Concerning the possibility of a finite number of conceptual primitives: (01)
John Sowa stated (among other things): (02)
[JS] > The world is a continuum (at least as far as human perception is
> concerned) and languages consist of discrete worlds. That implies
> that the number of potential percepts and concepts is immensely
> greater than any human language can designate.
>
The conclusion does not follow from the premise: if the world is
continuous in quantitative terms, then a small number of arithmetic
primitives will still suffice to allow division of some dimension into an
infinite number of different regions, each of which can be labeled by some
word in a human language, and which may overlap, giving ambiguity to the
linguistic terms. It should be clear that an infinite number of objects or
terms can be represented by combinations of a small finite number of
primitive concepts (objects, relations, functions). Whether or not human
language can be mapped to a set of fixed concepts based on such a finite set
of primitives is still an empirical question. The continuity of reality
does not preclude finding primitives that can specify the boundary points
for useful concepts lexicalized in human languages. (03)
[JS] > I'm glad that you put double stars around IF, because that is a huge
> assumption to swallow. There is not the slightest shred of evidence
> that the number of primitives is discrete and finite. In fact, there
> is overwhelming evidence that the meanings of words tend to shift in
> gradual, continuous ways.
>
I consider several phenomena as valid presumptive evidence (and a lot more
than just a shred) for a finite number of conceptual primitives:
(1) the ability of dictionaries such as Longman to define all words using
a small (e.g. 2100 word) defining vocabulary;
(2) the need for only 4,000-5,000 basic characters (most representing one
or a small number of concepts) in Chinese or Japanese to allow creation (by
combination) of all of the words of the language;
(3) the need for only 2,000 -3,000 signs in sign languages such as
AMESLAN to allow deaf people to communicate effectively. (04)
This does not **prove** that the same principle will work with
logic-based ontologies for communication among computers, but it provides
**evidence** that is meaningful. The proof will have to come from the
engineering process of building an ontology system based on the
representation of conceptual primitives and testing it to see if it is
capable of representing concepts in many diverse fields, as combinations of
the primitives. (05)
The arguments against fixed semantic primitives tend to rest on the
ability of words in human languages to have multiple meanings, and to change
their meaning. This argument confuses the roles of a logic-based ontology
of fixed concepts, and a human language of terms whose referent concepts are
not fixed. The fact that terms in human languages can change their meaning
does not mean that the terms in an ontology must change meaning, because the
terms in the ontology can (at least in theory) be grounded in procedures
that assure their unchanging meaning. (06)
Exactly how to provide that conceptual grounding for ontologies is, in my
opinion, a very important topic that should be investigated actively. To be
easily usable, a good mapping of any foundation ontology to human language
will probably be necessary. The **mapping** of the ontology to the human
language will need to be updated frequently. Once created and refined by
thorough testing in multiple applications, the foundation ontology itself is
likely to evolve very slowly, as new primitives become recognized. (07)
Pat (08)
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx (09)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: Saturday, December 12, 2009 2:08 AM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Language and logic
>
> Pat, Ferenc, and Rich,
>
> I'm merging the comments about form and content with the thread
> on language and logic. And I'm also trying to reduce the amount
> of off-topic noise on this forum. But I'll add a few comments.
>
> PC> Perhaps you could provide us with an example of some more or
> > less "rare" logic that is inspired by some particular culture?
>
> First-order logic appears to be universal in all cultures that
> have to deal with money. People tend to be very careful in their
> dealings with money, and they use the simple, regular, and highly
> reliable FOL to keep the details straight.
>
> But when you get into modal logics, the number of modalities and
> their interpretations is extremely language dependent. Even among
> common European languages, the modal terms don't line up exactly in
> translations between any two of English, French, German, or Russian.
> When you move to Asian languages, exact translations become even
> more difficult and dubious. Chinese, for example, has no way of
> accurately translating any English sentence that contains the
> combination "would have".
>
> When you get to fuzzy terms, hedging, emphasis, approximations,
> nonmonotonic reasoning, etc., things get even worse. The terminology
> that people use is not only language and culture dependent, it tends
> to vary among different businesses, professional fields, and even
> different applications within a given profession.
>
> PC> I believe that there is a finite number of conceptual primitives,
> > and that interoperability depends on sharing the same conceptual
> > primitives, with which the non-primitive terms can be defined.
>
> The world is a continuum (at least as far as human perception is
> concerned) and languages consist of discrete worlds. That implies
> that the number of potential percepts and concepts is immensely
> greater than any human language can designate.
>
> Work by linguists, such as Anna Wierzbicka and Len Talmy, show that
> there are common "primitives". But those so-called primitives are
> vague generalities. They designate a vague field or aspect rather
> than something that could be axiomatized in a formal ontology.
> Anna W. insisted that her primitives were very different from any
> of the proposals by logicians. I certainly agree.
>
> PC> **IF** there are a finite number of conceptual primitives,
> > **THEN** any two systems using the same conceptual primitive
> > representations can interoperate accurately by sharing their
> > definitions as well as the data they want to exchange.
>
> I'm glad that you put double stars around IF, because that is a huge
> assumption to swallow. There is not the slightest shred of evidence
> that the number of primitives is discrete and finite. In fact, there
> is overwhelming evidence that the meanings of words tend to shift in
> gradual, continuous ways.
>
> Peirce was very clear about the point that "symbols grow" over time.
> Following is one of many comments he made about such issues:
>
> CSP> By his system of nomenclature, Sir William Hamilton has conferred
> > an immense boon not alone on his own school but on all English
> > philosophers who believe in anchoring words to fixed meanings. I
> > deeply regret that I am not one of these. That is the best way to
> > be stationary, no doubt. But, nevertheless, I believe in mooring
> > our words by certain applications and letting them change their
> > meaning as our conceptions of the things to which we have applied
> > them progresses.
> >
> > --Charles S. Peirce, Writings 1, p. 58 (1861)
>
> Note the word 'stationary'. If you want to freeze all development,
> then it is possible to have static definitions. But just look at
> any kind of computer application. As software progresses from
> version 1.0 to 3.5, the same words are used at each stage, but their
> definition changes with every update. The kinds of primitives that
> Anna W. proposed are like the vague terms that change with every
> new release of a software application. They are definitely not
> suitable as a foundation for a formal ontology.
>
> Ferenc and Rich were hoping to find precise definitions of terms,
> but I'm sorry to disappoint them. Those terms cannot be defined
> precisely, except within a fixed formal theory. Outside any such
> theory, we just have to muddle through with what you can find in
> your favorite dictionary.
>
> FK> What is formalism? A language?
>
> Short answers:
>
> 1. formalism -- any kind of mathematical notation.
>
> 2. language -- a dialect with an army.
>
> The long answers and debates are off topic.
>
> FK> Why call a verbal string/cluster a linear pattern?
>
> Why not?
>
> FK> What is a triad?
>
> A pattern of three.
>
> FK> A concept? An object? What do you mean by beginning? A boundary
> > in space or time?
>
> Please use a dictionary or try Google.
>
> FK> What is a statement? A proposition? What is a logical operator?
> > An object? A relation? A property?
>
> If you want a tutorial on mathematics and logic, I recommend:
>
> http://www.jfsowa.com/logic/math.htm
>
> RC> but this topic leaves a lot of unspecified terms open for
> > misinterpretation.
>
> It most definitely does, and I have no desire to write a tutorial
> on every term.
>
> RC> You have a view of foreground and background which seem to be
> > less well thought out than your usual deep viewpoint.
>
> I'm sorry that I had mentioned form and content, and I definitely
> did not want to open up another discussion about foreground and
> background. There is an immense literature about those issues
> in psychology and linguistics. Please use Google.
>
> John
>
>
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