A. Alparslan wrote:
> Dear Barry,
>
> First I ask to excuse my English.
If you'll excuse mine!
> I am neither a sociologist nor I am well-experienced with
> simulation. But I have some questions/remarks concerning your note:
>
> You wrote:
> > So, if it is possible to have multiple, mutually contradictory
> > simulations "from" (or inspired by or "built on top of") the same
> > theory, then such a theory is logically worthless. (Remember
> > elementary logic? If you can derive a contradiction from a given
> > argument, then that argument is invalid.
> (1) I do not understand your example of elementary logic. Is a
> simulation a (logical) derivation of a theory: theory -> simulation?
No, not necessarily. I was making the point that *if* a simulation is to
have any bearing on a theory (such as revealing inconsistencies, or
supporting the theory by testing the simulation), *then* it must be
logically consistent with the theory. That could mean the simulation is
derived from the theory (such as a component or subset of the theory),
or that it is logically equivalent to the theory. In my argument, I
stated that this is virtually never the case when simulations are
inspired by discursive theories.
> If yes, then I do not understand the introduction of "gap-filling"
> axioms (see below)!
> Either the simulation is a logical consequence of the theory and
> is a theorem of this theory. Then you can use your example from
> elementary logic: "If you can derive a contradiction from a given
> set of axioms, then that axioms are invalid."
> Or it is an entity which is something like a theory with its
> "own" axioms and theorems:
>
> theory: axioms(T) -> theorems(T)
>
> sim(1): axioms(sim(1)) -> theorems(sim(1))
> .
> sim(n): axioms(sim(n)) -> theorems(sim(n))
Yes, when the simulation and theory do not conform logically, then the
simulation (to use your words) "is something like a theory with its
'own' axioms and theorems.
> (2) What's about the relationship between the axioms of T and
> sim(1).sim(n)?
The relationship may be logically consistent or not, but whether or not
they are so has the sort of consequences I mentioned.
> You wrote:
> > How does this relate to the original theory? At best,
> > VERY loosely. The simulation introduces functional relationships
> > that the theory does not specify, and usually specifies gap-filling
> > assumptions that the theory never made.
>
> and:
>
> > The simulation introduces functional relationships that
> > the theory does not specify, and usually specifies gap-filling
> > assumptions that the theory never made. This breaks the logical
> > connection between theory and simulation. They become distinct
> > logical entities. That there may be some shared terms, and perhaps
> > some correspondence in the directions of some specified functional
> > relationships, still is insufficient to establish a consistent
> > logical connection between the theory and simulation.
> In the philosophy of science there are several attempts to
> clarify the relationship between theories and models (here:
simulation). ...
<material deleted>
Thanks very much for the references. I'll read them, and hopefully they
will be clearer and more comprehensive than my little analysis! :) I
don't fully understand the meaning of the terms you quoted, but at
first-read the argument does seem consistent with my understanding.
Barry
=== === === === === ===
Barry Markovsky
Dept. of Sociology
University of South Carolina
Columbia, SC 29208
(803) 777-0804
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