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Re: Tech Plenary: agenda Best Practices

From: Christopher Welty <welty@us.ibm.com>
Date: Mon, 8 Mar 2004 14:55:30 -0500
To: Pat Hayes <phayes@ihmc.us>
Cc: public-swbp-wg@w3.org, public-swbp-wg-request@w3.org
Message-ID: <OF3C8066FE.4B42441C-ON85256E51.006CFAF4-85256E51.006D743F@us.ibm.com>
Pat,

Unfortunately, we are in complete agreement.  Not to worry, I'm sure we 
will find something else to argue about.

Chris

> <speech>
> 
> The problem with mereology (and things like it) as a guide to practice 
is that, 
> like most philosophically motivated theories, it tries to be a universal 
theory of 
> everything. Varzi's excellent article 
http://plato.stanford.edu/entries/mereology/ 
> makes this quite clear: it is a theory of parthood IN GENERAL, and is 
supposed to 
> cover every possible sense of 'part', including things like physical 
parts, parts 
> of space and time, pieces of text, parts of abstracta, parts of the 
human soul (one
> of Brentano's primary concerns), parthood in static settings, in dynamic 
settings, 
> in Platonic worlds, etc. . The practical trouble with this motivation is 
twofold. 
> First, there isn't very much you can reliably say about things at this 
level of 
> generality. It is too easy to find intuitive objections to almost any 
axiom from 
> some source or other (which is why general mereology is so weak as a 
formal system,
> and even at its strongest only gets to be similar to a theory of 
subsets, rather 
> than a theory of set membership.) Second, whatever you do come up with 
isn't much 
> real use anyway, since any particular application of a theory of 
parthood will be 
> about one sense in particular, and most of the utility comes from the 
> characteristics of this particular sense of 'part', the ones that 
distinguish it 
> from other senses. This last is a very general point, which I learnt 
from Doug 
> Lenat: the very high levels of an ontology are of little importance in 
practice. 
> Its the middle levels where the axioms do the real work. Philosophers 
rarely 
> descend to these middle levels; the concepts are too dense and 
complicated for them
> to handle. (There is also another reason, which works in the other 
direction: 
> philosophers will often modify or reject an idea for philosophical 
(often described
> as 'principled' or 'foundational') reasons, when in fact, in practice, 
it is quite 
> OK to use it. The general philosophical-foundational desire to keep the 
conceptual 
> universe parsimonious is a frequent cause of this.  Cyc has axioms in it 
about 
> arbitrary combinations of stuffs being a stuff that would leave many 
philosophers 
> shaking their heads about all those crazy stuff-kind individuals. The 
Cyc attitude 
> is pragmatic and works fine in practice: if you don't think those things 
exist, 
> don't use the axiom. See also Jerry Hobbs' writings on 'ontological 
promiscuity' 
> for more on this theme.)
> 
> Now, don't get me wrong, I don't mean to imply that everything called 
'mereology' 
> is useless. If one is interested in axiomatizing a real notion of part 
in, say, a 
> machinery catalog, then it is probably worth knowing about some of the 
applied 
> mereology work. It also has applications in ontologies for geographical 
space, for 
> example, because geographical space is indeed very mereological-ish: it 
can be 
> carved up arbitrarily, combined arbitrarily, and is kind of defined by 
its extent. 
> But these applied theories aren't useful because they are mereologies 
(and 
> 'parthood' is some kind of magic key to the universe): they are useful 
because they
> fit their intended domain quite well.  Take mereology and geographical 
space, for 
> example.  A colleague and I once developed a basic ontology for 
geographical space 
> which turned out, after a lot of work, to be almost exactly like 
Tarski's 1935 
> axiomatization of 'general extensional mereology'. I could have saved 
some time by 
> just knowing more about Tarski, except that what I found out was a 
genuinely 
> *geographical* motivation for those axioms: you can derive the 'unique 
fusion 
> axiom' (P12' in Varzi's article) from the requirement that map 
projections are 
> invertible, which is needed in order to make sense of the idea of a map 
having a 
> well-defined semantics. So I don't see this as a mereological axiom at 
all: in this
> application, it is essentially a *cartographical* axiom. In this 
application, all 
> that stuff about parthood being fundamental to the universe is baloney: 
the 
> intuitions come from the idea of rendering a map on a surface as a 
description of 
> geographical space. And this kind of insight is genuinely useful, 
because it ties 
> the formal ontology to intuitions that are robust in the application 
domain, 
> instead of to very abstract, evanescent ideas that one quickly loses 
confidence in,
> so cease to be useful guides to what axioms to write. (Similar comments 
apply to 
> the notion of a 'boundary' in geography, as opposed to in philosophical 
generality.
> You want to find out about geographic boundaries, ask a surveyor or a 
civil servant
> or a soldier or a map-maker: don't read Aristotle.)
> 
> A good guide needs to tell users that they should not assume that their 
problem has
> been solved by virtue of some Great Thinker having made a Universal 
theory, and 
> they can just take the solution off the shelf and run with it. They need 
to think 
> it through, to see if it applies where they need it to apply, or if it 
needs to be 
> modified. They need to think about whether their notion of parthood is 
really 
> transitive or not., and maybe be given some guidance on how to find out. 
They need 
> to think about issues like, what it means to replace a part (does the 
whole with 
> the replaced part stay the same thing or does it change? Or both, in two 
senses 
> that we probably need to distinguish? Or is this just not an issue?) 
They need to 
> be warned about the places where an apparently obvious axiom (if the 
parts are all 
> the same, the whole is the same; a part of a part is a part) might turn 
around and 
> bite them (a disassembled lathe isn't a lathe; a ballbearing might be 
part of a 
> bearing assembly but not part of an engine.)  Being told that the guys 
who publish 
> in the journals that *real* philosophers read are of the opinion that 
parthood is 
> necessarily transitive and non-diachronic is kind of beside the point.
> 
> </speech>
> 
> Pat
> 
> <snip>
> -- 

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Received on Monday, 8 March 2004 14:56:06 EST

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