FOM: Feferman wet blanket for f.o.m.?

[Robert Tragesser]

        I write because no one more
able has risen to defend Feferman --
which I find startling indeed.

        To begin on a "professional" note and
with a "professional" judgment (since,  e.g.,
H.Friedman puts so much stock in that, as nauseous
as the very term makes me],  I
suggest as a professional philosopher who
has been around the block a few times
and down a number of strange byways:
Friedman's [even if "affectionate"] attack on
Feferman as the arch wet-blankateer of f.o.m.
points up better than any comments I have yet seen 
the philosophical puerility [professional
judgment,  not rhetoric] of the ideology
of "general intellectual interest"--a
cunningly designed slogan for levering all
manners of evading the most
difficult philosophical problems we face.

        In his "Feferman a notorious wet blanket for
f.o.m." posting,  Friedman mocks Feferman for saying
(apparently recently?) that he (Feferman) is not
clear about the significance of the proof of the 
independence of CH.  One does notice that Friedman
has a one dimensional sense of "significant".  One
can not as much as imagine that Feferman does not
think this f.o.m. result to be important/significant.
What surely is at issue is what its import is.  What,
for example, does it say about the definiteness or
determinateness of the continuum problem as a mathematical
problem?  What is its import for mathematics?

        I do not think that it is too much to say that
Feferman has spent a lifetime attempting (among other things)
--judging entriely by his writings -- to disclose,
unfold,  get right,  the import of Goedel's 1931
PM I.  Feferman is by far more illuminating than any
other writer I've seen in his subtle articulation of
what is going on in that paper,  and above all for
giving us ways of exploring the import for mathematics
of that paper:  How does it make us wiser about
mathematics (rather than just about, e.g., the limitations
of, e.g., "finitary inductively presented logics")?
        As Feferman has repeatedly and ever more
elaborately revealed,  this is an extremely difficult question.
Indeed, it is perhaps (still) the central and most radical question
in the philosophy of mathematics.  (Where one does
not take the "philosophy of mathematics" to be
that in-bred academic discipline,  but "philosophy" in
Plato's sense,  as a thinking about mathematics that
aims to make us wiser about and at mathematics -- that
aims to make mathematicians fully GOOD mathematicians. --
It is in this spirit that one can see Feferman's
"Working Foundations"-- especially in the light
of Feferman's reflections on the course of his own
thought in "Three conceptual bugs" and "Math.need
axioms?" essays, as among the best that philosophy
in the Platonic sense has to offer us now.)

        Philosophy in this Platonic sense is extremely 
difficult, and so one could see why someone who is genius at
f.o.m. but who also has revealed quite obviously that he
has little time and energy for hard philosophy might deeply
value and need to displace it,  hide it way,  by the
philosophically subversive ideology of "general
intellectual interest". 
        I have in mind H.F.  Judging by his postings,
it is easy to imagine that he has little appreciation
of the nature of philosophical problems (or at least no
patience with them).  Here are two examples:
 
        [1] Earlier,  I had introduced what I
called "Boolos' Conjecture" (which he made in
conversation with me circa 1990):  "an
intuitive [informal] proof that p is an
intuition that p is demonstrable in ZF". This
amounted to: if you begin with an informal proof
and develop it into a perfectly rigorous proof,
one would end up in ZF.  Friedman's response to
this was that it was not a conjecture at all,
but (not an empirical but a) fundamental truth.
Alas Boolos can't explain himself,  but my sense was
that Boolos was being a good philosopher,  that
is,  he was making a problem to be taken seriously
and meticulously solved of what Friedman was quite happy 
to dogmatically declare as wholly true and wholly
unproblematic.-- It was instructive to notice that
Friedman could look at Hilbert's Foundations of
Geometry and be wholly blind to (what say someone
with the phenomenological acuteness of Wittgenstein
would see right away), that Hilbert's proofs
there often trade on the as it were syntax
of geometric drawings/figures,  and not on logical
syntax.  That is,  there is indeed a very difficult
problem of understanding exactly how those
proofs (their informal content) are related to
formal-logical derivation. [This is very different
from its being easy to formally-logically re-do
Hilbert's FoG!!! -- A strange confusion of Friedman's] 
        [2] Friedman mocked [in an affectionate way,
we're told] Feferman for not considering
Goedel's claim that one important way of 
choosing axioms is by virtue of their being
fruitful in consequences.  First,  why
'should Feferman accept this simply because Goedel
declared it?  It is rather than Friedman
owes us an explanation of just what "fruitful"
should mean,  and under what circumstances this 
criterion is genuinely viable and cogent,  and when it
is not. 
        [I do not venture a comment on the
philosophical vapidity of HF and SS's satisfaction
in the "gii" of HF's "big cardinal/finite statement
results -- I haven't been able to access them. Except
to notice that on FOM one sees a lot of emphasis
on importance and very little on import.]
 
        
Robert Tragesser
Class of '43 Professor in the
Hiustory and Philosophy of Science
and Mathematics at Connecticut College