Meta-metamathematics

[martdowd at aol.com]

 FOM:
Joe Shipman wrote:

direct evidence for CH itself will not be something that correct physical theories can provide
 I'm a confirmed "CH'er".  I think there is a simple mathematical argument that CH is true.  Namely, there is no self-evident way to construct an embedding of $\aleph_2$ in the 0-1 functions with domain $\omega$.  It is even possible to suggest that physical evidence for this might exist, although a physical manifestation of $\aleph_2$ is more elusive than one of the unit interval.
I recently read 
 G.\ H.\ Hardy, A theorem concerning the infinite cardinal numbers,
 {\it Quarterly Journal of Pure and Applied Mathematics} {\bf 35} (1904), 87--94.
This provides a second embedding, to the usual one via well-orders, of $\aleph_1$.  Both embeddings rely on AC.

Martin Dowd
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