[OPE-L:7252] [OPE-L:777] Re: In what sense does exchange "establish" an

Gil Skillman (gskillman@mail.wesleyan.edu)
Fri, 26 Mar 1999 18:51:49 -0500

Brendan wrote (a while ago--sorry about that):

>I'm starting to get the hang of Gil Skillman's problem with Marx's
argument... I think. :-)
>In my reading, Gil sees Marx's argument as having the following structure.
Marx defines a kind of equality (congruence) between commodities which
purports to prove the existence, underlying this relational structure, of a
quantity (value) which is different from the quantity defined by the
exchange relationship itself.

I'd rather put it that Marx *asserts* the inference from commodity exchange
relations of a relationship of *equality*, supporting the subsequent
inference of "a common element of identical magnitude" in exchanged
commodity bundles, which turns out to be value as determined by abstract
labor. But what is established *at most* by the fact of commodity exchange
is a relationship of congruence, which is insufficient to support Marx's
subsequent claims.

>This argument doesn't work for him because "there is no evident sense in
which exchange establishes an 'equation' in a sense sufficient to support
Marx's inference that 'a common element of identical magnitude exists in
two different exchanged things'. Now, one could [...] *define* exchange
[...] to establish a sort of equality, in which Marx's inferences follow as
a simple tautology." [OPE-L: 627]. But (if I read Gil right) this would
still be unsatisfactory as a justification for Marx's Chapter 1 argument,
because under this interpretation Marx would only find in his inferences
the result he had pre-determined in his premises (the axiomatic
presentation of exchange).

Worse than that: if we take seriously Marx's initial restriction of focus
to exchange of *commodities*, i.e. products of labor, then we *already
know* that the only thing they necessarily have in common is being products
of labor. We don't need to inquire *at all* into the properties of
exchange, contrary to his argument.
>This leads Gil to pose for his opponents a dilemma. Did Marx presuppose
labour as the content of value (in which case his Chapter 1 argument is
irrelevant) or is the Chapter 1 argument supposed to allow us to infer
labour as the content of value from properties of exchange (in which case
it only appears to do so because this conclusion has been smuggled into the
premises of the analysis of exchange)?

I'd put my point one step more strongly: there's no grounds, on the basis
of Marx's Chapter 1 argument, for validly inferring that there exists a
thing called "value" which has content, whether or not labor is that
content. So *two* things have been smuggled into the premises of the
analysis of exchange.

>I see my own position as embracing both horns of this dilemma.
>I think Marx pre-supposed labour as the content of value. I think that
this pre-supposition determines the choices that Marx made in Chapter 1,
viz. to focus on the commodity (rather than "exchange", which he put off to
Chapter 2), and to focus on the "forms of value" rather than concrete
exchanges. Nevertheless, I think that the Chapter 1 argument does allow
Marx to show that exchange only brings to light a quantity (value)
associated with the commodities, which is equal in both commodities, and
different from the use-values of either commodity.

I don't see this. In particular, *nowhere* in Marx's Chapter 1 argument
does he establish that *commodity* exchange has these unique properties.
Therefore, so far as we know from his argument, if exchange can "bring to
light" any such quantity, it must be able to do so with respect to any
exchangeable good. Thus, if his argument about the properties of exchange
is valid, it must be true that exchange involving *non-*commodities "brings
to light a quantity (value) associated with" them, since he's never
established that exchange enjoys this property *only* respect to
commodities. But trying to extend the argument to non-commodities leads to
a contradiction, as I've argued.

An illustration of the point. Suppose somebody says that yeast makes rye
bread dough rise, but gives an argument to explain this phenomenon which
refers only to the effects of yeast on bread dough in general, and not on
rye bread alone. It would be illegitimate, on the basis of this argument,
to conclude that yeast makes *only* rye bread dough rise; in terms of the
logic of the argument, the fact that *rye* bread dough is being used is
purely incidental. By exactly the same token, the fact that it's
*commodities* that are being exchanged has no demonstrable connection to
Marx's inferences that "the valid exchange-values of a particular commodity
express something equal", and subsequently, that "a common element of
identical magnitude exists in two different [exchanged bundles]. Thus, if
the argument is valid, it must apply with equal force to exchanges
involving non-commodities. And this leads to the contradiction, because
the argument isn't valid.

I need only add the footnote that while, yes, Marx is expressly talking
about "commodities", the argument I'm criticizing is manifestly based on an
analysis of the *exchange* of commodities.

> Marx goes on, in Chapter 2, to discuss exchange. Here his argument takes
a >more conventional form, since the form of exposition matches the
direction of >the implication: from value determined in production to price
in exchange >(whereas in Chapter 1 the argument was inverted with respect
to the implication >that Marx wanted to show).
>My justification is as follows.
>Taking Marx's characterisation of the properties of exchangeability as
valid, we can show that they entail certain properties of the
exchangeability relation: reflexivity, symmetry, transitivity and composition.

[Reflexivity can only hold by definition, since as a matter of fact,
commodity bundles are never exchanged for themselves. And I'm willing to
grant the possibility that exchange conditions allow transitivity and
composition, but I don't see Marx assuming this in Chapter 1.]

> This means that they define a kind of equality. What kind?


>The properties of exchange assign to each commodity a positive integral
number (of units of the universal equivalent commodity) that is conserved
when commodities are aggregated. In this sense the price behaves just like
the mass of physical objects, as if it was a scalar physical property of

For what it's worth, physicists no longer think mass behaves this way. See
my comments on Duncan Foley's recent post.

> This is the basis for fetishism. But, unlike mass, the assigned property
is equal >in two exchangeable commodities. This evident close link between
exchange and >value leads to the fallacy that exchange determines value.

*What* "close link between exchange and value"? All that's been
established is that some set of commodity bundles share the same exchange
ratio with another commodity. No inference of a separate "value" dimension
follows from this fact. This must be *proved*, not asserted.

> But Marx's analysis >allows him to disprove this.
>If you look at the properties of the commodity that Marx uses to
characterise the value forms, you can see that he ignores at all times the
concrete use-values or actual prices of any commodity. This means that,
given his analysis, the properties of exchange that define the "equality"
(or "congruence" or whatever) do not include use-value or price.

I don't see this. If they don't include price, i.e. exchange-ratios, then
the equivalence (or congruence) relationship could not have been asserted
in the first place.

> This implies that the "scalar quantity embodying" property of exchange
would >apply equally well to a set of commodities embodying *any*
use-values, and >exchanging with *any* vector of prices.

So long as prices were such that the defined equivalence relation held.

>This means that the definite price vector of commodities in real life can
*not* >have been determined by the exchange relation and hence *must* have
come >from outside it, from production.

This does not follow. And here, again, the counter-example using exchange
of non-commodities applies. Note that nothing in Brendan's preceding
analysis of the properties of exchange is shown to emanate specifically
from the fact that it is *commodities* that are being exchanged. Thus,
suppose that exchange relations include exchange for unimproved land. But
then it obviously can't be true that the price vector "*must* have come
from outside it, from production", since unimproved land isn't produced.

> He achieves a neat trick: he shows that exchange defines the necessity of
a >definite positive scalar quantity associated with each commodity
*without* >defining what the value of that quantity is.

Either that "positive scalar quantity" is simply the common exchange ratio
(relative price) of a given set of commodities, which tells us no more than
we already knew by asserting exchange relations with given properties, or
Marx achieves no such neat trick.

>Then the fact of definite prices shows that prices formed in exchange are
the form of expression of something else, i.e. not just that the values are
formed elsewhere, but that prices formed in exchange express them.

No it doesn't, so far as I can tell.

>Because the actual use-values of commodities have also been ignored, Marx
can show that no use-value can be the source of the common property that
allows two commodities to exchange. What is left but their common existence
as produced things, i.e. products of human labour? Nothing.

1) If we accept the (relevance of the) premise that "no use-value can be
the source of the common property that allows two commodities to exchange",
then we already knew that "nothing is left of [the] common existence of two
commodities" other than labor, *from the definition of commodities*, not
from any properties of exchange.

2) But, as an aside, I'd like to note a fallacy in the premise. Granting
that exchange abstracts from the *particular* use-value of given
commodities, it doesn't abstract from the fact that they *have* use-value.
Thus the "common property that allows two commodities to exchange" is just
their common property of having *abstract use value.*

In any case I *know* it's not being "products of human labor" that allows
two commodities to exchange. Proof: I know commodities also exchange with
non-commodities like tracts of unimproved land or insurance policies, and
the latter are not products of labor.

Notice I can't make the same proof by contradiction for use-value: if
bundles don't have use-value, be they commodities or not, then they
wouldn't exchange.

Thus, *either* Brendan's claim about the common property of commodities
results simply because he assumed it to begin with--commodities are, after
all, *by definition* products of labor--or his claim is simply false.

>At the risk of being long-winded here, I'd like to suggest an analogous
form of argument. Consider the theory that the marginal productivity of
factors of production determines the income shares of the classes of factor
owners. It's well known that this theoretical construct is circular: the
measure of capital goods depends on the profit rate and hence on the income
shares of the classes which it purports to explain. Hence, even if the
various assumptions required for the theory to work were valid, it could
not serve as an *explanation* of the income shares: if the income shares
were changed, the marginal productivity of the factors would also change.
The theory could still be true as description, but false as explanation. To
pursue the analogy, Marx's Chapter 1 argument shows that the exchange
relation defines a vector of prices that necessarily describes values
without explaining them.

As explained above, I don't see this. The argument assumes what it must
prove, that the equivalence established by an exchange relation allows an
inference about a dimension or property outside of or beyond that relation.
But mere equivalence, or even congruence, doesn't allow you to do this.

>Now I can return to Gil Skillman's dilemma: Marx can presuppose and also
infer the labour content of value because he shows that the exchangeability
of two commodities demands a "third thing" (a scalar quantity associated
with each commodity which is conserved in exchange and aggregation) and
also fails to explain it.

But he *doesn't* show this. He *can't* show this on the basis of
equivalence (or even congruence) relations arising from exchange.

>Now for the relevance of Marx's restriction of his analysis to the
commodity, the product of labour. This allows him to avoid the distinction
between the "definite prices" of Chapter 1 on one hand and values on the
other, which comes into play later in his analysis of capitalist relations.

What this restriction "allows him" to do is beside the point. The question
is whether the restriction to commodities is demonstrably central or
incidental to Marx's inference of equality, and thus of the existence of a
"third thing." And Marx offers *no* demonstration that the "equalizing"
properties of exchange depend on the fact that it is specifically
*commodities* being exchanged. And if his inference of the existence of a
"third thing" is invalid, as I argue, then it doesn't matter what he avoids
now and brings into play later.

>In this sense, the Chapter 1 argument presupposes the determination of
values >by labour time.

It also presupposes, since it doesn't establish, that there *is* such a
thing as "value" understood independently of "exchange-value."

Bottom line: Brendan's position depends on the premise that commodities
have a thing called "value" which can be understood independently of
use-value (concretely or in the abstract) and exchange-value. But Marx
gives no valid grounds for believing such a premise. Positing transitivity
and composition is not sufficient to do the trick, since that only
establishes relations of congruence, not equality as Marx claims.