ABSTRACT

Although most of the questions studied in this work are approached in terms of psychogenesis, they are closely related to fundamental epistemological problems. Insofar as one is inclined to consider knowledge in general as a more or less schematized copy of reality and logicomathematical truth as an adequation to entities given in advance, 1 the role of correspondences or morphisms as instruments of comparison will be overestimated whereas transformations themselves will be reduced to metaphors expressing relationships given in reality in the form of “operations” (an idea that Couturat qualified as anthropomorphic). By contrast, if one is neither empiricist nor apriorist but rather constructivist or paritsan of dialectic as source of novelties, the problems of relationships among comparisons and transformations and in particular among operatory and morphismic transformations acquire a new meaning of some importance. That is why we have sought to clarify the extent and nature of their respective contributions in the continuous elaboration of knowledge from elementary levels onward. That is also why we have sought to elucidate the coherence between the psychogenetic facts and the analysis of the same questions on the plane of scientific thought (see the chapters by G. Henriques and E. Ascher). All of these analyses aim, therefore, at more closely encompassing these two aspects of knowledge, adequation, and construction, at once inseparable and apparently opposed.