  Probability theory can be modified in essentially one way while maintaining
consistency with the basic Bayesian framework. This modification results in
copies of standard probability theory for real, complex or quaternion
probabilities. These copies, in turn, allow one to derive quantum theory while
restoring standard probability theory in the classical limit. The argument
leading to these three copies constrain physical theories in the same sense
that Cox's original arguments constrain alternatives to standard probability
theory. This sequence is presented in some detail with emphasis on questions
beyond basic quantum theory where new insights are needed.
