The paper presents some brief notes regarding the theory of hypothesis testing and the characteristics of inductive procedures of statistics by critically rethinking two basic themes: identifying false assumptions and selecting, amongst the likely assertions, those which are most consistent with a given system. The methodological demarcation between rejection of a statistical statement, because it is “false”, or its exclusion, because it is “less probable”, lies in the fundamental premises of inferential procedures. In the first class we find the methods proposed by Fisher and Neyman and Pearson; in the second one, the Bayesian techniques. Any particular solution has a limit of validity strictly bounded by the conventional procedural rules on which it is based. In this sense, different theories can be used for solving real inferential problems.