Re: Skolem Again

Herman Jurjus says...

>Very good. Do you happen to have a similar falsifiable prediction that
>is implied by the existence of large cardinals?

Sure: con(ZFC). That's a falsifiable prediction that follows
from the existence of a large cardinal.

In general, set theory uses some "unobservable" objects
(uncountable sets, for example) but then it allows one to
make predictions about things that *are* observable (that
certain computations halt, or don't halt). That seems in
the scientific spirit.

Of course, I think that the actual falsifiable consequences
of high powered mathematics all follow from the assumption
that the high powered mathematics is *consistent*. It's not
necessary to assume that it is *true*. On the other hand,
there is no reason for someone to *conjecture* that ZFC is
consistent other than contemplating the standard model, and
seeing that the axioms all seem true for that model.

So these unobservable, possibly imaginary objects are a rich
source of true falsifiable conjectures. That's in contrast
with belief in the supernatural, which generally doesn't
produce falsifiable consequences.

--
Daryl McCullough
Ithaca, NY

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