# [FOM] Tait on constructive mathematics

Mark van Atten Mark.vanAtten at univ-paris1.fr
Wed Feb 15 05:36:27 EST 2006

On Sat Feb 11 14:41:10 EST 2006, Bill Tait wrote in Haney and Tait on
intuitive sources of mathematics':

>Weyl, who was a better philosopher than Brouwer, understood that the
>successor operation was not the issue, but rather that then basis of
>arithmetic is the notion of a finite iteration of *any* operation,
>and he took that notion of finite iteration as what is given in
>intuition.

Brouwer describes exactly this in his dissertation, where he writes of
the intuitively clear fact that in mathematics we can create only
finite sequences, further by means of the clearly conceived and so
on'' the order type \omega, but only consisting of equal elements'.

In a footnote he explains further:

The expression and so on'' means the indefinite repetition of
one and the same object or operation, even if that object or that
operation is defined in a rather complex way'

This is on p.80 of Collected Works I.

Mark van Atten.

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