Modus tollens probabilized: deductive and inductive methods in medical diagnosis

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, i.e. by modus tollens, i.e. deductively. By drawing on a case history, this paper aims to clarify some points on the issue. And namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in pearcean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) Medical diagnosis uses both modus tollens and abduction, preferably in this order; 3) Medical diagnosis also uses a kind of “probabilistic modus tollens” in that signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/e1 & e2 & e3): especially at the beginning of a complicated case, odds are between the hypothesis which is potentially being excluded and a vague “other”]; 5) Bayes theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis in the presence of relatively unambiguous evidence or when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a long process of “trial and error”; 6) Bayes theorem is however indispensable in the case of litigation in order to assess the doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposition.