Silviu-Constantin Federovici | From Genesis to Normativity in Brouwers Intuitionism

For the second session of the year, we are pleased to invite a speaker who is currently a Junior Fellow at the Descartes Centre, Utrecht University. Silviu’s talk will be on Intuitionism – a topic we decided on based on popular vote last session. See below for details of the talk.

Speaker: Silviu-Constantin Federovici
Affliation: Alexandru Ioan Cuza University of Iași, Romania

Intuitionism is considered a systematic challenge to certain classical principles of mathematics, yet its viability as a substitute remains widely contested (e.g., Tait 1983).

While this objection concerns its capacity to supplant classical results, Brouwer’s intention to explain “how mathematics is rooted in life” (Brouwer 1906, in van Dalen 2011, p. 27) invites another interpretative approach, namely a more fundamental epistemological inquiry into the relationship between mental experience and the constitution of mathematical constructions.

Building on genetic investigations into Brouwer’s philosophical works (van Stigt 1990, p. xii; van Atten 2004, pp. 2–3), this talk examines two interconnected dimensions of his intuitionism: the mental background from which mathematics emerges as a distinctive field of knowledge and the norms governing constructions within it. More specifically, the analysis centres on a tripartite genetic model of intuition, volition, and reflexivity, exploring how these faculties furnish evidence for the legitimacy of intuitionistic constructions. Selected mathematical examples will help trace this connection.

Finally, the talk addresses the issue of psychologism: can the genetic-normative structure be coherently articulated without reducing mathematical reasoning to contingent states of mind, and what remains philosophically valuable even if the full complementarity of these two dimensions cannot be established?