  Bayesian probability theory is used as a framework to develop a formalism for
the scientific method based on principles of inductive reasoning. The formalism
allows for precise definitions of the key concepts in theories of physics and
also leads to a well-defined procedure to select one or more theories among a
family of (well-defined) candidates by ranking them according to their
posterior probability distributions, which result from Bayes's theorem by
incorporating to an initial prior the information extracted from a dataset,
ultimately defined by experimental evidence. Examples with different levels of
complexity are given and three main applications to basic cosmological
questions are analysed: (i) typicality of human observers, (ii) the multiverse
hypothesis and, extremely briefly, some few observations about (iii) the
anthropic principle. Finally, it is demonstrated that this formulation can
address problems that were out of the scope of scientific research until now by
presenting the isolated worlds problem and its resolution via the presented
framework.
