Modes du continu dans les sciences

Abstract

Ways the continuum comes into play within scientific areas The paper, taking into account the actual trends towards the adoption of a continuous framework in cognitive science, especially under the influence of connectionnism, addresses simply the question whether this reference to continuous mathematics goes the same way as in the classical case of newtonian mechanics, and whether it is legitimate to speak of a cognitive continuum sharing its epistemological status with the spatio-temporal continuum. We therefore first try to explain what the epistemological status of continuum in classical mechanics is, making appeal both to Kant and to Montague. Speaking with kantian words, we call this way of the continuum comes into play in the area of science (in that case, of physics) the way the esthetical continuum. We contrast it essentially with what we term way of the tool continuum, exemplified by the continuous approximation of a Bernouilli distribution by a Gaussian one in probability theory. In between, we evoke the hermeneutical relation that mathematics — especially recent mathematics — bear to the enigma of the continuum, as well as the construction of derived mathematical problematics on the basis of the canonical model R. Finally, we examine the status of the continuum within the area of cognitive science in the light of these criterias and distinctions. By commenting some technical moves in current research literature, as well as the methodological position sustained by authors like Minsky or Smolensky, we come to conclude that there is actually no evidence of an esthetical continuum in cognitive modelling.