Ceteris paribus

glevy at acnet.pratt.edu glevy at acnet.pratt.edu
Thu Jul 27 19:34:19 MDT 1995

I'm back.  I just finished reading (i.e. skimming) the 637 messages that
I received in the last two weeks.

Before I left, I sent a post responding to Lisa that referred to the
ceteris paribus (other things being equal) assumption in Marx.  I am not
entirely satisfied with what I wrote then and want to expand upon this
theme now. This discussion relates in some ways to the threads on logic
and dialectics that have been discussed in recent days by Hans Despain,
Juan Inigo, Ralph D., Rakesh, Chris B. and others.  As I am rather tired
and am  sweltering from the heat and humidity in NYC, I will try to make
this  post rather brief with the understanding that others may have some
things that they wish to add (or dispute).

Firstly, I don't recall that Marx ever used the words "ceteris paribus"
in _Capital_, although, I haven't attempted to review his writings on
political economy for these words. Yet, there can be no doubt that he
used this assumption, called by other names, in many sections of _Capital_.
For instance, in the reproduction schemes in Book 2, the general law of
capitalist accumulation in Book 1, etc.  The question that I will pose in
this post concerns how Marx used this assumption within the context of
his overall methodology.

To express the issue simply: I believe that Marx used *both* formal and
dialectical logic in _Capital_ and that the c.p. assumption is part of
his formal analysis. As an example:  Marx stated equilibrium conditions
for both simple and extended reproduction in Book 2 using the "other
things being equal" assumption. That analysis was intended in part to
counter J.B. Say (and Say's Law) to show the "abstract formal possibility
of crisis" (a paraphrase, I believe).  The *actual* way in which
capitalist crises are manifested could not be developed at that level of
abstraction or with the c.p. assumption.  Similarly, Marx's explanation of
the general law of capitalist accumulation was intended in part to
counter Malthus's theories on overpopulation.  Marx made it clear that
the general law of capitalist accumulation was contingent upon a number
of variables that had not been addressed yet in Book 1.

How then are we to understand Marx's use of the c.p. assumption?

Firstly, it was intended as a simplifying assumption and was a necessary
step in the process of abstraction.  By first developing formal
relationships, Marx could then go on to show how the variables that he
was analyzing are dynamically related (more later).

Secondly, (as can be seen from the above) Marx's use of this assumption
was often intended as a critique of political economy.  It has to be
remembered that Marx not only intended to show the "laws of motion" of
capital but also to critique the writings of other political economists
(such as Ricardo, Quesnay, J. and J.S. Mill, Say, Malthus, etc).  By
using the c.p. assumption Marx was able to differentiate his theory from
others and to point out logical inconsistencies and shortcomings in
others' analyses.  Yet, this *formal* analysis was not intended as a
complete analysis or critique but only as a logical *step* towards
"dialectical investigations" (for lack of a better term).

Thirdly, Marx's formal analysis was supplemented by his dialectical *and*
materialist method. Let me give a couple of examples.  In Book 1, Marx
presents the concepts of abstract labor and the organic composition of
capital.  Concerning abstract labor, Marx took great pains to explain
that this was *not only* an abstract concept but was a mirror or
reflection of an actual historical process.  In fact, in many places in
_Capital_ Marx took pains to give many, many historical examples of how
the abstract processes that he was explaining manifested themselves in
reality.  In so doing, he was clearly trying to explain that his analysis
was *not* entirely logical but was rooted in material/historical reality.
It was a combination of formal, historical and dialectical analysis which
could  not be *entirely* grasped by formal analysis.  Later in Book 1, Marx
distinguishes between the technical composition of capital(TCC), the value
composition of capital(VCC) *and* the organic composition of capital(OCC).
The organic composition of capital was said to reflect changes in the
technical composition of capital, that is, whereas the TCC and the VCC
are formally distinct, the OCC is a dialectical relation. It *appears*
that the TCC and the VCC are formally separable but they are united by
the processes of accumulation and centralization which
bring about changes in the composition of capital.  This is explained
both as a dialectical relation and a mirror of social reality.

Another example: in Book 3 Marx states the "law of the tendency for the
general rate of profit to decline" (which I prefer to abbreviate as
LTGRPD rather than FRP).   It has often been argued by Neo-Ricardians
and others that the LTGRPD is in error because of unwarranted assumptions
on Marx's part (for instance, they claim that the LTGRPD is dependent on
the assumptions that the OCC will rise and the rate of surplus value is
constant).  As I recall, Marx stated the LTGRPD *first* be presenting it
in *formal* terms, i.e. that general rate of profit will fall if the
organic composition of capital rises, *other things being equal* (ceteris
paribus). The c.p. assumption in this case holds the value of the
elements of constant capital and the rate of exploitation and other
variables constant.  This is what the Neo-Ricardians most frequently take
exception to. *But*, Marx then went on to list the "counteracting
influences" to the "law" and to explain that although, for instance, an
increase in the rate of surplus value causes an increase in the general
rate of profit in formal terms, the *actual* mechanism that causes an
increase in the rate of surplus value also brings about the LTGRPD. Thus,
while it *appears* that changes in the rate of surplus value counteract
the decline in the general rate of profit, these two categories (and
others) are dialectically related.  This is a logical process which is
very difficult to capture in formal, mathamatical terms precisely because
it posits a dialectical relation which can not be expressed adequately
with the tools of formal logic, including the c.p. assumption.

Thus, Marx's use of the c.p. assumption is part of his *formal*
analysis.  Yet, as we have seen, there is both formal and dialectical
logic in _Capital_.  Marx attempts to show not only what is formally
logical but the contradictory ways in which those categories relate.  In
some case (e.g. critique of Say's Law and reproduction schemes), Marx
used formal logic to discuss the "abstract formal" possibility of
crisis.  Using dialectical logic, he was able to explain in Book 3 that
what *seemed* inconsistent and illogical from the standpoint of formal
logic was actually a dialectical relation.  So, Marx uses the c.p.
assumption as a step in his analysis but the greater insights and
relations are revealed dialectically.

I trust that the above (which I make no claim to be a complete analysis
of this subject) will spurn further discussion ... and that is my intent.


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