# [OPE-L:7048] [OPE-L:543] RE: Re: How mathematicians think about equality [OPE523]

Brendan Tuohy (reg@reddfish.co.nz)
Sun, 28 Feb 1999 15:51:54 +1300

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Steve Cullenberg writes:

b. But maybe you are not thinking about direct exchange of commodity
monetized
or "priced" world, where the question of value has already been settled =
in
some sense. Then, I agree it does make sense to think about commodity
exchange as an exchange of equality. Two dollars of oranges will =
exactly
equal two dollars of bread. OK....even those vile neoclassicals would
agree that exchange at this level of abstraction is a relation of =
equality.
But isn't this like wondering which weighs more, one hundred pounds of
feathers or one hundred pounds of steel?

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.

[end quite]

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.=20

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 therefore 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".

Brendan
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