FOM: Feferman on inherent vagueness of CH

penelope maddy pmaddy at
Tue Dec 2 11:00:30 EST 1997

>From: Torkel Franzen <torkel at>
>  This open and indeterminate character of the notions involved in CH
>does not in itself rule out the possibility that some convincing
>principle (i.e. one that appeals to us as being in accordance with our
>general understanding or picture of the world of sets, as do the
>axioms of ZFC) will eventually turn out to settle CH, but to
>CH of being "inherently vague" is, I would assume, to
suspect that no
>such principle will ever appear, that there isn't anything
in our
>picture of the world of sets that settles the matter.

Here's a straightforward answer to Neil's question (what does it mean to say
that CH is 'inherently vague'?).  NT might object that it has nothing to do
with vagueness, or any other semantic notion, but as a gloss on what's
actually intended, it seems worth considering.


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