Marxism and Mathematics
Julio Huato
juliohuato at SPAMhotmail.com
Wed Feb 7 20:34:44 MST 2001
John Landon <nemonemini at yahoo.com> wrote:
>I do know the math, up to a point, and have a
>sense of 'smell' (?) which is say, life is short,
>these subjects are not so hard, but take time, which
>is in short supply. Is it worth mastering these
>subjects? My unconscious answer was always, not unless
>you have to refute this propaganda! So my instincts
>were born out in this case. Study some good physics,
>this other stuff is junk.
Remarkably, this passage is quintessential "neoclassical" reasoning.
Translated into the jargon it becomes:
<My conscious lifetime as a Marxist is a scarce resource. Therefore I, a
rational individual, will try to allocate it according to the rule that
marginal benefits from all the possible uses of each unit of my lifetime are
approximately equal. And this is so, whichever the "value system" I use to
measure these marginal benefits, and however imperfect my measurement.>
This seems like (implied) calculus to me.
Now, how come is it always mathematical economists who misunderstand the
nature of mathematics and stretch its scope to the point where it becomes
irrelevant or misleading? Is it that mathematical economists are constantly
challenging the way in which physicists use mathematics in dealing with
physical phenomena, while showing little or no knwoledge of the subjects
involved? No! It is the other way round -- some physicists and pure
mathematicians (but, wait, is this right?) challenge the use of mathematics
in economics.
By the by, Mitchell's "theory-free," inferential method to do economics was
contested by the bad guys. If interested, look for the relevant articles at
the Cowles Commission's site, http://cowles.econ.yale.edu/P/cd/cfdpmain.htm.
In addition, take a look at Debreu's address to the AEA meeting and
Arrow's article on math relevance in social sciences -- they are there too.
The anti-Mitchell response doesn't have Marxist echoes... unless we remember
that Marx advocated for some synthesis of induction and deduction,
historical research and logic, with no anti-logic bias (to say the least).
Nowadays, for good or bad, logic appears to be a subset of mathematics. It
seems to me that the math Marx used in Capital reflected his mathematical
background (which, in turn, is to be assessed in its context) rather than
any fundamental, methodological rejection of mathematical reasoning.
But back to my thesis, if mathematics contains today's logic, then every
science is a "mathematical science" (just as every Gramscian person is a
philosopher), explicitly or not, and the question is whether the mathematics
embeded in its reasoning is sound mathematics or not.
And it doesn't seem to me that what has been traditionally called
"dialectical logic" escapes this. After all, as hinted in a previous e-mail
from this thread, modern mathematics deals with the very issues that
distinguished our venerable "dialectical logic" (change, ambiguity,
interdependence, etc.). If it deals with them successfully or not is not
for me to say, but modern dialecticians are not giving us any better
option... or are they?
Julio
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