John F. Sowa schrieb:
> Ken and Ingvar,
>
> I just wanted to make a supportive clarification of one point:
>
> KC> One can, I think, consider the truth not only of a statement, but
> > of a (the) mental model associated with the statement, as a statement
> > is typically an expression of a mental model of reality. The two (the
> > statement and the associated mental model it expresses) can be
> > considered themselves to be corresponding.
>
> IJ> I have used the term "statement" in such a way that a statement
> > contains both a sentence (as a pure graphical or oral sign) and
> > a proposition (mental or Platonic). I have no qualms about talk
> > of models corresponding or not corresponding to reality.
>
> I agree with both of those statements. But I would like to restate
> them in terms of propositions,  (01) 
That's very much o.k. as far as I am concerned.  (02)
> although the word 'proposition' is
> also considered to be in some need of clarification. The definition
> of proposition that I prefer  (03) 
Why do you write "prefer" without any further qualifications? Your 
definition fits only formal languages, but a notion of 'proposition' is 
just as needed in relation to natural languages.  (04)
best,
Ingvar  (05)
> is one I stated in
>
> http://www.jfsowa.com/logic/proposit.htm
>
> The basic idea is summarized in the abstract of that paper:
>
> Informally, different statements in different languages may mean
> "the same thing." Formally, that "thing," called a proposition,
> represents abstract, language-independent, semantic content.
> As an abstraction, a proposition has no physical embodiment that
> can be written or spoken. Only its statements in particular
> languages can be expressed as strings of symbols. To bring the
> informal notion of proposition within the scope of formal treatment,
> this paper proposes a formal definition: a proposition is defined
> as an equivalence class of sentences in some formal language L
> under some meaning-preserving translation (MPT) defined over the
> sentences of L. This paper defines a series of six MPTs f0,...,f5
> and recommends f4 as the most useful for most purposes.
>
> According to various traditions, the only things to which the words
> 'true' or 'false' can be applied are propositions or their statements
> in particular sentences. The notion of 'model' or 'mental model' is
> widely used in many different fields, and it is itself in some need
> of clarification.
>
> My preference is to associate each such model or mental model with
> a *theory* that characterizes the propositional content of the model
> (mental or not). Each theory is a conjunction of propositions (or
> their statements in some language). That conjunction is itself a
> large proposition (or sentence). Therefore, the terms 'true' or
> 'false' could be applied to the theory directly and indirectly to
> the model, which it characterizes.
>
> And by the way, this approach can accommodate models that are
> continuous geometrical or even dynamically evolving continuous
> geometrical structures. Such structures are routinely represented
> by theories in physics and engineering.
>
> John
>
>
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>  (06) 
-- 
Ingvar Johansson
IFOMIS, Saarland University
 home site: http://ifomis.org/
 personal home site:
 http://hem.passagen.se/ijohansson/index.html  (07)
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