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No. Classically, LEM and double negation are equivalent. Intuitionistically the situation is more complicated, see the discussion in this thread by IngoBlechs
by mafribe 11y ago
No.
Classically, LEM and double negation are equivalent.
Intuitionistically the situation is more complicated, see the discussion in this thread by IngoBlechschmid: We can prove that LEM implies double negation, but not the other way around. Intuitionistically, we can only prove that ⊢¬¬A⊃A, then ⊢A∨¬A, but not ⊢(¬¬A⊃A)⊃(A∨¬A).
For these and related reasons, double negation is not considered constructivistically valid.