FOM: background on incompleteness I

Stephen G Simpson simpson at
Sat Sep 5 09:34:18 EDT 1998

Harvey, your posting "background on incompleteness I" is excellent and
I am looking forward to parts II, III, ....  Many FOM subscribers
already understand the general thrust of your research in this area,
but a fuller statement may help clarify some points.

For instance, many people may benefit from an elaboration of your
points about the incremental nature of progress in this area:

 > 4. Progress has been far more incremental than the early work of Godel and
 > Cohen.
 > 5. Progress will continue to be incremental.
 > 6. Progress is already more than sufficient to expect continuing long term
 > success of the program.

And if anyone is taking Shoenfield seriously, it will surely be
worthwhile to elaborate on:

 > 7. Progress is sufficiently clear so that lack of formal criteria for
 > progress is not serious nor is it an impediment to progress.
 > 8. Some formal criteria for progress can be given, but is not as important
 > as continued progress.
 > 9. Progress has been, and will continue to be informally tested by
 > interaction with mathematicians outside f.o.m. and mathematical logic.

And I need you to explain this one:

 > 10. There are prototypical results (unfortunately, demonstrably false)
 > which indicate anticipated future stages of progress.

And of course everybody is eager for your upcoming announcements:

 > 11. Over the next couple of months I will make some announcements which
 > represent a next stage of progress.

-- Steve

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