Ken and Ingvar, (01)
I just wanted to make a supportive clarification of one point: (02)
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. (03)
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. (04)
I agree with both of those statements. But I would like to restate
them in terms of propositions, although the word 'proposition' is
also considered to be in some need of clarification. The definition
of proposition that I prefer is one I stated in (05)
http://www.jfsowa.com/logic/proposit.htm (06)
The basic idea is summarized in the abstract of that paper: (07)
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. (08)
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. (09)
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. (010)
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. (011)
John (012)
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