Brendan closes his post 594 as follows:
>This is the background that saves Marx from having to "prove" the labour
theory of value in chapter 1. His project is a different one, to analyse
the core determinations of exchange production relations to show how they
generate, "compute", this approximation to social labour contents of
commodities in the prices that are formed in exchange. Then by adding more
determinations to construct a more concrete analysis of exchange as a
social relationship, he can show how the divergence of prices from values
arises.
I believe I've shown that no such "approximation" is generated by the chain
of argument Brendan advances, and thus there is no demonstrable relevance
in "show[ing] how the divergence of prices from values arises", since
neither Marx's argument in Chapter 1 nor Brendan's reverse argument
successfully demonstrates why values should be considered at all.
>Marx's abstraction from e.g. arbitrage or the positive price of unimproved
land in Chapter 1 is not a selection of a desired set of exchanges from
among all real exchanges. It's a selection among some of the properties of
the social relationship of exchange.
That's simply not true. The "properties of the social relationship of
exchange" are not dependent *in general* on the particular goods being
exchanged, and in any case neither Brendan nor Marx attempts any
demonstration of this claim.
>Properties that determine exchange's ability to generate prices embodying
abstract labour are expounded first in order, and the properties that
modify this identity to an approximation are brought in later.
This order begs the central question at hand, since no fundamental
connection between exchange values and abstract labor has been established
in the first place, either by Marx's Chapter 1 argument or the alternative
argument advanced by Brendan and Marx in his letter to Kugelmann.
Brendan's remaining comments assume that the relevance of value as Marx
defines it has been established, and since I think I've shown that it
hasn't, I won't go any further. Gil
>But if exchange considered as a production relation is not the set of all
concrete exchanges, then what is it? Exchange the relation of production,
exchange as a social relationship, exchangeability, is a nexus of socially
constructed roles, at base the roles of exchanger (and later, with money),
buyer and seller.
>
>Let's look at the "forms of value" in Chapter 1. They amount to analyses
of definite stages (or moments) of the roles of buyer and seller. In the
first "Elementary or accidental" form of value, Marx introduces the
qualitive fact of alienation of use-values. The exchanger is one who has
unwanted use-values that can be alienated in return for wanted use-values
owned by the other. This weak (and early) form of the social role of
commodity exchanger already defines some relational properties of exchange,
without recourse to generalisation from concrete exchanges. For example,
the fact of exchange directly implies symmetry, and the fact of exchange
ratios (arbitrary though they may be in this form) imposes linearity.
> "It therefore follows that the elementary value-form is also the
primitive form under which a product of labour appears historically as a
commodity, and that the gradual transformation of such products into
commodities, proceeds pari passu with the development of the v!
>alue-form".(p67).
>
>The elementary form of value has "relative" and "equivalent" subforms that
correspond to the two distinct roles in exchange, the one who alienates the
unwanted use-value and the one who provides the wanted use-value.
>
>The second, "Total or expanded" form of value corresponds to the
generalisation of the first form. The exchange relationship broadens to the
point that the exchanger sees their commodity as exchangeable with
"numberless" other commodities in definite proportions. Here
exchangeability of a particular use-value extends to a wide range
(potentially all) of other use-values, and hence the given use-value
appears as the embodiment of social labour. The value of their commodity
(embodied form not in a scalar but in the vector of exchange ratios with
other commodities) appears now to the exchanger as distinct from its
use-value.
>
>The "General" form of value corresponds to the stage of equating the value
of all commodities through the ratios with which they exchange with a
particular commodity, a universal equivalent. It's this stage where the
social relation of exchange becomes able to enforce transitivity (more or
less successfully), and hence calculate a consistent vector of exchange
ratios. Here value begins to obey the all the 4 axioms of of RST and
composition, and thereby becomes a definite positive scalar associated with
each commodity.
>
>The Money form corresponds to the specialisation of a particular
commodity, money, in the role of universal equivalent. The universal
exchangeability of money now becomes its primary use-value, and the social
role of exchanger diverges into buyer and seller (the "relative" and
"equivalent" subforms of the money form).
>
>I won't go further with this interpretation here, it's pretty clear how it
works, and how it extends through further specification to the roles of
worker, capitalist and landowner.
>
>How does this reading of Marx's theory relate to our project of
formalising and developing conceptual models? To me it suggests that our
formalisation should start from a formal specification of the social roles,
as algorithms or repertoires. Our theory should start from the simulation
(and analysis) of the results of the interaction of multiple interacting
processes implementing definite (and simple) roles.
>
>Simulations of populations of commodity exchangers with appropriate
programs should be able to generate actual exchanges that obey e.g. the
equivalence relation laws; in particular they could evolve definite prices.
These "evolved" laws would not take the form of binding rules, disprovable
by a single counter-example. They would be attractors in the space of
possible sets of concrete exchanges computed by the simulacra.
>
>For example, suppose that our simulated exchangers were simple commodity
producers. The vector of values of their products would be an attractor
within the space of price vectors that they actually did compute during
simulation.
>
>Since Marx never had a computer, the option of simulation was not
available as a way of demonstrating the implications of the social roles he
described via people's concrete behaviour to systemic properties. He had to
use analysis. We can use both techniques and use one to inform the other.
>
>To wind up, I can now return to Gil Skillman's accusation of tautology.
Marx's argument runs from a description of a subset of the properties of
the social relation of commodity exchange to the existence of commodity
fetishism, the appearance of the social labour content of products as an
"objective character stamped upon the product of that labour". That's the
kind of "tautology" that deserves the name "theorem".
>
>As for the relationship between actual price ratios and embedded labour,
that quite validly appears at a later stage of the analysis, after the
social relations (surrounding the commodity "labour-power") which govern
the divergence between these vectors have been added to his incremental
analysis of capitalist production relations.
>
>Brendan
>
>
>