[OPE-L:2450] Re: John and Jerry on Dynamical Systems

glevy@acnet.pratt.edu (glevy@acnet.pratt.edu)
Mon, 3 Jun 1996 11:11:03 -0700

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---------- Forwarded message ----------
Date: 03 Jun 96 13:09:26 EDT
From: Alan Freeman <100042.617@CompuServe.COM>
To: "INTERNET:glevy@acnet.pratt.edu" <glevy@acnet.pratt.edu>
Subject: Re: John and Jerry on Dynamical Systems

Jerry; could you forward this when appropriate? Alan

I'm happy to reply to Jerry's request for clarification in post
#2437 and John's in #2436. Can I apologise in advance for being
both telegraphic and longwinded in the same post. This is a
complex issue.

To avoid setting off alarms, I am not trying to saddle Marx
with a new terminology; the only way to understand Marx is read
what he wrote.

Concepts such as paradigm, model, axiom system are for me a way
of discussing systematically the relation which theories bear
to each other.

My historical judgement on the current state of economic theory
is that its principal deficiency is the way it is discussed and
used. In this century, due to the material dominance of capital
in the sphere of intellectual production, it has gone backward.
The first step in the creation of new theory is the adequate
reappropriation of the old theory. This in turn demands an
adequate mode of theoretical activity, which capital has
displaced by its mode of organising the intellectuals.

Conversely, now that the working class has become a universal
class at least in itself if not for itself, progress in theory
requires not brilliant leaders or inspired individuals but
disciplined collective activity.

This runs directly counter to the academic tradition of setting
up shop as a thinker and sounding off until someone listens. It
can only be established in an actual practical, as well as
theoretical struggle, against this tradition.

As opposed to this kiosk model of thinking we require what I
would call a co-op model; a mode of working together which
prioritises engagement and mutual understanding, but not at the
expense of clarity. At this time we need to know not just the
relation of each theory to reality, but to every other theory.
The immediate practical task is not merely (or even mainly) to
decide whether Paul C, Gil or Andrew - not to mention Marx,
Keynes or Friedman - are right or wrong but to define as
clearly as possible what they *think*, and what conclusions
follow from their theories.

Since we must do it, we must do it well. We need to categorise
theories and find where they agree and disagree.

Thus, at a purely descriptive level, Gil, Paul and Allin use
vertically-integrated labour embodied magnitudes as the measure
of value whereas Bruce, Fred, Andrew, Ted, Alan and John do
not; Alan, Ted, Simon, Andrew and Duncan think the value of
labour power is measured by the value of the money wage but
Paul and Allin do not; Bruce, Fred, Andrew, Ted, Alan, John
think the value of constant capital is measured by the value of
the money paid for it, Duncan is considering this possibility
and so is Simon; Alan, Andrew, Ted, John and I think Duncan
consider the value of fixed constant capital is represented by
its historic cost whereas Bruce, Fred, Simon, Paul, Allin, and
Gil do not.

First, note this tells us nothing about the the people
concerned. It is a property of the theories they hold.

But these coincidences express more than a purely accidental
relation. Why do Andrew, Ted and Alan conclude that Okishio is
wrong, and not Bruce, Fred or Paul? After all, Paul and Fred
disagree on many other things. Bruce and Fred consider constant
capital in its money form, and Paul does not.

I would say, because Andrew, Ted and Alan evaluate capital not
only as money, but at historic cost. Thus, their view on the
rate of profit is deducible from their theories and follows
from a definite, identifiable postulate. It is a property of
these theories. There is a systematic relation between the
theories involved, which has a structure. We cannot just remain
at the level of saying that we agree on A but not B. We also
have to locate and if we can, mutually agree, the assumptions
which lead to these conclusions.

The description and classification of this structure is a
legitimate and necessary form of knowledge, above all because
we need a combination of both understanding and clarity.

I am not saying we should not study the real world; I am saying
that at those times where many theories coexist, this prior
knowledge, of the relation between them, becomes an essential
prerequisite for studying the real world.

I think the concept of a paradigm is of use in facing this
task. It arises from a study of how in practice, in the history
of thought, theories have replaced other theories. Kuhn's
studies show that the Popperian theoretical ideal, according to
which each theory is tested separately against the facts, does
not actually happen.

Kuhn classifies scientific activity into two types: 'normal'
science when a common set of concepts and procedures (including
measurement procedures) regulate all investigations, and
'abnormal' science when rival theories struggle for hegemony.
Rival models within a given paradigm can be tested by the
methods of normal science only because there is agreement on
these regulating methods and procedures, including empirical
methods. Rival models between paradigms cannot be so tested
because the prescribed empirical method is precisely what
differentiates the theories.

Moreover any given paradigm does not, contrary to the Popperian
ideal, commit suicide when it comes against a single fact that
it cannot explain. All paradigms actually tolerate many
unexplained facts. They give way only when another paradigm
comes along which explains these unexplained facts. Practical
science does not therefore consist of simply testing hypotheses
but of a struggle for hegemony between rival paradigms.

Political economy cannot hope to do 'normal' science. This is
the deep meaning of the eleventh thesis. Bourgeois society
cannot concede hegemony to a theory which explains it must die,
before it actually dies. 'Positive' economics is a logical
contradiction. For this reason Kuhn's study of 'abnormal'
science refers to the 'normal' state of economics; a struggle
for hegemony between rival theories.

There is no normal economic science or rather, it cannot be a
normal science in the sense of the physical sciences before
capitalism is overturned (whether it can be afterwards, we do
not yet know). Those theories which serve the interests of the
capitalist class cannot stabilise because their apologetic
goals doom them to ignore fundamental features of reality which
impose themselves at all the most awkward moments. But
conversely those theories which defend working class interests
cannot 'win' but exist only as embryos of the new forms of
thought which only a new society might fully develop.

The former is thus in a permanent state of disintegration and
reconstitution, while the latter is engaged in a constant
struggle for survival. The thing we need to understand is that
this struggle for survival is the only practical means of
advance under present conditions. The debate between theories
therefore *is* the principal means, for the whole of the
capitalist epoch, by which working class theories constitutes
themselves as independent. Debate is not a luxury but a
practical necessity. Every time in the history of our class
when debates stop, theory stops too.

This makes the study of theory *as such* a necessary aspect of
economic study. Philosophy as such is necessary to economics.
It does not reduce to pure scholasticism. Moreover it does not
consist of the study of pure, idealised or apostasised ideas,
but of actual ideas, the real things which real people think.
That is, each other's theories.

In my view Kuhn's idea of paradigm (or Bachelard's of
Problematic), goes beyond social observation. The mortal blow
he dealt Popperianism was to show that science is actual and
social, not ideal and individual. He went even further and
identified the actual process of struggle, which consists not
in the production and testing of hypotheses but of a struggle
between rival theories. An indispensible part of this struggle
consists in identifying the relations *between* these theories,
*in order* to devise practical tests of their actuality.

This idea goes back a long way and in this sense I think there
is a connection with Marx. In my view the most successful and
productive thinkers in history were precisely those whose mode
of being consisted of the most acute and heightened sense of
their social relation to other thinkers.

Marx wrote Capital after an exhaustive survey of current
economic thought, as an intervention into that body of thought.
Hegel never claimed to create a new philosophy but sought to
summarise and codify existing philosophy. The common feature -
the real 'secret' of their method - is that they considered
their own ideas in relation to all other ideas.

I think that anyone who sets out to create a 'system' of
thought independent of any relation to existing thought, no
matter how strong their claim to use Marx's or Hegel's method,
simply hasn't understood the problem, never mind the answer.
This very procedure negates the main finding of the materialist
method, which is that thought itself originates in the material
conditions of life, and therefore the study of actually-
existing thought is indissociable from the study of material

I reject, however, the opposite conclusion that can be drawn
from the existence of many contradictory theories, that all
such theories are equally valid and we can conceive of no
systematic method for testing one theory against another. This
eliminates the activity of debate just as effectively as
suppression. It constitutes a form of peaceful class
coexistence. Nothing ever becomes clear or definite, there is
no critical engagement, everything just floats on a Sargasso
Sea or as Marx puts it 'an eclectic pap' of ideas.

Therefore I think we need *procedures* for debate, for
estimating and comparing theories. And here I think that, among
many other useful procedures, the axiomatic method is helpful.

First and foremost the axiomatic method is a helpful way of
organising debate. All it does is categorise the assumptions of
each theory, so we can see where their starting point is common
and where it is not. It was for this purpose, after all, that
it was first introduced by the Greeks - with whose work as St
Croix points out, Marx was extremely familiar.

A second point is that by understanding what the axiomatic
method consists of we can escape the commonsense but false idea
that the purpose and function of logic is to establish truth.
The great majority of readings of Volume I seem to me prey to
this idea; they treat it as if it were a logical deduction of
value. It isn't, as has been remarked on OPE. Value is deduced
by Marx from observed reality, not from theoretical
speculation. The function of theoretical speculation is to
order the categories derived from reality in a systematic
manner so that when used for practical purposes, errors of
circularity, contradiction or petitio principii cannot be

And therefore third, there is here too a connection with Marx.
Any practical mathematician recognises the structure of Volume
I. No-one who has read a work in abstract universal algebra or
projective geometry can fail to notice the striking similarity
between Marx's logical procedure and the method of laying out
categories, axioms, systems and postulates adopted in these
works. One of the problems in the understanding of formal logic
which has come down to us from the early part of this century,
is that many people do not realise just how dialectical modern
mathematics has become when *properly* practiced.

This is not to deny that *bad* mathematics is every bit as
awful as it ever was. Since there is very little other
mathematics in economic theory, it is sad but not surprising
that many honest people wish to set up a counterposition
between Marx and mathematics. I can understand this but would
plead that they consider whether what is usually presented as
mathematics really deserves the title. It is certainly not like
anything I was ever taught.

Thus in promoting procedures such as axiomatisation I wish to
suggest that such systematic methods not only exist, but were
well-known to Marx and have been geatly developed by modern

A fourth point is this: there is a tendency to throw logic
around in debates and even construct entire arguments about
'what Marx must have thought' that are, quite simply, bad
logic: failing to quantify predicates, failing to distinguish
constructive proofs from reductio ad absurdam, and so on and so
on. Indeed it is becoming clear there is a gigantic such error
in Steedman, who nails his colours to the mast of arguments in
logic. But we cannot hope to set this right, unless we use
logic properly ourselves.

One of the aspects of economics we need to get away from is its
tendency to borrow badly. Academic economics has the habit and
reputation of soiling everything it lays its hands on and we
should be very careful not to take responsibility for this. If
we are going to import concepts then we first should understand
how they work in their native environment. So, if we're going
to use formal logic then let's use it properly.

I'm not trying to impose this on anyone. If Mike W, for
example, were to say to me 'the whole idea of model is useless
and I don't think we should use it' then my reaction would be
'fair enough, if it offends, I won't use it in company'.

I am only saying to those who *do* choose to use arguments in
logic that this should be done properly. If we use formal
logic, we should use good formal logic, or at least the best

This takes me back to one of the most important, but least
understood issues in logic, which is the following: the subject
of logic is not the structure of *truth* but the structure of

This allows me neatly to answer John E's question because it
illustrates this point quite well. John asks me, in effect,
what grounds I have to believe axiom (6).

My answer to this is at this point I have no answer because it
is not relevant to the question I am trying to pose. Axiom (6)
is not at this point intended as a statement about what is
true. It is intended as a means of separating, without
judgement, one type of theory from another, just as the axiom
of distributivity distinguishes an algebraic ring from an
algebraic field, or the axiom of parallelism distinguishes
Euclidean from non-Euclidean geometries. Some people believe
this axiom to be true, some believe it to be false. One
conclusion follows from one belief, another conclusion follows
from the other belief. We can always, of course, test these
beliefs and the conclusions against reality but *independent*
of these tests, the logical relation between the beliefs has to
be established if we are to achieve mutual understanding and

For me it is just as important to understand what someone
thinks, as to decide whether they are right. The first thing I
always try to do when I meet a new theorist or theory is to
find out what they believe, and why. I can't understand why so
many people consider this a secondary, tedious or irrelevant

My point here is not whether axiom (6) is wrong or right. My
point is that if we want to understand what differentiates
different theories, this axiom tells us. Moreover, once we know
this is the difference between them, we can logically predict
the answers they will give to a vast range of questions, simply
exploring the deductions which follow from this one axiom. A
Post-Keynesian, for example, who does not accept this axiom,
will assert that a capitalist can impose an arbitrary markup. A
Marxist, who does not, will deny it. A simultaneist will give
one set of answers, and sequentialists another set of answers,
to the question 'does the profit rate fall?' A dualist will
give one set of answers, and a nondualist another set of
answers, to the question 'is the sum of values equal to the sum
of prices and the sum of profits equal to the sum of surplus-

Rather than remaining at the purely descriptive level of
listing these answers, which often leads to simply going round
and round in circles, my general approach is identify the basic
postulates from which these answers flow so that we can clearly
and unambiguously state what distinguishes the two theories

*Then* we can set about devising tests to discriminate between
them. But how can we discriminate between them, if we do not
know firmly where they definitely and necessarily give
different answers?

If we study carefully the actual discussions that have been
taking place on OPE, we see that most discussions do not
consist of X saying 'the world is like this' and Y saying 'no,
the world is like that'. They consist of X saying 'I think Z
implies, believes, or claims the world is like this' and Y
saying, 'no, 'Z does not believe, imply, or claim this.'

In some cases X is the same as Z in these dialogues and in some
cases Z is the same as Y. In many cases Z is Marx. In some
cases Z is the Statistical Office. But the essential structure
of all such discussions is what, in Aristotle and also in
modern mathematics, is known as modal. In logic, modal
statements refer to belief, necessity, probability and
possibility, rather than directly to truth.

The point of departure of an axiom system is a set of
statements of belief. The question of whether this belief is
accurate or justified does not enter into it. But what can be
asked is '*If* this is what you believe, what else must you
believe? What follows from your beliefs?' This kind of
discussion is often confused with a discussion about what is
true. But it is not the same thing. I can perfectly
legitimately enquire into, and discuss with, another person
about what they believe, or what follows from their theory,
without having to agree with that theory.

Now, this is exactly the kind of discussion we have with each
other all the time. We enquire into the presuppositions,
beliefs and conclusions, of the theories we each hold. This is
an exercise in logic, whose purpose is not the discovery of
truth - a common misconception. The function of logic is to
assess the consequences of belief. There is no such thing as a
truth that can be established purely in logic. On this I am a
hundred percent against Kant. There are no synthetic a priori

I think that logic has often been wrongly used in economic
discussion as a means of establishing truth. Part of the reason
is that apologetic and academic political economy has so little
other connection with reality that, like the Jesuits, there is
little left to working economists but the deployment of reason
for the endorsement of torture. But in fact, we should treat
logical discussions for exactly what they are, which is a
systematic way of examining the structure of thought.