The interpretation of negation is different in intuitionist logic than in classical logic. In classical logic, the negation of a statement asserts that the statement is false; to an intuitionist, it means the statement is refutable (i. e., that there is a counterexample). There is thus an asymmetry between a positive and negative statement in intuitionism. If a statement P is provable, then it is certainly impossible to prove that there is no proof of P . But even if it can be shown that no disproof of P is possible, we cannot conclude from this absence that there is a proof of P. Thus P is a stronger statement than not-not-P.
The interpretation of negation is different in intuitionist logic than in classical logic. In classical logic, the negation of a statement asserts that the statement is false; to an intuitionist, it means the statement is refutable . There is thus an asymmetry between a positive and negative statement in intuitionism. If a statement P is provable, then P certainly cannot be refutable . But even if it can be shown that P cannot be refuted, this does not constitute a proof of P. Thus P is a stronger statement than not-not-P.
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(i. e., that there is a counterexample).
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it is certainly impossible to prove that there is no proof of P
P certainly cannot be refutable
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no disproof of P is possible, we cannot conclude from this absence that there is
P cannot be refuted, this does not constitute