FOM: methodology

[Harvey Friedman]

I just read Holmes 2:18PM 3/25/99: properties, in which he responds to Sazonov.

Their interchange, which has been going on for some time, centers around
issues concerning objectivity and meaning, often going under the names of
realism, platonism, formalism, finitism, etcetera.

I have always found such discussions unsatisfying, where people rarely seem
to change their mind. I, personally, have always felt more comfortable
trying to produce results that clearly bear on these issues. I try to sense
what is relevant and doable - and try to do it.

At a later stage in my career, I may well move towards dealing more
directly with such matters. But I am still inclined to think that,
personally, I have a better chance of doing something of permanent
intellectual value under my present mode of operation. Nevertheless, I like
to read what people have to say, as it frequently suggests new kinds of
results.

With that preamble, let me suggest a somewhat different thread for the FOM.
WHAT KIND OF MATHEMATICAL DEVELOPMENTS WOULD BEAR ON THE ISSUES THAT ARE
BEING DISCUSSED?

Just to get the ball rolling, let me throw out an obvious one. THAT NEW
KINDS OF INCONSISTENCIES ARE DISCOVERED.

How would that change the discussion? Obviously, it depends on where these
inconsistencies lie. But, also: WHAT IF NO NEW INCONSISTENCIES ARE EVER
DISCOVERED? How would that effect matters?

Here is a perhaps impertinent question: WHAT IS CURRENTLY BEING WORKED ON
BY LOGICIANS THAT COULD EVER OR MIGHT EVER EFFECT THESE DISCUSSIONS?