[OPE-L:7044] [OPE-L:539] Equality and Equivalence: Response requested

Alan Freeman (a.freeman@greenwich.ac.uk)
Sat, 27 Feb 1999 09:46:19 +0000

Gil, Steve, Brendan (and anyone else that wants to respond)

A small point where a response would be useful

Gil writes
> I'd like to point out for the sake of clarity that *I'm* not translating
> "equality" as "exchange in proportion to abstract labor." ...My point
> is that exchange relations, with or without the law of one price, do not
> establish a relationship of *equality* in a sense sufficient to support
> Marx's Chapter 1 argument that abstract labor is in some *qualitative*
> sense the basis of exchange value.

One of the reasons that we keep going backward and forward on this question
is that we have not established what we all think Marx means by 'equality'.
One of the reasons we have not done this is that each comes to the
discussion with her/his own prior concept of equality, and then attributes
it to Marx, or attempts to establish that Marx could not reasonably have
meant anything else.

I think my [OPE 529] establishes a precise sense in which exchange
relations establish a relationship of equality which conforms to standard
mathematical thought, and matches a possible reading of Marx's argument.
That is, one may read Marx as saying exchange-relation is RST; that basket
decomposition holds and that by 'equality' he means the relation between
exchange-equivalent sets of baskets.

I want to know whether you consider this a *possible* statement of Marx's
argument. Not the only one, not the true one, but a *possible* one. I'm
happy to reciprocate by considering any definition of 'equality' that you
wish to propose. Then we have a *variety* of possible definitions of
equality and a *variety* of readings of Marx, which we can assess and

I haven't yet argued that my definition supports the chapter 1 argument
because I think the definition of equality as such is prior. But if we can
agree that [OPE 529] establishes something which, for the sake of argument
at least, I can specify as an initial axiom, then I'm quite happy to
proceed from there to discuss whether and how these axioms support the
chapter 1 argument.

Steve has started to answer this question but I'd like to know what others
think to minimise talking at cross-purposes.

Do you agree