Intellectica 2009/1, n° 51

The Mathematical Continuum. New Conceptions, New Challenges

Jean-Michel Salanskis

The Continuum in Cognitive Philosophy

Abstract: The paper addresses the question of mathematical continuum in cognitive contemporary context in large. It first reviews the epistemological debate about continuous modeling and its ontological significance in cognitive science, comparing it with the same debate concerning physics. It then deals with the foundational problem pertaining to continuum inside mathematics. Coming back to cognitive issues, it accounts for some continuous approaches in cognitive matters: namely morphodynamic modeling as Petitot sustains it, Cadiot’s and Visetti’s theory of semantic forms, and continuous biophysics of the brain. Finally the paper considers naturalist apprehensions of mathematics, be it in a programmatic way or on the basis of empirical psychological investigation.

 Key words: Continuum, connectionism, morphodynamics, hermeneutics, language, semantics, epistemology, constructive, formalism, dynamical system, naturalism, psychologism.