FOM: wider cultural significance, part 1 (postmodernism)

[Martin Davis]

At 03:06 PM 3/3/99 -0500, simpson at math.psu.edu wrote:

>However, let's not go off on a tangent.  This is the FOM list, so
>let's keep the discussion close to foundations of mathematics.  It
>seems to me that there is a logic tie-in here, via Marx.
>
>Martin Davis 1 Mar 1999 21:36:30 said of the postmodernists:
>
> > These folks are neither "neo" nor "Marxist." Marx thought to have
> > found the truth. These folks deny its existence.
>
>I disagree.  Marx was no truth-seeker.  Indeed, Marx made a major
>contribution to truth-denial, with his theory of *polylogism*, i.e.,
>the theory that there is no one absolute or universal logic.
>According to Marx, logic is conditioned by non-logical factors.  In
>Marx's specific version of the theory, the determining factor is
>social class.  According to Marx, there are competing logics such as
>`bourgeois logic', `proletarian logic', etc., based on social class,
>and the only arbiter among them is raw power or historical necessity.
>(This predated the Nazi theory of `Jewish logic', `Aryan logic', etc.)
>The economist Ludwig von Mises dubbed Marx's multiple-logic theory
>`polylogism'.  According to von Mises, Marx devised this theory in
>order to spare himself the necessity of refuting the arguments of the
>classical economists; he simply dismissed those arguments as being
>based on `bourgeois logic'.  But clearly it goes deeper than that.  In
>my opinion, Marx was actually hostile to all reason and objectivity.
>In this respect Marx was a forerunner of postmodernism, and obviously
>all the postmodernists pay a great deal of attention to him.
>

Oh Steve!

Please show me where *Marx* said anything of the sort.

Marx (and especially) Engels said many foolish things, especially about
mathematics. But he never denied the existence of objective truth. He
claimed to have established a theory of *scientific* socialism based on
objective laws of the development of human society. That this theory was
largely in error is beside the point. I said that he claimed to seek truth
(not that he had found it) as opposed to pomo-ists who deny its existence.

What you and von Mises are confusing is Marx's thought expressed in the
elliptical sentence: "Being determines consciousness" which stripped of the
Hegelian language means simply that the way someone sees the world is
inevitably largely a function of the place in society such a person finds
him/herself. In particular one's socio-economic class has a major effect on
the way one will see the world.

Since you bring up economics, Marx's economics suffered from a grave flaw at
the outset: the idea that in some sense the value of an object should be
proportional to the human labor input to it (labor theory of value). There
is a straight line of deduction from that assumption to the conclusion that
the capitalist mode of production is doomed. Recognizing that this
assumption did not correspond to reality, in a remarkable footnote (in
Capital vol. I), Marx indicated that this mystery that would eventually be
cleared up was like the mystery that 0/0 can represent a finite quantity
(i.e., differential calculus). The task of explainimg the mystery fell to
Engels writing in vol. III of Capital after Marx had died.
Needless to say, his arguments were quite unconvincing. They were torn to
pieces by the classical economist Bohm-Bawerk. It is possible that some
"Marxists" felt they could dismiss this by calling it bourgois economics,
but you can hardly blame Marx for that. In fact, vol. I of Capital was
deeply influenced by such economists as Adam Smith and Ricardo and contains
scholarly discussions of their ideas.

I should also mention, having talked about the flaws in his economics, that
vol. II of Capital represents the first attempt to understand an economy in
the large (what is called macro economics). In particular it anticipates
(and likely provided the inspiration for) Leontief's important input-output
analysis. Without modern linear algebra Marx was constrained to work in
terms of a small number of economic sectors, rather than the large array of
commodities in current versions, and to engage in rather tortuous reasoning
that would have been helped by a little mathematics. (It's all a matter of
an economic conservation law: whatever comes out here was put in there.)

So what does this have to do with f.o.m.? Nothing. With post-modernism? Also
nothing.

Martin