[Clinical cases, trials, and the problem of the colored socks. Or the problem of induction in medicine]

The medical prevision is based on the induction, that is the logical procedure trying to get a general truth starting from pooling and analysis of single cases. A first type of induction is defined complete or mathematical, since it allows a switch from a finished to a wider and endless set of cases. The mathematical induction is a logical procedure, completely consequential and that's why the derived demonstration is always true. Instead the knowledge in medicine is founded upon empirical induction, inferred from the observation of a sufficiently wide number of real cases. But the conclusions which are induced empirically introduce an inevitable degree of uncertainty, because they cannot be deduced logically. Statistics is the tool employed for "weighing" somehow the degree of confidence in a conclusion induced from the observation of numerous single cases. But it presents the limit of quantifying global behaviors, so the generalization derived from statistical inference reflects only the final mean effects that occurred under some specific conditions. Here are presented the problems that arise when switching from conclusions induced by the observations of a wide sample to the management of the single patient. On the other side the limits, but also the complementary value of case reports, are presented.