From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Wed Jul 25 2007 - 05:55:18 EDT
Ian, I agree that the issue of whether on uses finite arithmetic or allows real numbers is relatively secondary, so let us leave that aside. What I am mainly arguing against is the following " An important property of the dated interpretation of labour-values has not been su±ciently emphasised. At every stage a net product is produced but it is productively invested rather than consumed by workers and capitalists." I think that this is just wrong. This is not what Sraffa means by the dated labour interpretation, though it is an accurate account of von Neumanns growth model. There is no growth assumed in the Sraffian dated labour interpretation, and you have not demonstrated that it must involve such growth. Merely showing that at each cycle of production fewer means of production are required to be used than are produced, which is all your equation 6 rests on, does not amount to such a demonstration -----Original Message----- From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Ian Wright Sent: 18 July 2007 23:47 To: OPE-L@SUS.CSUCHICO.EDU Subject: Re: [OPE-L] a paper on Marx's transformation problem and Ricardo's problem of an invariable measure of value > 1. That no growth is implied in dated labour values, what is implied is a diminishing fraction of the total labour of past time intervals being necessary for the current output. Under my interpretation there is a process of growth. But if your proposed "finite" interpretation make sense of the mathematics then feel free to translate my argument into terms you are more familiar with. The standard and nonstandard formulae will denote different economic processes under your interpretation too. But as already stated the argument is independent of the chosen interpretation. It is purely a matter of presentation. > 2. This diminishing fraction terminates within a finite time horizon because all units of means of production are integers not real numbers. 0.3 of a hydraulic press is not a means of production. Note that Kantorovich certainly realised this and was careful to present all his quantities as integers. So yes, this integral analysis of linear production processes has been in the literature since 1938. Any integer can be represented as a convergent infinite series. It is eccentric to reject infinite series representations on such grounds. > The example you give from electrostatics is classical electro mechanics which is cast in Newtonian form with continuously differentiable fields. This has been rejected by physicists as only an approximation since Einsteins 1905 paper on the photo electric effect. All physical quantities are quantised - thus integer rather than real. You are mixing up so many issues here it is difficult to know where to begin.
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