>After following with some awe the explosion of posts on Gil's critique of
>Marx's "derivation" of the labor theory of value in the first pages of
>Capital, the following thoughts occurred to me.
>
>1. The Marx passage in question is not very well-drafted, at least in the
>English translation. I don't read German, but I wonder whether there might
>be some tiny changes in tone in translation. For example, it makes a big
>difference whether one says the common element among the commodities "can
>be no other than" labor time, or "is nothing other than" labor time.
I was called on this point some time ago, probably on PEN-L, and since then
I've checked the translation of key passages with a German-speaking Marxist
friend. An example of Duncan's point: I was getting worked up over the
term "valid" in the phrase "the valid exchange-values of a particular
commodity express something equal", but found out that in this context the
word means something innocuous like "actually obtaining".
>2. It might be more useful to point the discussion of the "common
>substance" type of argument at scientific rather than mathematical issues.
>The paradigmatic case of this kind of reasoning is the physical concept of
>mass, which I think Marx is invoking in this passage. Because we have an
>operational way of equating two objects (that they balance in a scale) this
>_suggests_, but does not prove, that they have some conserved substance in
>common (mass). Now in fact physicists have never satisfactorily explained
>mass, although the conservation of mass has been a fruitful theoretical
>principle for them. This isn't true all the time. For example, some
>physicists tried the same idea with heat, assuming that because one can
>operationally equate two systems through the equality of their
>temperatures, they must have the same amount of some conserved substance
>(which some of them called "phlogiston".) This turned out to be wrong, when
>thermodynamic analysis showed that heat was a form of energy, and linked to
>the degree of disorganization (or entropy) of the system.
I'd like to add some details to this, courtesy of Roger Penrose, Professor
of Mathematics at Oxford, from his book THE EMPEROR'S NEW MIND. Here he
describes the understanding of the concept "mass" that emerges from "the
classical world" of physics, which he defines as everything prior to the
quantum mechanical revolution:
"It is worth while to be somewhat more explicit about the viewpoint that we
have been led to. The conserved quantity that takes over the role of mass
is an object called the *energy-momentum four-vector.* This may be
pictured as a ...(vector) at the origin 0 in Minkowski space, pointing
*inside* the future light cone at 0...
"The Minkowskian 'length' of this arrow is an important quantity, known as
the *rest-mass.* It describes the mass for an observer at rest with the
object. One might try to take the view that *this* would be a good measure
of "quantity of matter.' However, **it is not additive** [emphasis added]:
if a system splits into two, then the original rest-mass is not the sum of
the resulting two rest-masses
[contrast this with Alan's "(de)composability axiom--GS] Recall the
pi-(super naught) meson decay considered above. The pi-(super naught)
meson has a positive rest-mass, while the rest-masses of each of the two
resulting photons is zero. However, this additivity property does indeed
hold for the whole arrow (four-vector), where we must now 'add' in the
sense of the *vector* addition law...It is now this *entire arrow* which is
our measure of quantity of matter.'
[GS: Contrast this with Alan's assessment of the role of mass in physics:
>If this was sufficient, why has physics developed the category of mass? Why
>has it found it necessary to define precisely 'another dimension' than
weight?
Whatever it is that physics has found it 'necessary' to do, the result is
much, much messier that a *one* dimensional thing. But wait, it gets more
interesting...]
"Think now of Maxwell's electromagnetic field. We have noted that it
carries energy. By E = m (c squared), it must also have mass. Thus,
Maxwell's field is also matter!....What about Einstein's gravitational
field? In many ways it resembles Maxwell's field....Yet this energy is not
measured in the standard way...
The energy--and therefore the mass--of a gravitational field is a slippery
eel indeed, and refuses to be pinned down in any clear location.
Nevertheless, it must be taken seriously. It is certainly *there*, and has
to be taken into account in order that the concept of mass can be conserved
overall. There is a good (and positive) measure of mass....which applies
to gravitational waves, but the non-locality is such that it turns out that
this measure can sometimes be *non-zero* in *flat* regions of space--time.....
"In such cases, we seem to be driven the deduce that if this mass-energy is
to be located at all, it must be in this *flat empty space*--a region
completely free of matter or fields of any kind. In these curious
circumstances, our 'quantity of matter' is now either *there*, in the
emptiest of empty regions, or it is nowhere at all! This seems to be pure
paradox. Yet, it is a definite implication of what our best classical
theories--and they are indeed superb theories--are telling us about the
nature of the 'real' material in our world. Material reality according to
classical theory, let alone in the quantum theory that we are about to
explore, is a much more nebulous thing than one had thought." [pp 219-221]
GS: I draw two inferences from Penrose's discussion. First, "mass" is a
much less tidy and more multi-dimensional physical notion than Alan
suggests--and this is before quantum mechanics gets ahold of it, mind you.
I'm not sure that anybody knows exactly what "mass" is in quantum-land.
And second, the physical notion of mass does not in any case seem to be a
secure analogue for asserting the existence of "value" underlying commodity
exchange, since entirely different issues (curved vs. flat space-time,
anyone?) seem to be at stake with respect to the former phenomenon.
Gil
>3. I agree with the point that what Marx's very brief remarks support is
>the tentative identification of a substance common to the commodities,
>which I would call "value". Whether this actually exists or not is like the
>problem of phlogiston. Neoclassical economics, in my reading, explicitly
>denies the reality of value as an independent substance, and argues that it
>is like heat, just a result of aggregating price relations in the economic
>system. What, if it exists, it arises from (labor time, for example) is yet
>another question, and I agree with Gil that this paragraph of Marx's really
>offers no coherent argument in favor of the link. When I've read this in
>the past I've thought that Marx assumed the reader would be familiar with
>the labor theory of value, and that the purpose of this brief remark is
>merely to contextualize his discussion in terms of what the reader already
>knew.
>
>Duncan
>Duncan K. Foley
>Department of Economics
>Graduate Faculty
>New School University
>65 Fifth Avenue
>New York, NY 10003
>(212)-229-5906
>messages: (212)-229-5717
>fax: (212)-229-5724
>e-mail: foleyd@newschool.edu
>
>
>