[FOM] CH and mathematics

[Arnon Avron]

On Sat, Jan 19, 2008 at 05:37:07PM -0500, joeshipman at aol.com wrote:
> 
> >-----Original Message-----
> >From: Arnon Avron <aa at tau.ac.il>
> >
> >The fact that CH cannot be decided in the strongest
> >systems that the overwelming majority of  the mathemaricians
> >can claim to have some intuitions about,` casts even stronger
> >doubts that CH can be said to have a definite truth value.
> 
> I don't see why our inability to know something should cast any doubt 
> on its definiteness. That's epistemological arrogance.

For itself, as a unique piece of data, such inability is a very weak
argument. However, when it is about a claim whose definiteness
is independently strongly doubted (and before this inability was
proved), then the proof of such inability is a strong confirmation 
of these doubts.

 You may ask why. My answer would  be: for a reason similar to the
importance that scientists attached to experiments in which 
new predictions of a theory are tasted, although in principle
support by known facts and by new facts should be equally valuable.
Another analogy: each evidence for CT taken alone is quite weak.
Together they make a strong case.

  In addition, the inability to know eliminates an attempt
to make CH definitie using a formalist criterion (i.e. replacing
the quest of its truth by the question of its decidability
in some natural theory).

Arnon Avron