Observables, Disassembled

How should we characterise the observable aspects of physics? This paper makes a start on this question by analysing the concept of an observable in quantum mechanics, arguing that philosophers and physicists should jettison a standard dogma: that observables must be represented by self-adjoint Hermitian operators. Four classes of non-standard observables are identified: normal operators, symmetric operators, real-spectrum operators, and none of these. The philosophical and physical implications of each are explored