[OPE-L:6997] [OPE-L:489] Sequiturs?

Gil Skillman (gskillman@mail.wesleyan.edu)
Tue, 23 Feb 1999 20:23:50 -0500

Alan insists that a commodity is a produced good that exchanges on the
basis of the "law of one price." I have two responses to this, developed
further below in response to his specific comments:

1) I see no grounds for the assumption that Marx defined a commodity in
this way, and several grounds for the belief that he did not in fact define
it this way. Furthermore, I think it is not useful to proceed on the basis
of such a definition, but of course Alan is free to do so if he wants to,
subject to the same caveat he extends to me:

>However, [Alan's response to my] criticism of Marx is in turn a
non-sequitur, >because Marx's plan was a different one [than the one Alan
suggests]. You can't >really [defend] Marx for [doing something he did not
evidently do]; all you can >say is that you are trying to do different things.


2) But **even if** we accept the condition that commodities exchange on the
basis of the law of one price, it does not follow that exchange expresses a
relationship of equality in the sense required by Marx's argument in Volume
I. I made this argument in detail in the much earlier exchange Alan
alluded to, and he has never addressed it, now or before. Furthermore, he
is quite wrong to suggest that I "didn't reply to" his specific argument
this time; I refer Alan to OPE-L post #472.

>My point is not however entirely irrelevant to other points which Gil has
>not responded to, which I'll call 'non-non-sequiturs'
>Point 1: the law of one price
>I fortunately found a precise reference in [OPE-L 746 of 1996] so it's
>obvious the issue is an ongoing one. Brendan also introduces this. Gil
>>Referring to 'the' exchange value of a quarter of wheat begs a
>>serious question. Unless the "law of one price" holds, i.e.
>>something like perfectly competitive markets exist, it is meaningless
>>to speak of "the" exchange value of a quarter of wheat, or any other
>>good. It may simultaneously have multiple exchange values conditional on
>>idiosyncratic transaction conditions faced by the various possible
>>pairs of exchangers. For example, a transaction of the silk owner
>>with some other owner of a quarter of wheat may yield an entirely
>>different exchange ratio."

[Yes. Notice my statement in the passage just cited that the law of one
price corresponds more or less to the condition of perfectly competitive
equilibrium, and recall Alan's opening admonition in his previous post that
"markets are never in equilibrium." Thus Alan's position is implicitly, but
unavoidably, contradictory. More on this in a second.]

>My point is straightforward and Gil hasn't answered it: the 'law of one
>price' holds whenever we are studying commodities, because that's what a
>commodity is; something with one price. If Gil wants to drop this
>assumption, then he isn't studying a commodity economy, or he is at best
>re-defining commodity in a very different way to Marx and, I think it's
>fair to say, most of economics.

But I did answer this assertion; see my earlier post OPE-L 472. Let me
elaborate by making 4 points:

1) It is not part of the standard definition of "commodity" that its
exchange obey the "law of one price (LOOP)". Furthermore, I see no
evidence in etymological analyses of this word that LOOP was part of its
standard definition in the mid-1800s. There are two standard definitions
of "commodity," corresponding in fact to Marx's own two-sided analysis: it
is on one hand a good or use-value, and on the other hand an item produced
for exchange (with no conditions adduced concerning the character of

2) Therefore, including LOOP as part of the definition of "commodity"
constitutes a radical departure from standard usage, both now and in Marx's
time. Consequently one might reasonably expect that Marx would have
stipulated this extra condition *explicitly* in Volume I of Capital, which
so far as I can tell he never does.

For example, Volume I opens with the statement that "The wealth of
societies in which the capitalist mode of production prevails appears as an
"immense collection of commodities." In Alan's reading, Marx has just
announced a meaning which is very different from that which anyone would
reasonably take, i.e. to the effect that capitalism appears as a system of
market exchange in which the law of one price holds throughout. Now,
first, I don't think it plausible that this is the meaning Marx meant to
convey (since capitalism has, I trust, never "appeared" to anyone as a
system in which the law of one price in fact prevails) and second, if he
did, he would immediately and explicitly have said so. But he didn't.

He does often refer to a commodity's *exchange value*, i.e. in singular
rather than plural terms, but it does not follow from this that he
considered LOOP as part of the *definition* rather than simply an aspect of
a given level of analytical abstraction. For example, "exchange value" has
a qualitative dimension, meaning "the capacity to be exchanged for other
goods", and in this interpretation singularity cannot be seen to refer to

3) To the contrary, there are indications that Marx *does not* consider
LOOP as part of his *definition* of a commodity. Consider, for example,
when Marx first introduces the notion of exchange-value in Chapter 1: he
says that "Exchange-value appears first of all as the quantitative
relation, the proportion, in which use-values of one kind exchange for
use-values of another kind. This relation changes constantly with time and
place." [I, p. 126, Penguin]

Very well, and three reasons that exchange-values can change "with time and
place" are (a) disequilibrium in an otherwise competitive market (in which
anything goes, subject to some version of Walras' law); (b) price
discrimination; and (c) transaction-specific bargaining power, all of which
allow violations of LOOP. Thus if Marx intended to rule out *these
particular* variations "in time and place" it seems he would have
immediately and explicitly done so, but he didn't.

4) Alan's reading of Marx creates a number of puzzles. First, if LOOP is
part of the *definition* of a commodity, what did Marx (or, for that
matter, what does Alan) call a use-value which is produced for exchange,
but exchanges under conditions other than LOOP? Second, we know that Marx
referred to labor power under capitalism as a commodity. Under Alan's
reading, wouldn't he have had to *stop* calling labor power a commodity as
soon as some workers with a given quality of labor power are unionized,
given others aren't, since this creates a violation of LOOP?

Third, and not least, Alan's reading of the term "commodity" logically
contradicts his insistence that "markets are never in equilibrium." There
is *no* reason to think that LOOP holds in a market out of equilibrium,
since in that case anything goes with respect to exchange ratios, subject
only to Walras' law, i.e. that aggregate purchases must equal the aggregate
value of endowments. Thus, according to Alan's two postulates, *we must
understand Marx to be studying capitalism under economically inconsistent
and thus jointly irrelevant conditions*, that is, a system of commodity
exchange in which LOOP holds although there is absolutely no logical basis
whatsoever for believing that it would. This strikes me as an infinitely
more damning take on Marx's analysis than anything I've had the temerity to

So I don't think it's *me* who's "re-defining commodity in a very different
way to Marx," and I know for a fact that Alan's definition of "commodity"
differs from that of "most of economics." For example, let's take a poll:
what do the comrades on this list take as the definition of a "commodity"?

However, in the end it doesn't matter. Even if I grant Alan what I take to
be his radical re-definition of "commodity", it still doesn't get around
the point of my earlier critique: exchange, even exchange based on LOOP,
establishes a relation of *equivalence* not *equality.* And it's *Alan*
who's not responded to *my* quite specific and detailed argument from the
earlier OPE-L discussion.

On to point 2---

>If he wants to say that a more general enquiry is needed into non-commodity
>exchange, which I think on the whole is his general plan, then who can
>disagree? I support this enquiry, which leads to interesting results.
>However the criticism of Marx is in turn a non-sequitur, because Marx's
>plan was a different one. You can't really criticise Marx for not doing
>what you want to do; all you can say is that you are trying to do different
>Point 2: an exchange-relation is more than just an equivalence relation
>The second point which Gil doesn't reply to has cropped up in all these
>exchanges and I think it's time to address it frontally.

[Ah, but I have. See post 472 and my posts in the earlier exchange.]

>In my view, I
>repeat, some very sloppy math enters some of these discussions. An
>exchange-relation is *not* just an equivalence relation. It's a *linear*
>equivalence relation. Straight away, this rules out most of the
>counter-examples that Gil and also Brendan provide.

We'll see, but unless it rules out *all* of them, then the remaining ones
still serve to illustrate the central point adverted to above.

>To repeat the point in my last post, here's what Gil says again:
>>As a counter example, consider a preference ordering R. A preference
>>relationship among bundles which satisfies reflexivity, transitivity, and
>>symmetry establishes a relationship of indifference, not equality. To say
>>that I am indifferent between two bundles in no way implies the two bundles
>>are equal in the sense required by Marx.
>Here's what I replied, and Gil hasn't answered:
>But if I am indifferent between bundle A and bundle B, this does not imply
>that I am indifferent between two As and two Bs. If A exchanges with B,
>then two As exchange for two Bs; this is why an exchange relation is
>not the same as an indifference relation. Don't forget that; it makes all
>the difference.

Of course if Alan insists I won't forget it, but it makes no difference
whatsoever for the point of my (and others') argument. That is, even
granting this additional "linearity" property, it does not follow that
exchange based on LOOP establishes a relation of equality in the sense
required for Marx's chapter 1 argument. It is Alan's burden of proof to
establish this positive claim, and he never does this.

>We have more than just
>(1) aRb->bRc
>(2) aRa
>(3) aRb -> bRa
>we *also* have
>(4) aRb -> (ka)R(kb) where k is any scalar.

[*Any* scalar? Even one such that the total quantities exchanged exceed
the total goods available for exchange?]

>More prosaically we can explain the same point with reference to Brendan's
>example of a grey sweater swapping for a green sweater. The point is that
>we are not entitled to deduce, because a grey sweater can be swapped by
>brothers for a green sweater, that the same brothers (or anyone else in
>society, don't forget) would exchange two grey sweaters for two green
>sweaters. If one brother is a risk-avoider and worries about losing
>sweaters, and the other brother doesn't like to clog up his wardrobe, they
>wouldn't swap two for two, even though they would swap one for one.
>Moreover you can't go to a shop and say 'You must sell me two sweaters for
>the price of one-and-a-half, because I'm not over-fond of grey sweaters.'
>Postulate (4) is an independent postulate. It follows from the
>commodity-relation, not from equivalence.

Rather, it follows from exchange given LOOP, which establishes a particular
form of equivalence relationship, but still not a relationship of equality.
To repeat the counter-example from the earlier discussion that Alan never
addresses: nothing in Marx's Chapter 1 argument about the properties of
exchange relations depends on the conditions that only *human products* are
exchanged. Very well, then imagine that plots of unimproved land are
exchanged for units of boot-polish, and suppose such exchanges, as well as
all others, obey LOOP. Then according to Marx's analysis, it *must* follow
that "a common element of identical magnitude exists" in the exchangeable
bundles of unimproved land and boot-polish, and according to his subsequent
argument the *only possible* common element is human labor, which is of
course impossible in the case of unimproved land. Contradiction.

But this is almost beside the point: it is up to *Alan* to establish the
theorem that says that reflexivity, completeness, transitivity, and
"linearity" jointly imply "equality" in the sense required by Marx's
Chapter 1 argument, and this he does not do.

>The entire discussion about equivalence classes and magnitude amounts to
>this: (1), (2) and (3) don't imply (4).

Not at all. It is that (1), (2) and (3), with or without (4), do not imply
that "the valid exchange-values of a particular commodity express something
equal" in the sense required for Marx's Chapter 1 argument.

> Sure they don't, but Marx never
>says they do. Marx says, since we're discussing in a commodity economy, all
>four rules apply, and that's what I, Marx, am analysing, as I said on page
>one of my work.
>My reading is that Marx deduces from the fact that a linear function of
>use-value is conserved in private exchange, that it is also conserved in
>the totality of exchanges among all members of society. I don't think
>that's trivial. If it was, more people would have recognised the argument.

But that is not what he deduces in the argument under discussion. What he
deduces is rather the claim that abstract labor is the basis in some sense
of exchange value.

>A postscript on tautologies
>Gil hasn't dropped a position which I think militates against clear
>discussion: he says either Marx is tautological, or he is wrong. I
>challenged him at the time and he came off the fence; he seems to have
>gotten back on it. Gil, you have to say which.

I think Alan's charge here is a red herring. Here is the passage he
objects to:
"In Chapter 5, it is *Marx*, not me, who asserts the significance of
explaining surplus value on the basis of price-value equivalence, and he
bases this assertion only *partly* (and invalidly) on a stipulation that
*might* be read as a form of market equilibrium--i.e., that price-value
equivalence corresponds to the "pure" case of commodity exchange (I, pp.
260-61 Penguin ed.). As I've argued elsewhere this characterization is
either completely tautological and thus contentless or else demonstrably
wrong in general. But in any case, my critique of Marx's analysis in
Chapter 5 does not depend on any assumption that markets are in equilibrium."

Now, I have not "come off" or "gotten back on" any fence (nor did I in the
earlier exchange Alan alludes to), simply because there is no "fence" in
the first place. It is surely legitimate, and surely consistent with the
dictates of "clear discussion," to state that a set of arguments is subject
to a *dilemma*, i.e. that any given argument from the set is either a
simple tautology (i.e., circular--see below) or invalid.

Here's the point: Marx says in Chapter 5 that price-value equivalence
constitutes the "pure case" of commodity exchange. He doesn't ever define
what he means by this, so its meaning **is a matter of interpretation, not
dogma**. What I'm saying is that of the set of defenses which might be
given for such a claim, any member of the set is either a simple tautology
or invalid in general. This is a perfectly straightforward, perfectly
"clear" characterization. Thus there is no "fence" that I've been straddling.

Now, if Alan wants to know which characterization applies in our particular
discussion, I invite *him* to get off the fence and tell me what grounds he
favors for Marx's Chapter 5 claim that that commodity exchange on the basis
of price-value equivalence constitutes the "pure form" of commodity
exchange, and I'll gladly identify which horn of the dilemma he's run afoul

> Either he is tautological,
>or he is false. He can't be both, and if no-one can reply to you adequately
>unless you say which, or at least deal with one at a time.

See above.

>Moreover, I think the accusation of tautology is in any case a very dubious
>and rather sloppy one. In logic, every valid deduction is a tautology. It's
>just another word for valid deduction.

Not exactly. If you check the dictionary, there are two definitions
potentially applicable here. "Tautology" in the language of formal logic
is just as Alan describes it above--any valid inference from a given set of
premises. But there's another, "layperson" definition of the term as an
instance of circular reasoning, or simply restating a particular assumption
as one's conclusion. In the latter reading, for example, exchange on the
basis of price-value equivalence might be understood as the "pure form" of
commodity exchange simply because Marx defined it that way. It goes
without saying that no body of reasoning we typically honor with the word
"theorem"--much less Fermat's last theorem!--is merely a tautology in this
latter sense.

Now, if Alan wants my *opinion*--which is all it can be, since Marx never
defined what he meant by the term, and is now inconveniently dead--I
suspect Marx meant to express something other than simply a definition in
this passage. Consequently, I take him as expressing a claim which is
demonstrably invalid in general, according to the one horn of my dilemma.

But I don't insist on this reading; if Alan reads Marx the other way, then
the other horn of the dilemma applies. What's *your* position on this,
Alan? "You have to say which."

In any case, I believe the original critique of Marx's Chapter 1 argument
still stands. Gil