Jamie Dallaire on Tue, 23 Dec 2008 12:40:24 -0700 (MST)


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Re: [s-d] [s-b] Ballot for Nweek/152


On Tue, Dec 23, 2008 at 2:23 PM, Jay Campbell <bnomic@xxxxxxxxxxxxxxx>wrote:

>
>  Even then, that would be impossible. You can't define every single words
>> within a ruleset inside of that ruleset, just like you can't develop a
>> logically consistent, non-circular system of (e.g.) geometry without
>> relying
>> on some unproven axioms. The ruleset requires the use of terms that are
>> defined externally.
>>
>>
>
>
> Dictionaries are self-contained.


They are, but they're not logically coherent, IMO. Which a
ruleset-as-dictionary would have to be. The problem, to me, is that
dictionaries will invariably rely on some version of the following:

mountain: *n*. a large hill
hill: *n.* a small mountain

Of course, it's usually not that simple (though you can find a few instances
this blatant in many dictionaries). But no matter how complex your
definitions get, they rely on the use of other terms which are defined
within the same system. It's very incestuous, in a way. The mountain-hill
issue ends up becoming a problem even if it takes a longer chain to get
there. Ultimately, then, the definition of many terms depends on definitions
that include themselves...

I think the only reason it's not an actual problem, in a dictionary, is that
we DO cognitively have knowledge of the meaning of thousands of words
independently of their definitions in terms of other words (I've got direct
access to a "table" concept which, even though the edges are fuzzy in that
some objects are only ambiguously tables, I understand without recourse to
definitions of all the constituent parts of tables. Therefore other
objects/concepts can be defined in terms of a table, and I will know what
they mean even if the "table" ends up being defined in terms of those same
objects, in the dictionary).

So basically, I see us as being able to deal with this self-contained
circularly-defined dictionary because we don't actually treat it that way.
We take a lot of the terms for granted, in an axiom-like fashion, and only
because we do that can we build other definitions on top of them.

BP
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