Inductive reasoning: Problems, methods of justification and interaction between mathematics and computer science.

Abstract

Our paper reports on the  the fondations  of inductive reasoning, more precisely,  the reasons for the conflicts betwen several scientists around the place, the notion of induction and its role in differents sciences, in particular mathematics. We start from an epistemological and didactic reflection of this reasoning to understand this concept. First, we present the epistemological problem of induction in relation to its meaning and validity. These problems highlight the complexity of induction.This leads us,in a second step,   to set up a typology of the notion of induction developed by philosophers,linguists,empiricists and mathematicians. Finally ,we present a didactic analysis of mathematical induction which highlights the specific comprehension difficulties of learners and emphasizes the interaction between mathematics and computer science , in particular the relationship between mathematical induction and recursion.