[FOM] Embedding intuitionistic logic in classical

Joao Marcos botocudo at gmail.com
Fri Sep 23 15:51:40 EDT 2011

>> (i) Embedding intuitionistic propositional logic in classical propositional logic.
>> (ii) Embedding intuitionistic predicate logic in classical predicate logic.
>> (iii) Embedding intuitionistic S4 propositional logic in classical S4 propositional logic.
> The first and third of these questions are answered in the negative in my book Propositional Logics.

Someone pointed out to me what seemed to be an inconsistency between
Epstein's reply and mine ("no" to both (i) and (iii) versus "yes" to
both (i) and (iii)).  There is no contradiction, though.  Epstein uses
a specific notion of *conservative translation* in his book (chapter
X, if I remember it right) that has the extra property of being
*grammatical* in a certain precise sense.



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