Chris M. and Pat, (01)
As I said in a previous note, I seriously doubt that any legal
system (including the rules and regulations of Texas A & M)
are perfectly accurate statements of what actually happens. (02)
CM> However, many physical situations involve, *at a desired level
> of granularity*, NO vagueness and NO intractable complexity at
> all, as in my previous example involving faculty and administrators
> Texas A&M. (03)
Following is the relevant quotation from my earlier note: (04)
5. Legal systems of any kind (which include the administrative
structure of TAMU) have the nature of artifacts, which are
specified by a finite set of laws and therefore capable,
in principle, of being modeled precisely. (05)
6. But humanly defined laws are rarely run through a theorem
prover to check consistency. Even those that happen to be
consistent rarely anticipate all possible interactions with
natural phenomena (floods, earthquakes, etc.), all other
social institutions (governmental and nongovernmental), and
human variations and foibles (e.g., a mathematician like
Erdos, who would be a prize that any university would bend
the rules to hire). (06)
Do you really and truly believe (a) that the Texas A & M rules
are 100% consistent among themselves and with the relevant laws
of Texas & the US and (b) that every administrator observes them
to the letter without the slightest exception? (07)
I have no data one way or the other, and I'll take your word for it.
But in any case, my diagram does not preclude the possibility that
the level of approximation is a continuum with perfect at one extreme. (08)
PH> Tarskian models/interpretations do not (better, need not) 'model'
> the world in this sense, of being a simplified alternative version
> of the world. They can be actually PART of the world, constructed
> from real things and real stuff. (09)
How do you do that construction? How do you identify the individuals?
Perhaps by labeling the parts or by specifying their coordinates.
In that case, the model consists of those labels, which can never
represent more than a tiny fraction of what actually exists in the
selected chunk of reality. (010)
PH> You are muddling up conceptual analysis, with questions of
> empirical verification for certain kinds of physical theory. (011)
I am making explicit what some armchair philosophers prefer to
sweep under the rug. Philosophers like to compartmentalize
ontology, epistemology, and philosophy of science in different
textbooks and courses. But when you're designing a robot,
you have to face the questions of how that robot relates its
mental (or computerized) models to its sensory inputs and
motor outputs. You can't just declare that certain things
in a crowd scene magically become part of its internal models. (012)
PH> Its meaning in "model theory" aka Tarskian semantics is almost
> exactly the opposite or dual of its sense as in "to make a model
> of something". A Tarskian model/interpretation is a called a
> model of the SENTENCES it interprets, not a 'model' or reality
> in the sense of being a simplified artifact representing something
> more complicated, as in 'model aircraft'. (013)
I agree that the source of the information is different, but the
result is equivalent. When a child builds a model airplane, the
goal is to model an existing physical object. But when Boeing built
a model of the 777 in their computer, they began with a specification
in math & logic (SQL, etc.) from which they generated pictures and
templates of how the nonexistent airplane would look. After they
constructed physical embodiments of the model, the result fit
very nicely into my tripartite diagram. (014)
PH> I maintain that this diagram is SERIOUSLY misleading, suggesting
> as it does that there is some kind of categorical distinction or
> difference between the Tarski model/interpretation and the Real World. (015)
I truly believe that there is a major categorical distinction between
a mathematical structure and a physical object. The former is abstract,
has zero mass, and does not have a location in space-time. The latter
most definitely has mass and location. Furthermore, there is only a
homomorphism, not an isomorphism between them, since the physical object
has much more detail than any model we are capable of specifying. (016)
PH> Why did you choose to represent the [model] as an unlabeled graph?
> This is tendentious. I could just as well use a photograph of a crowd
> scene, or a view through a telescope, as an illustration of a
> relational structure. (017)
I used a graph because it's a clearer illustration than a table, and
the reason why I omitted the labels is that there wasn't enough space
to write them in (although I personally prefer labeled graphs). (018)
A crowd scene or a view of anything physical is not a relational
structure until you identify the individuals and the relations.
The number of individuals depends on your preferred model. Do you
consider the individuals in a crowd to be the people in it? What
about body parts, such as hands and noses? And do you want to identify
body parts by their English labels or by their Russian labels, which
consider the "ruka" to include the hand and forearm? (019)
PH> I bet I can beat you at this one if we need to settle who is
> misrepresenting model theory. (020)
I only said there was a bimodal distribution. I didn't say how many
people are in each category. Unfortunately, two of my supporters are
dead: Jon Barwise and Joseph Goguen. (021)
John (022)
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