From the standpoint of the theory of medicine, a formulation is given of three types of reasoning used by physicians.
The first is deduction from probability models (as in prognosis or genetic counseling for Mendelian disorders). It is a branch of mathematics that leads to predictive statements about outcomes of individual events in terms of known formal assumptions and parameters.
The second type is inference (as in interpreting clinical trials). In it the arguments from replications of the same process (data) lead to conclusions about the parameters of a system, without calling into question either the probabilistic model or the criteria of evidence.
The third is illation (as in the elucidation of symptoms in a patient). It is a process whereby, in the light of the total evidence and the conclusions from the other types of reasoning, one may modify, expand, simplify or demolish a conceptual framework proposed for deductions, and modify the nature of the evidence sought, the criteriology, the axioms, and the surmised complexity of the scientific theory. (The process of diagnosis as applied to a patient may in extreme cases lead to the discovery of an entirely new disease with its own, quite new, set of diagnostic criteria. This course cannot be accommodated inside either of the other two types of reasoning.) Illation has something of the character of Kuhn's scientific revolution in physics; but it differs in that it is the nature, not the degree or frequency of change that distinguishes it from Kuhn's normal science.