Marxism and mathematics
Julio Huato
juliohuato at SPAMhotmail.com
Thu Feb 8 08:46:42 MST 2001
John Landon <nemonemini at yahoo.com> wrote:
>Your comparison of my statement about allocating study
>time to economics is interesting and amusing, but I
>don't ascribe any mathematical theory to that.
It doesn't matter, John. My point is that your reasoning is amenable to
mathematical treatment. Philip Jourdain, the mathematician, used to say
that mathematics is logic with symbols, and symbols are abbreviations for
words. Life is short, use abbreviations. That you verbally conceptualize
your reasoning doesn't trouble you. What troubles you is to try and corner
the paradoxes and ambiguities of day-to-day language (since no math can
eliminate them altogether) by using symbols and by connecting them with some
"algebraic" grammar.
>As to why mathematical economists have troubles and
>not physicists so much is the Big Enchilada Question
>that has haunted science since Newton. The reason I
>brought Kant into the question, although that seems
>odd, is that he saw the trouble coming early on and
>attempted to determine the boundary between questions
>that have answers and those that are
>crypto-metaphysical. Economists must, maybe, be
>crossing the boundary here. Not hard to find where.
>Utility is a substitute for free choice, I didn't say
>free will necessarily. That doesn't tell us much, only
>why we failed, not how to succeed. This is one of the
>'Whatch out' points in Kant. Are you going to choose
>pure causality and eliminate free choice, to get one
>law, one answer, a science? Or, are you going to allow
>two answers, a causal and a free choice answer. If the
>latter, you lose the math, and can only 'write
>history', describe, not predict. Period. So to get the
>math, you must eliminate the right question.
>So I would guess somewhere in there the answer to your
>question is that a Kantian 'idea of reason' is
>concealed in the foundation, which is like bad cement
>for a building.
>I don't know, really, it makes no sense.
Conventional economics is as distrustful of scientific incursiones in
ontological territories as Kantians. Thus, it holds a trivial, tautological
view of value only because the existence of some "substance" of value is
pure metaphysics. But in all fairness to them, theirs is a mathematical
framework to analyze choice under constraints. Not unbounded, free choice,
but choice under the restrictions imposed by scarcity (i.e., the fact that
the productive force of labor is never infinite). This rings a historically
materialistic tone to my ear. Is the interplay between natural-social
conditions a zero-sum Kantian antinomy or a Hegelian-Marxian "true"
contradiction, one of those that cannot be suppressed, but merely find and
evolve their own forms of motion? Why are the historical outcomes of this
interplay beyond the reach of mathematics?
>As to Wesley Mitchell, I merely meant to suggest that
>the study of how economies actually behave is just as
>important as spinning theories from books of
>differential equations.
>One of the achievements of Marx and Engels, with
>Sismondi one of the first, is to bring home this
>behavior of actual systems. I am sure you are right
>and that Mitchell's ideas may have flaws. But my point
>was only that, if theories are suspect, then
>experience is the best guide, and that's what it boils
>down to in the end. We are always satisfying Kant's
>antinomy, i.e. in this case making choices about
>economies, and, to some degree, reacting to economic
>processes.
>The confusion arises from the simplicity and good luck
>of physicists. You have one small blob of matter and
>you can write a nice equation to predict what it will
>do. This nice math got everyone confused into thinking
>they would do the same thing to social science.
If theories are suspect, try harder. Come up with better theories. The
best guide is a better theory. There's nothing more practical and reliable
than a good theory. Is "experience," as dealt with by statistical inference
and/or historical research, theory-free anyway? I doubt it. Am I against
these methods? No.
>As to dialectics, I don't know. It is likely to
>confuse the study of math. Hegel's dialectical logic
>is not built on Either-Or, while mathematics is. There
>is certainly a resemblance of dialectical processes to
>contexts of change, but it could be confusing to mix
>the two domains.
If joining the dots is confusion, then it must be a good one. Math and
dialectics are not discourses about two different and separate worlds. Not
that it matters, but I don't think this is what Hegel had in mind when he
wrote about the math of his time. It seems to me that there is a lot of
gratuitous hair-splitting to justify our alienation from, distrust in, or
fear of modern math. Today's math has "either-or," "neither-nor," "none,"
"both," "all," "infinitely large," "infinitely many," different orders of
"infinity," "infinitesimally small," "undecidability," and what not. Just
to name a recent, hyped outgrowth -- ever heard of "fuzzy logic"? Well,
mathematicians "discovered" it. Does it apply fruitfully to computer
programs only or also to human issues? You bet.
Thanks!
Julio
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