[From Bill Powers (980406.0748 MST)]
There is a difference between PCT and many other explanatory schemes that
tends to be left out of discussions. PCT is an example of _system
analysis_, whereas few other psychological theories belong in that category.
In system analysis, a system is thought of in terms of variables that
interact via functions. In a true system analysis, every variable is
accounted for in terms of other variables, or as an independent variable.
Nothing "just happens".
The force exerted by a spring on its attachment depends on -- is a function
of -- the length of the spring, for example. The form of the function is
Hooke's Law, stating that force is proportional to the difference between
actual length and some resting length characteristic of the spring. In a
system of interconnected springs (for example, a bedspring), the length of
each spring would be determined by the sum of forces from other springs,
and the force generated by each spring would depend on the amount by which
it is stretched or compressed by forces from other springs. Some of the
springs would be attached either to fixed objects (the frame of the
bedspring) or to movable ones outside the network of springs (weights
pressing down on the network of springs); there we would find forces and
positions that are independent of what goes on inside the network of
springs, and those would be the independent variables.
The first rule of system analysis is that _every variable must be accounted
for_. Each variable must be some function of a set of other variables,
unless it is an independent variable determined by arbitrary processes
outside the system. The second rule is that each effect of one variable on
another must be mediated by a function: that is, a rule or equation which
allows the value of a variable (other than an independent variable) to be
stated in terms of the values of all the other variables that affect it.
And the third rule is that the parameters of functions must either be fixed
by the physical nature of the system, or be determined by system variables
that must in turn be accounted for.
To pick a recent example, one might propose that "attention" has some kind
of influence on the behavior of a system. What criteria must be met to
allow "attention" into a system analysis?
First, we must specify what sort of thing attention is. Is it a physical
quantity, a signal, or a function? If it is none of those, it is not
physical, and can't be part of a system model. If a variable, it must be
either an independent variable determined by something outside the system,
or a dependent variable determined by a function relating it to all the
other variables that affect it. If a function, the form of the function
must be specified, if possible, along with the variables that are related
through the function, as well as the parameters of the function that are
either physically fixed or dependent on system variables.
Now consider the following proposal: "attention is what determines loop
gain in a control system." By our usual definitions, loop gain is the
product of all steady-state proportionality factors encountered in one trip
around a control loop. This tells us immediately that if loop gain is to be
determined or influenced by attention, it is the steady-state gain factor
in one or more of the functions in the loop that is affected. In other
words, a parameter of one or more functions is being affected by attention.
The influencing agency, then, must be some other variable of which the
parameter is a function. This tells us that attention is a physical
variable, the state of which must be accounted for in terms of other
physical variables; if outside the behaving system, physical quantities,
and if inside it, (neural) signals.
If we don't mean that attention is caused by external physical variables
through a physical law, or that it is simply a neural signal for which we
still have to account, the only remaining choice is to say that "attention"
is just another word for "loop gain," turning the original proposition into
an identity and making it meaningless. All that has been proposed is that
loop gain determines or influences loop gain. The basic rules of system
analysis end up showing that we have proposed a dormitive principle:
something defined only in terms of its effects, and then used as an
explanation of the effects.
PCT is fundamentally a system analysis. Every variable is accounted for,
every relationship among variables is represented as a function. There are
no loose ends. Even in HPCT at the highest level, there are no loose ends.
The highest reference signals must be either outputs of higher functions
(ruled out by "highest"), fixed physical properties of the comparator
function at that level, dependent on physical variables outside the
hierarchy, or zero. Those are the only choices granted under system analysis.
Of course in doing a system analysis of a system with many unknown parts
and parameters, we must guess at many of the functions and variables. But
guess we must, because to end up with a complete analysis we have to make
sure that no variable or function is unaccounted for, even if we must
conjecture to do the accounting. Unless the accounting is complete, it is
impossible to make any predictions from a system model. System analysis
forces us to make our assumptions explicit, because unless we do we don't
have any analysis.
All models in the hard sciences abide by these rules of system analysis.
Essentially no models in the psychological sciences do, other than PCT.