[FOM] philosophical literature on intuitionism

[mark van atten]

Bill Tait Thu Oct 16 11:31:57 EDT 2008 wrote:

> Of course, this subjectivist element in Brouwer's theory  can be  
> eliminated and the theory of choice sequences can be tamed--- this  
> is done in the Kleene-Vesley paper on intuitionistic analysis and   
> in Dummett's book on intuitionism.

No so-called elimination theorem has ever been produced for the  
general notion of choice sequence; only for very specific classes. The  
creating subject is wholly free to generate sequences that fall  
outside of them.

Moreover, these theorems yield equivalences, so they work in both  
directions. For this reason, Kreisel has made the sound suggestion  
that such translations, when they do exist, should not be understood  
(as they usually are) as 'elimination theorems', but as giving `a  
complete analysis' of the notion of sequence in question.

I discuss this topic somewhat further in my book `Brouwer meets  
Husserl: on the phenomenology of choice sequences'.

Mark.



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