Re: [OPE-L] Ajit Sinha and equality versus equivalence

From: Andrew Brown (A.Brown@LUBS.LEEDS.AC.UK)
Date: Thu Jul 12 2007 - 06:53:11 EDT


Paul,

I think you are right except for your last point. Logically, society would certainly collapse if the underlying scalar were not labour-time. This 'logic' stems from a characterisation of the nature of human society, not something that formal logic recognises but that is so much the worse for formal logic.

Andy

-----Original Message-----
From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Paul Cockshott
Sent: 12 July 2007 11:44
To: OPE-L@SUS.CSUCHICO.EDU
Subject: Re: [OPE-L] Ajit Sinha and equality versus equivalence

Ajit
-----
Paul, as you know, a relation of equivalence and
equality are not the same thing. Equality is one
specific kind of equivalence relationship. You also
know that a relationship between two goods cannot be
transitive, you will need to introduce another good.
But, of course you know all this better than I do. The
point is, what is one doing by representing exchange
relation as equality relation. Of course, Marx tries
to deduce both money and labor out of it. The
deduction of labor is seriously problematic and as I
claim, equalization relation presupposes money of some
kind.  
--------------------------

Paul
----
We need to distinguish contexts of discussion here.

Context 1 - the immediate exchange with Jurrian
I would generally sympathise with your point in discussion with
Jurrian with respect to 'unequal exchange', which I think is a very
Problematic concept.

Context 2 - the derivation of labour as the common substance
In marxs argument in capital 1.

Here I am not convinced that the argument Marx makes actually assumes equality rather than the more general category of an equivalence relation. Note that he writes :

"Elementary or Accidental Form Of Value

x commodity A = y commodity B, or
x commodity A is worth y commodity B.

20 yards of linen = 1 coat, or
20 Yards of linen are worth 1 coat."

Here the = sign is being used as a short hand for 'is worth'. Trivially, is worth, means 'of equal value' or 'equi-valent', so one could reasonably argue that his use of the equality sign here is as a generalisation from arithmetic equality to the more abstract notion of equivalence.

His argument to derive labour as the common substance :

"Let us take two commodities, e.g., corn and iron. The proportions in which they are exchangeable, whatever those proportions may be, can always be represented by an equation in which a given quantity of corn is equated to some quantity of iron: e.g., 1 quarter corn = x cwt. iron. What does this equation tell us? It tells us that in two different things - in 1 quarter of corn and x cwt. of iron, there exists in equal quantities something common to both. The two things must therefore be equal to a third, which in itself is neither the one nor the other. Each of them, so far as it is exchange value, must therefore be reducible to this third."

He is here using Euclids Common Notion " things that are equal to the same thing are equal to one another ", which was arguably expressing the general notion of an equivalence relation. 

Obviously the relationship between two commodities in the accidental form of exchange is not transitive, but what Marx calls the total or expanded form is:
"Total or Expanded Form of value

z Com. A = u Com. B or v Com. C or = w Com. D or = Com. E or = &c.
(20 yards of linen = 1 coat or = 10 lbs tea or = 40 lbs. coffee or
= 1 quarter corn or = 2 ounces gold or =  ton iron or = &c.)"

It seems to me that he is setting out a definition of an equivalence relation here ( he does not bother with reflexivity, since this is obvious in the case of commodities ). Here he is giving an example of an equivalence set induced by the relation.

Consider then the argument that there must be something common and conserved in the exchange:
" A simple geometrical illustration will make this clear. In order to calculate and compare the areas of rectilinear figures, we decompose them into triangles. But the area of the triangle itself is expressed by something totally different from its visible figure, namely, by half the product of the base multiplied by the altitude. In the same way the exchange values of commodities must be capable of being expressed in terms of something common to them all, of which thing they represent a greater or less quantity."

The example here is an explicit instance of dimension reduction - reducing triangles - a two dimensional figure - to area, a scalar.

His argument seems to be that behind the equivalence relation there has to be a   scalar quantity - strictly speaking he also needs to assume that the value of

 z Com. A > y Com. A

when z>y to establish that behind the equivalence relation and its associated equivalence sets, there is a scalar, since this now allows us to say that one equivalence set is more or less valuable than another.

I think he iw right to argue that it is this structure that allows the existence of money as a dimension reduction device. The assertion that the common scalar is labour, is only an assertion, it is not proved in the argument. There are obviously other possible common scalars - weight, volume, carbon content etc, but none of these had the same immediate empirical plausibility as labour.

I would argue that the logic of commodity exchange implies a common conserved scalar value, and that hypothetically systems of commodity exchange could exist in which something other than labour provided this conserved scalar, ( some system of robot production for instance ), but that in contemporary human society it actually is labour that is the underlying scalar. But this is something to be empirically tested, not something to be logically deduced.


-----Original Message-----
From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of ajit sinha
Sent: 11 July 2007 15:06
To: OPE-L@SUS.CSUCHICO.EDU
Subject: Re: [OPE-L] Ajit Sinha and embodied labour/indirect labour

--- Paul Cockshott <wpc@DCS.GLA.AC.UK> wrote:

> Ajit
> ----
> My point has nothing to do with "unequal exchange"
> etc. When you say "10A exchange for 5B" there is no
> problem. But you are
> mistaken in jumping from here to a mathematical
> equation such as: 10A =
> 5B. There is nothing in the exchange that tells you
> that you could put
> two bunch of commodities as "equal".
>
> Paul
> ----
> Depends how abstract your algebraic concept of an
> equality or
> equivalence operation is.
> I would argue that if an operation induces a
> relation that is reflexive
> , symmetric and transitive,
> Which the exchange relation is, then it is an
> equivalence operation.
>
> This is pretty standard abstract algebra
____________________
Paul, as you know, a relation of equivalence and
equality are not the same thing. Equality is one
specific kind of equivalence relationship. You also
know that a relationship between two goods cannot be
transitive, you will need to introduce another good.
But, of course you know all this better than I do. The
point is, what is one doing by representing exchange
relation as equality relation. Of course, Marx tries
to deduce both money and labor out of it. The
deduction of labor is seriously problematic and as I
claim, equalization relation presupposes money of some
kind. Cheers, ajit sinha
>
> -----Original Message-----
> From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On
> Behalf Of ajit sinha
> Sent: 10 July 2007 17:41
> To: OPE-L@SUS.CSUCHICO.EDU
> Subject: Re: [OPE-L] Ajit Sinha and embodied
> labour/indirect labour
>
> Jurriaan,
> Right now I find myself more busy than I have ever
> been in my life, so I'm afraid my answers to your
> comments would have to be cryptic.
>
> --- Jurriaan Bendien <adsl675281@TISCALI.NL> wrote:
>
> > Well thanks Ajit for your clear opinions, I am
> just
> > trying to figure out
> > what you really mean what you are driving at. It's
> > not that I think I am
> > "completely incoherent", most people understand
> what
> > I mean very well, it's
> > just that my interpretation is different from
> yours
> > (as I said, I am not a
> > professional economist). I am trying to understand
> > better how you see the
> > issues, whether you are really saying something
> > profound, or whether you are
> > just reproducing old arguments (a lot of the
> points
> > you make are not
> > original, but what matters is, what you actually
> > infer from them).
> ________________________
> I never claim to any profundity or originality. It
> is
> for others to decide. I just do my work as well as I
> can.
> ____________________
>
> > I guess the big problem for me is, that your paper
> > in Westra/Zuege as a
> > whole is a very cryptic summation, of a whole lot
> of
> > research on the
> > quantitative implications of different ways of
> > conceptualising Marx's claims
> > about the relationship between production and
> > distribution under capitalist
> > conditions. It seems to me that you claim that
> > Marx's value-ontology is
> > mistaken, because quantitatively it is not
> adequate
> > to explain... what?
> ____________________
> I don't even know what "value-ontology" means? So
> how
> can I believe that it is mistaken or not?
> ______________________
> >
> > 1) What do you mean by "embodied labour"? Have you
> > defined/formalised this
> > in an article, or is it discussed in the archives
> > somewhere? The biblio in
> > Westra/Zuege cites 11 publications by you, but
> some
> > of these I cannot easily
> > get hold of.
> ______________________
> When you write a journal article, you have to assume
> that there are certain terms and concepts there is a
> shared understanding of. You cannot go on "definig"
> every term or concepts in your paper. It is well
> known
> that Marx and even classical economists calculated
> the
> labor-value on the basis of prevalent techniques and
> not the techniques actually used to produce fixed
> capital elements if there has been change of
> technology in the meanwhile.
> _________________________
> >
> > 2) Dated labour - not exactly the same as embodied
> > labour, I know (have to
> > check Sraffa on this)
> ____________________
> Please do.
> ______________________
> >
> > 3) If values, prices of production and market
> prices
> > can in reality deviate
> > from each other in any direction semi-autonomously
> > from each other across
> > time, I think a lot of your models wil not work
> > anymore since they assume
> > accounting identities to be able to establish a
> > systematic relationship
> > between values and prices.
> __________________________
> I didn't know that I had any model in my paper. I
> have
> a feeling that you don't have a good understanding
> of
> the terms and conditions of the theoretical
> problematic of value and that's why you are unable
> to
> understand my arguments.
> ____________________________
> >
> > 4) Products have values, but not prices, if they
> are
> > not being offered for
> > sale. At any time, the majority of products and
> > tangible assets in society
> > are not being traded. For example, means of
> > production being used in
> > production have no actual price, and what their
> > market price might be, at
> > any point in time, could only be estimated on the
> > basis of what similar
> > goods currently trade for on average. That price
> > would be an ideal price,
> > i.e. an assumed price, not a trading price.
> ________________________
> You say, "Products have values, but not prices, if
> they are not being offered for sale." Then the
> product
> is not a "commodity" and therefore has no "value" in
> Marx's theory. If a product is produced for sale,
> i.e., it is a commodity then it has value. If a part
> of this product is utilised by the firm which
> produces
> it, then it amounts to self-buying and its value is
> the same as it is for others. Same is true for
> inventories.
> ______________________
>
> >
> > 5) The question is, why does Marx not talk simply
> > only about prices? Why
> > does he utilise a series of "forms of value"
> > (individual and social values,
> > exchange values, market values, production prices,
> > market prices)? What is
> > you answer to that? In other words, what do you
> > think the theoretical reason
> > is, why he doesn't simply talk about real prices
> and
> > ideal prices, period
> > (since you can devise a concept of surplus and
> > exploitation without any
> > reference to values)?
> _____________________________
> How can I talk for Marx? But the fact of the matter
> is
> that he didn't know how to get to prices or surplus
> without going through labor-values. He died before
> Sraffa was even born! Secondly, he might have
> thought
> he was proving exploitation in a system based on
> equality through labor-values. The question is
> whether
> he succeeded in it or not. May be it will be of some
> help if you take a look at my 'A Critique of Part
> One
> of Capital Vol. 1: The Value Controversy Revisited'
> in
> Research in Ploitical Economy vol. 15, 1996.
> ________________________
> >
> > 6) The two sector model, you discuss in chapter 10
> > of the Westra/Zuege book
> > ("revisiting the theory of value"), p. 178. The
> idea
>
=== message truncated ===



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