FOM: Re: intuitionism, Tennant, McLarty, et al

[Colin McLarty]

        Neil Tennant wrote, following the discussion of the non-linguistic
intuition that Mic Detelefsen and I attribute to Brouwer:

>What is peculiar about this brand of intuitionism is that it does not do
any justice at all to the slow but extensive accumulation of steps so
characteristic
>of mathematical reasoning.
>
>Any help in understanding this "unitary intuition" conception would be useful.

        I think "unitary intuition" does reasonably get at Brouwer's idea.

Brouwer as a student wrote in his notebook: "Understanding between two
people is a matter of degree, but mathematical understanding is like being
asleep: your either are or are not." (quoted in van Stigt, BROUWER'S
INTUITIONISM. p.400)  

        But I don't think there is a very good understanding to be had. I
differ very much from Mic (as I understand him) in that I think Brouwer's
developed ideas on intuition, in essays after 1907, are poor and get worse
with time. Of course topos theorists benefitted from the formal
intuitionistic logic of Heyting and later. But you can see already on the
first page of the preface of my book I was eager to point out that topos
logic has none of the philosophic motives of Brouwer.  

Colin