 The negation \(\neg A\) of a formula \(A\) is proven once it has been shown that there cannot exist a proof of \(A\), which means providing a construction that derives falsum from any possible proof of \(A\). Thus \(\neg A\) is equivalent to \(A \rightarrow \bot\). The BHK-interpretation is not a formal definition because the notion of construction is not defined and therefore open to different interpretations. Nevertheless, already on this informal level one is forced to reject one of the logical principles ever-present in classical logic: the principle of the excluded middle \((A\vee \neg A)\). According to the BHK-interpretation this statement holds intuitionistically if the Creating Subject knows a proof of \(A\) or a proof that \(A\) cannot be proved. In the case that neither for \(A\) nor for its negation a proof is known, the statement \((A \vee \neg A)\) does not hold. The existence of open problems, such as the Goldbach conjecture or the Riemann hypothesis, illustrates this fact. But once a proof of \(A\) or a proof of its negation is found, the situation changes, and for this particular \(A\) the principle \((A \vee \neg A)\) is true from that moment on.