[FOM] Is CH vague?

laureano luna laureanoluna at yahoo.es
Fri Feb 1 19:10:19 EST 2008

Joe Shipman wrote:

>You are missing my point. "Definite" and "vague" are
>not opposites. 
>"Definite" and "indefinite" are opposites, as >are
"vague" and "clear". 
>The Sherlock Holmes example is supposed to
>illustrate " indefinite but 
>not vague" because there is no dispute about >what
"whether Sherlock 
>Holmes had blue eyes" MEANS, even though there may
>even in principle be
>no "fact of the matter". I agree that CH may be
>indefinite, but it is 
>not "vague", as Martin illustrates by reducing CH to
>simpler and 
>clearer concepts.  A statement cannot be vague if it
>is built up 
>logically from terms and concepts that are
>themselves clear and being 
>used appropriately.

I don't think I missed your point. I was arguing that
it is not clear that any well formulated question
could have no definite true answer. The example of
Sherlock Holmes is most probably wrongly formulated,
as I showed.

I think that any proposition is either true or false
and that any non vague (and non paradoxical) sentence
expresses a proposition, so that there is a
corresponding 'fact of the matter'. 

Finally, I'd say that CH is not less clear than the
concept of the set of all reals, so that if we accept
that concept as clear we should accept that CH is


Laureano Luna

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