>I am going to break my own plea to drop the subject by asking Chris if both
>of these senses - the Model of an airplane, as well as a Tarskian Model,
>exhibit some "lossy"-ness?
>Model, now matter how it is used, seems to be some sort of extended
>implementation from an original (whether it is an abstraction, like a
>mathematical, computer, or physical model - or some instantiation of a
>series of axioms). In doing this extension, something is lost from the
>original (in the case of the model plane, it is reduced in size,
>functionality, and fidelity - in the case of a Tarskian model it is reduced
>from an ideal state explained in axioms to something that can change and
>lose some of its adherence to those axioms).
>But it might be better to not make this observation . . . (01)
In fact, in the case of the relationship between
a Tarskian 'model' (ie satisfying interpretation;
I will use scare quotes for this sense from now
on, when I am obliged to use it) and the axioms
it 'models', this is indeed backwards. The
'model' can be vastly more complicated than the
structure defined by the axioms themselves: it
can contain arbitrary amounts of irrelevant
'waste' structure which does not affect the truth
of the axioms. So for example the axioms might
require only a finite universe, but have 'models'
in which the universe is uncountably infinite.
Any possibility not actually ruled out by the
axioms explicitly is allowed to be present in
such a 'model'. On the other hand, in order to
satisfy the axioms, the 'model' must contain all
the structure that these axioms explicitly
describe, so in a very precise sense it cannot be
of lower fidelity than the axioms, but it can
well be of much higher fidelity. (03)
>ontolog-forum-bounces@xxxxxxxxxxxxxxxx wrote on 02/09/2007 02:01:57 PM:
>> On Feb 9, 2007, at 12:26 PM, Pat Hayes wrote:
>> > ...I think (as I said in
>> > an email response a few days ago) that the usages
>> > of "model" in "model theory" and "modelling"
>> > (respectively realization and prototype) are at
>> > best unrelated, and at worst almost directly
>> > opposite in meaning.
>> I guess I don't see that, Pat. Don't, say, a physical model of a
>> Boeing 777 and my Tarskian model of the faculty and administration at
>> Texas A&M both represent (hence, in some sense, "model") relevant
>> structural features of complex real-world things?
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