The Equation of Knowledge: From Bayes’ Rule to a Unified Philosophy of Science

Arriving in a small town, with a heavy suitcase, you head for the taxi station, where only one car is parked. Unfortunately, by the time you get close to it, a faster traveller has already taken it and disappeared before your eyes. What conclusion can you draw from this misadventure? That there seem to be taxis in this city - given its size, it was far from certain? And that thus, if you wait patiently, another taxi will eventually show up? Or should you conclude that one of the few taxis in the city has just driven away from you and that, given the size of the city, such a chance will not come back soon? These two interpretations are correct, but both depend on what you knew - or believed - before you got off the train.