FOM: Re: pointless numbered postings?

charles silver silver_1 at
Sun Jun 30 10:57:53 EDT 2002

>From Harvey Friedman:

> Some time ago, I made a flurry of numbered postings about incompleteness,
> things have calmed down considerably since then. Questions were raised
> the point of them, their significance for f.o.m., etcetera. See
> charles silver" <silver_1 at>
>        Date: Wed, 27 Mar 2002 06:40:58 -0600

> >From Silver:
> >    I have a question: Whatever is "foundational" about Harvey Friedman's
> copious, exceedingly technical postings?

> They are meant to address the question "Does normal mathematics need new
> axioms?" positively by means of examples. There are criteria for
> according to current mathematical culture. These criteria have evolved
> their present state over hundreds of years, in fits and starts. There is
> than can be said about this notion of "normality".

    I'm a bit puzzled what is meant by "normality".  Does it mean something
like "present day consensus," and if so, consensus of what group?   One
should, I think, take into consideration that "normal mathematicians"
typically neglect foundational concerns entirely.

> The choice of systems, and the philosophy behind the whole enterprise, is
> obviously not purely technical. Some aspects are largely nontechnical.

    Sure.  I'm just asking for this to be spelled out.   Incidentally,
though I'm unconvinced that ZF set theory is **the** one and only foundation
for mathematics, I've never doubted for an instant Harvey's sincere
philosophical concerns in foundations.   I've just wanted to read more of
the views that underly his results.   (For example, off-line several times,
I've found myself in the unfortunate position of *defending* some extremely
critical comments Harvey's made that several ex-subscribers found offensive.
My defense, such as it was, relied on my--admittedly shallow--understanding
of some of Harvey's underlying philosophical views on certain foundational

> All that
> seems clear to me is that there is nothing or at least relatively little
> >his posts to explain their "foundational" content.

> As I said earlier on the FOM, I hoped to come back to explain this.

    Periodically, I wish you would.

> Do the postings of Martin Davis and Richard Heck form an adequate
> for you?

    Both of them have been helpful, but you are the best expositor of your
own underlying philosophical motivations.   I do understand that you would
prefer to concentrate on achieving results of foundational interest, rather
than spelling out the views motivating those results.   Nonetheless, I'd
appreciate an occasional tip of the hat toward philosophical concerns.
Actually, a book, or something like one, on the philosophy of mathematics by
you would be especially welcome.    And, it seems to me that in the back of
your mind you have already "written" such a book.

Charlie Silver

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