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To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Fri, 13 Feb 2009 13:03:00 -0600
Message-id: <39BB8147-1E60-4341-AFA6-6192E76DDA83@xxxxxxxx>
On Feb 12, 2009, at 3:48 PM, Chris Partridge wrote:
>> CP> I think John was espousing in an earlier set of emails (in
>>> relation to Aristotelian syllogisms), which is that logic is
>>> a formalism for describing the way the world is - or more
>>> grandly, what exists. And that in some way the form of the
>>> logic reflects the structure/nature of the world.
>> I didn't claim that logic reflects the structure of the world,
>> but that logic in combination with an ontology can be used to
>> describe someone's conception of the structure of the world.
> Apologies. I may have been a little unclear. My point was intended  
> to be the
> well-known one that it is extremely difficult to eradicate ontological
> commitment from a form of representation - and that the form of a  
> logic
> being used for description is likely to imply some ontological  
> commitment to
> the form of what is being described. And you are right, you did not
> explicitly make this point, though hopefully you do not disagree  
> with it.
> So, for example, in the case of the syllogism, the form of the  
> syllogism
> reflects the transitive nature of the subsumption/subtype relation  
> between
> types in the world.    (01)

There are 256 syllogistic forms; what do you mean by the form of THE  
syllogism?  It is, in fact, the case that universal affirmative  
statements "All As are Bs" expresses, in effect, that {x | x is an A}  
is a subclass of {x | x is a B}, so what you *might* mean is that the  
form of a universal affirmative statement represents the subclass  
relation.  And it is indeed in virtue of the transitivity of subclass  
that, e.g., a Barbara syllogism is valid.  Is that what you have in  
mind?    (02)

Be that as it may, I think your general point is well taken.  Every  
logic worth the name comes with a semantics that will involve some  
very high level of ontological commitment.  FOL, in particular, is  
committed to, at least, "things" (the range of the quantifiers) and  
"predicables" (the values of predicates).  That's pretty thin,  
ontological gruel, however, since things and predicables are the basic  
ingredients of *any possible* ontology, and hence don't distinguish  
one ontology from another.  So logic certainly reflects a little  
something about the structure/nature of the world; just not that much.    (03)

-chris    (04)

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