Normativity in logic

Jean-Yves Girard

pp. 243-263

in: P. Dybjer, Sten Lindström, Erik Palmgren, Göran Sundholm (eds), Epistemology versus ontology, Berlin, Springer, 2012

Abstract

Incompleteness—the absence of alternative natural numbers—can be ascribed to a ready-made normativity, inducing a rigid departure syntax/semantics. Geometry of Interaction, set in the non-commutative universe of von Neumann algebras, makes normative assumptions explicit, thus rending possible their internalisation, a possible way out from the semantic aporia. As an illustration, we define an alternative "model": logspace integers.