 To refute or undermine this ‘proof’, Wittgenstein says that if you have proved \(\neg P\), you have proved that P is provable (i.e., since you have proved that it is not the case that P is not provable in Russell’s system), and “you will now presumably give up the interpretation that it is unprovable” (i.e., ‘P is not provable in Russell’s system’), since the contradiction is only proved if we use or retain this self-referential interpretation (§8). On the other hand, Wittgenstein argues (§8), ‘[i]f you assume that the proposition is provable in Russell’s system, that means it is true in the Russell sense, and the interpretation “P is not provable” again has to be given up’, because, once again, it is only the self-referential interpretation that engenders a contradiction. Thus, Wittgenstein’s ‘refutation’ of “Gödel’s proof” consists in showing that no contradiction arises if we do not interpret ‘P’ as ‘P is not provable in Russell’s system’—indeed, without this interpretation, a proof of P does not yield a proof of \(\neg P\) and a proof of \(\neg P\) does not yield a proof of P. In other words, the mistake in the proof is the mistaken assumption that a mathematical proposition ‘P’ “can be so interpreted that it says: ‘P is not provable in Russell’s system’”. As Wittgenstein says at (§11), “[t]hat is what comes of making up such sentences”.