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Re: [ontolog-forum] The Relation Between Logic and Ontology in Metaphysi

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Fri, 16 Mar 2007 12:32:02 -0500
Message-id: <p0623090dc22080dad071@[]>
>JFS> For example, the quantifiers of predicate calculus
>>  (or any equivalent form, such as Peirce's graphs) are
>>  not well suited to dealing with continuous stuff,
>>  such as water.
>PH> I beg to differ. In a very old paper, whose title I
>>  believe may have been the first use of 'ontology' in its
>>  modern sense in a refereed publication,    (01)

OK, I withdraw the implicit claim to precedence. Still, anything from 
the 80's has a pretty good patina by now.    (02)

>  I used classical
>>  first-order logic to describe liquids in some detail:
>>  water in particular.
>Yes, I know that paper.  I didn't say that it was impossible
>to use the usual quantifiers, but that they are "not well
>suited".   As you and others have shown, it is necessary
>to add a lot more machinery, such as measures and careful
>distinctions about how various lumps are subdivided and
>combined.    (03)

But this isn't "more machinery" at least in the sense that 
quantifiers are "logical machinery". It is simply a part of the 
ontology itself. Of course one needs think hard about what exactly it 
is that one is quantifying over, what the 'pieces' actually are; and 
one should expect to get this wrong at first: its often not obvious, 
and requires a certain kind of willingness to examine ones own 
intuition critically, which can be difficult to master. I was 
surprised to discover that I needed two notions of a 'chunk' of 
liquid with different identity criteria. (Who knew?) But I really do 
think this was a genuinely *ontological* discovery, not something 
that the use of FOL forced me into by restricting my metaphysical 
imagination. (The hallmark experience of such a discovery, BTW, as Im 
sure you know, is that once one has bitten the bullet and decide to 
make the odd distinction, suddenly a whole lot of puzzling or 
confusing matters become easier to describe.)    (04)

...    (05)

>PH> All the formal and I would suggest informal evidence seems
>>  to point to FOL, in some incarnation, as the single best
>>  'ontologically neutral' logic. This is because the *only*,
>>  repeat ONLY, assumption that FOL makes about its universe is
>>  that is is a nonempty set...
>I would agree that FOL is the most neutral formalism that anyone
>has ever proposed.   But that little word "set" raises much
>more debatable ontological assumptions than the word "logic".    (06)

We have argued about this many times. I profoundly disagree. Saying 
that something is a set is a nontrivial claim: but to say that 
something is a *member* of a set is to say, literally, nothing at all 
about it. ANYTHING can be a member of a set. Set theory is simply a 
language for talking about conceptual collections of things. The 
things in the collections can be anything at all. If you can talk 
about it, it can be in a set.    (07)

>That is why so many people have been proposing some version of
>mereology as a way of avoiding the issues raised by set theory
>(at least the popular versions that build on Cantor's work).    (08)

What issues raised by set theory? Bear in mind that one needs only a 
very simple set theory to support Tarskian semantics. An 
interpretation is a set, and some subsets of the iterated power set 
of that set: no more.    (09)

BTW, if anyone reading this wants to try using mereology as a 
foundation for practical ontology, good luck. I have tried. It's like 
trying to build a skyscraper out of marshmallow. You would do better 
starting with topology.    (010)

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