A Constructive Paradox
Become an Omega or Aleph Member on Youtube and help us keep this going! 🙏
<a href="mailto:https://www.youtube.com/@aboutlogic">https://www.youtube.com/@aboutlogic</a>
Or you can buy us a coffee here: 
<a href="https://buymeacoffee.com/aboutlogic">https://buymeacoffee.com/aboutlogic</a>
Further Reading &amp; Resources:
Get the HoTT Book for free (no advertisement): <a href="https://homotopytypetheory.org/book/">https://homotopytypetheory.org/book/</a>
Thorsten Altenkirch: <a href="http://www.cs.nott.ac.uk/~psztxa/">http://www.cs.nott.ac.uk/~psztxa/</a>
Deniz Sarikaya: <a href="https://www.denizsarikaya.de/">https://www.denizsarikaya.de/</a>
Creative Production: Jan-Niklas Meyer: <a href="http://www.jammos.com/">http://www.jammos.com/</a>
Join the Discussion: Have questions or thoughts to share? Drop a comment below and engage in a discussion with fellow viewers and experts.

Choice vs. Excluded Middle: A Constructive Paradox | aboutlogic: premises #08
Constructive mathematics is all about building things explicitly — so why does it reject the Axiom of Choice, which sounds trivial in a constructive context. In this Premises episode, Thorsten walks Deniz through Diaconescu's theorem: the surprising proof that the Axiom of Choice implies the Law of Excluded Middle, turning a seemingly innocent principle into full-blown classical logic.

Using an intuitive type-theoretic explanation (starting with a very relatable glove-matching example), Thorsten builds up to Diaconescu's classic argument, touching on propositional extensionality, the difference between intensional and extensional predicates, and why the Axiom of Choice turns out to be a stronger form of "magic" than Excluded Middle itself.





aboutlogic: premises #08 | Choice vs. Excluded Middle: A Constructive Paradox

Description