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Re: [ontolog-forum] open knowledge

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 24 Nov 2010 22:47:40 -0500
Message-id: <4CEDDC5C.9070906@xxxxxxxxxxx>
Chris and Leo,    (01)

Before responding to your comments, I'd like to add some comments
about Frege, Russell, Wittgenstein, et al.:    (02)

  1. I certainly agree that Frege was a far better logician with
     far more nuanced views than Russell.  But his major work
     was on the foundations of arithmetic.  His remarks about NLs
     were interesting, but I believe that compared to Peirce and
     Wittgenstein, they are limited and often misguided or false.    (03)

  2. Example:  Frege (1979) set out "to break the domination of the
     word over the human spirit by laying bare the misconceptions
     that through the use of language often almost unavoidably
     arise concerning the relations between concepts."  With that
     attitude, he was constitutionally incapable of correctly
     understanding how NLs relate to logic and the world.    (04)

  3. Wittgenstein's _Tractatus_ was an elegant little book, which led
     Tarski and others to their model-theoretic semantics for logic.
     Therefore, it made a historically important contribution to formal
     semantics for logics.  But for NLs, it was oversimplified to the
     point of being a parody of NL semantics, and its ontology was
     embarrassingly naive.    (05)

  4. The ontology of the Tractatus was close to Russell's logical
     atomism, which was also an embarrassment by today's standards.
     For the 1925 edition of the Principia, Russell added a long
     introduction along the lines of logical atomism.  But Whitehead
     rejected it completely.  He wrote a letter to _Mind_ saying that
     he had no part in producing the second edition, and he did not
     want his name associated with it.  I don't blame ANW for being
     disgusted with that introduction.    (06)

  5. I also agree with Wittgenstein himself, who apologized for the
     poorly structured _Philosophical Investigations_, but I agree
     even more strongly with his desire to correct the "grave errors"
     in his first book.    (07)

  6. But LW's contributions in his later philosophy include much
     more than just the PI.  One book, which I believe is essential
     for understanding the relationship between TLP and PI, is his
     transitional writings in the _Philosophical Remarks_.  See the
     end of this note for some points I wrote elsewhere.    (08)

  7. In short, TLP is an elegant introduction to model-theoretic
     semantics.  That makes it historically important, but it is
     not a significant contribution to modern theories of NL.
     But LW's later work (of which PI is a major part) is still
     a fundamental contribution to the ongoing research.  Anybody
     interested in NL semantics and NLP technology ignores it
     at their peril.    (09)

> Unfortunately he dug himself a much darker and deeper hole of his own.
> By my lights, W. was a lot closer to right in the Tractatus than he
> ever got in the Investigations.    (010)

I agree that TLP was closer to modern theories of model-theoretic
semantics, but model-theoretic semantics is a small part of NL.
And the term "much darker and deeper hole" is not a bad way to
characterize the complexity of NL semantics.  But if you really
want to do NL understanding, you can't avoid it.    (011)

> I find more substance in early Wittgenstein than later.    (012)

As I said to Chris, early W is just model-theoretic semantics.
And as LW himself said, PI is not as well written as TLP --
primarily because LW was plowing virgin territory whose
boundaries were (and still are) largely unknown.    (013)

> Personally, I think that without Frege and Russell, philosophy
> of language would have been delayed many years.    (014)

Please read the following article (and if that doesn't convince
you, please follow the references):    (015)

    Peirce's Contributions to the 21st Century    (016)

I believe that AI would be doing true NL understanding today
if Quine had devoted equal time to teaching Peirce and Frege.    (017)

> ... much of contemporary corpus-based computational linguistics tends
> to explicitly side with later W.; perhaps not surprisingly, I tend to
> disfavor such comp ling where e.g., morphology has become "stemming"
> and meaning becomes purely collocational].    (018)

The corpus-based work has *nothing* in common with what LW was doing.
In any case, I completely agree with your "disfavor" of what most
corpus-based work has degenerated to.  (I subscribe to Corpora List
because they sometimes have some useful stuff.  But at VivoMind,
we definitely do not do anything like typical "corpus linguistics".)    (019)

> I couldn't find the original posting of this message, nor the citation
> to Spectre's work that Ferenc provided. Do you have this?    (020)

In any case, I quoted the entire abstract of Spectre's talk (and the
talk itself was not posted):    (021)

http://philosophy.ceu.hu/events/2010-11-23/levi-spectre-open-university-of-israel-inference-and-fallible-knowledge    (022)

As I said in my note, I agree with the sentiments in the abstract,
but I don't believe that the ideas are new.    (023)

_______________________________________________________________________    (024)

Excerpt from Section 5 of http://www.jfsowa.com/pubs/rolelog.pdf    (025)

5. Steps Toward Formalization    (026)

In his _Philosophical Remarks_ from the transitional period of 1929-30, 
Wittgenstein analyzed some “minor” inconsistencies in the _Tractatus_. 
His analysis led to innovations that form a bridge between his early 
system and the far more flexible language games.  Shanker (1987) noted 
two new terms that are key to Wittgenstein’s transition:    (027)

  1. Satzsystem:  a system of sentences or propositions stated in
     a given syntax and vocabulary.    (028)

  2. Beweissystem:  a proof system that defines a logic for
     a Satzsystem.    (029)

Formally, the combination of a Satzsystem with a Beweissystem 
corresponds to what logicians call a theory — the deductive closure of a 
set of axioms. Informally, Wittgenstein’s remarks about Satzsysteme are 
compatible with his later discussions of language games. In 
conversations reported by Waismann (1979:48), Wittgenstein said that 
outside a Satzsystem, a word is like “a wheel turning idly.” Instead of 
a separate mapping of each proposition to reality, as in the Tractatus, 
the Satzsystem is mapped as a complete structure: “The Satzsystem is 
like a ruler (Maßstab) laid against reality. An entire system of 
propositions is now compared to reality, not a single proposition.” 
(Wittgenstein 1964, §82).    (030)

For a given logic (Beweissystem), each Satzsystem can be formalized as a 
theory that defines the ontology of a narrow subject. The multiplicity 
of Satzsysteme implies that any word that is used in more than one 
system will have a different sense in each. For natural languages, that 
principle is far more realistic than the monolithic logic and ontology 
of the Tractatus. Yet Wittgenstein illustrated his Philosophical Remarks 
primarily with mathematical examples.    (031)

That turning point, as Shanker called it, implies that the goal of a 
unified foundation for all of mathematics, as stated in the Principia 
Mathematica, is impossible. The implication alarmed Russell, who 
observed “The theories contained in this new work of Wittgenstein’s are 
novel, very original, and indubitably important. Whether they are true, 
I do not know. As a logician who likes simplicity, I should wish to 
think that they are not.”    (032)

 From the mid 1930s to the end of his life, Wittgenstein focused on 
language games as a more general basis for a theory of meaning. But he 
continued to teach and write on mathematical topics, and he compared 
language games to the multiple ways of using words such as number in 
mathematics:  “We can get a rough picture of [the variety of language 
games] from the changes in mathematics.” These remarks imply that 
Satzsysteme can be considered specialized language games.    (033)

The crucial addition for natural language is the intimate integration of 
language games with social activity and even the “form of life.” As 
Wittgenstein said in his notebooks, language is an “extension of 
primitive behavior. (For our language game is behavior.)” (Zettel, §545) 
The meaning of a word, a chess piece, or a mathematical symbol is its 
use in a game — a Sprachspiel or a Beweissystem.    (034)

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