Re: Trying again to respond
Message-id: <>
Date: Thu, 29 Apr 1993 15:24:11 +0000
To: sowa <>
Subject: Re: Trying again to respond
Cc: interlingua@ISI.EDU,,

Hi John

Sorry about the mailer problem. I hope there are enough newlines in this
letter. (By the bye, archaic Unix mailers using
punched-card line lengths are certainly a nuisance. Does anyone 
know of a way of setting parameters on Eudora which would insert 
these newlines automatically?)


>After beginning my last note, I tried to go into vi to edit your note,
>but vi also got hung up on the 80+ character lines.  So I gave up and
>I'll just start a fresh round of comments:

OK, but theres a danger of us getting off track (or maybe onto
several tracks simultaneously). I have sent you a version of 
the last message which I hope is readable, and will respond to 
this one insofar as it is relevant to the earlier discussion. 
Again, dots indicate material removed to keep length down.

>In your earlier note, you labeled my approach as "eccentric".  That is
>a debating ploy to put me on the defensive, so that you can dismiss 
>the position as inappropriate for a proposed standard for kn. rep.

Correct. As I have repeatedly said, you are welcome to whatever 
philosophical positions you like - and this is not the forum to
argue about them - but I am anxious that they do not interfere
with the sensible development of a Krep standard.

>In developing a theory of concepts, I am starting from the evidence
>of language, not from introspection or psychology.  When I talk about
>concepts as the mediating level between word and object, I mean the
>formal structures that I can represent on paper or in a digital
>computer.  Their possible parallels to mental states or neural processes
>are an interesting topic for psychology and neurophysiology, but nothing
>in my approach critically depends on those parallels.

I believe this is not true, since your approach takes it that these
formal structures are the objects of belief assertions. But this is not 
really important and is aside from the central point at issue here.

>To avoid dealing with such elusive, nonobservable things as thoughts,
>Frege developed his Begriffsschrift (concept writing), which along with
>Peirce's algebraic notation became the foundation for modern systems
>of logic.  Although I prefer Peirce's graphic notation, all of these
>systems can be construed as formal ways of talking about that elusive
>level of thought or concepts.

That sounds like a reasonable statement, although one needs to be
rather careful with such words as 'about'. I take it that these systems
are intended to be ways of writing the content of whatever is in these
elusive levels. (One might say that Harry's thoughts are confused. 
That would be ABOUT his elusive level, but it wouldnt be trying to 
express its content.)

>You seem to claim, however, that logic should be related directly
>to real-world things without any intervening level of "concepts"
>or "models".  

Yes. (Well, strictly, I want to say that logic CAN be so related,
not SHOULD be; but let this pass for now.) This is quite 
consistent with the reasonable statement above. The expressions 
in a Begriffsschrift - in modern terminology, a Krep formalism - 
are intended to express the content of a thought or proposition. 
Krep expressions ARE the intermediate level that your philosphical
tradition puts between language and the world. Model theory IS an 
account of how the 'correspondence' between that and the world it 
purports to describe should be structured.

I know you disagree with this, since you want to identify krep
with natural language. I disagree, and think that this is not 
the right way to fit knowledge representation to work in language
comprehension. I recognise that others disagree (Yorick Wilks, for 
example, takes your position), and am willing to argue my side 
until the cows come home. But my only point here is that any position
on these issues should not be allowed to affect the syntax of a 
Krep standard.

>Although you use the word "model", you identify
>at least some of those models with aspects of the real world.
>I prefer to make a very clean distinction and say that none of
>those models are the real world. 

I know you prefer to make this distinction, but I don't want 
your preferences to be incorporated into a language I might 
be forced to use.

I don't want to insist that formalisms MUST be interpreted in 
the 'real world' (whatever that really means), only that they
CAN be. In fact, I want the semantic theory of the formalism to be
as agnostic as possible about the intrinsic nature of the possible 
interpretations. TMT makes very few such ontological assumptions;
fewer in fact than any other semantic theory I have ever seen. 
Thus, a TMT interpretation (I carefully avoid 'model', since 
you confess to having deliberately  confused two distinct 
meanings of this overloaded word) might be 
over a domain of integers or bacteria or ocean liners 
or concepts or whatever else one might decide to try to describe.

The mistake in this 'clean distinction' of yours, it seems 
to me, arises when one notes that TMT refers only to the 
structure of a possible interpetation. Thus, if we have an 
'abstract' interpretation and a 'correspondence' between that 
and some part of a more concrete world, this presumably means 
that that part of the real world is similarly structured to 
the abstract model. But if that is true, then that part of 
the world IS a valid TMT interpretation (since to be one, it 
only has to have the appropriate structure...) So if your notion 
of 'correspondence', the last link in your three-way chain, 
makes any sense, then it is simply TRUE that the formalism 
could have been interpreted as referring directly to the 
world, regardless of what your philosophical sensibilities 
lead you to prefer. 

>..........  I keep insisting that you
>are taking Tarski's name in vain, since he never related symbols
>directly to physical objects; he only related symbols to abstract
>set-theoretic constructions (or to mereology, which he used in some
>of his writings instead of set theory). 

Check my earlier reply for the error in talking of 'set-theoretic 
constructions' in this way.

>That approach should more
>properly be associated with Richard Montague, who tried to identify
>Tarski's abstract models with the real world.  And even Montegovians
>like Godehard Link and Nino Cocchiarella have been much more
>sympathetic to my three-part distinction between language, model,
>and reality than you have been.

Lets be clear: I am very much in favor of distinguishing language, 
thought and reality, which is what many of the philosophers you cite 
were concerned with. Your dropping all these Big Names is a 
debating ploy: we both know about debating. But that is not 
the essential difference between us. You want to identify 
Krep formalisms with language and their interpretations with 
thoughts, while I want (to oversimplify somewhat) to identify 
Krep with thoughts and its interpretation with the world: or, 
in this context, I want a Krep standard to allow such an interpretation.

>As I said in my previous note, I was a mathematician in my youth,
>but I also took a lot of courses in physics. 

Me too. Aren't we alike? :-)

> And I think that the
>three-way distinction comes naturally to both physicists and
>engineers.  They do not think of mathematics as a "science of
>reality".  Instead, they think of it as a tool for constructing
>abstract models.  Then physics is the science that uses those
>models to study reality, and engineering uses those models to
>manipulate or change reality.

So, if we try to represent engineers or physicists knowledge, 
we are encoding beliefs about reality (not about an abstraction 
which 'corresponds' to reality). Exactly my point, thanks. 

Russell said that mathematics was the discipline in which we did not
know what we were talking about, nor whether what we were saying 
about it was true. I think this captures the essence of mathematics. 
You can't say what much mathematics is aboput because it can be 
interpreted in all sorts of ways. One might say that it has been 
abstracted from specific content. But there's a subtle mistake 
in moving from that, to saying that it is about something abstract, 
so being forced to hypothesise a new domain of 'abstract things' 
standing between the mathematical language and the world. When I measured
the lengths of kitchen cabinets, added these numbers together and 
concluded that I would have to move a wall, my calculations
referred to the actual world, not an abstraction.

>I also claim that the three-part distinction is an accurate 
>description of AI practice:  language (either formal or natural)
>is mapped to abstract models constructed from data structures in
>the machine; and those models are mapped to the real world by
>pattern recognition systems and robot manipulators.

And now this is just an error. The data structures in a Krep 
system ARE (a suitable encoding of) the expressions of the 
formal language. That mapping is not one between a logic 
and its models (in the sense of TMT). 

This is just the kind of confusion which carelessness 
about words like 'model' gets us into. (While we are giving 
opinions, I find your careless lumping together of formal and 
natural language quite unacceptable. Natural languages and 
Krep formalisms must be carefully distinguished, in 
my view.)

>Summary:  The three-way distinction of language, model, and reality
>has a long and honorable tradition ranging from Aristotle to
>Ogden and Richards, from Frege to the analytical philosophers,
>and from common practice in physics and engineering to common
>practice in AI.

In order to make this case, you have to change the meaning of 'model' 
at least twice. But I'm not arguing against your honorable tradition, 
but the idiosyncratic (and I believe confused) conclusions you 
are wanting to draw from it for a Krep standard.

>I will acknowledge that there have been some philosophers who
>have tried to blur the distinction between models and reality,
>but I don't believe that they deserve the sobriquet of TMT
>or "Tarskian Model Theory".  Tarski never blurred that distinction,
>and he would probably respond in the same way as Karl Marx, who
>said "Je ne suis pas Marxiste."

Call it what you like. I don't give a damn about the name. 
I invented 'TMT' to try to not get involved in this kind
of amateur-scholarly debate. As I said, I was referring to 
standard 'model theory' of logic, found in any textbook; 
or more exactly, to this general approach to defining meaning 
of formal languages in extensional set-theoretic terminology.

Pat Hayes

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