[OPE-L:1427] Re: Math and numbers

Iwao Kitamura (ikita@st.rim.or.jp)
Mon, 11 Mar 1996 07:13:51 -0800

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Dear OPE-Lers,

the current debate about math is very interesting to me
and reminds me of Marx's manuscripts and notes on mathematics.
The availables are published by Nauka, 1968(#1).
His concern with mathmatics was centered on "analysis",
especially on diffrencial calculus in later years. He sees
differencial calculus a process of negation of negation.
For Marx, dy/dx is a expression of a "process", and thus
it distinguishes itself from 0/0. What do you think?

Paul C [1365] pointed that Hilbert hoped that " * Mathematics *
by definition* is an expression of formal logic" (Jerry [1353])
and it is invalid today. Cynically, Hilbert's formalism needs
substantial Super-mathmatics. His attempt to build a complete
system of mathematics, however, was proved un-representable by
Goedel's famous two theorems. Regarding this, Ruzavin(#2) wrote
that expelling substances from mathematics has no hope. I tend
to agree with this.

I don't think it's right to say that mathematics can never describe
dialectical processes. But to describe dialectical processes in
mathematics requires our strong consciousness and restructuring
of mathematics.

#1 K. Marx: Matematicheskie Rikopisi, Nuaka, Moskow, 1968
japanese edition is translated by Takashi Sugawara, Otsuki, 1973

#2 G.I.Ruzabin: O Prirode Matematicheskogo Znaniya, Moskow, 1968
japanese edition is tranlated by Saburo Yamazaki, Yasumitsu Shibaoka
Iwanami, 1977

in OPE-L solidarity,

Iwao Kitamura
E-mail: ikita@st.rim.or.jp