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Re: Is the meaning of order intrinsic ?

From: Bill Andersen <andersen@ontologyworks.com>
Date: Sat, 26 May 2001 05:23:34 -0500
To: Seth Russell <seth@robustai.net>, pat hayes <phayes@ai.uwf.edu>
CC: RDF Logic <www-rdf-logic@w3.org>
Message-ID: <B734EE56.E08%andersen@ontologyworks.com>

Hi all.  I'm new to the list and usually I like to read for a while before
writing but ... I just can't help myself!  Please forgive me.

On 5/25/01 11:36, "Seth Russell" <seth@robustai.net> wrote:

> From: "pat hayes" <phayes@ai.uwf.edu>
> 
>> It depends what you mean by 'define'. There is no definition of the
>> truth-value 'Truth', of course. But there is a (fairly elaborate)
>> definition of satisfaction of a set of sentences in an
>> interpretation. Being mathematics, it does not provide metaphysical
>> definitions of its basic terminology; but then mathematics never does.
> 
> Actually I think it is quite easy to define the truth-value 'Truth'.  It's
> simply an attitude adopted by an agent towards a particular statement.  Look
> ma, no metaphysics :)

You don't have a metaphysics?  Then what are "attitude", "agent", and
"statement"? 

If a planet explodes on the other side of the universe where there are no
"agents" is it in fact "seth-russel-true" that there is one less planet than
before the time of the explosion?

Ok ... I'm an "agent" and I have the "seth-russel-true" "attitude" toward
the following "statement" (which we will call S):

  "S is false"

Seems your theory of "truth" needs some work.

>> (A1 . (A2 . (A3 . (..... (An .  END)...))) The same kind of thing can
>> be done with functions, or sets, or whatever. Eg using functions, one
>> encodes an n-ary function - whichis interchangeable with an n-ary
>> sequence at this level of abstraction -  as a single-argument
>> function whose value is an (n-1)-argument function (a trick invented
>> by a logician called Curry, and hence known as currying.)

Cool, Pat.. I never knew where that term came from.

> Yeah this is pretty much the way numbers are defined with set theory.   But
> I still have a trouble with using this technique of defining a sequence.  My
> thesis is that 'ordering' is a first principal, is prior, is axiomatic (at
> least to humans and the systems they tend to construct).

Look out - words like "prior [to mathematics]" are getting awfully close to
metaphysics!

> It seems to me
> that to disprove this thesis you would need to be able to define an order
> without using anything that presupposes that order already.  Your syntactic
> string (sequence of characters) above of course contains that
> presupposition.  

You are confused.  The sequence of characters is irrelevant.  It is meant to
encode a representation of a set, which is not presupposed to have any such
ordering.  It is the properties of that set, interpreted via the axioms of
set theory (particularly equality), that make the representation conform to
our intuitions about orderings.  Note this makes no metaphysical appeal to
the notion of an order whatsoever -- it simply is one way (as Pat pointed
out, I think, there are many) to represent the notion of order.

If you want to talk about metaphysical order, then you will have to invoke
an appropriate theory of states-of-affairs, which has nothing to do with
what Pat talked about.

> But let's forgive that trespass for a moment, because I
> know what this string means and have interpreted it in a graph [1] quite
> apart from the ASCII string you used.

What topological properties does your graph have?  Sounds like it "contains
a presupposition".  So you want to use the axioms of graph theory instead of
set theory, go ahead.  You win a cookie.

> But here again I still have problems
> arriving at an unambiguous interpretation of the order without presupposing
> some known order already.  In particular (1) we need to establish the
> sequence {begin, end} ... iow try explaining that sequence to an alien life
> form that doesn't understand time;

"'tupid metaphysics" [H. Simpson, 2001]

  ..bill

-- 
Bill Andersen
Chief Scientist, Ontology Works
1132 Annapolis Road, Suite 104
Odenton, Maryland, 21113
Mobile 443-858-6444
Office 410-674-7600
Received on Saturday, 26 May 2001 06:24:06 UTC

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