[OPE-L:7183] [OPE-L:701] Re: Use and abuse of mathematics [OPE 574]

Gil Skillman (gskillman@mail.wesleyan.edu)
Thu, 18 Mar 1999 18:14:02 -0500

Andrew writes:

>Gil Skillman's post is very long, but almost all of it either says
>that the point is not yet proved, or was not proved where it was
>supposed to be proved. Hence, the whole thing reduces to one point,
>Marx's proof in the paragraph at the top of p. 127 (Capital I,

I apologize for the length, but actually the point was a little stronger:
Andrew suggested that my critique of Marx's Chapter 1 depended on my
particular reading of that argument, and that the alternative
"interpretation" offered by Andrew voided the critique. The point of my
post is that, for all its merits, Andrew's interpretation took as *given*
that commodities have a thing called "value", understood to be distinct
from use- or exchange-value, and that some form of "equality" was
established by exchange. But these are exactly the points I criticize
Marx's argument on. Therefore, whatever we may think about Marx's
argument, the bottom line is that *Andrew's* interpretation doesn't get
around my critique.

>Gil writes:
>"This passage from Marx establishes only that there are various
>bundles which have the equivalent property of being exchangeable for
>for a quarter of wheat. Andrew, like Marx, takes for granted what
>must be proved, i.e. that this equivalence establishes that exchange
>value can validly be thought of as the mode of expression or form of
>appearance 'of a content distinguishable from it.'"
>I think much more is established than what Gil says. Marx BEGINS
>with the exchange of a qtr. of wheat for various other
>commodities --
>not bundles, BTW. Several moves occur between this and the
>conclusion that exchange-value is simply the form of appearance of a
>content distinguishable from it. The whole thing together
>constitutes a demonstration.

I agree that several steps occur between the opening and closing sentences
of the paragraph in question. I disagree that the conclusions of the
paragraph have been "demonstrated." The whole point is that no such
demonstration has taken place.
Specifically, the words

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

do not, contrary to Marx's claim, support the inferences that

"the valid exchange-values of a particular commodity express something equal",
where "equality" is interpreted to signify "that a common element of
identical magnitude exists in two different things"

or that

"exchange-value cannot be anything other than the mode of expression, the
'form of appearance' of a content distinguishable from it",

since no basis for positing such a "content" has yet been given.

>Perhaps Gil can prove that Marx's demonstration is invalid.

It's not clear why this is necessary, since no "demonstration" has yet been
established in the first place, even given "the initial move from 'being
exchangeable for' and 'being the exchange-value of' ". But in fact I have
given a counter-demonstration, since none of the claims in that first
paragraph are shown to depend on the fact that only *commodities*, are
being exchanged. So let one of the traded-for bundles be a non-commodity,
like acres of unimproved land. Then any valid conclusion one draws from
the fact of exchange must hold for this bundle as well. Since, contrary to
Marx's ultimate conclusion, unimproved land does not have the property of
being a product of abstract social labor, the argument is invalid.

Alternatively, if one *restricts* the field to commodities, i.e. products
of labor, as a pre-condition, then one need not talk about exchange at all
to conclude that all bundles have in common the fact of being products of
labor. The conclusion was assumed already.


As yet,
>however, neither he nor anyone else has done so. What Gil has done
>is to ignore the intermediate steps -- in particular, he seems not
>to notice the initial move from "being exchangeable for" and "being
>the exchange-value of" -- and thus to argue that Marx's conclusion
>isn't immediately deducible from his starting-point. Of course not,
>but this has no bearing on the validity of Marx's own demonstration.
>Andrew Kliman