Linearity is not the issue here. As I, and Gil, argued a few months back
at length there is no self-evident, a priori reason to conceive of the
process of exchange as a relation of equality.
Yes Steve, I'm familiar with the debate; it's been going on a while, and
from time to time I've been involved in it, starting with the old 1995
PEN-L debate and continuing in the 1996 OPE debate. I didn't intervene in
the current round because I had nothing new to say but I followed it with
interest and not a little sadness, since it seems that each time around it
merely covers the same ground, which always suggests that people aren't
reading what each other says carefully enough.
I came in recently because I did have something new to say.
By and large I don't disagree with your central point in it, or at least I
haven't until now when you say that linearity isn't the issue, because I
think linearity is the issue.
However before we get onto that, there's a prior point of clarity; it seems
abundantly clear from all your contributions that what you mean by equality
is exchange in proportion to magnitude of abstract labour. If you mean
something different, then perhaps we should get that clear before
proceeding onto linearity.
Here's a list of citations from your post that suggest to me that when you
speak of equality, you mean exchange at values. I hope you'll enlighten me
if your own meaning is different from that which I attribute to you.
[OPE 298]
The question I have been pressing is: does Marx (and many others since)
define exchange values this way because he/they feel that there is
something about the nature of exchange that either theoretically or
empirically enforces such an exchange of equality, or, is it the case that
Marx considers exchange as an equality as a simplification and sets up
exchange ratios between commodities so that in fact they are equal in
abstract labor. And, if the latter, the question becomes just how robust
this simplification is.
I want to stress this point. There is nothing obvious about the claim that
exchange should be understood as an equality.
[OPE 288]
(ii) Is there a theoretical proposition that under fairly non restrictive
and general conditions will guarantee that exchange ratios will necessarily
be governed by equal magnitudes of abstract labor contained in each
commodity. I don't know of any such propositions.
[OPE 270]
I have no problem with this as far as it goes. My concern is why should we
expect the process of exchange to be one of equal amounts of abstract labor
time. That is, do the 2 apples exchange for the 3 oranges "because" they
have equal amounts of abstract labor time contained in them?
[OPE-241]
That doesn't make any sense. But
obviously many Marxists want to see exchange characterized by the relation
of equality, which brings us into the realm of a third substance, different
from each commodity, but common to both (abstract labor).
[OPE-164].
But defining these maps is a very different exercise than arguing that
exchange produces or creates through arbitrage (of what?) the equivalence
class of the equality of values, for example. I don't see the process
whereby that would occur.
[OPE-172]
It seems to me that the motivations for exchange, and the acceptance of
particular exchange ratios (nb, I'm not saying not exchange values) as
"fair" (by which all I mean here is that the exchange occurs without
physical force), will always be culturally and politically inflected, as
well as individuated.
[OPE 184]
Another relation which satisifies the conditions of an equivalence class is
the relation of indifference, and there is no presumption of equality
there. There are others as well. My question is, what is it about a
market exchange that would make us think that exchange should be the
characterized by the particular equivalence class of equality, and that the
metric of this equality should be abstract labor.
[OPE-203]
I am not sure what you, or others, mean by an exchange of equivalents, if
that is not also equality. My question again is why is it (a) obvious, or
(b) insightful, to conceive of exchange as an exchange of equals. As to
references, I said it before, 99% of economists who think about exchange
formally do not begin by presuming exchange as an equality. Why should
marxist economists do so?
(Alan adds: amen to that)
Alan