Very often arguments are not made fully explicit: some premises are supposed by the speaker to be too well known to be worth being stated. Such a form of reasoning is called an "enthymeme". First, the story of this Aristotelian concept is sketched and the possible reasons for the evolution of its meaning discussed. Secondly, I argue for its relevance for the understanding of varieties of reasonings, and for its capacity for enlightening the very notions of "inductive inference" and of "argument by analogy". In the former case, it is claimed that a certain "local" form of the "Fair Sample Hypothesis" can be regarded as the missing link between the evidence and the universal conclusion; unlike the conclusion and contrary to the views held by ...