Analyse sémantique d'un mot polysémique: La fonction

...... fungar vice cotis, acutum Reddere quae valet ferrum, exsors ipsa secandi. Horace “Je serai comme la pierre à aiguiser, qui peut rendre le fer tranchant, mais est incapable elle-même de trancher.” Epigraphe d'un article célèbre de Giovanni Schiaparelli “Forme organiche naturali e forme geometriche pure” (1900) sur la modélisation mathématique en Biologie.

Abstract

It is our intention in this article to reconsider a text written shortly before his death by the founder of our Society, Pierre Delattre. In it he apparently proposed that the biological meanings of the word ‘function’ were derived from the mathematical use of the word, a particularization.

We claim, on the contrary, that it is the mathematical use of ‘function’ that comes from its sociological and biological meanings. For this we go back to the etymology of the word. Function comes from the Latin verbfungi (in the first person,fungor). Fungor (a deponent verb form) already has a factitive meaning, “I am made to do”, and it applies to a ‘functionary’, a civil servant engaged in some specific social (or political, or military) task. Hence such a meaning presupposes the existence of a social structure able to compel individuals to undertake a specific task of common interest. The Latin verb can also be applied to a tool, made to ‘function’ in the interest of man. Thus the meaning offungi requires a preexisting social or biological organization. The function aims to correct the dysfunctions of the global system, whether political or biological.

The notion of function cannot be dissociated from the corresponding notions of structure and organization, the former being geometrical and the latter of a finalistic nature. If one wants to define the organ, or the function, in a descriptive manner without recourse to finality, one has to get back to the ‘phenomenological’ point of view, which relies on a phenomenological equivalence relation, the ‘homoeomeric equivalence’ of Aristotelian terminology as used inDe Partibus Animalium. See also the paper (Thom, 1990) which offers some extension of the present article by showing that body parts, as they are usually perceived and described linguistically by words like ‘head’, ‘trunk’, or ‘limbs’, cannot be defined in terms of homoeomeria alone. Hence the necessity of introducing Aristotle's ‘anhomoeomeric parts’. The anhomoeomeric parts are associated with some phenomenological discontinuity and are the support of physiological functions. In general they are associated with a ‘bifurcation’ command.

This article develops some criticism of the present use of the word ‘function’ in modern Biology, which puts on the same level a tiny local biochemical event (such as dehydrogenation) and a global biological function such as sensation, digestion or reproduction. We also propose an exercise on the use of the word ‘function’ as applied in a scientific discipline.

Résumé

Les emplois du mot fonction peuvent se grouper en:

• - Biologie: fonction physiologique

• - Socio-Politique: la fonction du fonctionnaire

• - Mathématique:y=f(x)

Tous dérivent d'un emploi unique: Fonction d'un instrument vu comme le controle d'une bifurcation.