Fonseca on math and explanation

[GREG RANSOM <GRANSOM@xxxxxxxxxxxxxx>]

I have been following the Davidson-Fonseca et al. conversation with
great interest.  From my own perspective much has been learned about the
background understanding tacitly contained in our use of the language
of uncertainty and logical determination -- and perhaps we are even seeing
progress made in the development of new lines of significant language
use (and the giving of misfired attempts at significant uses of language).
My question has to do with the possible role of pure formal systems and
mathematics in explantions of empirical problems in our experiece (e.g. the
problem of explaining the undesigned process that pushes prices toward
costs of production) and in the clarification of language use (e.g. the
use of the words 'capital goods' for the future use producing non-permanent
means like scaffolding on a construction cite).  As far as I can see there
are only three possible contingent causes for explaining the undesigned
order found in the prices->costs pattern or for the institions of several
property, the evolved sense of justice described by Hume, or that of money.
These are (1) human learning and discovery; (2) human imitation of the
behavior patterns of others, or (3) pure chance or incidence.  The work of
Kuhn, Popper, Wittgenstein, Hayek, Polanyi, Weimer, etc. etc. suggests that
none of these three alternative contigent causal explanations for undesigned
social order, whether in the research community of the natural sciences
or in the language of a small community, can be capture in a bird's eye view
or fully specified formal system of posited or given abstract or concrete
objects or functions.  First Hayek in the 1940s, then Popper in the 1950s,
and others since (most importantly G. Edelman) have pointed out that from
the point of view of learning (and most particularly in science) the future
is conceptually open-ended and yet to be imagined and discovered.  Hayek and
Wittgenstein and Kuhn have shown why rule learning by imitation will in the
same way be conceptually open-ended -- and similarly yet to be imagined and
constructed.  I take it that Davidson's point about uncertainty and its
role in the explanation of undesigned social institutions is of a similiar
kind -- the causal uncertainty that is of interest here is conceptually
open-ended and beyond what we can imagine or construct.

Typically the argument for mathematical modeling in economics takes what
can be called the Hahn-falacy.  Mathematical modeling is justified for its
ability to talk us out of our blind-ness to the obvious which no-one but
those under the spell of another mathematical model ever suffered from (e.g.
the bizarre efficiency standards of Pareto or Pigue welfare economics).
Gonzolo suggests that the case for mathematics in economics has already
been made.  Of course, so also has the case for the use of tarot cards been
made in the field of the para-normal and the case for star-gazing in
astrology (accepted by most astronomists pre-Copernicus).  My question for
Gonzalo is to explain the case for mathematics in the contintent causal
explanation of undesigned market patterns of the sort we all experience in
the use of money, exchangin the stores and banks, and in following the
unanticipated patchwork framework of the rules of several property and the
sense of liberal justice.

I don't doubt there is an answer, but I would like something more than
a shear assertion of institutional power and control by the mathematical
economists.

Greg Ransom