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Re: [ontac-forum] Re: owl:Class and owl:Thing

To: Azamat <abdoul@xxxxxxxxxxxxxx>
Cc: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: Chris Menzel <cmenzel@xxxxxxxx>
Date: Fri, 7 Apr 2006 13:18:18 -0500
Message-id: <20060407181818.GG900@xxxxxxxx>
On Thu, Apr 06, 2006 at 11:42:24PM +0300, Azamat wrote:
> Bertrand Russell, The Problems of Philosophy, in Great Books of the Western 
> World, V.55
> ''Speaking generally, adjectives and common nouns express qualities or 
> properties of single things, whereas prepositions and verbs tend to express 
> relations between two or more things. Thus the neglect of prepositions and 
> verbs led to belief that [every proposition] can be regarded as attributing 
> a property to a single thing, rather than [expressing a relation between 
> two or more things]''. ''...we can prove that there must be relations, 
> i.e., the sort of universals generally represented by verbs and 
> prepositions''. ''it seems plain that the relation subsists independently 
> of our knowledge of it''. p.272    (01)

Azamat,    (02)

This passage does not support your claim.  Your claim was that Russell
asserted that "every proposition should be regarded as expressing a
relation between two and more things', like in the from R(x,y, z,...)."
He says no such thing above (nor did he believe any such thing).
Rather, he is pointing out only that syllogistic logic erred in
*neglecting* relations, since in that logic (roughly speaking) one can
only attribute *properties* to individuals.  Thus, for example, in
syllogistic logic, there is no way to represent the logical form of such
simple arguments as "John gave the book to Mary; therefore, John gave
something to Mary."  The best one can do is a kludgy reconstruction that
buries "the book" within the predicate and treats the argument as
enthymematic (i.e., as involving a suppressed premise).  But even that
case is the exception; it is easy to prove theoretically that the great
majority of arguments that can be expressed in first-order logic cannot
be expressed in any way, kludgily or otherwise, in syllogistic logic
(i.e., more generally, monadic predicate logic).    (03)

For Russell, logical form encompassed far more than merely atomic
(relational) statements.  It included all forms expressible in first-
(and arguably, second-) order logic.    (04)

Chris Menzel    (05)

----- Original Message ----- 
From: "Chris Menzel" <cmenzel@xxxxxxxx>
To: "ONTAC-WG General Discussion" <ontac-forum@xxxxxxxxxxxxxx>
Cc: "Hans Teijgeler" <hans.teijgeler@xxxxxxxxxxx>
Sent: Wednesday, April 05, 2006 9:28 PM
Subject: Re: [ontac-forum] Re: owl:Class and owl:Thing    (06)

>On Mon, Apr 03, 2006 at 06:37:45PM +0300, Azamat wrote:
>>''What exactly did you have in mind when you referred to "n-relational
>>ontology of things"? <HT/>
>>Relations should be analyzed not only with respect to the number of
>>terms they connect and formal properties as cardinality, symmetry,
>>transitivity, reflexivity. This is all the subject of a formal
>>relational logic. As old as Russell statement that 'every proposition
>>should be regarded as expressing a relation between two and more
>>things', like in the from R(x, y, z,...).
>It's hard to believe Russell ever said any such thing, as he (with
>Whitehead) wrote Principia Mathematica, the language of which includes
>not only atomic (relational) statements but boolean and quantified
>statements as well.
>Chris Menzel    (07)

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