> every classical theorem is equivalent to an intuionistic theorem.
I understand that every intuitionistic theorem implies a classical one: give the same proof, and see what theorem you end up with in the classical world. But how is every classical theorem equivalent to an intuitionistic one? Can we construct the equivalent intuitionistic theorem in a similar way from any classical one, or is this a nonconstructive proof?
The negation of the negation not being equal to what you started with always reminds me of the Hegelian dialectic, or dialectic (in the philosophical sense) in general.
I understand that every intuitionistic theorem implies a classical one: give the same proof, and see what theorem you end up with in the classical world. But how is every classical theorem equivalent to an intuitionistic one? Can we construct the equivalent intuitionistic theorem in a similar way from any classical one, or is this a nonconstructive proof?