Probability, an epistemological focus

Abstract

One of the basic assumptions of the meaningfull learning of a concept [J.B. Araujo y C.B. Chadwick, Tecnologia Educacional, Teorias de Instruccion. 2(a) edicion, (Paidos Educador, Mexico, 1993)] is its maximum contrastability with the preconcepts of the student. It is assumed that the axiomatic construction of the concept to teach is the neatest form of its presentation to the student. Starting from a "preliminary object". which is a collective of data generated by a physical system (like the positions of a brownian particle), the probability associated to the collective is constructed by means of a set of axioms. From the transitivity or zeroth axiom postulated for the "place selection" operation of von Mises [R. Von Mises, Probability, Statistics and Truth. (Dover Publications, Inc., USA, 1981)] it is deduced that probability exists as an objective property of the collective. The other axioms complete the remaining aspects of probability as an intrinsic property of the random systems, by means of which probability calculations or "predictions" could be performed, subjected to experimental testing.