Re: (OPE-L) Re: Hume and constraint based theories

From: Ian Wright (ian_paul_wright@HOTMAIL.COM)
Date: Mon Nov 17 2003 - 16:56:41 EST

Paul wrote:
>Such constraints based theories are also commonplace in
>physics. Both quantum and classical mechanics have the
>same structure at the level of abstraction you define.
>One has to be careful when one suggests that cause is
>something other than constraints plus boundary conditions.

Jerry wrote:
>This implies that Marxian theories where there are
>sets of simultaneous equations are also not causal
>theories.  Do you agree with that inference?
>Put in the context of some of the many discussions
>that we on OPE-L have had over the years, does this
>mean that your conception of value is temporalist (rather
>than  'simultaneist')?

Ajit wrote:
>A theory of value is essentially a timeless
>problematic. A dynamic theory of value is bunk. A
>problem of asertaining the reasons for changes in the
>price of a commodity over a period of time is not a
>theory of value but rather an entirely different

Let me try to answer all these issues at once.
There are so many interesting and deep issues here that
I won't be able to say anything completely satisfying
or comprehensive. But I'll have a go.

Pure constraint-based theories break down when the
constraints are contradictory: they don't have a lot to
say in such situations. For example, consider tiling
a plane with a set of tessellating shapes. The contraints
are the set of shapes. For some sets of shapes,
the constraints are satisfiable, and lead to a solution
which tiles the plane. For other sets, the constraints
are unsatisfiable, and the plane cannot be tiled.
So we can develop a constraint-based theory that can
identify sets of shapes that are impossible to tile.
But consider that we are not engaged in logical possibilities
for tiling the plane, but engaged in modelling actual causal
occurrences that occur in historical time, for example,
modelling a child trying to tile the plane given a set of shapes
that happen to embody contradictory constraints.
Now the child has a strong desire to tile the plane, but
does not know our constraint-based theory, and therefore
does not know its desire is unrealisable. So what
happens? The pure constraint-based theory has
nothing to say about what happens dynamically, only
that a complete tiling of the plane will never occur.
The constraint-based theory does not model the mechanism
by which the constraints are satisfied, which in this case is
the child's strivings, so this kind of theory in principle
cannot tell us what will happen, cannot theorise the
unfolding dynamics. (Clearly, the child will try lots of
different combinations, may repeatedly try different
solutions in a cyclical manner, come nearer to tiling a
large part of the plane only to fail in some corner, retreat
and repeat and so on).

Now it seems to me that the status of Sraffa's theory is
analogous to the situation just described. It is a constraint-based
theory of the economy, which identifies logically possible
(and logically impossible) economic configurations. But
it has nothing to say about dynamics, because it does not
model the mechanisms that try to satisfy the constraints
(it does not model the child, it only models the problem).
In my view this is a severe limitation of the theory, as I'm
interested in modelling what actually happens over time.

But a further limitation of this theory, or at least a
limitation of how it has been used, is that it does not
admit of contradictory constraints, for example Marx's
aggregate equalities. I don't want to argue whether
Marx's equalities do or do not hold. Instead I want to
point out that some interpreters of Sraffa's theory
deny the existence of contradictory constraints in reality,
for no other reason, it seems to me at least, than
sets of overdetermined equations cannot be solved (or
they think they cannot be solved).

Now if there are economic mechanisms that are in
contradiction (or opposition) to each other, and
strive to attain mutually incompatible configurations
of the economy, then a constraint-based theory will
be unable to theorise the resultant dynamics, and instead
will simply (and correctly) state that the constraints
cannot be satisfied simultaneously (just like the tiles
and the child). But unfortunately some interpereters of
this theory go further and commit a logical blunder: that
because the constraints cannot be satisfied simultaneously
then the underlying mechanisms that generate those
incompatible constraints do not exist, or cannot exist
together. For example, denying the law of value
is an active mechanism, or denying that there is a tendency
for profits rates to equalise. The fallacy consists
in reducing transfactually active mechanisms in open
systems to the effects they generate in closed systems.
For example, reducing the mechanism of the law of value to
the definition of value as embodied labour, or reducing
the mechanism of the equalisation of profits to the
assumption of equal profit rates. This is a real blunder,
particularly as it seems to me that the interesting dynamic
questions can only arise in theories that admit of
contradictory tendencies in the economy that interact
over time.

Paul: I take your point. It depends on what we include
as constraints, and what we include as solution methods.
The matrix inversion solution methods that solve Sraffian
economies clearly do not correspond to the dynamics of
an evolving economy, dynamics that could be viewed as an
unfolding solution to the same set of constraints.
The difference is between a logico-deductive model and
a causal model, between modelling the problem and modelling
how the child solves the problem.

Jerry: In general I think that models that employ
simultaneous equations are not modelling dynamics, and
are therefore unlikely to get the causality right. But I
really don't want to deny the utility of static, simultaneous
modelling, just the kinds of conclusions that may validly
be drawn from them. I do think that the concept of
value can only be fully understood in a dynamic
context, so I suppose that makes me a temporalist.

Ajit: I think you are compartmentalising things that
are in causal interaction with each other. For example,
I have a computer model of a simple commodity
economy. The causal interaction between labour values
and prices results in an efficient allocation of social
labour time, at which point prices are proportional to
labour values. Irrespective of whether this is a good
or bad, relevant or irrelevant model for understanding
real economies, it is nonetheless a real dynamical system,
which can be an object of scientific study. It just
so happens that I try to understand it by employing
ordinary differential equations, not simultaneous equations.
This leads me to explain what happens dynamically in
terms of a theorem that states that labour values are
global attractors for prices. Does your philosophy rule
out the existence of the object I have constructed?
Does it rule out my explanation for its behaviour
over time? Or does it have nothing to say about it?
Presumably the causal interactions that are instantiated
when the model is run are a figment of my imagination?
I would really like to know if I've been labouring under
such a delusion!


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