[FOM] Shelf life of inconsistent theories

Thomas Forster T.Forster at dpmms.cam.ac.uk
Sun Sep 16 03:59:36 EDT 2007

Probably not a large enough sample to get a sensible answer. The first
edition of Quine's set theory ML was discovered to be inconsistent within
two years.  I don't know if anyone ever considered adding to ZFC as an
axiom ``there is an elementary embedding from the universe into itself'' -
tho' i'm probably old enough to remember.  It would have been early 60's
if at all, and the proof that it contradicts AC was no later than the
early 70's. Randall Holmes found an inconsistency in Kieselevicz (? sp)'s
*double extension set theory* within a very small number of years.  Of
course we all know that the undecidabilty of first-order logic means there
is no computable bound on the time it takes to find inconsistencies in
inconsistent recursively axiomatisable theories so we must ttach too much 
significance to these examples.


Home page: www.dpmms.cam.ac.uk/~tf; dpmms phone +44-1223-337981.  In NZ
until october work ph +64-3367001 and ask for extension 8152. Mobile in NZ
+64-21-0580093 (Mobile in UK +44-7887-701-562).

More information about the FOM mailing list