Foundations and Foundationalism
Harvey Friedman
hmflogic at gmail.com
Sat Jul 9 22:05:16 EDT 2022
I wrote:
I do not believe in foundational advances by committee. E.g., this was
tried with Algol. What happened to Algol?
On Wed, Jul 6, 2022 at 7:30 PM <dennis.hamilton at acm.org> wrote:
>
> I don't doubt the belief. I do challenge the choice of an example and somehow
> dispensing with collaborative efforts, whether by committee or other
> structure.
> The rise and fall of these things does not
> generally have much to do with there being committees that had their hands on
> them. Many of them would not have been established but for committee
> arrangements.
I'm only talking about path breaking foundational advances, and not
other kinds of path breaking advances.
The reason I brought this up is that I was focused on the lack of a
working combination of mathematical and philosophical instincts and
that that combination is an essential component for major advances in
foundations of mathematics.
Chow and also you are suggesting that this can be replaced by a
community or committee of people some of whom have strong mathematical
abilities but limited philosophical abilities, and some of who have
strong philosophical abilities but limited mathematical abilities. I'm
suggesting that that it never was effective and is not going to be
effective in coming up with path breaking foundational advances in the
foundations of mathematics.
Only certain special and rare combinations of mathematical and
philosophical insights generate path breaking foundational advances,
at least in f.o.m., because of the delicate way that they need to
interact and be integrated. In such an integration there must a very
delicate flexible modification of the mathematical and the
philosophical ideas in order for them to blend productively. The
adjustments needed on both sides in order for them to blend
productively are not natural for each side alone. Mathematical people
would not be interested in those modified mathematical ideas, and
philosophical people would not be interested in those modified
philosophical ideas. So, at least generally speaking, a single mind
with both strong mathematical and philosophical instincts makes these
adjustments without hesitation seeing clearly how they greatly
strengthen the mathematical and philosophical aspects to create
something of path breaking significance for f.o.m.
In a way this is similar to what is involved in performing a piano
piece with a stunning new revelatory interpretation with a special new
effect on the listener.This always involves two things. First some
special physical technique going beyond the usual in certain
specialized ways. Second some conceptual musical idea also going
beyond the usual in certain specialized ways. Neither is particularly
natural from either side - the physical and the musical. But for
getting a new kind of combined effect, they are crafted to interact
with each other usually involving some experimentation. Not really
practically possible by committee. Of course for a musical piece
involving say 4 musicians, of course it involves 4 minds. But not 5
and not 10and not 1000 minds.
Harvey Friedman
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