Every Paradox That Breaks Your Brain, Explained

A barber who can't exist. A ship rebuilt plank by plank. A sentence that calls itself a lie. Each one sounds simple, and each one breaks something we were sure of. Seven paradoxes, each harder to escape than the last, and where every one of them comes from. This is every paradox that breaks your brain, explained. -- CHAPTERS -- 00:00 Every step goes up: what a paradox is 01:26 Level one: the barber who can't exist 03:44 Level two: the Ship of Theseus 06:29 Level three: the heap (sorites) 09:48 Level four: Zeno's race, Achilles and the tortoise 13:20 Level five: the liar paradox 16:20 Level six: Russell's letter that broke math 20:26 Level seven: the surprise test nobody can explain 23:24 The way out: where a paradox comes from 25:21 The atlas -- SOURCES, every quotation -- Every quotation is read from a public-domain edition; work, section, translator and edition are listed. Plutarch, Life of Theseus 23. The translation called Dryden's, ed. A. H. Clough. Gutenberg 674. Diogenes Laertius, Lives and Opinions of Eminent Philosophers II.108 (Eubulides). Trans. C. D. Yonge (1853). Gutenberg 57342. Aristotle, Physics VI.9, 239b. Trans. R. P. Hardie and R. K. Gaye (Oxford, 1930). archive.org/details/physica0000rpha Titus 1:12, King James Version (1611). Gutenberg 10. Bertrand Russell, The Principles of Mathematics, vol. I (Cambridge, 1903), Preface. archive.org/details/cu31924001610421 Gottlob Frege, Grundgesetze der Arithmetik, vol. II (1903), appendix: summarised, not quoted. -- IDEAS AND HISTORY (described, not quoted) -- Hobbes, De Corpore (1655) II.11.7; Russell's letter to Frege (16 June 1902) and Frege's reply; Russell, The Philosophy of Logical Atomism (1918); Tarski on truth (1933); Godel, On Formally Undecidable Propositions (1931); O'Connor, "Pragmatic Paradoxes", Mind 57 (1948); Sainsbury, Paradoxes (1987); Williamson, Vagueness (1994). -- QUOTED CLIPS (short excerpts for commentary, each named on screen) -- Tony Mann, "Bertrand Russell, Set Theory and Russell's Paradox", Gresham College:    • Bertrand Russell, Set Theory and Russell's...   Timothy Williamson in "Philosophy's Most Formidable Living Mind", Theories of Everything:    • Philosophy’s Most Formidable Living Mind   James Grime, "Zeno's Paradox", Numberphile:    • Zeno's Paradox - Numberphile   Bertrand Russell, 1959 interview with Woodrow Wyatt, via Philosophy Overdose:    • Bertrand Russell Interview on Philosophy (...   -- IMAGES (each also named on screen) -- Public domain: Thomas Hobbes (John Michael Wright, c. 1669-70, National Portrait Gallery); Gottlob Frege (c. 1879); Bertrand Russell (1907); Kurt Godel (c. 1925); Zeno of Elea (Escorial fresco, c. 1590); title pages of Plutarch (1888), Diogenes Laertius (1853), Frege (1893) and Russell (1903), via Wikimedia Commons and the Internet Archive. Aristotle, engraving by P. Fidanza after Raphael, Wellcome Collection, CC BY 4.0 (licence link below). -- FOOTAGE (bylines on screen) -- Pexels: ANTONI SHKRABA production, Alena Darmel, Andy Barbour, Barbara Olsen, Cedric Fauntleroy, Christopher More, Diva Plavalaguna, Giant Asparagus, Glenn Langhorst, Joolsmagools, Juan Riofrio, Kaboompics (karola-g), Karl Byron, Ketut Subiyanto, KoolShooters, Laker, Los Muertos Crew, Mikhail Nilov, Nishant Das, Paul Bill, Pavel Danilyuk, Ron Lach, Tima Miroshnichenko, Yan Krukau, Yaroslav Shuraev, cottonbro studio, khanhhoangminh. Pixabay: AlexKopeykin (Pixabay), Solarselle77, conte_public. Mixkit: Mixkit, highwayvideography (Mixkit). Archival film: Film: ENIAC (U.S. Army, 1946), restored by Computer History Archives Project. -- MUSIC -- "Lofoten" and "Steppe", Doc & Lena Selyanina (archive.org/details/DocLenaSelyanina-SongsOfVastnessmt027), CC BY 3.0. "Tension", Alex-Productions (onsound.eu), CC BY 3.0. "Transcend", Jason Shaw (audionautix.com), CC BY 4.0. Licences: https://creativecommons.org/licenses/... and https://creativecommons.org/licenses/... Sound effects: paper sounds CC0; motion sounds CC BY 3.0 (licence link above): "SWOOSH" by Extreme Sound Effects (   • SWOOSH - Sound Effect HD  ); "Thick paper Book handling page turning" by Sound Creating (   • Thick paper Book handling page turning sou...  ); "Paper Sound Effects" by Creator Assets (   • Paper Sound Effects (Copyright Free)  ); "Knock On Stuff: The Singing Bowl" by Knock On Stuff (   • Knock On Stuff: The Singing Bowl (small)  ). An atlas of philosophy, one question at a time. #philosophy #paradox #shipoftheseus #zenosparadox #liarparadox #russellsparadox #videoessay This video quotes only public-domain texts and uses licensed or public-domain imagery. Brief excerpts of the clips above are used for commentary, criticism and education, which is fair use under Section 107 of the Copyright Act 1976.