OpenLogicProject / OpenLogic

An open-source, customizable intermediate logic textbook
http://openlogicproject.org/
Creative Commons Attribution 4.0 International
1.08k stars 242 forks source link

Fix intuitionistic equivalent of LEM #353

Closed PeepNSheep closed 10 months ago

PeepNSheep commented 10 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 10 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 10 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 10 months ago

Thanks!