[OPE-L:7055] [OPE-L:552] Re: RE: Re: How mathematicians think about equality [OPE523]

Michael Williams (michael@mwilliam.u-net.com)
Sun, 28 Feb 1999 21:17:51 -0000

The following message from Brendan seems to me to be right on the button.
>From it I would also draw the conclusion that the equivalence of each
commodity exchange is determined by its embeddedness in a system of
universal capitalist commodity exchange. And, of course, Marx had no
interest in tracing any notional historical development from some primordial
exchange of useful objects in terms of some even more primordial substance
of value.

>But for Marx, the characterisation of exchange as an equivalence relation
depends on positing money, or at >least a "universal equivalent". In Chapter
1 this is discussed under the section "C. The general form of value" >where
Marx at first posits linen in the role of general equivalent.

>As he puts it (p71), "The value of every commodity is now, by being
equated to linen, not only differentiated >from its own use-value, but from
all other use vlues generally, and is, by that very fact, expressed as that
which >is common to all commodities. By this form, commodities are, for the
first time, effectively brought into >relation with one another as values,
or made to appear as exchange-values".

>That is, only by the existence of a universal equivalent is exchange
constituted as an equivalence relation.

>And later (p73), "Finally, the form C gives to the world of commodities a
general social relative form of value, >because, and in so far as, thereby
all commodities, with the exception of one, are excluded from the
>equivalent form. A single commodity, the linen, appears therefore to have
acquired the character of direct >exchangeability with every other commodity
because, and in so far as, this character is denied to eery other
>commodity." Marx continues in a footnote, "It is by no means self-evident
that this character of direct and >universal exchangeability is, so to
speak, a polar one, and as intimately connected with its opposite pole, the
>absence of direct exchangeability, as the positive pole of the magnet is
with its negative counterpart. It may t>herefore be imagined that all
commodities can simultaneously have this character impressed upon them,
>just as it can be imagined that all Catholics can be popes together. It is
of course highly desirable for the petit >bourgeois, for whom the production
of commodities is the nec plus ultra of human freedom and individual
>independence, that the inconvieniences resulting from this character of
commodities not being directly >exchangeable, should be removed. "

>Later, in the section, "3. Transition from the General form of value to the
Money-form" he states that it is only >when the General form of value
becomes restricted to a particular commodity, money, that "the general form
>of relative value of the world of commodities obtains real consistence and
general social validity".