[FOM] reply to martin davis

Gabriel Stolzenberg gstolzen at math.bu.edu
Tue Apr 18 23:44:20 EDT 2006

> Gabriel Stolzenberg has favored FOM with his ruminations which
> frequently take a subjective turn.

   Everyone's messages (indeed, all human discourse) frequently take
a subjective turn.  For example, Harvey recently called attention to
my use of the word "seems."  I then carefully explained why I used it.
Do you have a problem with this?

>    He assures us that he can be in one of two clearly distinct states
> or "mindsets" when thinking mathematically: classical and constructive.

   "Assures us" is you, not me.   Try "says."

>   We who haven't had this experience should just accept Gabriel's
>   assurance.

   I don't talk this way.  I don't think this way.  Yes, if Martin
has earned your trust, you may take seriously what he says about me
here.  Similarly, if I've earned your trust, you may take seriously my
statement about the two mindsets.  Unless you find either of them too
radical--like the European visitor's claim to the Indian prince that,
in Europe, in the winter, water becomes solid.  In that case, you will
roll your eyes and blow it off.  As I do with Martin's remarks about

>            We can't know until we experience it ourselves. This
> does remind one of things one is more likely to hear in a Church
> sermon than in a Mathematics colloquium talk - but no matter.

   I don't think churches get into Gestalt switches of the kind I'm
talking about.  The Pope doesn't shift back and forth at will between
Catholicism and atheism.  (At least, if he does, he doesn't advertise
it.)  Also, notice what happens if we say about classical mathematics
what you say above about constructive mathematics.

        "We can't know classical mathematics until we experience
         it ourselves."

Do you have a problem with this?  If you don't, why do you have one
with constructive mathematics?

> On the other hand he's quite unaccepting of other's subjectivity
> insisting on explicit explanations of just when a number theorist
> will find a bound interesting and even more asking for the "reason"
> why a particular result is of interest.

   I don't insist on anything.   Also, you might do something about
your rhetoric.  E.g., replace "insisting on explicit explanations of
just when" by "seeking explanations of when."

> Gabriel feels free to objectivize the subjective remarks of others.

> Thus he says:
> "Harvey believes that, at least for bounds and algorithms, increased
> knowledge, no matter what, is desirable."
> No matter what? What does this even mean?  But in any case, of course
> Harvey believes no such thing.

   How does a sentence that begins "Harvey believes" objectivize a
subjective remark of Harvey?

   I can think of only two things that are relevant here: the content
of Harvey's alleged belief and whether Harvey believes it.  If I'm
mistaken to think he does, I'm sure he will correct me.  I'm also sure
that he knows that I'll appreciate it, even if I ask him to show me how
to square his not believing it with other statements of his that led me
to think that he did.

   Finally, re "increased knowledge, no matter what," I mean any increase
in any knowledge about bounds or algorithms.


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