Re: uncountably many things to name

At 5:35 PM -0500 2/1/08, Jonathan Rees wrote:
>On Jan 25, 2008, at 10:11 AM, Williams, Stuart (HP Labs, Bristol) wrote:
>
>><Aside>
>>...though sometime ago there was an 'entertaining' exchange on 
>>quite whether there were enough URI's available to assign [1] 
>>(which I suspect repeats from time to time).
>>
>>"...In particular, how can RDF say something a particular arbitrary 
>>real number?  There just aren't enough URIs to provide names for 
>>them all." [1]
>>[1] 
>>http://lists.w3.org/Archives/Public/www-rdf-interest/2002Jan/0028 
>>(and ensuing thread).
>>
>></Aside>
>
>In the spirit of entertainment:
>
>There aren't enough URIs to simultaneously name all members of an 
>uncountable set - true. But I can use URIs to name arbitrary 
>countable subsets of that uncountable set. The set of everything 
>(which of course is nonsense, cf. Russell) may be uncountable, but 
>that doesn't mean that we can't name arbitrary particular members of 
>it.

Set theory has got beyond the Russell difficulty. But in any case, 
the set of real numbers certainly isn't nonsense, and its uncountable 
all by itself.

The point of examples like this is that the official line is, or once 
was, that anything that could be given an URI is a resource, even if 
it hasn't actually been given one yet. And there is this apparent 
difficulty with that declaration; that the set of things that could 
be given a name is provably bigger than the set of names you can give 
to them. IMO, the appropriate answer to this is to smile 
enigmatically and agree: no matter how many lifetimes you have to do 
it in, you will never manage to name all the reals. There will be 
some resources you could have named but didn't. I'll take my blessing 
with the lave, and ne'er miss 'em.

>Or, to prove that I can name anything: Give me an example of 
>something that can't be named. Let 
>http://mumble.net/unnameable-thing be that thing. Then it can be 
>named!

Nah, that argument fails: you can use this prove that all sets are 
countable. It might not be possible to give an example of a thing 
that cannot be named, yet still possible to prove that such a thing 
must exist. In fact, the basic argument of this area, Cantor's 
diagonal argument, is like this.

>This kind of talk is sophistry, of course, which is why I prefer to 
>ground discussions in how URIs are to be used in our Wittgensteinian 
>language-games, not in what they denote.

??? Whoa. All this cardinality-of-the-nameset stuff hasn't got 
anything to do with the fact that names denote, which is just another 
way of saying that a name of something is, well, a name of something.

>  I can say how I want a URI to be used, and it's then a political 
>question whether anyone else follows the rules I set out.

But its a semantic question whether the rules make any sense.

Pat

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