FOM: judging f.o.m.

Harvey Friedman friedman at
Sun Mar 15 04:25:56 EST 1998

In this posting, I may convince people that I am worse than Simpson. The
genesis of this is that I looked in the mirror and decided that I was
provoked by the postings of Franzen 2:19PM 3/13/98, 11:05AM 3/14/98, and
9:41AM 3/15/98. So here it is.

Franzen 9:41AM 3/15/98 writes:

>  Harvey Friedman says:
>  >I suggest that it is more reasonable for you to be asking questions rather
>  >than telling us about how complicated you find something, or how perplexed
>  >you are, or how perplexed you are that anybody would not be perplexed, or
>  >making judgments as to what is needed to convince people, or when what
>  >should be characterized in what way.
>  Yes, I know that you would prefer this.

So would everybody. You now have the opportunity to read your earlier
(initial) posting over and retract it (of 2:19PM 3/13/98). I.e., say that
you, too, would prefer also "to be asking questions rather than telling us
about ..." as I stated above.

>Also, I have no doubt that
>combinatorists are thrilled by your results.

This kind of scarcasm is out of place on the fom, especially since it
involves a whole class of people who are not on the fom. If you believed
that, then why did you write (2:19PM 3/13/98):

> My own tendency as I attempt to penetrate the combinatorial
>principles here at issue is to lapse into slack-jawed wonder that
>anybody can make sense of them, let alone formulate them. ... What is
>needed to
>convince people
>that these are "very natural combinatorial propositions" is to find
>some striking applications of them. ...

which says more about either your bias or your lack of mathematical ability
than about the work you seek to cast doubt on. Incidentally, I can now
announce that two combinatorists are writing a paper for publication in
which they apply one of my independent combinatorial statements to a
problem in partial orders that I have nothing to do with and don't even
know the statement of.

>  I'm sorry that you did not think my observation regarding Cardinal
>Granvelle significant.

What was significant was the fact that you chose to write about you found
and  did not find on AltaVista rather than simply ask what a k-subtle
cardinal is. You wrote:

>Also, it is a significant circumstance that the only occurrence of
>the phrase "subtle cardinal" on any web page indexed by AltaVista is a
>reference to Cardinal Granvelle. To establish Friedman's results as
>important progress in f.o.m., a principle that yields the existence of
>subtle cardinals must be established as a comprehensible and
>potentially acceptable addition to the axioms of set theory.

implying that there is any problem in this regard, which there is not, and
which you could easily have found out by asking. This points to your bias
or lack of understanding of set theory. Or perhaps to a sense of humor that
I didn't appreciate?

>But you underestimate
>what is needed to actually establish work in foundations as being of
>"general intellectual interest".

You continue to misunderstand the notion of "general intellectual
interest." I have already addressed this in this particular instance in my
reply of 7:14PM 3/13/98:

"A coherent body of discrete and finite combinatorial results, regarded as
interesting, natural, basic, and simple by relevant practitioners, has been
discovered and shown to be provable only by going well beyond the usual
axioms of mathematics via standard axioms of higher infinities." A
non-specialist can understand this finding.

E.g., remember the discussion on the fom about MRDP (Hilbert's 10th) stated
for non-specialists? They don't have to understand any actual model of

Franzen writes 11:05AM 3/14/98:

>  The comments by Bill Tait and Martin Davis in response to my remarks
>on Friedman's work are entirely reasonable, and I see no scope for any
>adversarial exchanges on this topic. ***However, my little piece may
>perhaps serve as a reminder that the best way to make people aware
>that an epochal advance has been made is not to underline that it is
>an epochal advance, but to patiently present and explain the work in
>such a way as to allow those qualified to judge (although not
>necessarily experts in the field) to arrive at this conclusion for

***'s are mine.
Here you try to resurrect something from the impulsive 2:19PM 3/13/98
posting (which I invite you to read over and retract) by beating up on that
poor whipping boy, Simpson, who "must have done something wrong" to get you
to write what you did. I say:

***However, this little incident may perhaps serve as a reminder that the
best way to judge something is not to make public pronouncements about your
doubts, but to patiently ask questions in such a way as to learn enough
about it to judge it.***

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