How can Randomised Controlled Trials (RCTs) change our beliefs? The fact that they do update prior beliefs to different posterior beliefs is explained by Bayesian philosophy. Crucial points in Bayesian analysis include setting the first prior expectation right and sequential updating of the prior in the light of new evidence. Bayesian analysis depends highly on the evidence included. RCT evidence can only falsify the placebo hypothesis, it cannot indicate which mechanism of action could be responsible for an intrinsic effect and therefore cannot overturn existing beliefs. Bayesian reasoning could structure further discussion, but subjectivity is an inherent element of this process. In the case of homeopathy the first prior is not a common prior shared by all parties to the debate, but a paradigm, this prevents common updating of beliefs. Only by keeping an open mind towards other paradigms and all possible hypotheses can a low Bayesian prior be elevated to the point of accepting a new paradigm, this is more relevant than Bayesian calculations.