Intuition, iteration, induction

Abstract

In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge; Brouwer disagrees on both counts. I will compare Parsons' argument with Brouwer's and defend the latter. I will not argue that Parsons is wrong once his own conception of intuition is granted, as I do not think that that is the case. But I will try to make two points: (1) Using elements from Husserl and from Brouwer, Brouwer's claims can be justified in more detail than he has done; (2) There are certain elements in Parsons' discussion that, when developed further, would lead to Brouwer's notion thus analysed, or at least something relevantly similar to it. (This version contains a postscript of May, 2015.)