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)
>It
> 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)
>
>John
>
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