[FOM] Is CH vague?

[joeshipman@aol.com]

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.

-- JS


-----Original Message-----
From: laureano luna <laureanoluna at yahoo.es>
To: fom at cs.nyu.edu
Sent: Wed, 30 Jan 2008 2:45 pm
Subject: Re: [FOM] Is CH vague?



Joe Shipman wrote:

>Martin, I agree that those who would argue that CH
>is vague ought
>identify which of the simpler concepts you
>identified are vague.
>However, my understanding is that we are discussing
>a slightly
>different question, whether CH is "definite".
>
>Indefinite and vague are not the same. "Whether
>Sherlock Holmes had
>blue eyes" may be indefinite if Conan Doyle's
>stories don't anwer it,
>but it is not vague. "Whether X is a great
>mathematician" is a vague
>predicate, but that does not prevent it from being
>definite when
>X=Archimedes or when X=Britney Spears.

The question about the eyes of Holmes seems ultimately
wrongly worded. The color of Holmes's eyes depended on
Conan Doyle's will; it is a question of artistic
creation. So the question about that color should be
re-worded as the question about whether Conan Doyle
described that color and, if so, how he did it. But if
we re-word it and pose: did Conan Doyle described
Holmes's eyes as blue? There is surely one definite
true answer to the question.

Is the question about CH similarly ill-worded? If so,
who is the creator of CH's biography? Whose is CH the
fictional creation? It depends on the will of whom?
Cantor's? Is it a question of copyright?

I don't think Holmes and CH are comparable topics. If
we agree on this, all we can require from CH in order
to accept it as a definite question is that it be not
vague.

I dare say that if we grant that reals and the set of
all reals are not mere fiction characters, CH should
be accepted as a definite and not vague question.


Laureano Luna




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