[FOM] RE: FOM Continuum Hypothesis
Miguel A. Lerma
mlerma at math.northwestern.edu
Sun May 18 20:40:26 EDT 2003
> Insall:
> [...] For example, if we could show
> that CH implies that some particular subatomic particle cannot exist, but we
> perform experiments and these show that such a particle does exist, then we
> would have physical ``proof'' that CH is false.
I do not think that any physical experience can decide anything
in pure mathematics. After Einstein we know that the universe
is not Euclidean, but that does not imply that the postulates
of Euclidean geometry are "wrong" in any absolute sense, it just
shows that Euclidean geometry is not an appropriate model for
our physical universe. If a physical theory made false predictions
based on the assumption of the existence of large cardinals, that
would not mean that there are no large cardinals, just that there
are no large cardinals in our physical universe. If CH implied
that certain particle cannot exists but we find it anyway, then
that would not necessarily mean that CH is false, just that it
does not hold in our universe (say because certain bijections
used to state equal cardinality among sets turn out not to have
a physical meaning). In any case physical theories depend on
many postulates and sometimes it is hard to tell which ones
must be changed.
By the way, since set theory is a product of our intuitions
and our intuitions do not seem to be clear enough to reach
an agreement about the "truth" or "falsity" of CH, I tend to
think that CH has no definite truth value; but if I had to
participate in a collective decision about it, my vote would
be with Cohen in support that it is "obviously false" and
that C is extremely large (at least inaccessible).
Miguel A. Lerma
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