FOM: Seismology

[Vaughan R. Pratt]

>From: jshipman at bloomberg.net
>Godel's results did not affect "business as usual"

Goedel's incompleteness result for arithmetic shook the foundations of
mathematics hard enough to bring down Hilbert's program, which made the
very strong assumption that we could in principle eventually know any
given mathematical truth.  What program today with a comparably strong
and fundamental assumption would be knocked down by the need to weaken
Replacement?

>since replacement used informally all over the place though not
>in a necessary way).

Jon Barwise answered this more comprehensively than I could have.  (I
was going to say that an implicit use of Replacement would only need
attention if it used Replacement at the strength causing
inconsistency.  Those uses of Replacement you have in mind that
implicitly perform replacement, but entirely within a given set, should
not need any attention.)

Vaughan Pratt