[FOM] reply to Panu's reply to my reply to his reply.

Gabriel Stolzenberg gstolzen at math.bu.edu
Sat Mar 4 20:32:56 EST 2006

   This is in reply to Panu Raatikainen's reply of February 28 to
my reply, "intuitions of logic in Helsinki and Cambridge" to his
reply to my message, "intuitions of logic in Chicago and Cambridge."
(I think I've got this right.)

   Panu quotes from my reply.

> > I just wanted to see how, in certain situations (chatting in a
> > common room, over dinner in a restaurant, etc.), classical
> > mathematicians would respond if they thought that this was what
> > I was doing.  And, in my very small sample, I found that it was
> > the involuntary, unreflective response that I described above.

> OK, I then misundertood your point. Obviously you're right here.

   For which I apologize.  I didn't make myself clear.

> > If, by "to argue against these ideas," you mean arguing in favor
> > of rejecting the law of excluded law, recall that, in constructive
> > mathematics, the law of excluded middle is happily neither accepted
> > nor rejected.  If you start out as a classical mathematician, as I
> > did, you don't acquire a constructive mindset by rejecting the law
> > of excluded middle.  It doesn't work that way!  (What intuitionists
> > do is another matter.)

> So how do you think it works?  (honestly, I am iterested.)

   To me, this is -the- question to ask.  "How do you get there from
here?"  But it almost never is asked, so, I'm very pleased to be asked
it now.  But, to do it justice, I'll answer in stages, starting with
my next message, in which I'll begin by describing what happened in my
own case.

> I had myself in mind people such as Dummett, Prawitz and Martin-Lof
> who argue against LEM by questioning the Principle of Bivalence. The
> attempts to make this more precise easily leads to all sorts of
> circularities (as I've tried to argue).

   I wouldn't be surprised to find that I agree with your arguments.
I don't know about Prawitz but, as you know, Dummett and Martin-Lof
have their own projects and conception of things.  In Dummett's case,
to put it somewhat crudely, it seems to me that he has been trying to
develop a constructivist theory of language within analytic philosophy.
And if he decides that it can't be done, it will be the former that
goes, not the latter.  (I think it has to do with the project of making
faith rational.)  To me, it looks like trying to fit a square peg into
a round hole.  But it would be great to be proved wrong.

   Finally, an anecdote that I think is relevant.  When I found that
Dummett had become a realist about the past (his past is now filled
with "facts of the matter"), I called him up and said, "Michael, I
see you're now a realist about the past but still an anti-realist
about mathematics.  What's going on?  Is it that you feel that the
past is too important to be an anti-realist about it but mathematics
is not?"  And he replied (something like), "Something like that."
Now, I don't know about anyone else.  But I find this very funny.
And I'm pretty sure that Dummett did too.

   Gabriel Stolzenberg

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