containing two projectors, where \(P\) corresponds to the case \(N=1\) in \eqref{eqn3}. The physical interpretation of \(P\) is that the energy of the oscillator is no greater than \((3/2)\hbar\omega\), whereas \(I-P\) means the energy is at least \((5/2)\hbar\omega\). If \(P\) is true it might seem reasonable to conclude that either \(n=0\) and the energy is \((1/2)\hbar\omega\), or else \(n=1\) and the energy is \((3/2)\hbar\omega\). After all, the energy can only take values \((n+1/2)\hbar\omega\), so does it not follow from the truth of \(P\) that \(n=0\) or \(n=1\)? No it does not, and understanding why it does not will expose an important principle of quantum reasoning. The point is that probabilistic reasoning, in quantum mechanics or in other disciplines, does not allow one to make inferences about matters which are outside the scope of discussion, i.e., which are not contained in the event algebra. The event algebra \(\EC_a\) corresponding to the sample space \(\SC_a\) in \eqref{eqn7} contains \(P\) and \(I-P\), but does not contain either \([0]\) or \([1]\), the projectors that correspond to the two lowest energy eigenstates. Consequently, this framework does not allow for the statement of a result which might seem intuitively obvious.