FOM: Pratt/Friedman on set/cat

[Colin McLarty]

Pratt  11:15PM 2/25/98 writes:

>Steve is like a pianist who has played only Beethoven all his life.
>Confronted with a Scott Joplin score, his fingers tell him that this is
>not even music.

Friedman replies:
    
>    I would rather say: Steve is like a painist who has played only music with
>    clear rhythm and melody all his life. Confronted with very modern scores
>    with neither rhythm nor melody, his fingers tell him that this is not even
>    music.

        I think Mozart/Joplin would be fairer. I would even argue for
Mozart/Tchaikovsky. But I suppose Vaughan has Beethoven's piano concertos in
mind. Harvey, when you say "modern" are you thinking more in terms of
Phillip Glass or Bob Dylan?

        Anyway, Vaughan aptly sees the anti-TOP arguments on fom as
esthetic. Like all arguments over taste they rest largely on name calling,
"challenges" and "total repudiations". Even this has its value. Historians
would love to know what Kronecker really said about Cantor, but it was
almost never public. 

        Harvey himself has done less name calling (perhaps none, if you read
"slavish imitation" as purely descriptive), and only normal repudiating. But
his arguments are still primarily esthetic:

>    at present there is no theory of structures (glued points) that meets
>    the high standards that the theory of sets (no glue) meets. What is so
>    disturbing is the lack of recognition of the special intellectual standards
>    that are uniquely met by the theory of sets.

        Can we articulate these standards? Or are they so high and so
special that the question is too disturbing to answer? In fact I admire
Harvey's standards, so far as I understand them, and I'd like to understand
them better. But they are not (yet, anyway) all I admire in foundations of math.
       
        I certainly won't argue when Harvey says

>    it is far more likely that people with my point
>    of view will make something serious out of something like category theory
>    as comprehensive foundations than people who mistakenly think that it is
>    already comprehensive foundations.

Give it a try and let's see.

Colin