[OPE-L:203] Re: abstract labor and OPE abstracts

Paul Cockshott (wpc@clyder.gn.apc.org)
Thu, 5 Oct 1995 11:59:21 -0700

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Jim has asked for an abstract of an argument
about the nature of abstract labour and
value. Here is a short summary of my

Marx first argues that echange value
is a mode of representation of something

"the valid exchange-values of a given commodity
express something equal; secondly exchange-value,
generally, is only the mode of expression, the
phenomenal form of something contained in it,
yet distinguishable from it." (Cap 1 p 37)

He then argues what the only common substance
is :

"there is nothing left but what is common to them
all; all are reduced to one and the same sort of
labour, human labour in the abstract." (Cap 1 p38)

The then identifies this with value:

"the common substance that manifests itself in
the exchange-value of commodities, whenever
they are exchanged is their value." (Cap 1 p38)

Thus we have that exchange-value is the form
of representation of abstract labour which
is the same thing as the value of commodities.
Thus abstract labour = value.

He then says that the magnitude of value is
dimensionally equivalent to the magnitude
of labour required for a use-value's production:

"A use value or useful article, therefore has
value only because human labour in the abstract
has been embodied or materialised in it.
How then is the magnitude of this value to be
measured? Plainly by the quantity of the
value-creating substance, the labour, contained
in the article." Cap 1 p 38

Note that he talks of articles or use-values
having value - not commodities having value here.
Since commodities are a subset of use-values the
above obviously applies to them in particular,
but the concomitant is that, use-values that are not commodities
also have value.

Thus the expression of value as exchange value
is a historically specific form:

"the 'value' of a commodity only expresses in
a historically developed form, what exists in
all other historical forms of society as well,
even if in another form, namely the social
character of labour, so far as it exists as the
expenditure of 'social' labour power. ... Herr
Rodbertus takes Ricardos measure of the quantity
of value; but just as little as Ricardo has
he grasped or explored the substance of value
itself; e.g. the mutual charact of the labour process
in primitive community life as the
community organism of labour powers allied
to one another" ( Notes on Wagner p 207, Carver 75)

Thus although the value ( in quotes ) of a
commodity is a historically specific form,
because the commodity is a historically specific
phenomenon, the underlying substance that
constitutes value is both common to different
modes of production, and a property of all
humanly produced useful articles.

However we can construct an outline argument
from 'first principles' to establish
this without relying on Marx. I will attempt
to put online a full form of this ( I currently
have it in Latex ), but here is the
argument very much in outline form:

We use the concept of metric spaces and
try to establish the law of value as
a conservation law

what is meant by the law of value -
phrase little used by marx
certainly no definition as one would expect
for some thing like Hookes law

Phrase came into general use this century
to refer to economic regulation

debates about socialism

Alternative definition:

The law of value states that:
In exchanges of commodities sums
of value are conserved.

It being understood that value is abstract embodied

Advantages of this definition:

1) It is cast in the normal form of a scientific law

2) It is empirically testable

3) It has a precise meaning.

4) It emphasises that value can not arise in

Metric spaces
A metric space (X,d) is a space X together with a
real-valued function d: X X r real , which
measures the distance between pairs of points x
and y in X where d obeys the axioms:

i) Commutivity
d(x,y)= d(y,x)

ii) Positivity
0<d(x,y)< if x1 y

iii) Self identity

iv) Triangle inequality
d(x,y) d(x,z) +d(z,y)

Examples of metric spaces

Euclidean 2 space
defined by the pythagorean metric:
d =( dx2+dy2)
the distance is root of the squares of the
distances in the x and y directions

Manhattan space
So called after the Manhattan street plan, the
metric is simply the sum of the absolute
in x and y directions
d = |x| + |y|

Equality operations in metric spaces

Let us define two points y, z I X to be equal with
respect to x if they are equidistant from x under the
metric d.


y =x z if d(x,z)= d(x,y)

Equality sets

If one has an equality operator E
and a member y of a set X, you can
define an equality subset ,

that is to say the set whose members
are all equal to y under E.

The equality set of y under =x
using the Euclidean 2 space metric is a circle.

The equality set of y under =x using a
Manhattan metric is a diamond.

The definition of the commodity bundle space

A commodity bundle space or order 2 is
the set of pairs [ ax, by] whose elements
are a units of x and b units of y.

A commodity bundle space of order 3 is
the set of triples [ ax, by , cz] whose
elements are bundles of a units of x, b
units of y, c units of z.

Etc ...

The set of all points equidistant with [r iron, s corn ]
from [p iron , q corn] under a Euclidean metric. Is
a circle centered on [p,q] with [r,s] a point on the

Clearly we have a distinct equality operator =[p,q]
for all points [p, q] in our corn iron space.

Let us consider the particular equality operator, that
of all points equidistant from the origin,

The observed sets constitute the isovalent contures
in commodity bundle space.

They are straight lines - called by economists
budget lines.

Why are they not circles centered on the origin?

Why does commodity space have a non-Euclidean

Spacial metrics are so much part of our mode of
thought that to imagine a different metric is
conceptually difficult.

Most of us have difficulty imagining the curved
space time described by relativity theory, Euclidean
metrics being so ingrained in our minds.

Conversely, when looking at commodities, a non-
euclidean metric is so ingrained that we have
difficulty imagining a Euclidean commodity space.

But there is something very strange about the
metric of commodity space.

d = | ax + by|

If value were just a matter of providing an ordering
or ranking of combinations of goods, then a Euclidean, or indeed
any other, metric would
pass muster. It is some additional property of the system of commodity
production that imposes this specific metric
characteristic of a system governed by a conservation law.
This fits in rather nicely with the labour theory of value,
where social labour would be the embodied
substance conserved during exchange relations, which in turn provides us
with some justification for casting the law of value in the
form of a classical conservation law.

Other examples - energy conservation
One dimensional 'substance' underlying the
What is the cause of this:
1 explanation due to unidimensional underlying

2 what is ruled out and what is ruled in
explanation due to logic of the exchange
arbitrage arguments

Representation mechanism only allows one
dimension to be represented thus value can only
have a single substance
Could it be something else - energy
show contradiction
Must be non produced input
Could it be land
trinity illusion
Labour only non optional non produced input