[FOM] Intuition, iteration, induction

[Mark van Atten]

A preprint of the following paper is available upon request:

Intuition, iteration, induction

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.

Best wishes,
Mark.