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[Xmca-l] Re: grosholz



Still, your experience allows you to richly interpret what is involved,
cognitively, socially, and affectively, Henry.

Very interesting.
mike

On Mon, Nov 10, 2014 at 6:17 PM, HENRY SHONERD <hshonerd@gmail.com> wrote:

> I just finished the Grosholz article (“Phil of Math & Phil of History”).
>
> I was thinking about conjectures regarding things that have not been
> proven) and discoveries of things that have may not even been imagined.
> Fermat’s theorem was a conjecture until Wylie proved it. I would contrast
> Wylie’s proof with the year of “pure math” I did at U of Texas at Austin in
> the program set up by E.T. Moore. I tried very hard to prove that such a
> thing as a Cantor set existed. I was not able to beat another student in
> the program to the punch, in fact made a fool of myself in front of a class
> thinking I DID have a proof when I didn’t. But that failure, and the
> struggle that went into it, made it possible for me to understand the other
> guy’s proof. So, on that occasion, he was better at math than me. But by
> the time the two of us worked on the problem it was neither a conjecture,
> nor a discovery. Somebody else had done it for the first time. Our job was
> not trivial, to trace the steps to the proof, but it was very different
> from what Wylie did. Cantor’s story, I think, ups the ante. The set in
> question may have been only a conjecture to Cantor at the time. His ideas
> on transfinite numbers were ridiculed and he was hounded much like Vygotsky
> by the cogniscenti at the time. In fact the It was a discovery of that set
> that has become the foundations of fractal mathematics (which I think is
> worth talking about in this thread). In analogous fashion, Vygotsky’s work
> was epic in analogous fashion and equally tragic. I sort of see us here
> today, with our crisis, working with LSV’s conjectures, finding the
> solution to the problems. I think it’s worth adding these kinds of
> narratives to the history of math and the history of philosophy, as
> Grosholz has construed it. And maybe it’s sort of what she was getting at
> on page 16:
> “…[T]his is the logical texture of everyday life, where the unforeseen
> constantly puts to the test our intellectual and moral resources, and where
> our ability to rise to the occasion must always remain in question: the
> insight of tragedy is that anyone can be destroyed by some unfortunate
> combination of events and a lapse in fortitude or sympathy.
>  Clearly my little piece of it amounts to very little. Still...
> Henry
>
>
>
> > On Nov 9, 2014, at 5:05 PM, Ed Wall <ewall@umich.edu> wrote:
> >
> > Thanks
> >
> > Yes, Wiles is a nice example of doing mathematics within a historical
> dimension.One part of the article bothered me when the author averred that
> Fermat would need to pick up the centuries between. Interestingly that is
> not what a student of mathematics who was born today would 'need' to do to
> enter the conversation.
> >
> > I was listening to a presentation, you might say, on the 'true but
> unprovable'  (in the sense of Godel) by John Conway and he kept saying "I
> don't know if this is true, but …"; "I don't have a proof, but …" It was a
> serious mathematical presentation.
> >
> > Ed Wall
> >
> > On Nov 9, 2014, at  5:26 PM, Vera John-Steiner wrote:
> >
> >> Hi,
> >>
> >> I am forwarding an article by a philosopher of mathematics who
> addresses issues of narrative and logic as well as the role of history
> >>
> >> in mathematics. Some of the article requires a familiarity with
> concepts in the field which are above my head, nevertheless it was a
> valuable
> >>
> >> piece in the context of the current thread.
> >>
> >> Vera
> >>
> >>
> >>
> >> From: reuben hersh [mailto:rhersh@gmail.com]
> >> Sent: Friday, November 07, 2014 7:44 AM
> >> To: Vera John-Steiner
> >> Subject: grosholz
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >> <Grosholz_Maths & History.pdf>
> >
> >
>
>


-- 
It is the dilemma of psychology to deal with a natural science with an
object that creates history. Ernst Boesch.