Re: Models Err

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• In-reply-to: Fritz Lehmann: "Models Err"

Date: Tue, 25 May 93 11:14:33 -0400
From: schubert@cs.rochester.edu
Message-id: <9305251514.AA18277@ash.cs.rochester.edu>
To: fritz@rodin.wustl.edu, interlingua@ISI.EDU
Subject: Re:  Models Err

> A Tarskian model can itself be WRONG.  It can include 
> Pat Hayes among U.S.  Presidents.  (The real world 
> itself cannot err this way.) 
> ....  Since a model may err, a 
> model is not the world.  Pretty simple, but 
> evidently disregarded by persons overly steeped in 
> the technical formal method (and maybe the 
> notation).  

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).

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

  US-president(Pat-Hayes)

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. 

-Len Schubert

P.S. I'm no logician, Fritz, but this seems like a pretty simple point,
even to someone underly "steeped in the technical formal method"