(I had vowed to not get involved in this endlessly-repeated discussion yet
again, but ...) (01)
There are, as people have noted, two different senses of the English word
"model" being used here. These really are different senses, and they do not
naturally fall under a single general heading. They have almost nothing in
common. One of them - the 'logical' usage of the word - is a technical use, and
just like many other cases where a word has been co-opted to serve in a
technical capacity , its technical meaning is essentially unrelated to its
pre-formal meaning. (Other examples include "field" , "modular" and "wreath" in
mathematics, which have nothing whatever to do with the English meanings of
those words.) (02)
The logical, technical, usage of "model" refers to a semantic interpretation of
a sentence which makes the sentence true: a satisfying interpretation. A
"model" in this sense *is* a satisfying intepretation of a sentence. In the
rest of this email I will use "satisfying interpretation" for this sense and
reserve the word "model" for its normal English sense, extended to such things
as engineering models, architectural models of buildings, etc.. (03)
Saying X is a model of Y implies that Y is some part of reality, and (as Petri,
quoted by John, says) that X bears some structural similarity to some aspect of
Y. In contrast, to say that X is a satisfying interpretation of Y implies that
Y is a set of sentences (*not* a part of reality) and X bears a particular
algebraic relationship to it which renders it true according to the semantic
rules of the language of Y. (This algebraic relationship is typically not a
"structural similarity" - which in algebra would be a homomorphism - but in
almost all cases is what is referred to as a Galois connection, which if
anything is a kind of complement to a homomorphism: the interpretations get
fewer as the sentences get larger.) (04)
There are cases of models where the model is itself language-like or symbolic.
A map or engineering diagram, or even a set of equations, can be called a
"model". At this point, however, one has to adjust the Petri definition: if the
model is a description, then the way it bears a 'structural similarity' to the
world it describes is not through its structure as a set of sentences, ie its
linguistic syntax, but rather through how that syntax is interpreted. The model
is accurate to the extent that what it says about the part-of-reality it
describes is in fact true. So we have come full circle: the modelling
"similarity" is the linguistic/semantic truth. But notice that (as often
happens when one goes in a circle) we have undergone a reversal of roles. The
"model" now is the sentences, not their interpretation: When a model is a
description, the X of [X models Y] is the Y of [X is a satisfying
interpretation of Y]. And, even more potentially confusing, the satisfying
interpretation of those sentences is not the model[1], but the part of the
reality it is a model of. So in this situation, where a model is a description
(in a language with a semantics), the logical sense of "model" and the
pre-formal, or engineering, sense of "model" are *exactly opposite* from one
another: X is an engineering model of Y just when Y is a logical "model" of X:
that is, just when Y is a (piece of reality which is) a satisfying
interpretation of X. (05)
Allowing models to be descriptions, and then using the logical terminology to
describe that situation, does more than simply muddle two meanings of "model",
it gets them exactly backwards from one another, an almost uniquely confusing
clash of usage. (06)
Pat (07)
[1] Logically trained readers, recall I am NOT using "model" in the semantic
sense here. (08)
On Jul 13, 2012, at 12:07 PM, John F Sowa wrote: (09)
> On 7/13/2012 12:43 PM, Burkett, William [USA] wrote:
>> A bit more to add to the discussion of "models", a "model"
>> may have several, likely overlapping, purposes...
>
> I agree.
>
> But all those purposes -- Inquisitive, Descriptive, Predictive,
> Informative, Prescriptive, and Representative -- are consistent
> with and can be supported by models that fit the basic definition:
>
> JFS
>> Petri... observed that when you say X is a model for Y, that means
>> X has some structural similarity Z to an important aspect of Y.
>
> The reason why people develop models is that they are usually easier
> to build, modify, and analyze than the real-world systems they model.
>
> That property makes them more convenient for all the above purposes.
>
> John
>
>
>
>
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