[OPE-L:746] Re: LTV an assumption?

Gilbert Skillman (gskillman@mail.wesleyan.edu)
Sun, 17 Dec 1995 10:45:55 -0800

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Andrew writes:

> On to Gil, responding in ope-l: 731 to my reply to his original post (ope-l:
> 710). At first the reply didn't make much sense to me, so I studied it
> carefully along with his original post. I've concluded that we've been
> talking past each other, partly because I missed some subtleties in the
> original post. So let me return to it. Gil writes (ope-l: 710):
> "one cannot infer from the former [an equivalence relation] that the elements
> of an equivalence set contain any other "common property" (much less "common,
> homogeneous property") other than that which placed them in the set--in this
> case, paraphrasing Marx, that x boot-polish, y silk, and z gold are all
> equivalent in being exchanged for a quarter of wheat."
> I do not consider the paraphrase of Marx to be accurate...

As we discovered in a mini-symposium on value theory we jointly
presented at the last URPE summer conference, Andrew and I face certain
problems of translation in arguing with each other. For my part, and
I suspect Andrew would say something similar, I don't always understand his
choice of terms, mode of argument, or choice of points of emphasis.
For example, Andrew takes exception here to my paraphrasing of Marx's
argument, but then paraphrases it himself using a new term,
"commonality", which is not defined relative to the terms
"equivalence" and "equality", so I don't see what's being gained with
his alternative wording.

I propose two steps to get around the immediate problem. First,
let's agree to drop, at least for the moment, references Andrew
introduces to subsequent arguments in Chapter 2 and to Part 3 of
chapter 1. Since these are subsequent to the argument in Part 1 of
Chapter 1 that we are addressing, they necessarily cannot inform the
logical basis of that argument, unless one reads Marx backwards.
They can perhaps *illustrate the sense* of the earlier argument, but
they necessarily cannot form part of the *logical basis* of this
argument; indeed, subsequent analysis presumes the validity of
antecedent results.

Second, to avoid translation problems, I'll confine myself to Marx's
own words. I argue that Marx's inferences in the disputed passage are
either close tautologies (i.e. alternative ways of stating what is
already given) or are invalid. In either case Marx's argument cannot
support his conclusion that exchange values "express something
equal" in such a way as to imply the existence of some measurable
common element. Marx writes (p. 127, Penguin edition):

"A given commodity, a quarter of wheat for example, is exchanged for
x boot-polish, y silk or z gold, etc. In short it is exchanged for
other commodities in the most diverse proportions. Therefore the
wheat has many exchange values instead of one."

The 'therefore' in the last sentence at best indicates what is
already known, i.e. that in a given system of commodity exchange at a
particular point in time it is observed that a quarter of wheat is,
in (necessarily) separate transactions, exchanged for x bootpolish, y
silk, z gold, and possibly other quantities of other commodities.
No argument has been presented for any other conclusion.

Marx goes on:

"But x boot-polish, y silk, or z gold, etc., each represent the
exchange-value of one quarter of wheat."

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 the
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. So unless Marx is simply repeating what is
already given, the suggested inference is in general invalid. It
appears from Marx's next line that he does indeed see the preceding
as more than a tautology:

"Therefore x boot-polish, y silk, z gold, etc. , must as exchange
values, be mutually replaceable or of identical magnitude."

Let's take each of these characterizations in turn. First, unless
"mutually replaceable" simply means that the indicated quantities are
part of the same equivalence class, i.e. "things that are exchanged for a
quarter of wheat", Marx's conclusion is invalid. It does not follow
from this equivalence, for example, that x is exchangeable for y, or
y for z, or x for z. So unless "mutually replaceable" simple
re-establishes the equivalence inititally postulated, it is an
invalid inference.

Similarly, it does not follow that x bootpolish, y silk, or z gold
are of "identical magnitude"; all we know is that they are equivalent
in being exchanged for a quarter of wheat under the above-stated
conditions. To speak of an "identical magnitude" in any stronger
sense assumes what must be proven, that there is a common,
well-defined "magnitude" in which *identity*, rather than mere
*equivalence*, is expressed. Again, if Marx is not simply restating
a tautology, his inference is invalid.

I repeat that such an inference, understood other than in a strictly
tautological sense, would necessarily support the conclusion that
this "identical magnitude" is shared by any good which might be
exchanged for a quarter of wheat, including a good which is not a
product of labor. [This is *logically* so *whether or not* Marx
intends to exclude such goods from the discussion a priori.]
So any such inference would lead to a contradiction with Marx's
ultimate conclusion. Finally, Marx writes:

"It follows from this that, firstly, the valid exchange-values of a
particular commodity express something equal..."

[An aside: how did the modifier "valid" creep into this conclusion?
he nowhere defines this term].

Here is where the earlier fallacies come home to roost. This
conclusion does not at all "follow" from what has already been
established, namely that x bootpolish, y silk, and z gold are
exchanged for a quarter of wheat. This "commonality" is simply a
relationship of *equivalence*, which is insufficient to support the
conclusion of "equality", as I've argued at length in an earlier
post. Since any non-tautological inference of "mutual
replaceability" or "identical magnitude" is invalid, so is this

Bottom line: Marx's inference that "[valid?] exchange values of a
particular commodity express something equal" is itself invalid,
based on the fallacious deduction of a relationship of equality from
a relationship of equivalence.

Some comments on Andrew's argument in light of the above--warning,
lots of excerpting:

> Having established that the equivalence of commodities implies that they
> all contain some "third thing,"

But that's just the problem: mere equivalence *cannot* "imply" that
all such exchangeables contain some 'third thing'.
> As I understand Gil, he acknowledges that the derivation outlined in my
> last paragraph is legitimate, given that the existence of a third thing
> has been established (which he seems to deny; or perhaps he asserts that
> exchange is the third thing that makes the commodities equivalent. [But if
> so, then how do you explain a price-list?])

Yes, I deny the "existence" of this common "third thing". It does
not follow from the equivalence established by the fact that x
bootpolish, y silk, and z gold exchange for a quarter of wheat. The
existence of price-lists in no way challenges this conclusion; to
assert that it does begs the central question at issue.

Gil Skillman