Re: value, labour and conservation laws

From: Paul Cockshott (wpc@DCS.GLA.AC.UK)
Date: Tue May 20 2003 - 04:49:38 EDT

Andrew Brown wrote:

> Hi,
> You wrote:
> > The existence of the field can be deduced from the metric
> > space imposed by commodity exchange itself. Whether the
> > field is induced by labour is an empirical question. I think
> > empirical studies have established that it is, but at
> > least in principle, as scientists we have to allow that
> > it might be some other input to production - say energy
> > that induced the field.
> >
> > > Indeed I am
> > > arguing that the only thing that can possibliy constitute it is
> > > abstract labour. Let be more precise: I do not think I would it is a
> > > 'field' at all; it is a substance. This takes us into the
> > > metaphysics of the (highly contested) notion of 'field', on which, I
> > > supsect, materialist dialectics has rather alot to say.
> >
> > The concept of a field is well defined in math as a space with an
> > associated value at each point, One usually assumes a vector space and
> > a vector value, but the extension to other spaces and non vector
> > values is fairly conventional.
> >
> > I am not aware of any materialist dialectical criticism of this, if
> > you want to critique it you are setting yourself against science since
> > Maxwell.
> I had in mind the notion in physics of a 'field' of potential. Like
> 'energy' and 'force' this notion raises many philosophical issues
> (see below). Regarding your exposition of the notion of 'field' that
> you are employing, any definition in purely mathematical terms is
> necessarily incomplete. My question is: what quality is involved? I
> am pointing out that some quality must be involved; to talk of a
> field, as you have defined that notion above, pressupposes a
> quality whose quantity is denoted by the values to which you refer
> (i.e. the values associated with the space constituting the 'field').

Consider the case of  potential energy, a scalar field that can be
associated with each point in the phase space of a collection of
particles, and kinetic energy another scalar field associated
with each point in phase space.

This seems to be very similar to value. We know of
energy through its effects, these can be explained by the abstract
mathematical concept of a conserved scalar, with the
property that for all state exchanges the constraint
C = K + P

where C is a constant and K and P are the scalars for
kinetic an potential energy.

In practice what we observe is exchanges between states
each of which is a 6n vector for the positions and velocities
of the particles in the system. The conservation is not
immediately obvious, since the scalars K and P are non
linear functions of the state vectors. But we do not
ask 'what is the substance of energy', we deduce its
existence from the metric properties of the phase space.

I contend that an exactly similar situation holds with
generalised exchange value - we can deduce the necessity
of its existence from the metric properties of exchanges
between commodities, with exactly the same non-euclidean metric
function that is used in the potential + kinetic energy case

Talk about 'substance' or quality is to introduce a pre-scientific
common-sense metaphysics into a scientific question.

> > > Now, perhaps, you can see what I am getting at, and where we
> > > disagree? You are presuming, at least from my point of view, that
> > > *something* is being measured. You have called it a field. In your
> > > analogy it is mass.
> >
> > If one is looking for an analogy I would chose energy, whose existence
> > we deduce from an exchange relation between forms of movement.
> >
> Certainly, we can deduce the specific presence of energy from
> specific movements. But we can only do this given the general
> concept of energy as such. The concept and use of the term
> 'energy' as such is emphatically not a simple deduction from forms
> of movement. It is a very difficult notion registering the unity of the
> very diverse things of the universe. It is a task of philosophy to
> elucidate the meaning of the term 'energy'. Physicists, and indeed
> everyone else, can and do use the term without having to worry
> about its philosophical aspects.

Why does anyone have to worry about its 'philosophical aspects'
other than philosphers who would be out of a job if they did not.

> >
> > > I am saying that we must first establish *what*
> > > is being measured. What is the equivalent of notion in economics to
> > > the notion of 'mass' in physics? We cannot just say 'it is a field',
> > > it is a 'something' and then get on with it.
> >
> > Why not, one can deduce the existence of the field
> > from observables, just as one can deduce the existence
> > of energy from observables.
> Your analogy does not seem to work. Deducing the existence of
> 'energy' entails deducing the quality that is being measured (viz.
> qualitative characteristics of energy). It entails answering the
> question I keep posing. Deducing the 'existence' of a 'field' does not
> answer the question. It begs the question: what quality is involved?

What is the 'quality' of energy other than being a conserved
scalar, which is of course something purely quantitative.

> >
> > There exists a scalar field of abstract exchange value, there
> > exist various other fields implied by the structure of prodution: the
> > field of labour contents, of oil contents, steel contents etc. Which
> > of these induces the exchange value field can only be established by
> > empirical tests.
> A 'scalar field of *exchange* value'??? Not value? Now you seem to
> be saying that there is a field of exchange value, *and* a field of
> value. For me, 'exchange value' must be the form, and the external
> measure, of something else, some quality being measured.
> Without this then 'exchange value' at best refers to
> 'exchangeability', something that can only be measured, in general,
> by a vector of all exchange values for a particular commodity, and
> which therefore is, in general, incommensurable between different
> economies (and different points in time of the same economy).

I use the term generalised exchange value for the conserved
scalar that operates in a system of commodity exchange. I use
the term value or labour value for the scalar field derived
from the constraints of the conditions of production.

The testable scientific hypothesis in the labour theory
of value is that the former field is caused by or closely
constrained by the latter.

Paul Cockshott
Dept Computing Science
University of Glasgow

0141 330 3125

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