OpenLogicProject / OpenLogic

An open-source, customizable intermediate logic textbook
http://openlogicproject.org/
Creative Commons Attribution 4.0 International
1.02k stars 234 forks source link

Fix intuitionistic equivalent of LEM #353

Closed PeepNSheep closed 6 months ago

PeepNSheep commented 6 months ago

By the BHK interpretation, $\lnot \varphi$ is a shorthand for $\varphi \implies \perp$. The original statement was just the definition of negation in intuitionistic logic, not the LEM.

rzach commented 6 months ago

You're right that the first one makes no sense. But your replacement isn't a well-formed formula. I think you meant (\not !A \lif \lfalse) \lif !A.

PeepNSheep commented 6 months ago

You're right that the first one makes no sense. But your replacement isn't a well-formed formula. I think you meant (\not !A \lif \lfalse) \lif !A.

Good catch. I just fixed the typo.

rzach commented 6 months ago

Thanks!