The defining characteristic of Bayesian statistics is that it considers probability distributions over statistical hypotheses as well as over data. It embraces the epistemic interpretation of probability whole-heartedly: probabilities over hypotheses are interpreted as degrees of belief, i.e., as expressions of epistemic uncertainty. The philosophy of Bayesian statistics is concerned with determining the appropriate interpretation of these input components, and of the mathematical formalism of probability itself, ultimately with the aim to justify the output. Notice that the general pattern of a Bayesian statistical method is that of inductivism in the cumulative sense: under the impact of data we move to more and more informed probabilistic opinions about the hypotheses. However, in the following it will appear that Bayesian methods may also be understood as deductivist in nature.