[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

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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