Gödel’s incompleteness theorem is often misrepresented in popular science. In this episode we cut through the hype, correcting misconceptions from figures like Neil deGrasse Tyson, Veritasium, Michio Kaku, and Deepak Chopra, and explain exactly what Gödel proved and what he did not.
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RESOURCES:
- Scott Aaronson | How Much Math Is Knowable?: https://www.youtube.com/watch?v=VplMHWSZf5c
- The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis (paper): https://www.pnas.org/doi/pdf/10.1073/pnas.24.12.556
- The Gettier Problem: https://plato.stanford.edu/entries/knowledge-analysis/#GettProb
- Jennifer Nagel on TOE: https://www.youtube.com/watch?v=CWZVMZ9Tm7Q
- Gödel’s First Incompleteness Theorem: https://en.wikipedia.org/wiki/On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems
- Roger Penrose on TOE: https://www.youtube.com/watch?v=sGm505TFMbU
- Curt talks with Penrose for IAI: https://www.youtube.com/watch?v=VQM0OtxvZ-Y
- Bertrand Russell’s Comments: https://en.wikisource.org/wiki/Page:Russell,_Whitehead_-_Principia_Mathematica,_vol._I,_1910.djvu/84
- Gregory Chaitin on TOE: https://www.youtube.com/watch?v=zMPnrNL3zsE
- Chaitin on the ‘Rise and Fall of Academia’: https://www.youtube.com/watch?v=PoEuav8G6sY
- Curt and Neil Tyson Debate Physics: https://www.youtube.com/watch?v=ye9OkJih3-U
- Gödel’s Completeness Theorem: https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem
- Latham Boyle on TOE: https://www.youtube.com/watch?v=nyLeeEFKk04
- Gabriele Carcassi on TOE: https://www.youtube.com/watch?v=pIQ7CaQX8EI
- Gabriele Carcassi’s YouTube Channel (Live): https://www.youtube.com/@AssumptionsofPhysicsResearch
- Robinson Arithmetic: https://en.wikipedia.org/wiki/Robinson_arithmetic
- Algorithmic Information Theory (book): https://www.amazon.com/dp/0521616042
- The Paris-Harrington Theorem: https://mathworld.wolfram.com/Paris-HarringtonTheorem.html
- Curt’s Substack: The Mathematics of Self: https://curtjaimungal.substack.com/p/the-mathematics-of-self-why-you-can
- The Church-Turing Thesis: https://plato.stanford.edu/entries/church-turing/
- Curt’s Substack: The Most Profound Theorem in Logic You Haven't Heard Of: https://curtjaimungal.substack.com/p/infinity-its-many-models-and-lowenheim
- Twitter: https://twitter.com/TOEwithCurt
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