This is to continue the discussion with Fred, who writes:
> Gil's main points seem to be the following, which I will discuss in turn:
>
> 1. exchange is not necessarily transitive.
> 2. transitive exchange does not necessarily imply equal exchange.
> 3. equal exchange does not necessarily imply a common property
of commodities.
No, my point is that Marx's argument with respect to exchange
establishes only a relationship of *equivalence*, not *equality*, and
the former does not support the inference that commodities share a
measureable common property. To speak of "equal exchange" begs the
question at hand.
> 4. an empirical test of the LTV is irrelevant to the assumption of the
> exchange of equals, since the LTV does not necessarily follow from
> the exchange of equals.
No, wrong direction of implication. I'm saying the LTV doesn't imply
the exchange of equals, not vice-versa, the latter being the basis of
Bohm-Bawerk's critique, not mine. Thus a result which appears to
confirm the LTV does not confirm the notion that exchange "expresses
something equal", contrary to Fred's suggestion.
Before we get into Fred's arguments, let me note 2 problems up front.
First, Fred hangs a lot of his argument on the putative implications
of the condition of "mutual consistency" in exchange, a term which
a) Fred never defines, and b) Marx never uses, at least not anywhere
in the passages at issue. My argument, now as ever, is with the
first paragraph on p. 127 of the 1977 Vintage edition or the 1990
Penguin edition. The phrase "mutual consistency" never arises there.
"Mutual replaceability" does, but as a result, not a premise, and
I'm arguing that that result is invalid, so it would beg the question
to *assume* it.
2nd, Fred's defense based on "Marx's method of abstraction" boils
down to this: suppose Marx's method involves assuming condition A
holds. Then condition A holds by assumption. [I'll point out
examples of this below.] This tautology clearly does not address the logical
problems at issue.
> 1. EXCHANGE IS NOT NECESSARILY TRANSITIVE
>
> Gil wrote:
>
> Furthermore, absent conditions similar to perfect competition, the
> equivalence established by exchange does not even establish
> transitivity, as mentioned before: even though q exchanges for x and
> x exchanges for y, it does not follow that q exchanges for y. So
> even on the weak grounds of transitivity Marx's argument fails in
> general. I doubt that by "mutual consistency" Fred or Marx means
> "perfectly competitive."
>
>
> My reply:
>
> According to Marx's method of abstraction, Marx in Chapter 1 is not
> analyzing exchange actual, concrete capitalist economies, with market
> imprefections, etc. Instead, Marx is analyzing a very abstract view of
> exchange in capitalist economies - considering only the fact that each
> commodity is in principle exchangble with all other commodities in a
> mutually consistent way.
No, wait. Now as ever my critique concerns the first paragraph on p.
127, where Marx begins his analysis of exchange value. Marx does not
specify any such initial conditions as Fred refers to in this
argument. He doesn't specify his level of abstraction, he does not
assume that "each commodity is in principle exchangeable with all
other commodities", and he certainly doesn't say anything about a
condition of "mutually consistent" exchange. Please tell me where Marx
introduces and defines this term in the passage at issue, Fred (or
anywhere before this passage in Ch. 1). If he doesn't, then it cannot
possibly inform the logical validity of the inferences in this passage.
Furthermore, in his previous post Fred equated "mutual consistency"
with "transitivity." In that interpretation, Fred is saying in the
above passage that Marx concludes that exchange is transitive because
he assumes that exchange is transitive.
>Market imperfections in actual capitalist
> economics may make exchange not intransitive. But, according to Marx's
> method of abstraction, market imprefections affect the distribution of
> surplus-value, and the distribution of surplus-value can be analyzed only
> after the production of surplus-value (i.e. the determination of the total
> amount of surplus-value).
Aside from the fact that Marx never says anything about ruling out
"market imperfections", statements such as "market imperfections
affect the distribution of surplus-value" beg the question at issue
in a major way, since they presume the very theory of value that is
being criticized. It's illegitimate to invoke Marx's theory of value
to defend the grounds on which Marx derives that same theory of
value.
> Thus, Marx abstracts from market imperfections in
> Chapter 1 (i.e. assumes there are none).
Where does he say he's doing that?
>This is not meant to be a
> realistic assumption, but is rather Marx's method of explaining a very
> complicated capitalist reality. One cannot explain everything at once.
Of course not. But one can still proceed from simple to complex
analytical cases without committing logical fallacies, so this does
not excuse or alter the invalidity of Marx's argument.
> 2. TRANSITIVE EXCHANGE DOES NOT NECESSARILY IMPLY EQUAL EXCHANGE
>
> Gil wrote:
>
> Transitivity does not imply equality; equality implies transitivity.
> Transitivity of relationship R states that if aRb and bRc, then aRc.
> It does not follow that a and c are equal, contrary to Fred's claim.
>
>
> My response:
>
> Really? I always thought that transitivity meant that:
> if: A R bB
> B R cC
> and A R dC
>
> then d = bc.
I gave the definition of transitivity in my previous post. I don't
know why Fred has introduced these additional variables, but let's
test his suggestion: let the relationship R be >, "is greater than".
So if A > bB, B > cC, and A > dC, then d=bc? No.
> However, the precise meaning of transitivity is not the crucial issue here.
> The crucial issue is whether d=bc.
Yes, and Fred's argument in the previous post was that transitivity
*implied* equality. We see that in neither his nor my definition is
this the case.
>* I think that this is what Marx assumed
> about mutually consistent exchange.* Marx did not simply assume general
> exchange, but mutually consistent general exchange, in the above sense.
> *Mutually consistent exchange in this sense implies equal
exchange.* (Emphases added)
What? What is this mysterious term "mutually consistent" which Fred
never defines and Marx never uses? And how does it imply these
wonderful consequences? In the previous post Fred equated mutual
consistency with transitivity, but we've seen that transitivity does
not imply equality. If one combines Fred's first statement with the
last statement in the above paragraph, one sees that his argument is
circular: define mutually consistent exchange as equal exchange.
Then mutually consistent exchange implies equal exchange.
Absent such a circular argument, no such conclusion has been
established.
> 3. EQUAL EXCHANGE DOES NOT NECESSARILY IMPLY A COMMON PROPERTY OF COMMODITIES
As pointed out at the beginning of my post, this is not my
argument; it is rather that *equivalence*, the only condition Marx
establishes, does not imply the existence of some measurable common
property.
> Here the main argument is the price of land.
No, it isn't. Land is simply one possibly counterexample to
illustrate the logical fallacy in Marx's argument. It is irrelevant
whether Marx intended to exclude land from his analysis in Chapter 1;
the fact remains that the *logical structure* of Marx's argument from
conditions of exchange to the conclusion that exchange values
"express something equal" must work with *equal validity* if one
includes unimproved land (or any other exchangeable which is not a
product of labor) among the exchangeables. In other words, Marx does
not demonstrate the lemma that "this argument works only for
equivalence sets whose elements are all products of labor, and
necessarily fails otherwise." But since including non-products of
labor leads to a contradiction with Marx's ultimate conclusions, this
demonstrates by counter-example the fallacy in Marx's argument.
But let's not lose sight of the fundamental point: the exchange
conditions posited by Marx establish relations of equivalence, not
equality. The former cannot support the inference of a measurable
element common to all commodities, contrary to Marx's claim. Fred
has not shown, indeed cannot show, otherwise.
> 4. AN EMPIRICAL TEST OF THE LTV IS IRRELEVANT TO THE ASSUMPTION OF THE
> EXCHANGE OF EQUALS, SINCE THE LTV DOES NOT NECESSARILY FOLLOW FROM THE
> EXCHANGE OF EQUALS.
I've already explained that this is not what I've argued.
>
> My response:
>
> As I have said before, I think the main test of Marx's LTV is its empirical
> explanatory power, not the logical arguments in Chapter 1. Marx said the
> same thing in the letter I quoted before ("all that palavar about the
> necessity of proving the law of value in Chapter 1 ...").
By the way, I referenced the same letter, and argued that the
alternative method suggested there does not rescue the LTV from its
logical contradictions, either.
> At most, the
> logical argument proves that the LTV necessarily follows from mutually
> consistent or equal exchange. In this argument is valid, then an empirical
> test of the LTV is also an empirical test of the assumption of equal
> exchange. But even if this argument is not valid, and the LTV did not
> necessary follow from equal exchange, as Gil claims, Marx's theory of
> surplus-value would be still based on the two assumptions of equal exchange
> and the LTV, even if the latter does not necessary from the former:
> The transformation of money into capital has to be developed on the basis
> of the immanent laws of the exchange of commodities, in such a way that
> the starting point is the EXCHANGE OF EQUIVALENTS.
> (C.I. 268; emphasis added)
Yes, he says this, BUT IT IS WRONG. (Emphasis added) Marx has simply
committed another fallacy here, possibly motivated by the conclusions
fallaciously established in Chapter 1.(For particulars,
see either my article in the lastest Economics & Philosophy, or
request my "Marxian Value Theory and the Labor-Labor Power
Distinction", forthcoming next year in Science & Society.) And note that
quoting this passage can't help Fred's argument in any case, since it
presupposes the legitimacy of what went before.
For example, the Fundamental Marxian Theorem establishes that theory
of surplus value has no particular connection whatsoever to the
condition of exchange of equivalents, contrary to Fred's --and
Marx's-- claim.
> Therefore, an empirical text of Marx's theory would still be an empirical
> test of the exchange of equivalents (or exchange of equals, in
Gil's sense). [No, my sense is not different than Marx's. I'm saying
that exchange doesn't establish anything "equal."]
But I don't consider this point very important.
It may not be important, but it's fallacious, for the reasons
suggested above.
>The main point is the
> validity of the labor theory of value, which has been the most controversial
> issue in the history of economics.
Perhaps, but this is a significant retreat from Fred's initial
position vis-a-vis Steve Keen: There he argued that the
relationships of general equivalence established by exchange *imply*
the existence of a measurable element common to commodities.
And that retreat is actually a step forward: if we could just finally discard the
belief that Marx's value theory has any logical basis, we could get
onto the real substantive issues: namely, that Marx's
value-theoretic argument as to the basis of capitalist profit is
essentially misleading, and inconsistent with his historical argument
in Volume III. The logic of capitalist exploitation and
profit is more coherently addressed through a historically contingent
strategic argument which runs as an undercurrent through Parts 3-6 of
Volume I, the RESULTATE, and Part 5 of Volume III.
But one step at a time....
Gil Skillman