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 >equilibrium? 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). -Ian. _________________________________________________________________ The new MSN 8: smart spam protection and 2 months FREE* http://join.msn.com/?page=features/junkmail
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