Re: (biassed) summary of the argument so far.

sowa <>
Date: Sat, 5 Jun 93 12:01:57 EDT
From: sowa <>
Message-id: <>
To: interlingua@ISI.EDU,,
Subject: Re:  (biassed) summary of the argument so far.

I'm glad that this discussion is winding down, since there are many
other issues that we both are busy working on.  A few comments:

> Our difference lies in what we think it is to 'apply' mathematics. You 
> seem to take this to involve far more than I take it to. All one needs 
> to do, in order to apply some mathematical ideas, in my view, is to 
> ensure that the area of application satisfies the assumptions made by 
> those ideas (which for set, and hence model, theory, is not much). You 
> seem to take it to involve far more than this.

Certainly for many applications, like counting apples and identifying
sets of people, dogs, and houses, the application is almost trivial.
But it is very far from trivial when you are working in a new domain,
especially one where you can't use unaided eyesight to recognize the
things you choose to call "individuals".  And when you trying to get a
computer to deal with those apples or people, the things that are trivial
for humans become some of the most difficult to simulate.

> This distinction is exactly that between use and mention.


>>But if you do accept the meaning triangle as a reasonable hypothesis
>>about intervening mental states in human use of language, I cannot
>>understand why you would object to an intervening level of surrogates
>>in a computational system that is used to relate a language (natural
>>or artificial) to the world.

>That suggests where we disagree. The use of 'language' to refer both 
>to natural language (which is used by humans to communicate) and 
>(hypothesised) representational languages (which are used by agents 
>to represent and infer) is little more than a pun, in my view, and 
>potentially very misleading. 

There are very many fundamental differences between a system of logic
and a natural language.  That is why I also showed my 4-part distinction
where I separated the NL from the logic.  But there are also very
fundamental differences between different kinds of "representations"
inside a computer system, either an AI system or a commercial DB or
an engineering simulation of some physical system.

As I said in my last note, I don't like to use the abbreviation "Krep"
because it blurs that distinction.  I prefer to say "KR language" or
even better to talk about a specific language such as KIF, CGs, or SQL.
That is the point of my insistence that a DB is not a language.  SQL
is a language that is used to define a DB, update a DB, query a DB,
and make assertions about the contents of a DB.  The DB is definitely
a kind of representation, but it is not a "language-like" representation.
I would prefer to call it a "model-like" representation or a depiction,
if you like.

> ... For example, I believe that there 
>are hundreds of billions of stars. Does this mean that I must have 
>a surrogate universe with hundreds of billions of surrogate stars 
>in my head somewhere?

No.  But it does mean that you can, if you choose, imagine or conjure
up mental images of as many stars as you like -- just as my computer
can compute prime numbers one at a time until either it runs out of
space or I lose patience waiting for it.

> This is easy to distinguish. What you mean by 'perceived reality' 
> is something like 'the way the world would (or might) be if my 
> perceptions were correct', I presume? That is a model of my 
> (perception-governed) representation of it.

Thank you.  That "model of your (perception-governed) representation"
is exactly what I meant by "depiction".  You may dispute the usefulness
of computing or storing such models, but that is precisely what I was
trying to get at.

>Just a side comment: there is only one reality, of course, so 
>'the perceived reality' is only a metaphorical usage. I hope we 
> agree on this.

Yes, of course.  But the number of perceived realities is open-ended.
Each perceiver (person, animal, or robot) would have a different one,
and the same person would have different perceived realities in the
daytime or the nightime or when using a telescope or a microscope.

>The theory of meaning isnt the kind of thing one would (usually) 
>seek to implement, its a theory of what such implemented 
>things might mean. 

Fine.  We have no disagreement on this point.  But what I was
trying to say is that many of the mathematical operations in model
theory can be implemented in a digital computer.  In fact, I was
pointing out that the operations that an SQL processor uses to
answer a query are exactly equivalent to the operations that Tarski
defined for evaluating the denotation of a formula in terms of a model.

>I agree with this general idea, although I am quite willing to 
>countenance a more platonic approach. (And agree with Quine that 
>it is very hard to avoid allowing some abstract entities into 
>ones ontology, such as the integers. Even the intuitionists 
>allowed the integers.) Part of the utility of set (and hence 
>model) theory is precisely that it is completely agnostic on 
>this issue.

Fine.  We have no disagreement on this point.  In fact, I believe
that the integers are more fundamental than set theory, and I would
prefer to see a foundation for mathematics that starts with the integers
as given rather than trying to construct the integers from sets.  But
that is another issue.

> ... The strenousness of my objections to 
>your messages has been motivated more by my strong belief that 
>it is necessary to maintain this freedom to be ontologically 
>promiscuous than by my disagreement with your particular views. 

That's fine.  As I said many times, I was not trying to stop anyone
>From saying anything they please in either CGs or KIF.  This whole
discussion has been at the metalevel of (a) how does a language like
CGs or KIF relate to the world, and (b) how can one implement such a
relationship in a way that can be useful for guiding a robot or
simulating virtual reality.

>To insist that logical representations must refer only 
>via some kind of computational surrogate seems to me to be an 
>unwarranted intrusion of a very particular philosophical stance on 
>semantic, and even computational, practice....

First of all, I never "insisted that... must refer only via...."
All this metalevel discussion is about my approach to constructing a
framework that has some useful computational properties.  We have been
arguing so long about philosophical issues that I have hardly begun
to list the computational reasons why I prefer this approach.  But
nothing forces you or anyone else to adopt my approach if you don't
like it.  And for comparison, I would suggest that you look at the
philosophical and computational "intrusions" caused by some other
metalevel approaches, such as Montague grammar.

Now, to get back to KIF, I would like to endorse your recommendation
that we avoid the extra levels of parentheses in the variable and type
declarations; i.e., for the sentence, "Yojo is one a mat", there were
two suggestions:

 1.  (exists ((?x mat)) (on Yojo ?x))

 2.  (exists (?x mat) (on Yojo ?x))

You preferred the second alternative, since the question mark is
sufficient to distinguish the variable from the type declaration.
I agree wholeheartedly.

I also agree with Len Schubert's suggestion that the commas be
dropped in variable references inside quoted expressions.

So we can agee on the syntax of KIF and how it can be used to
represent anything we want to say, even if we might disagree about
the most convenient way to implement it or the most philosophically
elegant way to talk about what it means.