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

From: paul cockshott (clyder@GN.APC.ORG)
Date: Thu Nov 20 2003 - 11:26:56 EST

>>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).


One of the things I am interested in at the moment is seeing
how one might construct a model of price determination that

1. Values
2. Prices of production
3. Random noise

and see how much better such a composite model would fit
observed data.

I had not thought of using generalised inverse for this ( I think
APL calls it 'solve'). It might be possible provided that
one could linearise both sets of constraints.

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