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In La Nouvelle Héloïse Rousseau states that everyone uses figurative expressions; he adds that only fools and geometricians express themselves without using metaphor. Can one allow even these two exceptions? It has become increasingly clear in the field of culture that metaphor can be used in a foolish manner: how many doctrines have a dominant analogy at the basis of their reasoning; how many metaphors have become dogmatic as the areas in which they may be applied increase? And if metaphor is central to faulty reasoning and foolish arguments, is it altogether absent from the geometrician's work? The geometrician's categories are certainly limiting in this respect, and it appears paradoxical to wonder whether geometrical concepts, such as a straight line or a point are not figurative expressions borrowed from other fields. However the problem becomes far less paradoxical when one moves from geometry to mathematical astronomy, mechanics and by degrees to the whole of physics. For in most fundamental categories, those which instigate a new field of knowledge, a metaphorical dimension, then become apparent. The further one descends Comte's ladder of science, the more the terminology retains the stamp of the transitional stage from which the concept originated. A straight line, a point, a circle are perhaps first concepts as regards expression and invention. But attraction, natural selection, physiological division of labour, or division of social work bear in their very names the mark of the intellectual transference through which they were formed. With the result that scientific invention does not use non-figurative concepts; it often finds its mode of expression through metaphor. Neither the fool nor the geometrician escape the metaphorical realm of thought, because it is the usual means of expression and conceptualisation. Because of this the metaphor used by the fool and that used by the geometrician link up, and it becomes possible with regard to certain predominating metaphors, to tackle the question of the quality of reasoning and the question of the discovery of knowledge, the study of argument and the study of conceptualisation, together: for beyond the general usage of metaphor, it is the expressive nature of speech itself with which we are primarily concerned.
