 What does it mean then for a state to be a superposition? First, it means that if an observable has value \(a'\) in \(\psi'\) and value \(a''\) in \(\psi''\) then any observation of the system will give either \(a'\) or \(a''\), each with probability 1/2. Second, the probability distribution of the outcomes of the measurement of any observable that is not diagonal in the \((\psi'\), \(\psi''\)) basis will be affected by interference: that is, it will not be the mean of the average values of the observable in \(\psi'\) and \(\psi''\). This and nothing else is the meaning of being in a quantum superposition. Hence, the answer to the question “Why don’t we ever see cats that are half alive and half dead?” is: because quantum theory predicts that we never see this sort of things. It predicts that we see cats either alive or dead. It also predicts that in principle we should be able to predict interference effect between the two states. These interference effects are strongly suppressed by decoherence in the case of macroscopic systems (like cats), hence the theory actually predicts that they are extremely hard to observe, in agreement with our experience.