[OPE-L:739] Re: exchange of equals

Gilbert Skillman (gskillman@mail.wesleyan.edu)
Thu, 14 Dec 1995 13:35:46 -0800

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Thanks to Fred for responding. I think his post makes the relevant
issues quite clear.

> 1. My understanding of Gil's distinction between equivalence and equality
> is that equality requires commensurability and equivalence does not. This
> seems to be the main difference for our purposes. Gil, please correct me if
> I am wrong.

That, but also that exchange expresses at best relationships of
equivalence, not equality. Thus Marx cannot validly infer the
commensurability condition from the fact of exchange, as he claims.

> 2. Gil argues further that Marx assumed in Section 1 that commodities are
> equivalents, in the sense that they are all exchanged against e.g. wheat,
> but that Marx did not assume or establish that commodities are equals, in
> the sense of requiring commensurability.

Marx begins with the case that x bootpolish, y silk, and z gold are
each exchangeable for a quarter of wheat; the former are thus
equivalent in this regard. He then says:" Therefore x bootpolish, y
silk, z gold, etc, must, as exchange values, be mutually replaceable
or of identical magnitude."

The first statement is in general wrong, except under exchange
conditions similar to perfect competition. For example, x, y and z
may exchange for a quarter of wheat, and yet not be exchangeable for
each other. The second claim, to the extent it is valid, is a
tautology: they are of "identical magnitude" only in the sense of
each being exchangeable for a quarter of wheat, but that was assumed
to begin with.

Marx then says: "It follows from this that, firstly, the valid
exchange values of particular commodity express something equal...";
this does not follow, as the counter-examples in my first post illustrate.
Equivalence in terms of being exchangeable for something else does not imply

Thus, Marx *begins* from the assumption of equivalence, and "deduces"
equality, but the deduction is fallacious.

> 3. To begin with, I think that when Marx said the exchange of equivalents,
> he meant the exchange of equals, in the sense of commensurability. The
> question remains whether Marx was justified in considering exchange as the
> exchange of equals, but this is what Marx meant when he said the exchange of
> equivalents
> (and also what I meant when I stated Marx's second methodological
> presupposition was the exchange of equivalents).

Yes, he said it, but it doesn't follow. See above.

> 4. Now to the question of whether Marx was justified in considering
> exchange as the exchange of equals: One could respond by arguing that Marx
> simply ASSUMED that the exchange of commodities is essentially the exchange
> of equals.

But he didn't. He ASSUMED an equivalence class and CLAIMED that
equality follows: "It follows from this that....". But it doesn't.

Gil would say that this is assuming what should be proved, but
> it could be argued that this is a fundamental methodological presupposition,
> which cannot be "proved",

(then why did Marx try?)

>and that the best way to test the validity of this
> presupposition - relative to the opposite presupposition of the exchange of
> non-equivalents (it has to be one or the other, doesn't it?) - is to compare
> the relative explanatory powr of the theories based on these two alternative
> presuppositions.

This sounds suspiciously like Milton Friedman's methodological dictum
that the appropriate defense of unrealistic neoclassical assumptions
is in the empirical success of the hypotheses derived from them, but
it doesn't really matter: since one can *assume* that values are in
some sense the basis of exchange value *whether or not* exchange
establishes relations of equality, the test Fred proposes is *necessarily

> 4. But I think a stronger argument can be made for Marx's assumption of the
> exchange of equals. Marx's assumption of the exchange of equals follows
> from his first methodological presupposition that capitalism should be
> analyzed in terms of its objective characteristics. If exchange is viewed
> as an objective process, i.e. as a SYSTEM of MUTUALLY CONSISTENT exchanges,
> rather than as an individual act of exchange from the perspective of
> individual exchangers and disconnected from all other exchanges, then it
> follows that exhange must be an exchange of equals (mutual consistency or
> transitivity requires equality).

No, equality does *not* follow from the fact of "mutually consistent"
exchanges. Fred's asserting this does not make it true.
Transitivity does not imply equality; equality implies transitivity.
Transitivity of relationship R states that if aRb and bRc, then aRc.
It does not follow that a and c are equal, contrary to Fred's claim.
Viewing exchange as an "objective process" has absolutely nothing to
do with it.

Furthermore, absent conditions similar to perfect competition, the
equivalence established by exchange does not even establish
transitivity, as mentioned before: even though q exchanges for x and
x exchanges for y, it does not follow that q exchanges for y. So
even on the weak grounds of transitivity Marx's argument fails in
general. I doubt that by "mutual consistency" Fred or Marx means
"perfectly competitive."

> But even this argument does not "prove" that exchange must be viewed as an
> exchange of equals.. The exchange of equals follows only from the objective
> method.

But that's just it: it *does not* follow from "the objective method."
Fred asserts this, but doesn't prove it. He equates "mutual
consistency" with "transitivity", but transitivity does not imply
equality, and exchange does not even imply transitivity.

Again, the counter example. Suppose unimproved land where among the
items exchanged. Then according to Fred's "objective" argument,
"mutually consistent" exchange establishes an equality between
unimproved land and, say, x units of boot-polish. But then they must
have some common measurable element, which Marx claims is

> One can still adopt the subjective method of individual choices and
> view exchange as an exchange of non-equals. But, similarly, one could not
> "prove" that exchange has to be viewed as an exchange of non-equals. So we
> would come back again to the relative explanatory power of these two methods
> as the best test of their relative validity.

Again, this is irrelevant and question-begging.

> 5. A note on the history of economics: the classical economists, especially
> the Physiocrats, also assumed that exchange is the exchange of equals, in
> the sense of requiring commensurability. Menger railed against the
> classical economists (in an Appendix to his Principles of Political Economy)
> for making this assumption, and based his neo-classical theory on the
> opposition assumption of the exchange of non-equivalents. (By the way,
> Menger also used "equivalence" to mean the same thing as "equal"). As Gil
> noted, Bohm-Bawerk made the same argument against Marx, but B-B's argument,
> like Menger's, assumes the subjective method.

And whatever you think of Menger or his brand of neoclassical
economics, he was right on this point.

The core of the dispute is now quite clear. Fred claims that "mutual
consistency", interpreted as "transitivity", implies equality. It
does not, as I show. Furthermore, absent special conditions, the
mere fact of exchange does not even imply transitivity.

Finally, Fred is wrong to suggest that we can "test" the assumption
of exchange of equals by checking the explanatory power of the
conclusion drawn from this assumption. But this is clearly not the
case; if one derives a true conclusion based on an invalid deduction
from a given premise, one cannot "test" the premise by showing the
explanatory power of the true conclusion invalidly reached.

Gil Skillman