Gil, you are still begging the question.
You write: "there is no interpretation of the term 'equality' that
I know of, other than by simple tautology, that is sufficient to
support Marx's inference from the fact of exchange (under whatever
conditions) that there exists 'a common element of identical
magnitude' in exchanged bundles."
I have put forth an interpretation of the text according to which
Marx DOES NOT infer the third thing from the *fact of exchange*.
Unless you prove that my interpretation is false, you are not
entitled to refer to "Marx's inference." That assumes what needs to
be proved.
Further, you write:
"It is *Marx* who insists on a *particular* 'equalizing' property of
exchange, so the burden of proof is on those who agree with this
assertion. ... if it can follow from Alan's 'RSTC plus a couple
additional axioms' or Andrew's 'alternative interpretation', it is
incumbent on them to demonstrate it. [For what it's worth, Andrew's
paper, for all of its other virtues, does not do so.]"
This is more petitio principii. I have put forth an interpretation
of the text according to which Marx DOES NOT insist on an equalizing
property *of exchange*. Unless you prove that my interpretation is
false, you are not entitled to refer to "Marx's insist[ence]." That
again assumes what needs to be proved.
You are right about one thing. My paper does not demonstrate the
proposition that is supposedly incumbent upon me to demonstrate.
There is a good reason for this: I think the proposition is false.
I repeat: I THINK THE PROPOSITION IS FALSE. So there is nothing
for me to demonstrate.
You continue to assert that Marx is deducing the existence of a
third thing from the fact of exchange. This assertion has been
challenged. I would suggest that it is incumbent upon you to prove
that it is true.
Andrew Kliman