelley9125]

@@crackedcandy7958 That's interesting. If we consider a foundational theory such as ZFS to be equivalent to quantum states in physics, is it possible for a theory to be superpositional? If so, Russel's paradox becomes a superposition, not a contradiction.

[@deandeann1541]

I have subscribed. This video was as clear and concise of a description of Russell's paradox as I have seen. It was enjoyable. Good work, Jade.

[@deryputra2586]

Your explanation is very clear and helpful. Thanks a lot

[@Young_Navigator]

Thanks, i really wasn't understanding it, but now i understand (Also: loved the drawings and the sound effect on the breakdown of Frege, astonished me! )

[@SeriousNERD1]

Frege's breakdown almost made me cry. I can't even imagine how it must have felt to have his life's work be disproved by a single sentence. Great video, you've earned a subscriber!

[@broffutt]

I literally laughed out loud when she said that.... Time to find the Ted Talk about why we laugh at other people's pain...

[@SeriousNERD1]

@@broffutt Well it is funny from a dark comedy point of view and also we are all different I guess. So I think there is nothing wrong with you 😄

[@harrymills2770]

He wouldn't be the only one of these clowns with a screw loose. Pondering different flavors of infinity defies all intuition, until you're deep enough into it to develop a new kind of intuition.

[@moadot720]

Same...

[@retry4z]

There is no evidence Frege had a breakdown due to Russel's letter.

[@stevien196]

A great little video so well scripted and cut and a testament to the ability of its creator. I got to the end without needing to rewind but I can call on a degree in Philosophy to help me. I have never seen set theory explained so well. Thanks and well done.

[@djangoworldwide7925]

You're such an intelegent and articulate math communicator. I subscribed and looking forward to endulgr more of your videos.

[@p382742937423y4]

Im new to your channel. Thanks for making these videos. I watched the one in Russel and Whiteheads book, which i learned about while studying philosophy. Its nice to learn more about it. Thanks for doing that. I really liked it

[@nielsen425]

I have a question observation. We routinely define math such that we exclude certain conditions because there isn’t a clean definition. We cannot divide by zero. We used to not be able to take the square root of negative numbers. And we used to insist on only rational numbers. We have determined a means to work around these issues, except we still say that dividing by zero is undefined. The other place I think we see the rules change is when we talk about sets of infinite size. We have limitations on what we can compare with these sets. Hence we exclude properties because of the paradoxes that arise. The Russel paradox looks like the divide by zero concern. He’s just pointing out that there are these cases that tend to act like dividing by zero. These cases are self referral cases. Any set that refers to itself can create this paradox. In fact, all of the paradoxes I’ve seen here have this same property that the rule because it applies to itself changes the state of the object and so self referral creates the same type of condition as dividing by zero. Hence, for the same reasons we exclude divide by zero; can’t we also just exclude cases of self referral that create the paradox? If it works for dividing by zero, it appears that it works here as well?

[@epicmarschmallow5049]

That's basically what happened in the future. Some dude's (Zermelo and Fränkel) developed a new axiomatic set theory (Zermelo-Fränkel set theory) specifically to exclude paradoxes like this.

[@nielsen425]

@@epicmarschmallow5049 Thx!

[@MrEmrys24]

"Apparently he didn't know about the breakdown?!" 😂

[@voodoochile7581]

An amazing video Jade. I ❤️ all your content.

[@13rolf]

I have no idea how to describe number, all I know is your explanation is awesome and I love Tifa.

[@ywenp]

12:50 WOW, did Russel clearly know his way about elegantly rubbing salt in the wound ^^!!

[@email4ady]

Russell s question was plain stupid n irrelevant. Idiotic man, overrated as f

[@Ivan_1791]

Frege: I'm finally done with my work! Russel: I'm about to end this whole man career.

[@shlovaski8393]

Lmao love this meme

[@hamman_samuel]

Story of PhDs

[@Deguiko]

Frege's work got known thanks to Russel though. And although the problem he found was at the base of the theory, most of the work still was very important for the future develpment of formal logic.

[@salaciousBastard]

@@Deguiko So he destroyed his mind in order to build him back up? I've heard of tough love, but savage love? Damn.

[@StevenNess]

Amazing video! You are so cool and explain things so well. If you could please do a video on Category Theory, that would be so helpful, I've been trying to learn it for a while now and most of the videos are pretty abstract. Thanks for what you do!

[@s888r]

The best answer you can possibly give to Russel's question is to modify the question a bit, because every question along the same lines and similar, creates a paradox. "Any unifying set, such as this, cannot be part of itself, as this means it has not unified everything"

[@chihebbaazaoui9388]

keep up the good work i really love your videos. I'm an enthusiast about physics and maths and it's hard to find people speak about actual interesting things like this.

[@zeinmahmoud9931]

I love your videos :) great explanation for complicated topics, and the animation is amazing and creative, thank you jade

[@xoiyoub]

Your explanation is much more clear and clean than that long video by Veritasium

[@awfominaya]

Great video. Thanks so much!

[@michaelmj1964]

This was a really good overview of some of the philosophical problems surrounding math, and I would love to see more on this subject.

[@djtomleeuwen]

"You're all individuals." "I'm not."

[@fakkmorradi]

Tom van Leeuwen but you are in the set of all individuals

[@AvanToor]

No, no. It goes: "You're all individuals." "Yes, we're all individuals!" "You're all different." "Yes, we're all different!" "I'm not..."

[@djtomleeuwen]

@@AvanToor I know, just tried to simplify so that it was easily read. :-) The ones who know the scene understand.

[@cosmojg]

@@fakkmorradi I am the set of all individuals.

[@happinesstan]

@@AvanToor The very best movie quote of all time.

[@joanofarcsinus]

an easy to understand communication of a complex concept without dumbing it down! lovel, and a rare sight :)

[@rambysophistry1220]

I love this. I would say, not having watched further in the video yet then the preposition to define a number without using number, that a number is: a mathematical object defined by a relation to the empty set and non-empty sets using logical operators.

[@rcb3921]

11:27 -- I love that Jade's gives the camera that same look you'd give anybody when you're pretty sure you've said something that's gone over their head.

[@mookrage]

Best visual representation of plato I've ever seen. You are also an amazing communicator

[@Samrushtonblight]

You a terrific explainer. Thank you so much.

[@ericvondell5157]

I've seen the Jeffrey Kaplan tribute to the Russel's Paradox, but, I got Way More value from your approach. Those adorable animated Thingies remind me a lot of those Delightful Saturday Morning Educational Interstitials. "Interplanet Janet", "Conjunction Junction ", "Bill ", Twelve Toes", "Hero Zero"... There Were So Many!🙀💕 You'd have Loved My Century!😻 THANK YOU FOR WORKING SO HARD ON THIS!💖 Tifa might not be able to smell things as well as when she was younger, but, we could Use Logicism to infer, correctly that "All Dogs Smell!" And, This is accurate to At Least, ONE POV concerning Dogs. How to describe a Number w/o using the Word "Number" Might be expressed as :the value and/or *"Quantity" (I know 🤪) of a something denotes how it may be combined with another Value and/or Quantity. Ie: I have a quantity of Shoes, but, only enough for One person at a time to Wear." I think that THIS is How Most animals determine if everyone in the family is present! NOT with artificial inventions, but, by direct Observation and memory. The Linnaean system of classification operates similarly by determining What items Belong together based on intensity and plurality of similarities. The Cow clearly doesn't Belong with Humans and Apes. But, Could belong with Cats and Dogs, but, moreso with Sheep and Goats. Phylogenetic classification deals with ancestral relationships between organisms. 1+1=3! Is True because there are Three value symbols shown. But, we know that This is Incorrect. The Quantity of All symbols in the equation would Be 5! Which is how an animal would perceive this equation's Value. 1+1=2 is logically correct to the purpose of combining integers. My Dyscalclia operates like this giving me an instinctive value of the symbols First and then resulting in everything getting all mixed up in my mind disrupting computation. *But, like you said: Words Such as "Quantity" are related to the Word "Numbers"! But, what if I use a Made Up term such as "Accumulation", but, here, again, we've got a number related word. Humans Are the ONLY Indigenous Species Currently Extant on Earth to Utilize Complex Structured Utterances to convey information. It's completely artificial and unnatural. That's Why It has to be taught and learned! But, a mother Duck determining if everyone in Her brood Are present, is Not Likely accomplished with artificiality. Even words Such as Concepts and Sets are, precisely The same sort of thing As Quantity and Value! And, again, we're back to the Linnaean system! Try conveying Any Information w/o employing Artificiality! Like That Party Game "Taboo"! And, that's At the Root of this type of Paradox: Just like with The Raven Paradox! Although, you might be able to Break it down with Sets, Subsets, Ifrasets, Quantum Sets. You can say "All Ravens in Subset A are black. But, NOT All Ravens in Set 1 Are Black. And, only some of the Ravens in Collection 3 10:06 are Black!" Er .........🤪😵‍💫 Does the Concept of "Nothing" have an Extension?!🙀😱💫 Getting Off Tangent... Sorry 😹

[@garybrisebois2667]

People: Imagine if everything was absurd!? Quantum Mechanics: Well hello there :)

[@JJ-kl7eq]

The Buttersotch Paradox - It tastes neither like butter or scotch. This Butterscotch Ripple is more upsetting to the foundation of life than Russell’s Paradox ever could be.

[@alex0589]

J J if you throw butterscotch hard enough, it tears space-time so you can step out of this reality and can taste thoughts and concepts instead. Try it.

[@Hydrastic-bz5qm]

@@alex0589 we've got a synesthete!

[@MisoMooch]

My butterscotch paradox is that my butter is usually messy while my scotch is always neat

[@selimseddiki430]

very enlightening and enjoyable video, thanks!

[@fig7047]

You've reminded me of binding loops in QML (a programming language for user interfaces). Binding loops highlight a bug in the code: you've crafted something that can't work / doesn't make sense. Much like the paradoxes you mention in the video.

[@JJ-kl7eq]

Deep philosophical question that comes to my mind from watching this video: Who shaves the turtle?

[@videofudge]

Achilles

[@EddieVBlueIsland]

Turtles all the way down to the Mock.

[@bobbimke82]

"Who shaves the turtle?" ==> Mitch McConnel's wife.

[@JJ-kl7eq]

One thing I am sure of, turtles don’t get electrolysis. That would leave them shell shocked.

[@kandysman86]

@@bobbimke82 yeah, he definitely is the turtle.

[@chuckm1961]

“Life” is immeasurably and incomprehensibly complex. Words are at best rough approximations of anything resembling “life” or “reality”.

[@htavli]

Thanks for this amazing video!

[@scottalbers9314]

I've enjoyed your video. It's well considered and very helpful.

[@RyanVJones]

Jade, you should get a Nobel prize for your teachings to a large audience on KZbin. A growing audience at that!

[@monjitchetia6768]

I am currently reading Logicomix and this video really helped me understand the novel. Thanks!!👍

[@10418]

I bought it thanks to you…

[@kaiblack4489]

Quick point: There isn't actually any paradox with Frege's theory of concepts and extensions at all (as it was presented in this video at least); that idea is used in ZFC set theory all the time (every well-defined property φ induces a class of sets satisfying φ). The reason this isn't a contradiction is that there is no notion of a class containing another class - so you can't have a class of classes that do not contain themself. The contradiction seems to just be in the way he defined "set". If you swap it for the modern idea of a set, then you get a perfectly good model for set theory.

[@thefuturist8864]

Whenever I meet anyone who has a favourite paradox, or favourite paradoxes, I know they can be trusted.

[@thecompanioncube4211]

Frege: I have the most fundamental theory about maths Russell: I'm about to end this man's whole career

[@briancotton]

I refuse to join any club that would have me as a member - Groucho Marx

[@MikeRosoftJH]

And this leads us to a different paradox. Imagine a town where every possible set of citizens forms a club. Would it be possible to name all clubs after a citizen, in such a way that every club is named and no two clubs have the same name? Of course, this can't be done with a finite town; it would have more clubs for than citizens. (For example, with just 10 people there would be 2^10=1024 clubs.) But could it be done in an infinite town? Turns out, the answer is: no, it can't be done either. Take any naming scheme (where no two clubs have the same name), and ask: does it cover all clubs? If every set is a club, then so is the set of all citizens who are not a member of their own clubs. But this club can't be named; otherwise, can the citizen who the club is named after be its member? It can be seen that he's a member of our club if and only if he isn't a member. This is an impossibility, so the club can't have a name.

[@Blox117]

@@MikeRosoftJH do these clubs come with membership benefits? otherwise I must decline your offer.

[@milanstevic8424]

@@MikeRosoftJH Anyways, you seem to be running out of letter combinations, so here I propose an infinite alphabet to go along with the naming.

[@WBoettchStevens]

​@@MikeRosoftJH The number of clubs is summation(n choose r) for 0

[@nicolaiveliki1409]

I thought that was Woody Allen

[@YuvrajSingh-nd2kd]

I really like your way to explain ...thanks for.making.such informative videos

[@vill824]

This is great. You speak so clearly about this. :) Does this translate or connect with Goedels theorem as well?

[@duggydo]

Up and Atom Kurt Gödel shed a lot of light on self referential statements with his work. You should consider a follow up video covering his work on meta-mathematics and consistency vs completeness. I really enjoyed this video btw! 😁

[@AgentOccam]

She's done Gödel I think, and the related Halting Problem. But yes, a follow-up video on how one led to the other would be well warranted.

[@RichardBronosky]

Because you didn't ask me to subscribe and hit the notification bell, I did. How's that for a paradox?

[@rolyf100]

Bruno Bronosky that is not a paradox. It was an exploitation of your nature. The fact that it simultaneously is and was, that’s a paradox.

[@force3413]

@@rolyf100 is and is not*

[@rodschmidt8952]

Try subscribing to the channels of all KZbinrs who don't subscribe to their own channels.

[@captainzork6109]

Russell's commendation of Frege is to me the most valuable from this vid

[@jonathanbickerton6645]

Upon first viewing, I got it. But if I'm being honest. I've heard it before... I will say I understand it a lot better now and now have more clarity on the subject. So, thank you! 😊

[@johnshioli1499]

Nice one, Jade! I can’t wait for the follow up! 😀👍

[@vmp916]

Russel’s paradox was always that quirky thing I was taught half way through a Discrete Math course. I didn’t know it basically ruined a dude’s life lol.

[@seanleith5312]

The femininity of her is remarkable. Who cares about mathematics?

[@Red-Brick-Dream]

@@seanleith5312 Dude, go away.

[@icefire6622]

@@seanleith5312 holy shit dude. touch grass

[@seanleith5312]

@@icefire6622 I came here for science, apparently, but ended up giving up on science. I am happy.

[@craZgirl1091]

Thank you!!! Very helpful as I’m trying to make my way through an advanced logic course in university 😅

[@ReallyVirtual]

I'm not a mathematician - I'm a programmer. The common thread from this and other sources I have read, is that a system cannot describe itself. It can only be described from or by another independent system. If a system attempts to describe itself, paradoxes seem follow. This video only seems to reinforce this point of view, which is a little unfortunate as we tend to use mathematics to model things. The things we tend to model are in this universe. Along with us and the mathematics we use to describe those models. Presumably, as all of these things are in the same system - the universe - it would be impossible to describe said universe with said mathematical models without introducing paradoxes. What got me into this, is that once upon a time I used to be assured in the truthfulness of logic until someone told me about the chap living on the island of Crete.... That one broke my logic box, much like your examples in this video. For those that don't know the Cretan's story.... Basically, this chap (or chapess) from Crete, proudly stood up and proclaimed that all Cretans are liars. That one statement floored me, and I wrestled with it and its implications for a long time. How could logic break so easily? Of course, one could resolve the above paradox by having somebody else, not from Crete, and outside of the system describe that system (Crete). For example, someone from mainland Greece could say 'All Cretans are liars'. Then you have a perfectly reasonable statement that in no way contradicts itself. It's pretty much like your hairdresser's example. Have a car mechanic make the statement about that hairdresser and all the paradoxes disappear. Having the hairdresser make exactly the same statement results in the whole world falling apart! As my job entails coding logic into software, I was naturally quite alarmed by these discoveries! :) PS: the answer to the number question posed above is: It's a symbol that describes a quantity!

[@UnkleRiceYo]

I’d argue the most shocking and interesting part of this story comes after, when Gödel throws a spanner in the works

[@nafrost2787]

Really interesting, what I like about this paradox is that in a way it’s the same as the problem with quantizing gravity. One of the problems with quantizing gravity is that it’s not a quantum field on top of space time, it is space time, I see here similarity to this paradox, the set of the sets that are not members of themselves is sort of different than other sets in the same way that gravity is from the other fundamental forces.

[@aparnaga1182]

Yes! I was thinking the same thing

[@shimashr1908]

God, videos like this are the reason why I love youtube, and math, and basically everything else in the world

[@zogger5281]

Very good video. It was a topic I had not heard about before. Interesting. Thank you! All math and science is an attempt for us to describe the world using ideas/concepts our brains self generate. So it should not be surprising that in creating concepts using our imperfect brains to describe a world we don't fully understand thru senses that give limited information and given our limited exposure to the universe that contradictions and paradox's should arise.

[@tiborkoos188]

Thank you, great explanation! ALso loved the graphics, especially the birds :)

[@atsmyles]

Great Video! Apropos, I happen to be in a reading group studying Homotopy Type Theory. I look forward to your take on it.

[@MeNanWazaHowitzer]

You know you’ve over done the science and math video binge when you get something like this in one take, i’d heard of the barber paradox and set theory before seeing this i guess thats why YT thought I’d like this video