# [OPE-L:993] Re: Definitions and Tautologies

Alan Freeman (100042.617@compuserve.com)
Wed, 7 Feb 1996 16:21:42 -0800

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Re; OPE-L 976 from Allin, 7 /2/96
Allin writes
===========================================================
A propos a recent posting of Alan's:

> 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 Marx's definitions have been replaced by other defintions.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
>
> v=vA+L
>
> But this definition applies only to the special case of both
> sale and purchase at values.

I'm now re-confused on something I thought we had agreed. The
_definition_ of value via the equation given above (whether or not it
represents what Marx meant) is surely independent of the issue of whether
sale and purchase take place at prices corresponding to values.
Schematically, step 1 is to formulate an adequate definition of value,
step 2 is to see whether exchanges take place at prices corresponding to
values so defined (on average or whatever).

============================================================

I kind of knew that once the cards were on the table, even close
friends would blanche at the hands displayed.

Let's recall our putative agreement, and I'll try to show that it
isn't affected. That is, I'll try to show that you don't need the
equation

v = vA + L

in order to sustain our agreement. This might seem like nitpicking,
but the much more important point is that Marx's derivation of value
does not presuppose this equation.

In OPE 925 of 2/2/96 I summarise the agreement thus (revised agreement 1):
============================================================
Marx's derivation of the category of value and its magnitude is
independent of the assumption of price-value equivalence.
============================================================

This arose (inter alia) from Allin's statement that
============================================================
"If one is to talk of the equivalence of prices and values
in any substantive way, value must be _defined_
independently of price; and of course we find this -- value
is defined in terms of socially necessary labour-time.
Equivalence is clearly not "the basis of his definition of
value"
============================================================
My interpretation - and, I think, Marx's - of agreement 1 is as
follows: with each commodity is associated a unique magnitude, its
value, which is defined independent of its price and is equal to
the labour time socially necessary to produce it.

Nothing in this definition says that socially necessary
labour time is given by the equation

v = vA+L.

Indeed, *no* further determination of the magnitude of value
is given.

My explanation for this is that Marx proceeds, like most
mathematicians, by laying out his most abstract and general
definitions and axioms first, without assuming what is later
to be proved.

The *definition* of value does not say how value is made up.
It does not say it is made up of a certain quantity of living
labour and a certain quantity of dead labour.

That comes later.

After Chapter 5.

The definition of value only says that it is equal to
a magnitude independent of price (as you say) and that the
substance, and measure, of this magnitude, is socially
necessary abstract labour time.

That is, axiomatically:

Axiom 1
=======

associated with each quantity of use-value is a unique
magnitude, its value; the dimension of this magnitude is
time and it is a linear function of use-value.

Nothing else is stated or assumed.

There are then a variety of 'models' to use a term from symbolic
logic, which may satisfy this axiom.

One such model (the word 'model' is *strictly* to be understood
in the technical sense of the predicate logic, that is 'an assignment
of truth values') is to define value by the equation

v = vA + L

if we write in time subscripts, this really says that

v(t) = v(t)A(t) + L(t)

This, we [the TSS guys] assert, is inconsistent, and incompatible with
any reasonable textual interpretation of Marx. Quite apart from anything
else it works only if there is no technical change.

Another such model is to define value dynamically by the equation

v(t+1) = v(t)A(t) + L(t)

This model would accept that the value at time t is not equal to the
value at time t+1, but would nevertheless claim that the value
transmitted to the outputs is given by the labour time embodied
in the inputs. This interpretation would be a pure sequentialist
interpretation. I don't know of anyone who currently holds this
view, but it is always a possible view. Paolo Giussani maybe
holds it. I once held it. If you think this, then you have to think
that by some means the inputs directly transmit their value to the
outputs, without the market getting in the way. That is, you
have to abstract from the C-M-C part of the circuit, as if the
capitalist obtained their inputs directly without the intermediary
of money.

A further possible view is to define value statically, but by the
equation

v = pA + L

but subject to the constraint that

p = (pA+L)(1+r)

that is, that the economy has attained a static equal-profit-rate
equilibrium. This is the view, for example, of Roberts-Wolff-Callari
and also of Ramos-Rodriguez: the nondualists. I think this is
also Fred's view but I am not certain of this.

Finally, the interpretation which I think is most rational, reasonable
and consistent with Marx's own words, is the equation

v(t+1)=p(t)A(t) + L (t)

where v and p are both given in hours.

Now, each such equation allows us to define a magnitude, x labour
hours, which is associated with y use-values. Each such equation
satisfies axiom 1.

I think that there is much in the first 5 chapters of Volume I
which make it impossible to accept

v = vA + L

as the definition of value. But our agreement, and axiom 1, is
minimalist enough that we don't have to settle this before
we have established the conclusion which for me is the most
central of all, namely that in simple commodity circulation,
the total value of all goods cannot change.

I suspect that this will not satisfy many people. The central
point is therefore the following: chapter 1 of Volume I *only*
says that the magnitude of value is a quantity of labour time.
It does *not* say how this magnitude is determined.

Alan