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Re: [ontolog-forum] Ontological Assumptions of FOL

To: Kathryn Blackmond Laskey <klaskey@xxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Sun, 18 Mar 2007 03:01:10 -0500
Message-id: <p06230906c2229c496274@[]>
>At 10:36 AM -0500 3/16/07, Pat Hayes wrote:
>>...the *only*,
>>repeat ONLY, assumption that FOL makes about its
>>universe is that is is a nonempty set ....
>More precisely, one can represent it as a set for purposes of
>defining truth-conditions for sentences.    (01)

If you can represent it as a set, then it is a set.    (02)

>>All other logics
>>seem to impose extra conditions on their
>>universes... Now, it is hard for
>>me to image what could possibly be *less* of an
>>ontological commitment than that the elements of
>>the universe can be viewed as members of a set:
>This is a very serious ontological commitment.    (03)

Perhaps it is serious, but my point was only that 
it is hard to see how one could make less of a 
commitment than this. In fact I don't think it is 
any more serious than, say, the commitment made 
by being able to refer to it in a natural 
language, or even to think about it coherently. 
Perhaps these are all equally serious, but they 
seem equally minimal.    (04)

>FOL makes the ontological commitments that:
>   - The universe of discourse is made up of elements or constituents.    (05)

Yes... but if you think about it, that really 
says nothing at all. It amounts to saying that 
the language is about entities. The *nature* of 
these entities is completely unspecified.    (06)

>   - These elements or constituents have properties and stand in
>     relationship to one another.    (07)

True, it assumes that they stand in relationships 
to one another. I used to think that this was 
nontrivial, but Ive come to see that it also 
really amounts to no commitment, since the nature 
of the relationships is nowhere specified. The 
logic only requires that for each relation there 
be a fact of the matter whether or not a sequence 
of entities stand in that relation: and this is 
simply a consequence of its being a two-valued 
Boolean logic.    (08)

>   - One can make statements about these properties and
>     relationships (e.g, that all, or some, elements have a given
>     property or stand in a given relationship)
>   - Any such statement has a definite truth-value.    (09)

Those are not ontological commitments. What 
Tarski showed was that they follow, in fact: the 
truth-recursions do this for you . The only 
'inputs' you need are the universe and the 
relational extensions.    (010)

>Tarski showed that one can define a precise set-theoretic semantics
>for such a universe.
>That doesn't mean the universe "is" a set.  To say that something can
>be represented as a set for purposes of defining truth-values of
>sentences is a very different thing from saying it IS a set.    (011)

I disagree. I think these are exactly the same 
thing to say. To say that a collection is a set 
is to say nothing about it at all.    (012)

>The universe is what it is.    (013)

Wait: you are making a pun on "universe". The 
Tarskian 'universe' (aka domain of discourse) is 
simply the collection of all entities being 
described. The actual universe, the cosmos we 
inhabit, is a much hairier beast, I will agree.    (014)

>  For many purposes, it is useful to
>describe it as a set with elements that have properties and bear
>relationships to each other.  But sets, elements, properties and
>relationships are mathematical abstractions.  The universe is real.    (015)

Quite. But (I insist), while a set may be an 
abstraction, its elements can be quite concrete. 
The set of my ancestors is an abstraction, but 
the people in it are quite real, or were when 
they were living.    (016)

>There was a comment in another recent post about the Chinese
>language, and how it appears to be based on a fundamentally different
>metaphysics as Western languages.    (017)

I would like to hear a defense of this idea made 
by a professional linguist. I do not believe 
there is any convincing evidence that different 
languages or cultures are based on fundamentally 
different metaphysics. The fact that rival 
metaphysics seem to arise in philosophical 
debates within a single language, and the 
resulting debates can be translated into other 
languages, seems like a priori evidence against 
this idea.    (018)

>If we go around saying the universe "is" a set, we are in danger of
>confusing a representation of the world with the world we are
>representing.  Tarskian semantics accords well with the Western
>scientific worldview. It is quite useful for mathematical
>formalization of the meaning of statements that can be given definite
>truth-values.  Formal ontology is most usefully applied to problems
>that can be described in terms of statements that can be given
>definite truth-values.
>But that doesn't mean nothing exists except that which can be
>described in terms of properties of or relationships among elements
>of a set.    (019)

It doesn't mean that, indeed. But I would defend 
this last proposition as being true, 
nevertheless. I don't think there is anything at 
all 'western' about this idea. Certainly, 
Japanese and Chinese and Indian folk seem to have 
no trouble with it.    (020)

(BTW, if you intend to come back with quantum 
theory at me, I will concede in advance that QT 
and especially QED might put some strain on the 
simple relational model. But that has got nothing 
to do with Chinese versus English.)    (021)

>I apologize for getting a bit metaphysical, but I think this is an
>important point.    (022)

I agree it is important.    (023)

Pat    (024)

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