>Pat,
>
>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)
Pat
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