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Re: resources, stuffs and individuation

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 21 Apr 2003 19:02:46 -0500
Message-Id: <p05111b14baca319b3362@[10.0.100.12]>
To: John Cowan <cowan@mercury.ccil.org>
Cc: uri@w3c.org

>pat hayes scripsit:
>
>>  Thus, for example, each of the sodium atoms in my body has an
>>  identity - it is identical to itself - in the first sense, even
>>  though none of them has an identity in the second sense, since we
>>  have no agreed-on scheme for referring to individual atoms (and there
>>  are too many of them to keep track of, in any case).
>
>This is peripheral to your point, but quantum mechanics tells us that
>atoms are truly Leibnizian indiscernibles -- there is not only no way
>to label all the sodium atoms in your body, but there is not even any
>sense in which they can be individuated from one another.
>
>(By "atoms" I mean only what physicists call atoms, not Leibnizian atoms.)

So do I, and I agree it is peripheral, but I think you are wrong 
about the atoms in my body.  Particular atoms are distinguishable by 
their relative location, if by no other means. These days, one can 
actually *see* individual atoms and even push them about in some 
cases. They obey Bose statistics, but that's another matter: that's 
like saying they have no *intrinsic* identities, that could be 
discovered by looking at them in isolation, like blemishes on an 
apple; but I didn't say that they did.

>
>>  First, I would suggest that the best road for the WG to take on
>>  issues like these would be to be as agnostic as you feel you possibly
>>  can be about the exact nature of 'resources'.
>
>+1
>
>>  Second, it is important for almost all reasoning engines that the
>>  general picture, of how URIrefs relate to whatever it is that they
>>  refer to, should also allow for the existence of similar things which
>>  are not referred to. That is, please do not say anything which
>>  restricts the universe of discourse to include only those things that
>>  have a URI or URI reference assigned to them (in whatever sense of
>>  'assigned' is appropriate.)  The reason for this request is that such
>>  a restriction effectively makes it impossible to use quantifier
>>  reasoning - that is, all kinds of formalized reasoning invented since
>>  about 1880, including most reasoning software - over the set of
>>  resources, so defined. The alternative logics that would be required
>>  (those with a "substitution interpretation" of the quantifiers) have
>>  been fully analysed and are known to be inadequate. This would be a
>>  crippling decision.
>
>I think you underestimate the power of substitutional quantification,
>unnatural as it seems, to work in the Real World, an essentially finite
>place.

If you wish to have a debate about the nature of quantification, I am 
willing to engage you in  one, but it will take a long time. I 
absolutely do not accept your implication that talk of the Real World 
is inherently suited to the substitutional interpretation, or indeed 
that the set of entities we need to refer to, in order to talk about 
the Real World, is finite.  For example, I am quite sure that there 
are things which have no names and which have never been, and never 
will be, referred to by names. In the substitutional interpretation, 
what I just said is *meaningless*.

But surely the point here is not which one of us is right in some 
absolute sense, but whether the central definitions of the Web should 
be posed in a form which renders vast areas of the intellectual 
landscape out of bounds. Most working mathematicians are Platonists, 
for example, who believe that their abstractions are real: try 
telling a Platonist that she is obliged to use substitutional 
quantifiers.

>  Objectual quantification is clearly neater in a formal sense,
>but provokes intractable computational difficulties.

Really? Can you say what those computational difficulties are? I know 
of none, and have been using formalisms with such quantifiers in 
computational settings for about 30 years now.  And the issue is not 
to do with formal 'neatness', but practical matters of interpreting 
normal language. Kripke's 1976 review seems to me to be a masterly 
demolition of substitutional interpretations in general, in fact.

Pat Hayes
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Received on Monday, 21 April 2003 20:02:49 GMT

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