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The paradox at the heart of mathematics: Gödel's Incompleteness Theorem - Marcus du Sautoy

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Explore Gödel’s Incompleteness Theorem, a discovery which changed what we know about mathematical proofs and statements. Consider the following sentence: “This statement is false.” Is that true? If so, that would make the statement false. But if it’s false, then the statement is true. This sentence creates an unsolvable paradox; if it’s not true and it’s not false– what is it? This question led a logician to a discovery that would change mathematics forever. Marcus du Sautoy digs into Gödel’s Incompleteness Theorem. Lesson by Marcus du Sautoy, directed by BASA. Support Our Non-Profit Mission Support us on Patreon: 🤍 Check out our merch: 🤍 Connect With Us Sign up for our newsletter: 🤍 Follow us on Facebook: 🤍 Find us on Twitter: 🤍 Peep us on Instagram: 🤍 Keep Learning View full lesson: 🤍 Dig deeper with additional resources: 🤍 Animator's website: 🤍 Thank you so much to our patrons for your support! Without you this video would not be possible! Dwight Schrute, Dianne Palomar, Marin Kovachev, Fahad Nasser Chowdhury, Penelope Misquitta, Hans Peng, Gaurav Mathur, Erik Biemans, Tony, Michelle, Katie and Josh Pedretti, Sunny Patel, Hoai Nam Tran, Stina Boberg, Kack-Kyun Kim, Michael Braun-Boghos, Ken, zjweele13, Jurjen Geleijn, Anna-Pitschna Kunz, Edla Paniguel, Elena Crescia, Thomas Mungavan, Jaron Blackburn, Venkat Venkatakrishnan, ReuniteKorea, Aaron Henson, Rohan Gupta, Begum Tutuncu, Ever Granada, Mikhail Shkirev, Brian Richards, Cindy O., Jørgen Østerpart, Tyron Jung, Carolyn Corwin, Carsten Tobehn, Katie Dean, Ezgi Yersu, Gerald Onyango, alessandra tasso, Côme Vincent, Doreen Reynolds-Consolati, Manognya Chakrapani, Ayala Ron, Samantha Chow, Eunsun Kim, Phyllis Dubrow, Ophelia Gibson Best, Paul Schneider, Joichiro Yamada and Henrique 'Sorín' Cassús.

Gödel's Incompleteness Theorem - Numberphile

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31.05.2017

Marcus du Sautoy discusses Gödel's Incompleteness Theorem More links & stuff in full description below ↓↓↓ Extra Footage Part One: 🤍 Extra Footage Part Two: 🤍 Professor du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy's book as mentioned... In the US it is called The Great Unknown - 🤍 In the UK it is called What We Cannot Know - 🤍 More of his books: 🤍 Discuss this one on Brady's subreddit: 🤍 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): 🤍 We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: 🤍 Numberphile on Facebook: 🤍 Numberphile tweets: 🤍 Subscribe: 🤍 Videos by Brady Haran Animation in this video by Pete McPartlan Patreon: 🤍 Brady's videos subreddit: 🤍 Brady's latest videos across all channels: 🤍 Sign up for (occasional) emails: 🤍

Roger Penrose explains Godel's incompleteness theorem in 3 minutes

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01.06.2020

good explanation from his interview with joe rogan 🤍

Math's Fundamental Flaw

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22.05.2021

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer. This video is sponsored by Brilliant. The first 200 people to sign up via 🤍 get 20% off a yearly subscription. Special thanks to Prof. Asaf Karagila for consultation on set theory and specific rewrites, to Prof. Alex Kontorovich for reviews of earlier drafts, Prof. Toby ‘Qubit’ Cubitt for the help with the spectral gap, to Henry Reich for the helpful feedback and comments on the video. ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ References: Dunham, W. (2013, July). A Note on the Origin of the Twin Prime Conjecture. In Notices of the International Congress of Chinese Mathematicians (Vol. 1, No. 1, pp. 63-65). International Press of Boston. — 🤍 Conway, J. (1970). The game of life. Scientific American, 223(4), 4. — 🤍 Churchill, A., Biderman, S., Herrick, A. (2019). Magic: The Gathering is Turing Complete. ArXiv. — 🤍 Gaifman, H. (2006). Naming and Diagonalization, from Cantor to Godel to Kleene. Logic Journal of the IGPL, 14(5), 709-728. — 🤍 Lénárt, I. (2010). Gauss, Bolyai, Lobachevsky–in General Education?(Hyperbolic Geometry as Part of the Mathematics Curriculum). In Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (pp. 223-230). Tessellations Publishing. — 🤍 Attribution of Poincare’s quote, The Mathematical Intelligencer, vol. 13, no. 1, Winter 1991. — 🤍 Irvine, A. D., & Deutsch, H. (1995). Russell’s paradox. — 🤍 Gödel, K. (1992). On formally undecidable propositions of Principia Mathematica and related systems. Courier Corporation. — 🤍 Russell, B., & Whitehead, A. (1973). Principia Mathematica [PM], vol I, 1910, vol. II, 1912, vol III, 1913, vol. I, 1925, vol II & III, 1927, Paperback Edition to* 56. Cambridge UP. — 🤍 Gödel, K. (1986). Kurt Gödel: Collected Works: Volume I: Publications 1929-1936 (Vol. 1). Oxford University Press, USA. — 🤍 Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the spectral gap. Nature, 528(7581), 207-211. — 🤍 ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Special thanks to Patreon supporters: Paul Peijzel, Crated Comments, Anna, Mac Malkawi, Michael Schneider, Oleksii Leonov, Jim Osmun, Tyson McDowell, Ludovic Robillard, Jim buckmaster, fanime96, Juan Benet, Ruslan Khroma, Robert Blum, Richard Sundvall, Lee Redden, Vincent, Marinus Kuivenhoven, Alfred Wallace, Arjun Chakroborty, Joar Wandborg, Clayton Greenwell, Pindex, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀ Executive Producer: Derek Muller Writers: Adam Becker, Jonny Hyman, Derek Muller Animators: Fabio Albertelli, Jakub Misiek, Ivy Tello, Jonny Hyman SFX & Music: Jonny Hyman Camerapeople: Derek Muller, Raquel Nuno Editors: Derek Muller Producers: Petr Lebedev, Emily Zhang Additional video supplied by Getty Images Thumbnail by Geoff Barrett ▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀▀

Gödel's Argument for God

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Kurt Gödel's argument for the existence of God, from his notebooks, as revised by C. Anthony Anderson. 🤍PhiloofAlexandria

Gödel's Incompleteness (extra footage 1) - Numberphile

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03.06.2017

MAIN VIDEO: 🤍 More links & stuff in full description below ↓↓↓ Extra footage part 2: 🤍 Professor Marcus du Sautoy is Simonyi Professor for the Public Understanding of Science and a Professor of Mathematics at the University of Oxford. Professor du Sautoy's book as mentioned... In the US it is called The Great Unknown - 🤍 In the UK it is called What We Cannot Know - 🤍 More of his books: 🤍 Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): 🤍 We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. NUMBERPHILE Website: 🤍 Numberphile on Facebook: 🤍 Numberphile tweets: 🤍 Subscribe: 🤍 Videos by Brady Haran Patreon: 🤍 Brady's videos subreddit: 🤍 Brady's latest videos across all channels: 🤍 Sign up for (occasional) emails: 🤍

Hitler against Godel's Theorem

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04.05.2014

Hitler faces the awful truth: arithmetic is incomplete.

Le théorème de Gödel | Voyages au pays des maths | ARTE

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20.11.2021

Dans cet épisode, on se penche sur le rapport entre maths et vérité. Les maths sont censées être le domaine de la certitude : soit c’est démontrable, soit c’est faux. Eh bien ce n'est pas si simple. Car le théorème de Gödel a prouvé qu'il existe des propositions « indécidables », qu’on ne peut ni prouver ni réfuter. Premier résultat limitant de l'histoire des mathématiques... Disponible jusqu'au 12/11/2026 #Maths #Vérité #ARTE Abonnez-vous à la chaîne ARTE 🤍 Suivez-nous sur les réseaux ! Facebook : 🤍 Twitter : 🤍 Instagram : 🤍

How Gödel Hacked US Constitution.

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23.06.2022

My interview with Mr. Guerra- Pujol, JD: 🤍 In this video I tell a story about Gödel, his US citizenship test and his analysis of the American constitution. Oskar Morgenstern' s original paper: 🤍 Consider becoming my Patreon ! 🤍 Join our Discord to engage with other Mathematics enthusiasts ! 🤍 #Gödel #logic

MIT Godel Escher Bach Lecture 1

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A (very) Brief History of Kurt Gödel

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07.11.2020

In this episode, we cover the history of 20th century Austro-Hungarian mathematician, logician, and philosopher Kurt Gödel, considered to be one of the most significant logicians in history. He is most notable for his incompleteness theorems, which showed in any axiomatic mathematical system, there are propositions that cannot be proven or disproved within the axioms of the system. As per usual, I don't go too deeply into the mathematics, largely just covering his history. Hope you enjoy! Sources: 🤍 DISCORD ►► 🤍 PATREON ►► 🤍

Godel- Porto Novo em coma

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07.09.2016

Limits of Logic: The Gödel Legacy

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21.06.2016

Kurt Gödel showed that mathematical thinking cannot be captured in a formal axiomatic reasoning system. What does this deep result mean in practice? What are the limits of computer thinking? Can beauty and creativity and a sense of humor be formalized? Introduction by professor Douglas Hofstadter.

Les théorèmes d'incomplétude de Gödel | Infini 18

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12.12.2016

Parlons des théorèmes les plus fous des mathématiques ! L'incomplétude de Gödel a fait faire des cauchemars à des générations de logiciens et de mathématiciens ! Et on en voit les grandes lignes de la démonstration. Playlist sur l'infini et les fondations mathématiques | Science4All 🤍 Les théorèmes d'incomplétude de Gödel | Science Étonnante 🤍 🤍 Incomplétude | Passe-Science 🤍 Logicomix (une excellente BD sur l'Histoire des fondations des maths autour de 1900) 🤍 The Technical Part of Gödel's Proof | Secret Blogging Seminar 🤍 Un site web pour taper des formules mathématiques : 🤍 4 paradoxes sur la logique mathématique | Infini 17 🤍 Les pages wikipédia sont très complètes sur l'incomplétude (lol) 🤍

Les théorèmes d'incomplétude de Gödel

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En mathématiques, il existera toujours des choses vraies, mais indémontrables. Merci Kurt Gödel... Sur mon blog, le billet qui accompagne la vidéo : 🤍 Vous y trouverez beaucoup de précisions et de compléments. Écrit et réalisé par David Louapre © Science étonnante * MES LIVRES : - "Mais qui a attrapé le bison de Higgs ?" 🤍 - "Insoluble, mais vrai !" 🤍 * ME SOUTENIR : 🤍 * SUR LES RESEAUX SOCIAUX : Facebook : 🤍 Twitter : 🤍 * LE BLOG : 🤍

Godel's Ontological Argument

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A quick description of the definitions and axioms of Kurt Godel's Ontological Argument for the existence of God. In future videos we will cover objections to this argument as well as the underlying logic. Sponsors: João Costa Neto, Dakota Jones, Joe Felix, Prince Otchere, Mike Samuel, Daniel Helland, Mohammad Azmi Banibaker, Dennis Sexton, Yu Saburi, Mauricino Andrade, Will Roberts, Greg Gauthier, Christian Bay, Joao Sa, and √2. Thanks for your support! Donate on Patreon: 🤍 Buy stuff with Zazzle: 🤍 Follow us on Twitter: 🤍CarneadesCyrene 🤍 Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more!

100% de Love ou Life - MC GODEL

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100% de Love ou Life - MC GODEL - do Ep Assalt Mental de 16 Junho 2016

Kurt Godel: The World's Most Incredible Mind (Part 1 of 3)

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Kurt Godel: The World's Most Incredible Mind. "Either mathematics is too big for the human mind or the human mind is more than a machine" ~ Godel Kurt Godel (1931) proved two important things about any axiomatic system rich enough to include all of number theory. 1) You'll never be able to prove every true result..... you'll never be able to prove every result that is true in your system. 2) Godel also proved that one of the results that you can never prove is the result that says that the system is consistent. More precisely: You cannot prove the consistency of any mathematical system rich enough to include the known theory of numbers. Hence, any consistent mathematical system that is rich enough to include number theory is inherently incomplete. Second, one of the propositions whose truth or falsity cannot be proved within the system is precisely the proposition that states that the system is consistent. " What Godel's proof means, then, is that we can't prove that arithmetic—let alone any more-complicated system—is consistent. For 2000 years, mathematics has been the model—the subject—that convinces us that certainty is possible. Yet Now there's no certainty anywhere—not even in mathematics. More... 🤍 Goedel's Ontological Proof. For those interested in a discussion of Goedel's reasoning for God, then I suggest starting with this heavily annotated work, which I recently stumbled upon. 🤍scribd.com/doc/95364925/Goedel-s-God-Proof-Annotated-Version "It's not that God is subject to the Freedom Proof or the Doubt Proof. According to Gödel, He's not. But we have to be, or else we are not free. So our truth game with God turns into something like Feynman had described. Feynman's Gods, every time physicists think they have the rules of the game figured out, throw in a new wrinkle. They let people like Feynman make progress, but if the Feynmans of the world learn too much, physics will stop being the joy and challenge that it is. The Gods don't let that happen. Gödel's God has to be very careful about how he lets our universe unfold. If the world becomes totally controllable and comprehensible, we'll be God. God does not object to that. In fact, according to Gödel, that is our destiny. But it is also the end of us as free human beings. And human freedom is an essential part of the beauty of God's universe." ~ page 251

Francesco Berto - Mente vs computer: Il Teorema di Gödel e l’intelligenza artificiale

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Internet Festival 2017 - Anelli, ghirlande e scale: a strange loop Capita che gli esseri umani vogliano misurarsi coi computer che hanno creato in qualche attività intellettuale, come quando Kasparov e il software di Deep Blue si sfidano a scacchi. Quando il campione del mondo di scacchi perde, alcuni di noi avvertono un certo disagio. Non occorre spingersi a temere che, una volta realizzata l’intelligenza artificiale, la creatura si rivolti contro il creatore, come Hal9000 in 2001: A Space Odyssey. Semplicemente, a molti dà fastidio l’idea che una macchina ci possa superare in intelligenza. Secondo alcuni, fra cui il fisico Roger Penrose, un risultato di logica matematica dimostrato nel 1930 da un ragazzo sui ventitré anni dovrebbe rassicurarci sul fatto che le macchine non riusciranno mai a superarci in intelligenza. Quel risultato è chiamato Teorema di Incompletezza dell’Aritmetica o, più semplicemente, col nome del suo autore: Teorema di Gödel. Ma cos’ha a che fare un teorema di logica con l’intelligenza, naturale o artificiale? In questa conferenza esploreremo la questione in un viaggio attraverso logica, macchine, algoritmi e creatività.

Godel Incompleteness Theorem and Ayn Rand | Yaron Brook and Lex Fridman

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Lex Fridman Podcast full episode: 🤍 Please support this podcast by checking out our sponsors: - Blinkist: 🤍 and use code LEX to get 25% off premium - ExpressVPN: 🤍 and use code LexPod to get 3 months free - Cash App: 🤍 and use code LexPodcast to get $10 PODCAST INFO: Podcast website: 🤍 Apple Podcasts: 🤍 Spotify: 🤍 RSS: 🤍 Full episodes playlist: 🤍 Clips playlist: 🤍 CONNECT: - Subscribe to this YouTube channel - Twitter: 🤍 - LinkedIn: 🤍 - Facebook: 🤍 - Instagram: 🤍 - Medium: 🤍 - Support on Patreon: 🤍

Visualization of the Gödel universe

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Video abstract for the article 'Visualization of the Gödel universe' by M Buser, E Kajari and W P Schleich (M Buser et al 2013 New J. Phys. 15 013063). Read the full article in New Journal of 🤍

Gödel's First Incompleteness Theorem, Proof Sketch

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Kurt Gödel rocked the mathematical world with his incompleteness theorems. With the halting problems, these proofs are made easy! Created by: Cory Chang Produced by: Vivian Liu Script Editor: Justin Chen Special thanks to Ryan O’Donnell, associate professor at Carnegie Mellon University (🤍 Twitter: 🤍 — Extra Resources: Ryan O’Donnell’s slide deck: 🤍 Wikipedia entry: 🤍 Rules of deductive calculus: 🤍 Proof that square root of 2 is irrational, in Metamath: 🤍 Mizar system: 🤍 Metamath: 🤍 Playlist to previous videos: 🤍

El Teorema de Gödel por fin Explicado Fácilmente

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Gödel´s theorem easy. El teorema de Gödel explicado de forma fácil. Esta historia, es una metáfora del Teorema de Gödel. Comparte el nucleo de ideas de este teorema. 1. Las cajas representan las proposiciones de lógica de primer orden de la aritmética de Peano. 2. El escaner representa la función recursiva que permite saber si una secuencia de proposiciones constituyen la demostración de la proposición de la caja. 3. Godel permite que los objetos , los numerales, definidos por la proposiciones de la teoría, se refieran a otras proposiciones de esa teoria (con la famosa numeración de Godel). Es lo que digo: "Inventó un método para que las cajas hablasen de otras cajas". 4. Crea una sentencia con una variable libre y luego introduce en esa variable el numeral de esa misma sentencia. Así crea una sentencia indirectamente autoreferencial que afirma que no existe una secuencia de numerales que corresponda a una demostración de ella misma. Esto corresponde a la caja que dice: "la caja del interior introduce una copia suya en su interior, y ya no pasa la barrera", el interior vacío de la caja es la analogía de una variable libre en una proposición. No digo, al final, que demuestre la incompletud de la aritmética de Peano, pero que esta arítmetica no puede ser completa y consistente a la vez. Y esta conclusión ya es un duro golpe para el Programa de Hilbert.

Gödel's Incompleteness Theorem - Professor Tony Mann

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21.02.2015

A short mind-bending trip through the wonderful world of Mathematical Paradoxes: An examination of some recent work on paradoxes by the Austrian-American Mathematician Kurt Gödel. You can watch the full lecture by Professor Tony Mann here: 🤍 Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: 🤍

Le théorème d'incomplétude, la révolution mathématique de Kurt Gödel - Passe-science #7

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Les mathématiques contemporaines sont devenues suffisamment puissantes pour démontrer que l'indémontrable existe. Présentation d'un des théorèmes les plus fascinant dans l'histoire des mathématiques, le théorème d’incomplétude de Kurt Gödel, 1931. Complément sur le récapitulatif (qui va un peu vite dans la vidéo!) a) Dire qu'un programme s’arrête, c'est une propriété mathématique comme une autre. b) On peut écrire un programme qui étant donné une propriété P qu'on lui fournirait en entrée, parcourait toutes les démonstrations existantes et s’arrêterait sur une démonstration soit de P soit de non P en temps fini. c) Si un programme tel que b) existait alors on pourrait lui fournir en entrée des propriétés correspondantes à "le programme p1 s’arrête", ou "le programme p2 s’arrête" et il saurait toujours en temps fini répondre à la question. (car ce sont des propriétés mathématiques comme les autres) d) Un tel programme d’énumération des preuves serait donc capable de répondre au problèmes de l’arrêt, mais on a démontré avant que c’était impossible. e) La seule manière de faire coller la chose c'est donc que l'arbre des démos que parcourt notre programme de l’étape b) ne contienne pas toutes les démonstrations des propriétés de la forme '"le programme x s’arrête" (ni les démos ni les réfutations, on a donc bien prouvé l’existence de propriétés qu'on ne pourrait ni démontrer ni réfuter, certaines dans la famille '"le programme x s’arrête") Pour en savoir plus: 🤍 🤍 🤍 🤍 Musique: 🤍 🤍 🤍 🤍 Retrouvez Passe-science sur Tipeee, Twitter et Facebook: 🤍 🤍 🤍

¿LA VERDAD NO EXISTE? | El Teorema de GÖDEL

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Hoy os voy a explicar el famoso Teorema de Gödel, un teorema creado por, seguramente, el más brillante lógico del Siglo XX y quizá de la historia. Y seguramente la persona que más desconcierto ha sembrado. Incluso a su gran amigo Albert Einstein. Y es que sus descubrimientos establecen auténticas e insalvables limitaciones al poderío de la matemática y de la mente humana. ¿Queréis saber más? Pues vamos a curiosear. 🔔 𝗦𝗨𝗦𝗖𝗥Í𝗕𝗘𝗧𝗘 𝗲𝘀 𝗚𝗥𝗔𝗧𝗜𝗦 → 🤍 🌐 𝗖𝗜𝗘𝗡 𝗣𝗥𝗘𝗚𝗨𝗡𝗧𝗔𝗦 𝗕Á𝗦𝗜𝗖𝗔𝗦 𝗦𝗢𝗕𝗥𝗘 𝗟𝗔 𝗖𝗜𝗘𝗡𝗖𝗜𝗔 → 🤍 📺 𝗟𝗢𝗦 𝗢𝗧𝗥𝗢𝗦 𝗖𝗔𝗡𝗔𝗟𝗘𝗦 𝗗𝗘 𝗝𝗝 𝗣𝗥𝗜𝗘𝗚𝗢: - 𝖧𝖨𝖲𝖳𝖮𝖱𝖨𝖠𝖲 𝖣𝖤 𝖫𝖠 𝖧𝖨𝖲𝖳𝖮𝖱𝖨𝖠 → 🤍 - 𝖤𝖠𝖲𝖸𝖯𝖱𝖮𝖬𝖮𝖲 𝖳𝖵 → 🤍 📱¡¡ 𝗦Í𝗚𝗨𝗘𝗠𝗘 𝗘𝗡 𝗥𝗘𝗗𝗘𝗦 𝗦𝗢𝗖𝗜𝗔𝗟𝗘𝗦 !!: - 𝖳𝖶𝖨𝖳𝖳𝖤𝖱 𝖩𝖩 → 🤍 - 𝖨𝖭𝖲𝖳𝖠𝖦𝖱𝖠𝖬 𝖩𝖩 → 🤍 - 𝖥𝖠𝖢𝖤𝖡𝖮𝖮𝖪 𝖩𝖩 → 🤍 ✳️ 𝗙𝗨𝗘𝗡𝗧𝗘𝗦 → 🤍 🤍 🤍 🤍 🤍 ✅ Espero que te guste el video, dale a 👍 y compártelo con tus amigos en tus Redes Sociales, eso ayuda a crecer el canal. ¡Ah! y no te olvides de suscribirte, subo mínimo, un vídeo a la semana. 𝓜𝓾𝓬𝓱𝓪𝓼 𝓰𝓻𝓪𝓬𝓲𝓪𝓼 😘😘😘😘 #CienciasdelaCiencia #JJPriego #Ciencia #CanaldeCiencia

Godel's Incompleteness Theorem (Doubting Math)

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A short description of how Zermelo-Fraenkel Set Theory Avoids Russell's Paradox, but falls into Godel's Incompleteness Theorem. Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more! Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy and more! (#Godel #Incompleteness)

AI Python ChatBot Tutorial with Microsoft Godel and Gradio UI

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GODEL (Grounded Open Dialogue Language Model), a large pretrained language model for dialog. In contrast with earlier models such as DialoGPT, GODEL leverages a new phase of grounded pre-training designed to better support adapting GODEL to a wide range of downstream dialog tasks that require information external to the current conversation (e.g., a database or document) to produce good responses. Experiments against an array of benchmarks that encompass task-oriented dialog, conversational QA, and grounded open-domain dialog show that GODEL outperforms state-of-the-art pre-trained dialog models in few-shot finetuning setups, in terms of both human and automatic evaluation. ChatBot Tutorial - 🤍 Paper - 🤍

EL MATEMÁTICO QUE LLEVÓ LA LÓGICA AL LÍMITE | KURT GÖDEL | Mr. Why | NICOLAS BOURBAKI | P. CUÁNTICO

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26.02.2021

Kurt Gödel ha sido uno de los más grandes lógicos de todos los tiempos. Ocupa, junto a Bertrand Russell, la más alta posición del siglo XX en cuestiones como los fundamentos o la filosofía de las Matemáticas. Gracias por ver el video. Twitter: 🤍 Instagram: 🤍 Facebook: 🤍 Visita el canal de física: 🤍 Comenta, puedes hacer sugerencias para futuros videos. Referencias y videos sobre KURT GÖDEL: 🤍 🤍 🤍 🤍 🤍 🤍 🤍 Publicaciones importantes En alemán: 1931, "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme," Monatshefte für Mathematik und Physik 38: 173-98. 1932, "Zum intuitionistischen Aussagenkalkül", Anzeiger Akademie der Wissenschaften Wien 69: 65–66. En inglés: 1940. The Consistency of the Axiom of Choice and of the Generalized Continuum Hypothesis with the Axioms of Set Theory. Princeton University Press. 1947. "What is Cantor's continuum problem?" The American Mathematical Monthly 54: 515-25. Revised version in Paul Benacerraf and Hilary Putnam, eds., 1984 (1964). Philosophy of Mathematics: Selected Readings. Cambridge Univ. Press: 470-85. #math #matemáticas #Gödel #IAS #bourbaki

Kurt Gödel: Il dio della logica, I fondamenti della matematica e i teoremi di incompletezza

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🤍 © Kurt Gödel / Quadro Film / RAI Educational / 2001 Argomenti: Kurt Gödel, La matematica è completa? La matematica è coerente? La matematica è decidibile? Logica matematica, Filosofia della matematica, I fondamenti della matematica, L'intuizionismo, Il logicismo, Il formalismo, I teoremi di incompletezza di Gödel, La vita di Kurt Gödel. In logica matematica, i teoremi di incompletezza di Gödel sono due famosi teoremi dimostrati da Kurt Gödel nel 1930. Gödel annunciò il suo primo teorema di incompletezza in una tavola rotonda a margine della Seconda Conferenza sull'Epistemologia delle Scienze Esatte di Königsberg. John von Neumann, presente alla discussione, riuscì a dimostrare il teorema per conto suo verso la fine del 1930 e, inoltre, fornì una dimostrazione del secondo teorema di incompletezza, che annunciò a Gödel in una lettera datata 20 novembre 1930. Gödel aveva, nel frattempo, a sua volta ottenuto una dimostrazione del secondo teorema di incompletezza, e lo incluse nel manoscritto che fu ricevuto dalla rivista Monatshefte für Mathematik il 17 novembre 1930. Essi fanno parte dei teoremi limitativi, che precisano le proprietà che i sistemi formali non possono avere. Con l'espressione crisi dei fondamenti della matematica ci si riferisce al fallimento del tentativo di dare una rigorosa giustificazione formale all'insieme di definizioni e deduzioni su cui si basa l'aritmetica (e conseguentemente anche la matematica nella sua interezza), il quale fu seguito all'inizio del Novecento da una radicale revisione dei concetti fondamentali della disciplina. In seguito al grande impulso ricevuto dalla formalizzazione nel corso dell'Ottocento grazie al lavoro di matematici come George Boole, Giuseppe Peano e Richard Dedekind, tra la fine del XIX e l'inizio del XX secolo un nutrito gruppo di studiosi si impegnò nel tentativo di dare una rigorosa fondazione logica ai contenuti delle proposizioni matematiche, con l'obiettivo di produrre una giustificazione assoluta della loro validità (in ciò fu importante specialmente il lavoro di Gottlob Frege); tuttavia l'insorgenza di difficoltà inaspettate (in particolare una serie di paradossi portati alle loro estreme conseguenze da Kurt Gödel nel 1931, Filosofia della matematica), finì per dimostrare l'incompletezza di tutta la matematica. È in generale riconosciuto il ruolo che la crisi dei fondamenti della matematica rivestì nella più ampia crisi che all'inizio del Novecento investì anche la fisica, la psicologia e la filosofia, provocando una perdita di certezze nel campo dell'epistemologia e della filosofia della scienza che portò in ultima analisi al crollo delle teorie filosofiche positiviste. La soluzione definitiva al paradosso di Russell, che costituì anche la risposta a tutti coloro che nei modi più vari avevano tentato di produrre una fondazione certa della matematica, giunse nel 1931, quando il logico austriaco Kurt Gödel dimostrò i suoi due teoremi di incompletezza. Il lavoro di Gödel prendeva le mosse dal Formalismo hilbertiano: il primo importante risultato del giovane austriaco, infatti, fu nel 1930 la dimostrazione del teorema di completezza, in base al quale nella logica del primo ordine una proposizione è vera se e solo se è dimostrabile. Questo risultato dimostrava che, dato un sistema di assiomi e un insieme di regole di deduzione valide per quel sistema, una proposizione vera è sempre dimostrabile in quel sistema (il quale, per questo motivo, è detto completo). Se il teorema di completezza sembrava suggerire che fosse possibile dimostrare la consistenza dei diversi sistemi assiomatici, e quindi arrivare a fondare formalmente la matematica, già nel 1931 Gödel ridimensionò tutte le aspirazioni degli studiosi che aspiravano a questo tipo di fondazione dimostrando i suoi famosi teoremi di incompletezza. La prova di Gödel si articolava in due parti: da un lato, egli dimostrò che se il sistema di assiomi dell'aritmetica è consistente, allora non è completo, cioè che un sistema coerente, in cui non sussistono contraddizioni, contiene delle affermazioni indecidibili (né dimostrabili né confutabili); dall'altro, dimostrò che non è possibile dimostrare la consistenza dell'aritmetica per mezzo del sistema di assiomi dell'aritmetica stessa. Di conseguenza, ogni dimostrazione concernente la validità di un sistema formale deve essere fatta ricorrendo a un diverso sistema formale più "potente" e complesso di quello di partenza, cioè a un metalinguaggio di "grado" superiore. Dovendo fondare una teoria, dunque, è sempre necessaria una metateoria che a sua volta non può essere convalidata se non da una meta-metateoria, e così via. Pertanto non esiste una "teoria ultima" capace di fondare compiutamente l'aritmetica, né a maggior ragione la matematica nella sua interezza. 🤍

Joel David Hamkins on Infinity, Gödel's Theorems and Set Theory | Philosophical Trials #1

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Joel David Hamkins is an American Mathematician who is currently Professor of Logic at the University of Oxford. He is well known for his important contributions in the fields of Mathematical Logic, Set Theory and Philosophy of Mathematics. Moreover, he is very popular in the mathematical community for being the highest rated user on MathOverflow. Outline of the conversation: 00:00 Podcast Introduction 00:50 MathOverflow and books in progress 04:08 Mathphobia 05:58 What is mathematics and what sets it apart? 08:06 Is mathematics invented or discovered (more at 54:28) 09:24 How is it the case that Mathematics can be applied so successfully to the physical world? 12:37 Infinity in Mathematics 16:58 Cantor's Theorem: the real numbers cannot be enumerated 24:22 Russell's Paradox and the Cumulative Hierarchy of Sets 29:20 Hilbert's Program and Godel's Results 35:05 The First Incompleteness Theorem, formal and informal proofs and the connection between mathematical truths and mathematical proofs 40:50 Computer Assisted Proofs and mathematical insight 44:11 Do automated proofs kill the artistic side of Mathematics? 48:50 Infinite Time Turing Machines can settle Goldbach's Conjecture or the Riemann Hypothesis 54:28 Nonstandard models of arithmetic: different conceptions of the natural numbers 1:00:02 The Continuum Hypothesis and related undecidable questions, the Set-Theoretic Multiverse and the quest for new axioms 1:10:31 Minds and computers: Sir Roger Penrose's argument concerning consciousness Enjoy! Apple Podcasts: 🤍 Spotify: 🤍 Google Podcasts: 🤍 Instagram: 🤍

Godel - Colors (Official Video)

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08.08.2022

Official music video for « Colors » by Godel Listen to « Colors » on all streaming platforms. Clip direction : Director: NilaProductions Editor: NilaProductions Resources: Vecteezy Follow Godel: Instagram: 🤍 TikTok: 🤍 Follow NilaProductions: Instagram: 🤍

Zona Pezod - MC GODEL

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DE BAI2R PA TUD ZONA PEZOD ! EN BREV TEN MES FICA ATENT!

Pile ou Face : Jérôme Godel et Stéphane Quéméneur

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07.07.2022

Directeur du Pôle Enfance Jeunesse de la ville de Bruguières, Jérôme Godel revient avec Stéphane Quéméneur, Responsable Vie Associative et Engagement à l'Ufcv en Occitanie sur les débuts de leur collaboration. Ils nous parlent également des (nombreux !) projets à venir et de la manière dont l'Ufcv peut accompagner les villes dans leurs différents besoins. Notre citation préférée : « Les associations comme l'Ufcv apportent une qualité dans l'action collective. Ensemble, on va faire de grandes choses ! » - Jérôme Godel

Kurt Gödel, O Maior Lógico da História

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29.09.2020

Kurt Gödel, Gödel também soletrado como Goedel, foi um matemático, lógico, e o filósofo auztríaco que obteve o que pode ser o resultado matemático mais importante do século 20: seu famoso teorema da incompletude. Sua obra o estabeleceu como um dos maiores lógicos desde Aristóteles, e suas repercussões continuam a ser sentidas e debatidas até hoje. • Acompanhe a Verve Científica nas mídias: instagram.com/Verve.Cientifica facebook.com/VerveCientifica e-mail: VerveCientifica🤍gmail.com * Este conteúdo teve a locução e a contribuição técnica e científica da Prof. Dra. Thaciana Malaspina (CV lattes.cnpq.br/2600060786895700) * Link para meu Curriculum Lattes: 🤍 Referências: [1] britannica.com/biography/Kurt-Godel [2] medium.com/cantors-paradise/kurt-g%C3%B6dels-brilliant-madness-84288dd96eda [3] page.mi.fu-berlin.de/cbenzmueller/2019-Goedel/PaperTakano.pdf [4] en.wikipedia.org/wiki/Kurt_Gödel [5] plato.stanford.edu/entries/goedel/ [6] usna.edu/Users/math/meh/godel.html

A Conjectura de Goldbach e o Teorema da Incompletude de Godel

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Nesse vídeo apresentamos a Conjectura de Goldbach, enunciada pelo matemático Christian Goldbach ao famoso matemático Leonard Euler em 1742. Aqui falamos também sobre os dois Teoremas da Incompletude de Kurt Godel e discutimos a questão da completude da matemática e se é possível demonstrarmos toda a verdade dentro da teoria. Inscreva-se no canal: 🤍 Redes Sociais: Facebook: 🤍 Instagram: 🤍

Gödel, quello che provo' che non sempre il vero e' provabile

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02.07.2022

Sul contenuto dei due celebrati teoremi del signor Kurt Friedrich Gödel. Art by Susanna Panfili 🤍 Liberi Oltre le Illusioni: 🤍

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