[FOM] why Kiselev's CLAIM of no inaccessibles may actually be a good thing

Tom Dunion tom.dunion at gmail.com
Sun Aug 21 14:18:10 EDT 2011

Two historical observations may be of some relevance here.

1) Before Special Relativity, who knows how many years, and how many
careers were largely consumed, exploring the properties of the
luminiferous "ether" by noteworthy scientists of that era?  If the
stupendously surprising claim that ZF proves there are no weakly
inaccessible cardinals can be validated, well, there goes much of the
whole Cantorian theory, crashing down, but no doubt we would
breathe a collective sigh of relief that another century of building
castles in the sky can now be avoided.   Umm...at least most FOMers
would, right?  (OK, yes, I was being a bit provocative there, but not
gratuitously so -- even scientists and logicians can fail to be
dispassionate when their own worldview is deeply challenged.)  That
observation leads me to my other point.

2) I recall as a teenager seeing books published at least a
half-century after Einstein became world famous, vehemently claiming
to refute his preposterous nonsense of Relativity.   I doubt one would
find such a tome on a library shelf today (except, perhaps, one with
an imprint like "Cranks R Us").   So it can take a very considerable
period of time until a scientific revolution (such as Cantor/Zermelo)
is consolidated.  If indeed Cantor broke through the walls of
theological, philosophical, and mathematical resistance to perceive
\omega as a "thing in itself" (as I believe he did), then *of course*
we may well believe in (even strongly) inaccessible cardinals.  Julius
Koenig's "refutation" of Cantor's Continuum Hypothesis was found to be
flawed, but his challenge led to new insights and strengthening of the
case for set theory.  Perhaps such will be the case, even if/when
Kiselev's challenge is overthrown.  I wish him well.


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