On Jul 26, 2012, at 6:43 AM, John F Sowa wrote: (01)
> Pat,
>
>> My point was that the various *kinds* of context have nothing in common,
>> so that any suggested *general* logic of contexts will be vacuous.
>
> I agree with McCarthy that there are an open-ended number of different
> kinds of logics that can use different criteria and axioms for what
> is in a context and what can be said in it and about it.
>
> But this is similar to the discussions we had about models. As you
> know, I tend to drag in Peirce and his method of analysis by triads. (02)
Indeed. And as you know, I tend to stop listening at that point. (03)
> His general principle is that whenever you find two kinds of things
> that are related in some way, look for the missing third.
>
> For example, many people use Peirce's terms 'type' and 'token', but
> they don't realize that they're using only two parts of his triad:
>
> 1. A *mark* X is anything observable that has not been interpreted. (04)
Which is absolutely anything, right? So "mark" has been introduced as a word
meaning "anything whatsoever", but if Peirce had phrased this honestly everyone
would have seen immediately how vacuous and content-free it was, so in a grand
intellectual tradition, he invented a technical-sounding usage to make it seem
like it had some actual content. (05)
>
> 2. A *token* Y is some mark X that has been interpreted as an instance
> of some type Z.
>
> 3. A *type* Z is a pattern, rule, or specification for interpreting
> a mark X as a token Y of type Z. (06)
All this is completely and totally circular. I can declare that my left hand is
a mark, my right hand is a type which makes my left hand into a token, and the
rule is that they are both connected to the same body. This fits the
"definition" and is completely meaningless. (07)
>
> In general, the same mark may be interpreted in many different ways
> from different points of view for different purposes. (08)
Anything can be interpreted in any way for any reason. True, but does not pass
the grandmother test. (09)
> The type is
> a specification based on that purpose or point of view.
>
> For models, I suggested the following definition. I was inspired
> by Petri, who suggested a commonality among the various meanings of
> the word 'model'. I stated the commonality in a Peircean triad:
>
> 1. An *object* X is any physical thing, event, situation...
>
> 2. A *model* Y of X is a physical or mathematical construction that
> resembles X according to some specification Z.
>
> 3. A *specification* Z is a statement of the way X resembles Y.
> Z may be single word, such as "shape", or it may be a detailed
> list of statements in some language, linear or graphic.
>
> An engineering model has all three parts. A Tarski-style model has
> parts #2 and #3, (010)
A Tarskian model (of a set of sentences) is an interpretation of the set of
sentences which makes the sentences true. I still do not understand how this is
supposed to relate to the idea of a mathematical structure "resembling"
something, or what the role of the specification is supposed to be.. (011)
> but it might be used to describe something #1. (012)
Since Y is defined in terms of X and Z in terms of X and Y, I fail to see how
anything can have #2 and #3 without #1. (013)
>
> In fact, you could even have a Tarski-style model in which Y
> was contained in X. For example, a model (D,R) could be
> a domain D of elements that are identified with parts of the
> object X, and R could be a set of relations defined over D.
> The model would still have three components X, Y, and Z,
> but Z would specify how parts of X were selected for Y.
>
> Given this preamble, I would use the notion of model defined
> above to state a general definition of a context for a text:
>
> 1. A *text* X is a statement in some language, natural or artificial.
>
> 2. A *context* Y for X is a model (X', Y', Z') plus a mapping of
> of every referring expression in X to something in Y'. (014)
?? How does this even remotely resemble the ideas that context theorists
mention? Take a time interval as being an archetypical context, for example. In
what sense can a time interval be seen as a model of a set of sentences? More
generally, surely the whole point of invoking a "context" in the first place is
that it is supposed to be something that influences the meaning of a sentence
but is NOT described directly by the sentence, or even mentioned in the
sentence's syntax. And given this, how can it be seen as 'resembling' the
sentence? (Even if that idea can be made to work in the first place, which I
doubt.) (015)
>
> 3. An *interpretation* of X in terms of Y is the truth value of
> X as determined by the model Y and the mapping in point #2. (016)
An interpretation is a truth value? That seems just plain wrong. (017)
>
> This is an informal, but very general statement that relates
> contexts to models. I believe that it can be formalized in a way
> that is compatible with the wide range of applications that various
> people have claimed -- including John McCarthy. (018)
I very much doubt it, but am willing to look at the details when you have them
done. (019)
Pat (020)
>
> John
>
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