Paola, Milton, and Azamat, (01)
First, I'd like to remind people that there is much more to thinking
than logic. Second, there is much more to logic than deduction.
And third, even when two people use the same logic, their starting
assumptions or axioms can lead them to totally different conclusions. (02)
PDM> JohnS and other writing referenced in the discussion say that
> logic (such as fol) is universal and does not differ across cultures
> and languages, (03)
FOL is the foundation for mathematics, and there are excellent
mathematicians in China, Japan, India, and Tibet who use exactly
the same FOL as all other mathematicians around the world. (04)
PDM> surely FOL is the top level logic for any logic, (05)
FOL is one very simple version of logic that happens to be expressed
as a subset of every language around the world. Every language
that has words for 'and', 'or', 'not', 'some', and 'every' uses
that subset to express sentences that could be mapped to FOL. (06)
However, the word 'logic' is often used in a very broad sense that
includes much more than what logicians call 'logic'. For example,
the Nyaya logic of India includes more than just FOL (although
versions of FOL are indeed present in it). (07)
For a quick overview, see the Wikipedia entry on 'Nyaya Sutra'.
There you'll find much more than a western textbook on logic
normally includes. Following is an example of a Nyaya syllogism: (08)
> The Nyaya Sutra supports a five-part syllogism, widely followed
> in the Indian tradition:
> 1. This hill is fiery (pratijna: a statement of that which is to
> be proved).
> 2. Because it is smoky (hetu: statement of reason).
> 3. Whatever is smoky is fiery, as is a kitchen (udaharana: statement
> of a general rule supported by an example).
> 4. So is this hill (upanaya: application of the rule of this case).
> 5. Therefore this hill is fiery (nigamana: drawing the conclusion). (09)
This format is longer than the western three-part syllogism, but
parts 3, 4, and 5 correspond to the western version: (010)
Everything that is smoky is fiery.
This hill is smoky.
Therefore, this hill is fiery. (011)
The basic deductive logic is the same, but the Nyaya school includes
more about epistemology, ontology, and practical reasoning methods
used in debates and discussions. (012)
MP> The Buddhists refrain from hard formal logic... (013)
The mathematical logic developed by Boole, Peirce, and Frege is
indeed much "harder". But it is a compatible extension to the
traditional logic from Aristotle to the middle ages in the west.
And as the example above shows, that traditional western logic
is very similar to the traditional eastern versions. (014)
MP> I humbly suggest to first borrow some commonsensical thinking
> from Tibetan Buddhist logic to simplify the formal discussion
> about entities, attributes and conceptual ideas laid down in
> the 100 plus standards. (015)
I like the Tibetan Buddhist approach very much, but I would hasten
to add that it includes much more than just logic. In fact, it
is strongly based on a theory of signs (semiotics). Peirce would
also approve of that approach, since he maintained that semiotics
is fundamental to all studies, including logic and ontology. (016)
MP> In the end the semantic web deals with natural languages and
> in most cases natural languages in restricted domains.
> The jury is still out on how to best formally describe the latter. (017)
I certainly agree with that statement, and I have been highly critical
of the methods of formal semantics by Richard Montague and others. (018)
My major criticism of formal methods is that they are far too narrow
to cover the full range of what people do with language. That was
also the primary criticism by Wittgenstein, with whom I strongly agree.
For more detail, see the following paper: (019)
Language Games, a Foundation for Semantics and Ontology (020)
That paper criticizes current methods of formal semantics as applied
to natural languages. For a presentation of my recommended alternative,
which we actually implemented in our VivoMind company, see (021)
Two Paradigms Are Better Than One,
And Multiple Paradigms Are Even Better (022)
And if you'd like to see some applications of these ideas to actual
problems that people were willing to pay money to solve, see the
following slides: (023)
Pursuing the Goal of Language Understanding (024)
AA> Strongly believe any standardization work involving ontology and
> semantic technology standards needs a deep fundamental research
> tested with effective knowledge and content systems and real world
> applications. (025)
I agree. That draft ISO standard merely addresses the conventions
for registering an ontology in a repository. That is useful, but
much more is needed. (026)
John Sowa (027)
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