[OPE-L:7149] [OPE-L:651] Re: Use and abuse of mathematics

Gerald Levy (glevy@pratt.edu)
Thu, 11 Mar 1999 12:04:44 -0500 (EST)

This must have been intended for the list./In solidarity, Jerry

---------- Forwarded message ----------
Date: Thu, 11 Mar 1999 11:14:23 -0500
From: Gil Skillman <gskillman@mail.wesleyan.edu>
To: Gerald Levy <glevy@PRATT.EDU>

In responding to the following passage from Steve,

>In [OPE-L:643] Steve C wrote:
>> Marx writes on page 127 of the Penguin edition of Volume I the following:
>> "....1 quarter of corn = x cwt of iron. What does this equation signify?
>> It signifies that a common element of identical magnitude exists in two
>> different things, in 1 quarter of corn and similarly in x cwt of iron.
>> Both are therefore equal to a third thing, which in itself is neither the
>> one or the other."
>> 1. This is the crux of the issue on equality that Gil and I have been
>> concerned with, not the later passages in Marx where he talks about a
>> universal equivalent, etc. Marx here is talking about what the
>> fundamental nature of the exchange is when two commodities trade hands.

Jerry writes:

>Perhaps you (and Gil) consider this the issue since you view the above as
>a *deductive* step for Marx.
>Let me suggest an alternative reading: Suppose Marx is asking how can we
>explain the apparent *enigma* or *riddle* that "1 quarter of corn = x cwt
>of iron"?

This formulation begs the central question at hand, since it assumes what
must be proved, namely that exchange establishes something that can be
expressed as an *equation*. Saying one bundle is exchanged for another is
not generically the same thing as saying that one bundle *equals* another.

>Putting it in another way, what explains the *apparently irrational basis*
>for the exchange-value of commodities?

I don't see anything irrational about this, once one gets rid of the
unproved assumption that exchange establishes a relation of equality.

Is it use-value? Marx says, no
>(Ibid, pp. 127-128).

[Although I don't want to make this point central to our discussion, Marx's
claim here is problematic as well. He says that since exchange represents
"an abstraction from" specific use values, that the "common element" cannot
be based on use value. But this doesn't follow. The common element
*could* as a matter of logic be "abstract usefulness", such as indicated by
neoclassical utility functions. Such a reading is exactly parallel to
Marx's claim that we must abstract from *specific* forms of labor to arrive
at abstract labor.] The point here is *not* to support a neoclassical
theory of exchange, but rather to state that *even if* one grants the first
step of Marx's argument (to the effect that exchange establishes a
relationship of equality),the conclusion does not necessarily follow.]

Then, what can it be?
>It appears, at first blush, to be a mystery. Yet, it is a "mystery" which
>has its origins in the [mystified] way in which social relations are
>veiled in the market under capitalism.

As mentioned above, the so-called "mystery" is entirely spurious, as is
Marx's "solution" to the mystery.

>>From this perspective, Marx is not trying to *deduce* value (at least in
>the normal sense understood by philosophers and economists). Rather, he
>is attempting to pose a *question* that is *itself* posed by the way in
>which commodity exchange presents itself to economic agents (and, no
>doubt, to readers of _Capital_ as well). Thus, we could read the above
>passage as an attempt to outline the _apparent_ *mystery* of the
>value-form rather than a logical proof for the LTV.

See above. There is no "mystery" to begin with.

>Perhaps part of the problem (in terms of our communicating with each
>other on this issue) might be that both Steve and Gil are rejecting
>possible Hegelian readings of the text.

Marx himself signals that he is arguing on grounds of Aristotelean logic,
not Hegelian dialectics, when he uses "entailment" phrases like
"therefore", "it follows from this", "must therefore", etc. Dialectical
premises don't *entail* specific conclusions. And even in Hegel-land, the
premise that exchange establishes a relationship of equality must be proved
rather than assumed.