Model vs. Worldfritz@rodin.wustl.edu (Fritz Lehmann)
Date: Thu, 17 Jun 93 05:41:34 CDT
From: firstname.lastname@example.org (Fritz Lehmann)
To: email@example.com, interlingua@ISI.EDU
Subject: Model vs. World
To my earlier note (during the model/world discussion),
>> One proof that a model is not the
>> real world itself is its capacity for error. A
>> Tarskian model can itself be WRONG. It can include
>> Pat Hayes among U.S. Presidents. (The real world
>> itself cannot err this way.) The model theoretic
>> evaluation of a KRep assertion may be flawless and
>> yield "T"; that alone does not make it true --- in
>> addition the model must be accurate. Some errors
>> do not arise in the sentence syntax nor in the
>> model-theoretic evaluation. The assertion is "true
>> in the model" but false. Since a model may err, a
>> model is not the world.
Len Schubert replied,
>A model, strictly speaking, can never BE the world. A model is a
>CORRESPONDENCE between symbols and things is the world, so it is the
>wrong sort of thing to BE the world. However, the correspondence can
>perfectly well be between symbols of the KREP and things in the ACTUAL
>world (and speaking loosely, one might sometimes say in such cases
>that one is using the world as a model).
When "strictly speaking" you are strictly right, Len, as
opposed to "speaking loosely", and I think KIF and CGs should be
founded on the strict view. Since when is a Tarskian model itself
a CORRESPONDENCE? It is a domain set with a set of predicates and
relations (sets of tuples) on the domain set. (This is an
abstract combinatorial structure, namely a relational structure or
directed hypergraph.) Nichtwahr? The correspondence you refer to
is the model-theoretic one between a KRep sentence and its
model(s). A model may have (or may not have) a further
correspondence to the real world.
>Relative to such a correspondence, there is assuredly no discrepancy
>between truth in the model and actual truth. For instance, if part of
>the assumed correspondence is that the predicate constant `US-president'
>corresponds to a set which includes the actual person, Pat Hayes, AND
>the individual constant `Pat-Hayes' corresponds to Pat Hayes, then
>is true in the model and true in actuality (i.e., the individual denoted
>by `Pat-Hayes' really IS a member of the set denoted by `US-president').
>Of course, this involves a use of the symbol `US-president' in a way
>rather far removed from the way speakers of English might prefer to use
>it -- but logic is very permissive in that regard.
Yes, and if a further "part of the assumed correspondence" is
that the predicate-constant `US-President' corresponds to being a
U.S. President, the sentence is true in the model and in fact false.
Again, this further possible "correspondence" or lack thereof is
between model and real-world; hence they differ. (This latter
correspondence is not only dependent on the referents of individual
names, but also on the referents of predicate/relation names, which
referents I take to be sets of relational instances or "tropes" in
the real world. So the "Pat Hayes" world-connection would have no
particular priority for me over the "US-President" world-connection,
outside of your particular definition.)
Also, Chris Menzel replied to me,
>I don't believe Pat et al. were quite as led astray by formal methods
>as you suggest. Pat is surely aware of the possibility of convoluted
>Tarskian models of the sort you discuss. The important point for him
>is that you can also define "accurate" or "intended" models out of
>real world objects and thereby provide a rigorous account of how
>models represent. John argued in response for the much stronger claim
>that one cannot properly form mathematical models out of real world
>objects *at all*.
Tarskian model theory is about how models are represented, not about
"how models represent". Purely formally, the model itself is the "dead end".
A Tarskian model is an abstract combinatorial structure as mentioned above.
Its parts may be named by us with symbols; any connection of those parts or
the symbols to the real world involves "grounding" (a can of worms properly
handled, I suspect, by Peircean causal semiotics). If Pat Hayes wants to say
a real tree is "in" the Tarskian model he is assuming the grounding without
worrying about it, which is fine. But Sowa is right to point out the
unstated assumption. And because a model is an abstract combinatorial
structure, it is not "formed out of" any physical things -- at all.
Hayes evidently disbelieves the latter. Maybe he thinks physical
objects do form actual combinatorial structures (as opposed to having
structures homomorphic to them).
To those who consider the whole discussion a big digression, I say
that KIF and CGs need to be careful about these things. If belief
spaces, situations, "contexts" and propositional attitudes are nested,
(or, worse, overlapped!) it is easy to go astray.
Yours truly, Fritz Lehmann
25 Seton, Irvine, CA 92715 714-733-0566