Pat, Ferenc, and Rich, (01)
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. (02)
PC> Perhaps you could provide us with an example of some more or
> less "rare" logic that is inspired by some particular culture? (03)
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. (04)
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". (05)
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. (06)
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. (07)
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. (08)
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. (09)
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. (010)
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. (011)
Peirce was very clear about the point that "symbols grow" over time.
Following is one of many comments he made about such issues: (012)
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) (013)
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. (014)
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. (015)
FK> What is formalism? A language? (016)
Short answers: (017)
1. formalism -- any kind of mathematical notation. (018)
2. language -- a dialect with an army. (019)
The long answers and debates are off topic. (020)
FK> Why call a verbal string/cluster a linear pattern? (021)
Why not? (022)
FK> What is a triad? (023)
A pattern of three. (024)
FK> A concept? An object? What do you mean by beginning? A boundary
> in space or time? (025)
Please use a dictionary or try Google. (026)
FK> What is a statement? A proposition? What is a logical operator?
> An object? A relation? A property? (027)
If you want a tutorial on mathematics and logic, I recommend: (028)
http://www.jfsowa.com/logic/math.htm (029)
RC> but this topic leaves a lot of unspecified terms open for
> misinterpretation. (030)
It most definitely does, and I have no desire to write a tutorial
on every term. (031)
RC> You have a view of foreground and background which seem to be
> less well thought out than your usual deep viewpoint. (032)
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. (033)
John (034)
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