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Re: [ontac-forum] Theories, Models, Reasoning, Language, and Truth

To: Chris Menzel <cmenzel@xxxxxxxx>, ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Thu, 15 Dec 2005 23:33:33 -0500
Message-id: <43A2439D.4090803@xxxxxxxxxxx>
Chris,    (01)

I certainly agree (and I believe Wittgenstein would also)
that the _Tractatus_ (TLP) was an elegant, tightly organized
little gem that presented a view of semantics that was
completely compatible with Tarski's model theory (actually,
more compatible than Tarski's own views of NL -- since T.
expressly limited his model theory to "formal languages".)    (02)

I also agree with W. that _Philosophical Investigations_ (PI)
was, comparatively speaking, a mess -- or as W. himself said,
"I should have liked to produce a good book.  This has not
come about, but the time is past in which I could improve it."    (03)

 > I can't think of a shred of evidence in TLP for the idea
 > that there is "one giant theory".    (04)

Start with Satz 1: "The world is everything that is the case."
That is equivalent, in Tarski's terms, to the claim that the
world is one giant model, which has a unique decomposition
into atomic objects that can be related by atomic sentences,
whose Boolean combinations assert all the possible "cases"
that make up the world.  That is certainly a "giant theory"
if there ever was one.    (05)

I agree that the picture theory of meaning was central to TLP
and that it is a decent elaboration of Aristotle's version.
For qualifications, see Section 7 of my theories paper:    (06)

    Theories, Models, Reasoning, Language, and Truth    (07)

 > TLP does contain a single, very influential theory of *meaning*,
 > viz., the "picture" theory, according to which a sentence has
 > meaning insofar as its internal structural corresponds in a
 > certain way to the structure of the objects denoted by its
 > referring terms.    (08)

The major problem, however, is that there is not just one true
picture of the world, but an infinite number of possible pictures
from different perspectives, at different levels of granularity,
for different purposes.  Take Jerry Hobbs' example of a road: a
map gives a one-dimensional picture for drivers who are planning
a trip, but the driver needs a 2-D picture for driving on it,
and the road builder definitely has a 3-D picture.    (09)

 > And his purpose was to circumscribe thereby the *limits* of
 > language, and in particular its powerlessness for expressing and
 > answering questions concerning what is in fact most important in
 > life, questions of life's meaning, questions about the good and
 > the beautiful.  Thus the towering, and ultimately tragic,
 > proposition with which W. closes the book: "Wovon man nicht
 > sprechen kann, darüber muß man schweigen!"    (010)

W. undoubtedly had multiple purposes, including a desire to complete
the project he and Russell had been discussing during the two years
before World War I.  The major part of TLP consists of W's version
of what Russell independently (and not as elegantly) published as
"Logical Atomism".    (011)

I agree that W. himself had much deeper thoughts, which he did not
(in 1920) believe could or should be expressed in language.  But
just before the conclusion, W. said "Everything that can be said,
can be said clearly" -- which essentially limits the useful subset
of language to just those sentences that express the giant theory.    (012)

In PI, W. presents example after example that cast doubt on (or
I would prefer to say "refute") every major Satz and most of the
minor ones in TLP.  W. refutes the claims that (a) there are atomic
objects, (b) any ordinary object (e.g., a chair) can be uniquely
analyzed into any unique set of elementary objects, (c) composite
sentences can be uniquely analyzed into Boolean combinations of
primitive sentences.  In PI, he also approves of unclear and
imprecise statements and many more kinds of sentences that are
not tied to some picture or some action (e.g., hoping, wishing,
expecting, praying, singing, joking, etc.).    (013)

 > For PI is a rejection, not of the idea of one giant theory, but
 > of the whole idea that meaning is representation.    (014)

W. did not use the word "representation" (or Vorstellung) in TLP,
and he did not reject in in PI.  I used the word "representation"
myself in the title of my KR book, but I now believe that word is
hopelessly misleading.  I now prefer to use Peirce's word "sign",
which I follow P. in applying to everything:  everything I see is
a sign, everything I feel is a sign, everything I think is a sign,
and everything I say is a sign.  It's all signs all the way down.    (015)

I don't claim that W. envisioned a lattice of theories, and given
the vehemence of his rejection of Waismann's attempt to summarize
his views, I wouldn't hold out much hope for his approval of my
version.  But I would claim that many of W's games -- including all
those that involve declarative language and queries and many that
involve commands -- could be mapped to theories of the lattice:    (016)

  1. Translate W's rules to the axioms (constraints) of a theory T.    (017)

  2. Every declarative sentence in that game would be compatible
     with T -- i.e., consistent with T and if not a theorem or axiom
     of T then an extension of T to a more specialized theory.    (018)

  3. Every question in that game would be a query that could be
     answered by methods similar to Prolog goals or SQL queries.    (019)

  4. Every command in that game could be interpreted as a request
     to start with theory T in the lattice and move by some sequence
     of theory revision operators to another theory T'.    (020)

Jerry Hobbs' examples would correspond to different and incompatible
theories about roads that would be suitable for different language
games that involve different ways of treating roads.    (021)

Many of W's remarks illustrate issues that are still open research
questions, but I believe that the subject matter of the various
domains could be characterized by theories in the lattice.  I would
handle intentional verbs (hoping, wishing, expecting, etc.) along
the lines of my laws paper:    (022)

    Laws, Facts, and Contexts    (023)

John    (024)

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