[mturmon]

Just for reference, not everyone is OK with the foundations of probability - what you might call "conventional mathematical probability" as axiomatized by Kolmogorov. See http://www2.idsia.ch/cms/isipta-ecsqaru/ for the most recent in a series of workshops.

One entry into this set of ideas is what Peter Walley has called the "Bayesian dogma of precision" - that every event has a precise probability, that every outcome has a known cost. There are real-world situations when these probabilities cannot be assessed, or may not even exist; same for utilities.

Some examples are in betting and markets (asymmetric information, bounded rationality), and in complex simulation environments having so many parameters and encoded physics that the interpretation of their probabilistic predictions is unclear.