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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Fri, 17 Oct 2008 12:40:41 -0500
Message-id: <FC90DE2E-F092-4A62-AB40-D82B5FD501BB@xxxxxxxx>
On Oct 17, 2008, at 5:35 AM, Rob Freeman wrote:
> You say:
> '...there are properties whose extensions are utterly random sets of  
> natural numbers, ones whose members cannot be picked out by any  
> finite expression or any computable process. If ever there were a  
> definition of a "meaningless" property or relation in the sense that  
> Rob seems to be groping for, that would be it.'
> The connection with randomness is well spotted. But why would you  
> characterize "properties whose extensions are ... random" as  
> meaningless, necessarily?    (01)

*I* would never characterize random sets as meaningless -- though I  
think there is a genuine question whether every such set is the  
extension of a property.  *You* were the one who introduced the idea  
of meaningfulness with regard to properties/relations and I was simply  
trying to provide a reasonable interpretation of the idea. If you  
don't like the suggested interpretation, fine.    (02)

> "Random" things don't obey rules, sure, but that need not mean  
> devoid of content, rather the contrary.    (03)

I wasn't talking about random *things*.  I was talking specifically  
about sets.  I also did  not propose that random means "devoid of  
content".  Let's get the context right here.  The semantic  
completeness of Common Logic depends on requiring at most that the  
relations one admits into one's ontology be closed under certain  
operations -- those corresponding semantically to the boolean  
operators and the quantifiers.  This means that, in a CL  
interpretation, there will always be sets of individuals that are not  
the extension of any property.  You proffered a vague objection to the  
effect that this might be a limitation that rules out certain  
meaningful relations as meaningless.  I challenged you to provide some  
substance to this claim by asking what role in ontological engineering  
relations beyond these would ever play.  Issues of randomness and the  
like are a red herring.  CL is perfectly capable of talking about  
random processes.  The question is whether relations beyond those  
noted are needed in its semantics to interpret the sentences of the  
language.    (04)

> Actually, instead of defining a sense for "meaningless",    (05)

Dude, again, that was your doing; all I was trying to do was help you  
out by providing a bit of rigor to your vague and impressionistic  
claims.    (06)

> you might take what I am saying here as exactly the suggestion that  
> we need to consider properties with extensions which are "random",  
> by one or other definition, in our representations of meaning.    (07)

You are confused here.  Again: my claim was that, in the semantics of  
CL, it is not the case that for every random set S of individuals,  
there is a property whose extension is S.  I did *not* say that there  
are no properties with random extensions.  There likely will be in the  
intended semantics of CL in any domain in which, e.g., random  
processes are part of the subject matter.    (08)

> Talking about growing evidence of a need for randomness in our  
> representations of the world (evidence from physics, Category  
> Theory, and not least natural language) was the other way I pursued  
> this thread earlier in the conversation (other than "many-body" or  
> set theory.)    (09)

Uh, ok.    (010)

-chris    (011)

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