[OPE-L:7043] [OPE-L:538] Re: Re: How mathematicians think about equality [OPE 523]

Andrew Kliman (Andrew_Kliman@email.msn.com)
Fri, 26 Feb 1999 22:23:15 -0500

A reply to part of ope-l 534.

Steve wrote

"2. The question I am getting at, and I believe Gil is too, is a
prior notion of equality in exchange, direct exchange, where such
exchange of two heterogeneous use values implies a third element,
something common to each, a substance....as discussed by Marx in
Chapter One."

I think this is the crux of the matter, and I think this is a
misreading -- unfortunately, a common misreading -- of Marx's
argument. He is not saying that exchange implies the existence of a
third thing. Indeed, in Ch. 2, he says that, at first
(historically), "commodities ... become exchangeable through the
mutual desire of their owners to alienate them" (Vintage, p. 182),
not due to the existence of any third thing, and their exchange
ratio is at first purely a matter of chance.

It also seems to me that the point is just too obvious. Marx would
have had to have been REALLY STUPID to thing that you have to have
a common element in order to have an exchange. In the exchange of
Christmas gifts, or favors, or prisoners, there's no third thing
(unless the relationships become *very* commodified), yet the
exchange does take place.

In Ch. 1, Marx instead proceeds from the equality of *commodities*
(not exchange). The equality of commodities, as I think Steve
agrees, is a fact. Marx points out that their equality to each
other implies an equality to a third thing, which is neither one
of them, but which is the substance of both.

Andrew Kliman