<excerpt> This is obviously not the case, since the elements of the first
bundle are units of corn, and of the second bundle are quantities of
iron. Thus they <italic>can't </italic>be equal, according to this
definition (which is standard).
</excerpt><<<<<<<<
...you write,
>>>>
<excerpt>
The equality cannot be (and is not) established in terms of "units of
corn" and "quantities of iron", as you suggest, because these are
"standards of measure for quantities of... useful objects."
The equality is actually established in terms of *units of value* or,
more precisely, in units of the *external* measure of value, i.e. of the
equivalent form of value, which is money when the value-form is
completely developed. This external measure of value expresses its
*internal* measure, abstract labor-time.
</excerpt><<<<<<
All right, let's consider this. First, if I understand you, you're
reading Marx not as meaning literally "1 quarter of corn = <italic>x
</italic>cwt of iron" (which I argue in my point (2) is nonsensical) but
rather something like V(1 quarter corn) = V(<italic>x </italic>cwt of
iron), where V(z) is interpreted as "the equivalent form of value of
bundle z," as expressed for example in money when the value form is fully
developed.
<excerpt>Such claims are the focus of my point (3), which considers a
system of exchanges in which, for example, 1 quarter of corn and
<italic>x </italic>cwt of iron might both be exchangeable for a third
bundle, denominated in terms of a money commodity. Given transitivity,
this can validly be asserted. But even given transitivity plus a number
of additional "regularizing" features, such as linearity, one cannot
validly infer a commonality between the commodity bundles along *any
other dimension* other than V. Thus your (and Marx's) claim ,"This
external measure of value expresses its *internal* measure, abstract
labor-time," does not follow from what came before. You're asserting
what must be proved.
</excerpt>
The Bohm-Bawerk/Knies counter-example works quite powerfully here to
illustrate the invalidity of Marx's claim, I think. Unless you first
*assume* Marx's conclusion, i.e. that abstract labor-time must be the
"internal" measure of equivalent value, then having an "equivalent value"
is not a unique property of *commodities.* Therefore, let us imagine the
same system of exchange as before, except this time 1 quarter of corn
exchanges for <italic>x</italic> acres of unimproved land, and thus V(1
quarter corn) = V(<italic>x </italic>acres land). But it *cannot* be the
case here that
<excerpt>"This external measure of value expresses its *internal*
measure, abstract labor-time," since unimproved land is not a product of
labor. Thus the inference is invalid.
</excerpt>
Gil