[OPE-L:7053] [OPE-L:548] How mathematicians think about equality [OPE 523]

Alejandro Ramos (aramos@btl.net)
Sun, 28 Feb 1999 14:35:14 -0600

In OPE-L 546, Gil writes:


I've illustrated this with the counter-example involving exchange of,
say, <italic>x </italic>boot-polish with <italic>z </italic>acres of
unimproved land. If the mere fact of systematic exchange (with or
without LOOP) were sufficient to establish "equality" in the sense
required by Marx, it must follow that boot-polish and unimproved land
share a "common element of identical magnitude," which according to
Marx's subsequent argument can <italic>only</italic> be abstract labor.=20
But unimproved land is not a product of labor. Contradiction.

One could easily multiply the counter-examples. Consider exchanges in
airwave frequency rights, such as have been established by auction in the
U.S. According to Marx's argument in Chapter 1, the equivalence
conditions established by systematic exchange imply a "common element of
identical magnitude" in different sets of air wave rights. Well, what
can that common element be in this case? It can't possibly be abstract
labor; neither the air waves nor claim rights to them are products of

Or consider markets in financial instruments, where one is much much more
likely than in commodity markets to see LOOP obtain, due to the relative
ease of arbitrage. What is the "common element of identical magnitude"
in different bundles of securities that are exchangeable for each=20


Gil, are you following here B=F6hm-Bawerk's argument in "KM and the close
of his system", pp. 68ff? B=F6hm quotes a related passage by Karl Knies:

"There is no reason apparent in Marx's statement why the equation
<italic>1</italic> quarter wheat =3D <italic>a</italic> cwts. wild-grown
wood =3D <italic>b</italic> acres of virgin soil =3D <italic>c</italic> acre=
of natural pasture-land, shold not be as good as the equation
<italic>1</italic> quarter wheat =3D <italic>a</italic> cwts. of
forest-grown wood." in B=F6hm, p. 70.

Regarding this, what do you think about Marx's argument in Capital I, p.