FOM: Awe

Harvey Friedman friedman at
Tue Jun 8 06:52:08 EDT 1999

As you notice, I feel obliged to defend the greatness of the f.o.m.
enterprise, and stand in awe of its acheivments and possibilities, as I
stand on the shoulders of giants such as Aristotle, Frege and Godel.
Apparently not all subscribers share this awe.

I have always respectfully responded to responsibly stated reservations
that people may have about the f.o.m. enterprise, and will continue to do
so. But because f.o.m. deals with many matters of the highest general
interest, far more people find themselves taking strong positions on f.o.m.
matters than, say, on the theory of knots.

The FOM is and has always been an hospitable place to engage in responsible
dialog about the f.o.m. enterprise. Under Simpson's moderation, it will
continue to be so.

There is no question that there are many vital issues that have not yet
been effectively addressed by f.o.m. For many of these issues, it may be
premature to try to make progress. For other issues, much may have been
said but much more needs to be said and can be said. For still other
issues, major breakthroughs may be around the corner that will open the

The FOM is a perfect place for responsible discussion of f.o.m. related
issues and questions. What issues do you think that f.o.m. should address
more effectively than you have seen f.o.m. do?

In the sharp interchange about Conway's book, On numbers and games, one can
positively focus on a quest for a formal theory of transfinite iteration
that includes set theory as a special case. This matter is quite ripe for a
substantial f.o.m. development.

Out of the latest postings which indicate the lack of approrpiate awe of
f.o.m., one can positively focus on a quest for a better understanding of
the choice of primitives to ground mathematics. It has recently become
clear to me that different choices of primitives lead to (potentially
important) new incarnations of reverse mathematics. That there is a wider
form of reverse mathematics where the choice of primitives becomes a
parameter, and that the present incarnation of reverse mathematics is based
on the particular (and crucially important) choice of natural numbers and
sets of natural numbers - which is the very best choice for the first
incarnation of reverse mathematics.

So don't misread what may be viewed as mindless argumentation on the FOM.
You can be assured that much of a positive nature is going on in the

With regard to my call for postings on:

"What issues do you think that f.o.m. should address more effectively than
you have seen f.o.m. do?"

I will be preoccupied with an upcoming talk on "The Future of Reverse
Mathematics" and will not be very active on the FOM for a while.

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