On 29.10.2012 20:44 meekerdb said the following:
On 10/29/2012 11:33 AM, Evgenii Rudnyi wrote:
On 29.10.2012 19:21 meekerdb said the following:
On 10/29/2012 10:21 AM, Evgenii Rudnyi wrote:
Some more quotes from From Scientific Representation: Paradoxes
of Perspective by Bas C Van Fraassen.
p. 45 "Agreed, we cannot demonstrate that in principle, as a
matter of logic, mathematical modeling must inevitably be a
distortion of what is modeled, although models actually
constructed cannot have perfection reachable in principle. But
on the other hand, the conviction that perfect modeling is
possible in principle - what Paul Teller calls the "perfect
model model" - does not have an a priori justification
p. 83 "Suppose now that science gives us a model which
putatively represents the world in full detail. Suppose even we
believe that this is so. Suppose we regard ourselves as knowing
that it is so. Then still, before we can go on to use that
model, to make predictions and build bridges, we must locate
ourselves with respect to that model.
If the model is complete it must already include us - as well as
what we will think about it and do with it. But then this will
run into Godelian incompleteness. If it is true it will be
unprovable within the model.
The question would be how it should be done practically. Say let us
imagine that such a model is the M-theory (I am still impressed by
Grand Design by Hawking). How do I find myself in the M-theory?
In practice, which I'm sure you're familiar with, we don't 'locate
ourselves in the model'. The model is in the objective world that we
share with others who are also not in the model. An engineer
In this chapter, Van Fraassen has considered a map as a model for a
typical model. A map is in the objective world, as well as a scientific
model, but to use the map one has to find out where on the map he/she is
located. I hope that you agree with that.
Yet, now this process, located oneself on a map, could be extended to
other scientific models. For example to those that engineers employ in
their practice. An engineer has a scientific model on one hand and real
things on the other hand. Similarly it is necessary to relate a model
and reality and one needs a human being to achieve this goal.
Along this line of thought we come to a "perfect model model" that also
is in the objective world, as for example the M-theory. The question
designing an airliner considers the airliner carrying other people,
but he doesn't model them completely - only their weight, size, use
of the restrooms, entertainment, etc. He doesn't try to model their
inner thoughts unrelated to the airliner. So a model, to be useful,
cannot be complete because part of its usefulness is that it can be
communicated and must be 3p, as Bruno would say. That's not to say
that someone's inner thoughts cannot be in some model (the often are
in novels), but only that they can't be in that same person's model;
just like a Godel sentence unprovable in one system can be provable
in some other axiom system.
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