[OPE-L:1374] Re: Maths

Allin Cottrell (cottrell@wfu.edu)
Fri, 8 Mar 1996 08:12:59 -0800

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My $.02 on mathematics, formalization and all that. First of all, I
think there's a problem that some people have in mind, namely the
tendency (very evident in modern neoclassical economics) to elaborate
mathematical models for their own sake, without much regard to the
substance of the analysis. I think we can all agree that is to be
avoided. Also, I suspect we can agree that there are qualitative aspects
of Marx's analysis that are important, yet not susceptible to
mathematization: for instance, his whole analysis of the conditions under
which products assume the form of commodities.

But that said, I tend to agree with Paul that our ability to express our
analysis of a particular domain in precise, formal terms is an index of
our degree of understanding. Alan points out that Marx uses lots of
numerical examples but little algebra, and says "jolly good too". Well,
yes, numerical examples can play an important pedagogical role, but they
are also quite limited. How far do the results of such exercises depend
on the particular numbers chosen? One can answer this only if one is able
to work out the issue in greater generality, that is to say algebraically.

I also believe that if we are investigating a domain (such as that of
"moral depreciation") where there is a lot of complex interdependence
among the variables, we can be sure that we have taken everything
relevant properly into account only if we can produce a general
mathematical treatment. Personally, I find writing down models of this
sort of thing very useful. Sometimes when you do the math it confirms
what you started out thinking; sometimes the results are quite
surprising, and that forces you to go back and figure out where the
mathematical result is coming from, which (if the math was right!) can
yield important new insights.

Allin Cottrell