[FOM] philosophical literature on intuitionism
somrh at yahoo.com
Tue Oct 14 22:15:34 EDT 2008
The philosophy of math anthology you mentioned has a few pieces on intuitionism including papers by Brouwer, Heyting and Dummett, IIRC.
One good place to start is to study Immanuel Kant, specifically Kant's view on mathematics. The intuitionists are an extension of that overall thesis. Kant's "Prolegomena to Any Future Metaphysics" is a good place to start and secondary literature is always good in any attempt to make any sense out of Kant.
The intuitionists do differ from Kant (they have to, with the advent of noneuclidean geometry, something had to be altered in Kant's thesis) but IIRC Brouwer made it pretty clear his thought was an extension to Kant's.
--- On Mon, 10/13/08, Thomas Forster <T.Forster at dpmms.cam.ac.uk> wrote:
> From: Thomas Forster <T.Forster at dpmms.cam.ac.uk>
> Subject: [FOM] philosophical literature on intuitionism
> To: "Foundations of Mathematics" <fom at cs.nyu.edu>
> Date: Monday, October 13, 2008, 6:27 PM
> I'm curious to know what the people who dreamt this
> stuff up actually
> thought they were doing.
> Where is the best place to start? Is it Dummett's
> book? Did Brouwer write
> anything one might want to read? I seem to remember there
> is an essay in
> one of the collections (Benacerraf and Putnam?). One of my
> here says that Intuitionism is really a form of solipsism,
> and that for an
> intuitionist to countenance any kind of interpretation into
> logic (or vice versa) is to undermine the solipsism and
> would not be
> welcomed by the true believers. I do remember reading that
> Brouwer was
> hostile to attempts to axiomatise constructive logic..
> Any useful steers?
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