[OPE-L:974] Definitions and Tautologies

Alan Freeman (100042.617@compuserve.com)
Wed, 7 Feb 1996 04:46:39 -0800

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This is the second of three preliminary questions prior to a
more general response to Gil (and others). It contains 2

Point 1: which crime, inconsistency or truth-by-definition?

Gil, it seems to me, has taken to hesitating between claims
that Marx is inconsistent, and Marx is true by definition. I
think he can't do both and I think he will have to settle for
one or the other.

The door remains open, of course, to the escape-route we have
always offered him, which is to say that the marxists are
inconsistent and Marx is true by definition. In this case we still
have a dispute, namely whether Marx is merely true by some
arbitrary whim or whether he has actually proved anything. But
at least we have a consistent dispute.

Either Marx is inconsistent, or Marx is true by definition. He
can't be both true and inconsistent. Particularly when the
assertion which is alleged to commit 'truth-by-definition' is
the assertion which abolishes the inconsistency.

What we actually need to establish is, as in any science

(i) whether his definitions are consistent,

(ii)whether these definitions arise properly from the subject-
matter and the observation of real life, or whether they
are arbitrary whims,

(iii)whether these definitions are developed in a correct
logical sequence which avoids circular argument, that is,
whether they assume what has to be proved or whether the
early definitions are the most general, and the later
definitions merely add extra determinations not initially

and it strikes me that this is what the debate of the nearly-
dead century is really about and what I conceive to be the
present debate.

In all existing proofs of inconsistency, our contention is that
Marx's definitions have been replaced by other defintions. For
example, value has been defined by the equation


But this definition applies only to the special case of both
sale and purchase at values. If this same definition is then
used to study the case of sale and purchase at prices not equal
to values, contradiction is obviously going to occur. But our
whole point is that Marx does not confine himself, in the parts
of Volume I where value is derived (chapters 1-5) to sale at
values. So this cannot possibly be his definition of value.
Moreover, it can be tested for consistency *only* under the
circumstances to which it applies, namely sale at values. It is
a grotesque insult to both Marx and common logic to take this
definition, that applies only for sale at values, and test it
for consistency in cases where goods are not sold at values. It
is, as I have said, testing on the moon a spring balance which
was calibrated on earth. And worse still, the definition is not
even Marx's.

Therefore Gil, I think, states the matter misleadingly when he
says in (OPE-L:960)

"In my reading, the "transformation problem" as presented in
Volume III of Capital is precisely Marx's attempt to
demonstrate the consistency between his disaggregate and
aggregate hypotheses, i.e. an attempt to show that the
translation of embodied labor values into prices of
production preserves certain aggregate equivalences.

"However, we know now that they are *not* in general
consistent; this may be the one true contribution of the
Bortkiewicz-Sraffa-Steedman tradition. Thus, if one is going
to affirm Marx's value-theoretic approach to understanding
capitalism, one of the two hypotheses has to go."

What we 'know' is that if one defines values on the assumption
of price-value equivalence, that is, by the equation

v = vA+L

and one then defines prices on a different assumption, namely
profit-rate equalisation, then inconsistencies result. This is
the 'one true contribution' of the Bortkiewicz-Sraffa-Steedman

The issue is, however, whether these inconsistencies cease to
exist if one defines value in the more general way that Marx
does in chapters 1-5 of Volume I where the assumption of price-
value equivalence is neither stated nor posited (as now seems
to be agreed: no citation to establish price-value equivalence
in this section of Volume I has been adduced, and there seems
to be an agreement which is holding between Gil, Allin and
myself on this issue. The disagreement is thus about what
happens next, in chapters 6, 7 etc)

In this case, Gil may argue that we or Marx or both commit
truth-by-definition, but he cannot prejudge whether the result
is inconsistent, using definitions which are precisely the
opposite of the alleged 'truth-by-definition'.

Now I can see that Gil might claim that the inconsistencies
cannot thus be abolished; that is, the inconsistency remains on
the basis of the temporal-single-system definition. Or, he
might claim that the argument which abolishes the inconsistency
is 'truth-by-definition'.

But I don't see how he can claim both.

The claim of the temporal-single-system definition of value is

(i) if value is defined in this manner, the inconsistencies

(ii)this is in fact Marx's definition of value.

If we are correct only on point (i) then it may be argued that
we have a consistent solution, but Marx does not.

If we are correct only on point (ii) then both ourselves and
marx are inconsistent

If we are correct on neither point (i) nor point (ii) then both
ourselves and Marx are inconsistent, and moreover in different

But only if we are correct on both points, can it be argued
that Marx has committed truth-by-definition - which I want to
deal with in my next post - and then it cannot be argued that
either the solution, or Marx, is inconsistent.

So I think Gil needs either to be more precise about who is
inconsistent and who commits truth-by-definition, or he needs
to drop one of the allegations.

Point 2: What did Bortkiewicz really show ?

I also think that Gil's 'proof' of inconsistency stated above
is weaker than he realises. This is not only because the
Bortkiewicz solution only applies to a special definition of
*value* (which is not Marx's) but because it also applies only
to a special definition of *price*.

Bortkiewicz et al discuss only one other special case, namely
sale at equal-profit-rate prices.

Gil may be working on the assumption that this is also the
special case dealth with by the TSS approach.

But this is not so, and this may be the source of

The TSS calculation is valid, on the basis of Marx's chapter 5
proof of the equality of total prices and values for any
arbitrary set of prices. Value is defined not just for prices
of production nor just for inputs purchased at values, but for
inputs purchased at *any* arbitrary prices on the basis of
Marx's volume I discussion.

This is precisely why the whole issue has surfaced in a Volume
I context: because, once we started examining the texts, that
the justification for Marx's famous 'first equality' appears in
Volume I, and in fact in Chapter 5.

The TSS and indeed the nondualist definition of value, I would
argue, effectively takes this as its point of departure. We,
with Marx, argue that the value of constant capital is
represented in the value of the product by the value of the
*money* which the capitalists pay for this constant capital,
not by the value of the *elements* of constant capital.

If Marx's first equality is already established, as I certainly
claim, by the time we reach chapters 6, 7 etc, and if - as I
also claim - inputs in these chapters are represented by the
value of the money paid for these inputs - then the resultant
definition of value is the following:

v = pA + L

provided, as indicated in my earlier post, all magnitudes are
expressed in the same unit, and provided that, if they are
expressed in monetary prices, correction is made for any
changes in the value of money.

This definition, incidentally, is the common property of both
the sequentialists and the nonsequentialists. It is a
consequence of nondualism - in fact this equation *is* the
nondualist position.

The sequentialists would merely add the proviso that v is
defined at time t+1, whereas p and A are defined at time t, and
L over the whole period [t,t+1].

On this basis it is quite easy to show that Marx's volume III
argument, and its further extension to rent and to monopoly
prices, consistently establishes his 'second equality'.
Moreover it is also easy to show that the same argument applies
to *any arbitrary set of values and prices*, that is, to
general, market prices.

The Bortkiewicz solution - or, to call it by its proper name,
the general equilibrium solution - only *exists* for equal
profit rates. The calculation which establishes unique relative
prices is simply meaningless without this assumption. There are
too many degrees of freedom.

Since for the general case the Bortkiewicz solution does not
exist, one is entitled to ask how it can be valid for the
special case it does discuss.