A reply to Allin's ope-l 4578.
Allin: "'Does it ... contain any abstract reasoning concerning quantity or
number? No. ... Commit it then
to the flames: for it can contain nothing but sophistry and illusion.'"
I think the shorter of Alan's recent papers, "Reply to some objections," has
answered this objection already. Let me quote.
"A question that certainly springs to my mind is, why 'accounting identities'
should be considered a lowly species of thought? Certainly any working
physicist, once s/he has constructed the Hamiltonian – the physicists' 'energy
accounting identity' seems to believe that all problems of the universe have
been solved. This is actually questionable but there is a marked contrast
between the two disciplines to be explained. Certainly since Hiroshima no-one
could possibly maintain that
E = mc^2
is an uninformative relationship; it is, nevertheless, precisely a 'mere'
identity. More generally (see below) the existence of a time-invariant
identity is more or less a proof of existence for core concepts such as energy
or mass. In general if any object does not persist over at least some period
of time, what basis is there for saying that such a thing exists? Hence if one
is to argue that there *is* such a thing as value, as Mirowski points out,
then it is rather important to identify the invariant relations in which it
participates.
"I think that there is good reason to believe this Marx himself has this
approach and I think it is poorly understood by economists. I emphatically
reject, for example, the idea that Marx's concept of value in Volume I of
*Capital* assumes exchange at values. Nothing in the first five chapters
supports this idea and several passages, as de Brunhoff notes, explicitly deny
it. Chapters 1-5 in my view make perfect sense if understood, just as Euclid's
axioms define the abstract properties of all geometries of lines and points,
as an attempt to define abstractly what all commodity circulation has in
common, regardless of the mode of production or stage of history. Exchange at
values is introduced in chapter 7 *after* Marx has established, in chapter 5,
what to me is exactly an 'accounting identity'; that value cannot be created
in simple circulation. It is precisely because of this identity that any
system of exchanges is homomorphic in respect of the relation of exploitation
to a system of exchange at values, and I find Marx's procedure very
mathematically coherent; since the Chapter 5 identity establishes that the
total magnitude of profit is an invariant with respect to all changes in
relative price and all nominal changes in the price level, it is perfectly
legitimate to study the special and simplest case where commodities exchange
in proportion to values, as the canonical form of all homomorphically
equivalent sets of actual exchange ratios.
[...]
"The deepest issue however concerns an objection raised at the last EEA by
David Laibman: without simultaneous determination, in what sense is there a
theory of economics? In the absence of any definite and determinate motion of
the economy, how can it have any laws? But an accounting identity *is*
precisely a law. It states what is invariant with respect to all possible
motion. That, in my view, is what a law consists of. The 'law' of gravity
cannot be understood as a definite prediction that any particular objects will
move definitely up or definitely down; it is simply a description of the
invariant relations that must hold between them, regardless of what they do. I
think that this is the concept of a 'law' which economics has simply lost
sight of.
"Finally there is an ontological issue also. What objects 'exist' in a
completely free-standing dynamic system? Equilibrium provides no clues. A
tornado has no equilibrium, but most definitely exists. The ontological
problem in a dynamic framework amounts to this: what is the basis for
asserting that something persists in time? An identity for me, and I think for
Marx, is precisely a statement of what persists in time and therefore has the
character of a *proof of existence*; a great deal of his work goes into
establishing that capital reproduces the conditions for its own existence –
the two classes, the use-values it requires, the money it requires, and so on.
The problem Marx sets himself is to *deduce* reproduction from the category of
value. The 'standard interpretation' reverses this, taking reproduction as
'given' (to borrow, with malicious intent, a term from Fred) and from it
deduce value."
Andrew Kliman