FOM: RE: Re: Are Harvey's postings "Foundational"?
montez at rollanet.org
Thu Mar 28 03:55:22 EST 2002
Wiman Lucas Raymond wrote:
``I share (to some degree) your annoyance with Friedman's frequent and
technical postings to FOM. I, like you, cannot really understand them,
and they do have a couple of problems:
(1) He claims they are self contained, but they frequently refer to
previous postings of his.
I'm not saying that there won't be significant results in foundations in
the future that might help shape mathematical thought. I'm saying that
such results would almost certainly be of a very technical nature--and
there's nothing wrong with that. Friedman's work may not (right now)
resolve deep foundational issues, but I would guess that it is
significant. I further doubt that Friedman is alone in understanding
I took a class at the University of Houston from professor Richard Byrd as
an undergraduate. The course was my first course in Abstract Algebra.
Later, as a graduate student in the same department, I was able to share
many conversations with professor Byrd. One phrase he frequently stated (I
believe he is now retired, for I recently visited UH and found no door with
his name on it.) was the following: ``It is well-known to those for whom it
is well-known that...''. I suggest that an appropriate way to deal with the
concept of ``self-containedness'' is to similarly preface claims made in
postings or publications with such a phrase (disclaimer?), or at least, for
those of us who do not always agree that some item or tidbit is really
self-contained, to imagine the author having intended actually just such a
phrase, instead of the much more brief ``The following post is
self-contained.'' Thus, when Harvey says such a thing, we may reasonably
read it as ``The following post is self-contained to those for whom it is
self-contained.'' In point of fact, I consider nowadays nothing to be
self-contained, but everything an author writes to be as self-contained as
the author deemed appropriate at the time of release. The work is the
responsibility of the author, but the appreciation of it is the
responsibility of a truly ``gentle'' readership, including referees and
editors. Harvey's ideas are worth archiving, even if I do not have time now
to delve into the appropriate literature searches, or to plow through his
posts in the detail necessary to provide the type of ``fill'' material
(examples, motivational discussions, etc.) that goes into a monograph or
textbook, and they are valuable even if he is mistaken in some results or
details or in some claims of self-containment or specific applicability.
There are, I daresy, enough people who understand one part or another of
Harvey's BRT, and/or the overall purpose of Harvey's posts, so that some
day, an analysis and synthesis of that material into a form almost all of us
will understand at some useful level will be made available.
Just my Ha-penny.
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