Methodological insights: fuzzy sets in medicine.

In this paper I wish to introduce some ideas about scientific reasoning that have reached the epidemiological community only marginally. They have to do with how we classify things (diseases), and how we formulate hypotheses (causes). According to a simplified and currently untenable model, we come to defining what a disease, or a protone or a chromosome, is by progressive simplification--that is, by extracting an essence from the individual characters of disease. At the end of this inductive process a single element, which guarantees the unequivocal inclusion in the category, is identified. This is what has been called "Merkmal-definition" (Merkmal meaning distinctive sign)--that is, the definition of disease would be allowed by the isolation of a crucial property, a necessary and sufficient condition, which makes that disease unique (and a chair out of a chair, a proton out of a proton, etc). However many objections have been raised by Wittgenstein, Eleanor Rosch and others to this idea: a Merkmal is not always identifiable, and more often a word is used to indicate not a homogeneous and unequivocal set of observations, but a confused constellation with blurred borders. This constellation has been called a fuzzy set and is at the basis of the semantic theory of metaphors proposed by MacCormac and the prototype theory proposed by Rosch. In this way the concept of disease, for example, abandons monothetic definitions, amenable to a necessary and sufficient characteristic, to become "polythetic." I explain how these concepts can help medicine and epidemiology to clarify some open issues in the definition of disease and the identification of causes, through examples taken from oncology, psychiatry, cardiology and infectious diseases. The definition of a malignant tumour, for example, seems to correspond to the concept of "family resemblance," since there is no single criterion that allows us to define unequivocally the concept of cancer: not morphology (there are borderline situations between benign and malignant), not clinical features, not biochemical or molecular lesions. In the case of schizophrenia, the problem of indetermination, as it has been defined, is even stronger. Mental disease probably cannot be distinguished from health in a clearcut way (according to a minimum set of necessary criteria), but it would have a fuzzy border with mental conditions that characterise normal subjects, through intermediate linking conditions.