Brouwerian Intuitionism and Husserlian Phenomenology - Dominique Pradelle (Philosophia Scientiæ)
How far can we go to establish a parallel between Brouwer’s intuitionism and Husserl’s transcendental phenomenology, especially when the latter deals with logic and mathematics? Positions on this question are diverse and sometimes quite divergent. For example, Mark van Atten considers that both advocate a reform of mathematics based on the inversion of the priority of logic over mathematics while Cavaillès considers that Husserl’s philosophy of mathematics is close to Hilbert and not to Brouwer. Where does the truth lie? We attempt to clarify the question by contrasting the notion of giving intuition as understood by Brouwer (in a Kantian framework referring to human finitude) and by Husserl (in a non-Copernican framework, freed from any reference to finitude and to the requirement of psychic effectuability of acts); by showing that, for Brouwer, intuition is tied to the conditions of the temporality of consciousness and to constructivist requirements, but not for Husserl, who admits a mutability of the forms of categorial fulfillment; then by showing that the Husserlian critique of the excluded middle and of decidability does not tend towards a reform of mathematics in the same way as Brouwer. It is instead viewed as a conservative critique aiming to reveal and understand the idealizing presuppositions that are necessary for mathematical practice. At stake in this clarification is the idea of the mutability, extensibility and historicity of intuition.