Gödel, constructivity, impredicativity, and feasibility
pp. 198-213
in: Pascal Boldini, Michel Bourdeau, Gerhard Heinzmann (eds), One hundred years of intuitionism (1907–2007), Berlin, Springer, 2008Abstract
This paper does not pretend to be an exhaustive survey of Gödel's interpretation of intuitionism. This long and rather complicated story has already been told and analyzed by others, for instance in (Kreisel 1987b) and (Tait 2006a, b). More modestly, our first aim here is to present a different appearance of a ghost during that story, the one of impredicativity, and to show that only one case is to be taken seriously from a strict anti-realist point of view: the impredicativity of the concept of natural number. This leads to our second aim, which is to present some of the feasible versions of Gödel's Dialectica interpretation.
