[OPE-L:24] [OPE-L:246] Re: Re: Chapter 1

Ajit Sinha (ecas@cc.newcastle.edu.au)
Thu, 29 Oct 1998 18:45:06 +1100

At 21:00 28/10/98 +0000, Chris Arthur wrote:
>Several posters deny that if one assumed exchange was ideally a net of
>relations characterised by relexivity, symmetry and transitivity anything
>interesting would follow. Russell and Tarski both seemed to think that
>equality followed. If anyone has a reference to more up to date literature
>on the logic of relations I would be interested to hear of it. There follow
>some key quotations.
>Russell *Principles of Methematics*
>p.166 "The principle of abstraction asserts that ,whenever a relation, of
>which there are instances, has the two properties of being symmetrial and
>transitive, then the relation in question is not primitive, but is
>analysable into sameness of relation to some other term.... Such relations
>... are always constituted by possession of a common property.... [a] third
>term to which both have one and the same relation."
>p.219 "Relations which are both symmetrical and transitive are formally of
>the nature of equality."
>p.220 repeats in other words the above on the principle of abstraction and
>adds: "Symmetrical transitive relations always spring from identity of
>Tarski *An Introduction to Modern Logic*
>sec 30 "Every relation which is at the same time relexivie symmetrical, and
>transitive is thought of as some kind of equality."
>{the above propositions seem strikingly similar to those employed by marx
>in section 1.}
> Chris Arthur

I don't think the idea of utility functions beeing RST has anything to do
with Marx's case of exchange of commodities to begin with. I don't think
exchange relation is necessarily an RST--a point I think Gil had made
earlier. x does not exchange against x, and if x exchanges against y and y
exchanges against z, it does not mean that x exchanges against z. You may
always require y to mediate. But let me try to turn the argumentation 180
degrees and see where do we get.

Let us suppose that commodity exchange relations are RST, and that RST
implies a relation of equality of some characteristic of the commodities.
The question then is, what is equal in the exchange relationship between x,
y, and z? Is it labor? Well, Marx says in the third volume that in a
capitalist economy it couldn't be labor. There has been no other
characteristic even thought up by anybody uptil now. Since we cannot find
anything equal in exchange relationship, it implies that it is not
RST--given our first proposition beeing true. Cheers, ajit sinha