SUO: RE: Defining words (was Problems in SUMO)
John,
Comments below.
-Ian
> -----Original Message-----
> From: John F. Sowa [mailto:sowa@bestweb.net]
> Sent: Tuesday, July 01, 2003 9:10 AM
> To: Ian Niles; 'sowa@bestweb.net'; Ian Niles; West, Matthew R
> SITI-ITPSIE; Patrick Cassidy; standard-upper-ontology@ieee.org
> Cc: cg@cs.uah.edu
> Subject: Defining words (was Problems in SUMO)
>
>
> Ian,
>
> I think that we both understand what can and cannot be
> expressed in languages like KIF or CGs.
>
> What we are disagreeing about is the definition of what
> constitutes a natural language, such as English.
No, actually we're not. I think you and I agree about most if not all of
the things that go into the class of natural languages. What we're arguing
about is whether any natural language can express any concept whatsoever.
This is not a definitional claim about natural languages; it is an empirical
claim which can be falsified by considering actual languages, e.g. languages
of stone-age cultures versus languages of industrialized cultures.
>My claim
> is that all natural languages are equally expressive in the
> same sense that KIF and CGs are equally expressive:
>
> 1. The syntactic and semantic features of KIF and CGs are
> equivalent in the sense that any statement in one could
> be translated to a logically equivalent statement in the
> other, provided that all the nonlogical constants (i.e.,
> the vocabulary) were defined by suitable definitions and
> axioms.
Number 1 is a trivial claim, and I of course do not dispute it.
>
> 2. The syntactic and semantic features of English and any
> other natural language are equivalent in the sense that
> any statement in one could be translated to a logically
> equivalent statement in the other, provided that all the
> words outside some "core vocabulary" were suitably defined.
This is true or false, depending on how you cash out the notions of "core
vocabulary" and "suitably defined".
>
> I certainly agree that "suitably defined" for most human
> speakers requires much more than giving them some axioms
> stated in the core vocabulary. But that is a question
> of how people learn -- they learn best from examples, not
> from abstract statements.
OK, this is where we disagree. You're arguing that all natural languages
are equally expressive. One consequence of this is that it should be
possible to express any English concept in any stone-age language without
using any extra-linguistic means, e.g. without pointing or other gestures.
It's true but irrelevant that people learn better when we teach them
ostensively. Your claim is about the inherent capabilities of languages, so
considerations about other matters only cloud the issue and, in fact, only
reinforce my point that all natural languages are not fully expressive.
>
> JFS>> All natural langauges have the full expressive power of
> >> first-order, modal, higher-order, and metalevel logics.
> >> Any ontology that can be encoded in those logics can be
> >> encoded in any NL.
>
> IN>This doesn't follow. The fact that natural languages have
> at least the
> >degree of syntactic expressiveness of the logics you mention
> does not imply
>
> >that natural languages can express any ontology and, hence,
> any semantic
> >content whatsoever.
>
> My claim is that the core vocabulary of any NL is capable of
> stating the definitions and axioms for any terms that could be
> defined in either KIF or CGs (or any other system of logic).
Introducing talk about KIFs and CGs is simply not necessary. The claim that
you made and that I am now disputing is that any natural language (given its
own syntax and semantics) can express any concept whatsoever. Some evidence
against this claim is the anecdotal observations of the anthropologists I
mentioned.
>
> I admit that there is a very serious question of whether the
> native speakers of that NL could understand those axioms
> without a large amount of traing.
This is not only a serious question, it is the crucial question. If the
training can only be accomplished extra-linguistically, then your claim is
false.
>
> But you don't have to go to a stone-age tribe. Just try to
> explain the notion of a charmed quark to somebody who has
> never taken a course in physics. Or try to explain the
> concept of puts and calls to somebody who has never made any
> kind of financial investments.
Exactly, because these concepts could not be expressed in the idiolects of
the people who had to learn about them. They required a an extension to
their semantics before they could accommodate the new concepts.
>
> The fact that certain terms exist in "the English language"
> doesn`t mean that a typical English speaker of average
> intelligence can understand them without a great deal of
> extralinguistic training.
If your claim all along was simply that any average language speaker can be
trained to understand any concept, I don't dispute this. However, I don't
think this is what you meant. I think you suppose that each natural
language has the same stock of core semantic primitives and the same logical
grammar, and, thus, everything in any natural language is in principle
intertranslatable. Correct me if I'm wrong, but this seemed to be the claim
you were making originally. If you've now backed away from this strong
claim and are simply making the trivial point about training, then we don't
have anything to argue about.
>
> JFS>> It is simply impossible to encode anything in KIF (e.g.
> >> SUMO) that could not be recoded in any stone-age language.
> >> How would you define book in KIF without assuming a lot of
> >> primitives that no stone-age reader would understand?
>
> IN>I don't follow you here. I was arguing that the concept
> of book presupposes
>
> >a set of concepts that are not available in many languages,
> e.g. those of
> >stone-age cultures, and that inculcating those concepts in
> the mind of
> >someone who is familiar only with one of those cultures would require
> >non-linguistic training, and, hence, that your claim that all natural
> >languages are fully expressive is false.
>
> My claim was that any term in English could be defined in any
> other NL by means that are similar to the way that term was
> introduced into English. But the fact that any particular
> term was introduced into any NL (including English) does not
> imply that an average speaker of that NL can understand it
> without a great deal of training.
>
> John
>