Andrew:
>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.
The paragraph Andrew refers to is follows.
"This law clearly contradicts all experience based on immediate appearances.
Everyone knows that a cotton spinner, who, if we consider the percentage
over the whole of his applied capital, employs much constant capital and
little variable capital, dows not, on account of this, pocket less profit
or surplus-value than a baker, who sets in motion relatively much variable
capital and little constant capital. For the solution of this apparent
contradiction, many intermediate terms are still needed, just as, from
the standpoint of elementary algebra, many intermediate terms are needed
before we can understand that 0/0 may represent an actual magnitude.
.." ( Penguin P421, chapter 11 Vol.1)
It's obvious that Marx concerned with the relationship between differential
calculus and dialectics when he wrote Vol.1. According to his notes on math,
he developed his thought on differential calculus further, studying Taylor,
Maclaurin, Lagrange etc.
Andrew:
>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.
I agree this is the most important point. Concrete logical (sometimes
also formal) descriptions are required to understand dialectical processes.
>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?
>
I believe it's not me who can shed light on that. I think Hegel is clear
about absolute negativity and the negation of the negation. For him,
pure 'Sein' is an un-determined pure direct form of ideal. So that
pure 'Sein' is its absolute negativity = 'Nichts'. The truth of them is
their unification. It is 'Werden'. This may be interpreted as a process
or motion. Such ideas are also found in Bhuddist philosophies.
in OPE solidarity,
Iwao
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Iwao Kitamura
E-mail: ikita@st.rim.or.jp