So let’s go back to the original imprecise case and consider what it means to have an imprecise belief in \(X\). Among other things, it means considering possible that \(X\) could be very likely. It is consistent with your belief state that \(X\) is such that if you knew what proposition \(X\) was, you would consider it very likely. In this case, \(Y\) would be good evidence for \(H\). Note that in this case learning that the coin landed \(\neg X\) uppermost—call this \(Y'\)—would be just as good evidence against \(H\). Likewise, \(X\) might be a proposition that you would have very low credence in, and thus \(Y\) would be evidence against \(H\).