I found Iwao's discussion of Marx's view of the differential calculus
as a negation of the negation quite interesting, though my knowledge
of calculus (as theory) is meager.
One thing I can point out is that Marx discussed dy/dx = 0/0 in _Capital_.
I don't remember the exact refence, but I think it is in Ch. 11 of Vol. I.
It occurs in the context of the "tranformation problem," i.e., Marx notes
that the equalization of profit per unit of capital advanced prima facie
contradicts the law of value, and then says that to resolve the prima
facie (or apparent) contradiction, "many intermediate terms" are needed.
Ricardo's method of "violent abstraction," saving the law of value by
abstracting from the phenomena that contradict it, is critiqued. In
bring up the needed "many intermediate terms," Marx says that the same
thing, i.e., mediation, is needed to understand how 0/0 can reprsent an
actual number.
It seems to me that this might have something to do with what Iwao was
saying. 0/0 is itself not an actual number, but understood as a *whole*,
not as a ratio of two independent (non-)quantities but as a *representation*
of the result of an operation, it indicates that the operation yields
a "real result." Without the process of mediation being conceived together
with the result, however, i.e., without mediation, 0/0 is meaningless.
It also seems to me that Marx's discussion is very important for understanding
how positivity (a "real result") can emerge in and through negativity. This
accords with Hegel--"the positive in the negative." As Marx notes, making
a change (e.g., a change in X that yields a change in Y) and then cancelling
the change (bringing x and thus Y back to their original values) brings
us back to the begining, yielding no new result. The hard thing to see is
that all negations are not of this type, but this can indeed be seen in
differentiation, he says.
My question is, what makes "absolute negativity," the negation of the
negation, different? How much does it rest on the concreteness of the
negations? (I.e., "the rose is a not-rose" contains an abstract negation,
"not-rose," a negation that lacks determinacy. But "the rose is red"
contains a concrete, determinate, negation, even though "red" is no more
"rose" than "not-rose" is rose.) I find it hard to understand the
"second negative," why it requires the "first negative" and *how* the
positive in the relation emerges. E.g., how can we comprehend the
movement from "not-rose" to "red"?
Can anyone shed light on this?
Andrew Kliman