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Re: [ontolog-forum] Visual Complexity

To: "John F. Sowa" <sowa@xxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Wed, 7 Feb 2007 11:14:03 -0600
Message-id: <p06230906c1efae3cdff8@[]>
John,    (01)

I profoundly disagree. As you know, this is an 
old debate we have had many times, at 
considerable length. (BTW, is that old email 
debate archived anywhere, do you know? It 
deserves to be.) I will not go over it all again, 
but just to put on record where I think you are 
(importantly) wrong:    (02)

>Chris and Patrick D.,
>I responded to this thread earlier this evening, but I
>didn't mention the following point, which may help to
>clarify the issues:
>   1. Model theory, as Tarski stated in the title of his
>      original paper, is intended to define "The concept
>      of truth in formalized languages."    (03)

Historically true; but his primary example used 
German ("Schnee ist weiss"); and model theory has 
since been applied to the analysis of NL by many 
philosophers, perhaps most notably by Montague.    (04)

>   2. Tarski later waffled on the subject and talked about
>      defining truth in general,    (05)

He did not waffle, and neither did all the other 
philosophers of language since. As I once 
documented in an old email to you, it is hard to 
find a philosopher of language (I am counting 
Quine, Tarski, Montague and others) who does not 
at some point take it to be simply obvious that 
model theory constructions apply to the real 
world. Every important mathematical philosopher 
who has written on set theory gives examples 
which make it abundantly clear that sets may be 
sets of real, physical, entities, not just pure 
abstractions.    (06)

>but it's best to make a
>      sharp distinction between an actual physical situation,
>      a model of that situation, and a theory stated in
>      some formal model.    (07)

This 'sharp distinction' is based on a conceptual 
mistake: the idea that mathematical language 
(here, the meta-language of the model theory 
itself, which talks of sets of individuals and 
relational structures and so forth)  must be 
describing something unreal or abstract, simply 
by virtue of its being mathematical in nature. 
One might call this view pan-Platonism. But this 
is clearly wrong: engineers every day use 
mathematical language to talk about physical 
structures: scientists use mathematical language 
to talk about nature. Everyone who uses numerals 
to say what time it is uses mathematical language 
to talk about the real world. I do not accept 
that there is any utility in making a sharp 
distinction between a "model of a situation" and 
the actual situation. (And, by the way, your 
multiple, clashing, uses of "model" here is 
highly confusing.)    (08)

>   3. Model theory only relates a statement in some formal
>      language to a formal model.    (09)

It relates it to a model in the technical sense - 
actually better, to an interpretation. (This 
terminology is both more accurate and less 
confusing, since "model" is so overloaded.) An 
interpretation is a universe - a set - of 
individuals and relations over them, a relational 
structure. Can this be a part of reality? 
Certainly. The set can be for example the set of 
all human beings living on Earth. Not a Platonic 
abstraction, but the actual living breathing 
human beings. Your usage "formal model" is 
tendentious and misleading, suggesting as it does 
that there is a corresponding (prior?) notion of 
"informal model". But model (better, 
interpretation) in this sense can BE a piece of 
reality. The fact that interpretations/models are 
*specified* formally in the meta-theory does not 
make the interpretations themselves somehow 
"formal" in nature or substance, any more than my 
use of numerals in saying "I spent 30 minutes 
answering this email" makes the observation into 
a claim about "formal times".    (010)

There is widespread tendency to treat this word 
"formal" as a kind of derogatory, dismissive 
qualifier, implying "not real", a kind of figment 
of a mathematical imagination. (The philosopher 
John Searle has made this into almost a cottage 
industry.) This tendency is regrettable, and 
seems to be American in nature: I suspect it is 
arises from the same lacuna in American education 
that makes most schoolchildren here equate having 
a grasp of elementary calculus with being 
unworldly. It is also completely mistaken, and 
very destructive to rational discourse. Allow me 
to quote a definition that I once wrote (in the 
RDF semantics glossary):    (011)

"Formal (adj.) Couched in language sufficiently 
precise as to enable results to be established 
using conventional mathematical techniques."    (012)

That is ALL it means. It does not imply that the 
subject-matter is "formal" in nature (which if 
you think about it is actually meaningless in any 
case) only that one is being fairly exact in 
describing it.    (013)

>  It does not make any
>      claims whatever about the applicability of that model
>      to any aspect of physical reality.    (014)

Of course it does. If I say that the universe of 
my interpretation is all human beings, and I say 
that this universe is infinite, I am thereby 
making a (false) claim about actual human beings.    (015)

>   4. The question of how well a particular model represents
>      physical reality is *not* a formal issue that can be
>      solved by laying down some formal definitions.    (016)

The structure of the model/interpretation is 
(better, can be) a claim about the actual world. 
How well it so 'models' - that is, how accurate 
this implicit claim is - cannot of course be 
decided using only mathematics: one needs to have 
some contact with the actual world, yes. Who ever 
said otherwise? (Not Tarski !)    (017)

>      involves all the hard work of observing, testing,
>      and devising experiments to determine what is real.    (018)

Well, ultimately, perhaps, but we really do not 
need to be so rigorously empirical for most of 
what passes as ontology design.    (019)

>In short, model theory makes no claims about reality.    (020)

On the contrary, the model theory of a formal 
theory is ABOUT the reality that the theory 
applies to. You are confusing "making a claim" 
with questions about how such a claim can be 
verified: which indeed does take some analytical 
and observational effort. But if model theory 
made NO CLAIMS about reality, observations of 
reality would be completely irrelevant to it.    (021)

>All the hard work lies in determining how well any
>particular model describes reality.    (022)

That can be hard work, but it is not ALL the hard 
work. There is plenty of other hard work to be 
done, much of it more directly relevant to 
ontology engineering.    (023)

>  And as Patrick D.
>said and I agreed, no model has an exact match to
>reality.    (024)

And I profoundly disagree. In fact, I think this 
kind of claim is not only false, but actively 
harmful, and that to urge this point in this 
forum without very close attention to explaining 
exactly what you mean, is close to irresponsible. 
It is very easy to read this kind of claim as a 
form of mysticism, along the lines of "no merely 
*formal* work, of the kind done by you logicians, 
can possibly apply to the non-formal Reality that 
we are talking about."  It serves only to 
obstruct and divert attention from the need to do 
some hard conceptual work.    (025)

Pat    (026)

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