Philosophical Foundations of Probabilities
Résumé
This document presents some views on the semantic of the probability notion. It's mainly a summary of different readings, in particular of a Stanford Encyclopaedia of Philosophy article. Probabilities are daily used in real world application, often without a clear understanding of their mathematical foundation and of the meaning we attach to them. This lack of understanding often leads to bad interpretations of statistical/probabilistic procedures (e.g. p-values of tests), and is an obstacle for research. Nowadays there is a debate opposing frequentists to bayesians, but we'll see that the problem of interpreting probabilities is broader, even if we'll present some strong clues in favour of bayesianism.