Re: (OPE-L) Re: Hume and constraint based theories

From: Ian Wright (ian_paul_wright@HOTMAIL.COM)
Date: Wed Nov 19 2003 - 13:54:40 EST

In reply to Rakesh and Paul:

>Hasn't Michele Naples' point been that the two equalities over determining
>an equilibrium set of equations does not logically invalidate Marx but only
>indicates that capitalist exploitation has to be incompatible with

I am unaware of this work. The logical point is impeccable,
I think, on condition that the distinction between events
and mechanisms is maintained. Contradictory events
cannot simultaneously occur, although mechanisms that operate
to attain contradictory events can simultaneously occur.
In the latter case, reality is overdetermined, and the
events that do in fact occur depend on how the mechanisms
interact. The distinction between "open" and "closed"
systems is shorthand for the distinction between situations in
which multiple mechanisms interact and situations in which
a single mechanism acts. In general, some work must be
performed, whether a real, computational or thought experiment,
in order to create a closed system that excludes the
interference of other mechanisms and allows the mechanism of
interest to act in isolation, and thereby hopefully reveal
more clearly what it is and what it does. This is of course
particularly difficult in the social sciences.

The interaction of the law of value and the law of equal
profits might be of this kind: they may be mechanisms that
operate to attain contradictory events. Now if one commits
the fallacy of reducing mechanisms to the events they
generate in closed systems (e.g., reducing the law of value
to the attainment of prices proportional to embodied labour
values, or reducing the law of equal profits to the
attainment of equalised profit rates) then it is natural
to conclude from the fact that contradictory events are
logically impossible that the simultaneous operation of
the mechanisms that generate them is also logically
impossible. So instead of determining the dynamic interaction
of the mechanisms, the reality of one or other of the mechanisms
is rejected (e.g., rejection of the law of value). Following Bhaskar,
this kind of reduction of mechanisms to events is characteristic
of philosophical positivism, such as Humean philosophies.

(I think Paul and Allin have presented empirical evidence
that real prices are sort of "inbetween" labour value prices
and prices of production, so this discussion has more than
philosophical relevance.)

>>Instead I want to point out that some interpreters of Sraffa's theory deny
>>the existence of contradictory constraints in reality, for no other
>>reason, it seems to me at least, than sets of overdetermined equations
>>cannot be solved (or they think they cannot be solved).
>Could you give an example of Sraffas interpreters doing this?

I have been reading Ian Steedman's "Marx After Sraffa"
recently because a reviewer asked me to relate my paper to it
(hence my paper has not been published yet). I wrote in haste,
and it is not quite accurate for me to say that contradictory
constraints are rejected by argument from the non-solution of
sets of overdetermined equations. That is never stated explicitly.
But there is no discussion of the possibility of contradictory mechanisms,
and hence no discussion of how to deal with contradictory constraints
in models based on linear algebra. It seems to be an implicit
assumption that contradictory constraints simply can't happen,
which is clearly false. But even for models based on linear algebra there
are techniques to solve overdetermined systems, in particular
the generalised inverse that provides least error solutions,
solutions that can be considered as "inbetween" all the contradictory
constraints. (Although I don't think this would be a good way
to go because the solution method of the generalised inverse
may have little or no relation to the dynamic interaction of the
underlying mechanisms).


The new MSN 8: smart spam protection and 2 months FREE*

This archive was generated by hypermail 2.1.5 : Fri Nov 21 2003 - 00:00:00 EST