Recursion, écriture, itération. Une proposition de fondation de la raison computationelle

In this paper we present a set of philosophical analyses to defend the thesis that computational reason is founded in writing; only what can be written is computable. We will focus on the relations among three main concepts: recursion, writing and iteration. The most important questions we will address are: What does it mean to compute something?What is a recursive structure? Can we clarify the nature of recursion by investigating writing?What kind of identity is presupposed by a recursive structure and by computation?Our theoretical path will lead us to a radical revision of the philosophical notion of identity. The act of iterating is rooted in an abstract space – we will try to outline a topological description of iteration. Writing and computation are two different interpretations of this imaginary use of space. So I want to propose a minimal philosophical account1 of computational reason.One of the main guiding ideas of this paper is that we need new philosophical tools to understand the roots of computation and computer science. It would be useful to apply mathematical models to express and clarify philosophical problems, but this would entail major consequences for our formulation of those problems.I will proceed as follows. The first part will be about recursion and the rule-following paradox elaborated by Kripke. I will give some basic definitions of recursion and algorithms, and I will present the paradox. The second part will treat the connection between recursion and writing from the point of view of the French philosophy of technology elaborated by Bruno Bachimont. The third part will focus on iteration and will include a formal definition of iteration