ȁȂȃ Partʺ: Economicseconomic theory or to other courses in the curriculum, or whether it might
duplicate existing courses. No, the overriding concern was with whether
the prospective instructor would teach the course with due “rigor,” mean-
ing, in the context, teach it as an application of advanced mathematics.
Rigor does have its proper place. In mathematics or formal logic—and
these of course can enter into an economist’s work—one does not want
lapses from due rigor; one does not tolerate either mistakes or steps in the
argument where crude appeal to intuition substitutes for logical entail-
ment.
Yet even in mathematics, excessive or premature insistence on rigor
can impede progress (LakatosȀȈȆȅ). Davis and Hersh identify a myth
of totally rigorous and formalized mathematics (ȀȈȇȅ, section on “Mathe-
matics and Rhetoric,” pp.ȄȆ–ȆȂ). No one knows exactly what constitutes
a mathematical proof. All proofs fall short of complete formal logic and
so of commanding absolute confidence. A mathematical proof written in
complete logical detail would be unreadable and incomprehensible. “Pro-
fessedly rigorous proofs usually have holes that are covered over by intu-
ition” (p.ȅȈ; an example follows). Proof simply means proof in enough
detail to convince the intended audience. Ļe competent mathematician
knows where his audience should focus their skepticism. Ļere he will
supply sufficient detail, abbreviating the rest. Most mathematical articles,
Davis and Hersh add, do not get close scrutiny from either referees or
journal readers.
Garrett Hardin identifies such a thing as “mathematical machismo”
(ȀȈȇȅ, p.ȂȈ). Arrogant numeracy can do harm. Lord Kelvin said, “[W]hen
you cannot measure it in numbers, your knowledge is of a meagre and
unsatisfactory kind” (quoted in HardinȀȈȇȅ, p.ȂȈ). Yet Kelvin radically
underestimated the age of the earth, predicted that man would never fly in
craft heavier than air, and predicted that any metal cooled almost to abso-
lute zero would become an electric insulator (p.ȃǿ). Many contributions
to science, as by Darwin, Pasteur, Kekulé, Harvey, Virchow, Pavlov, and
Sherrington, have been much more qualitative than quantitative (p.ȃȀ).
Even more so than mathematical proofs, knowledge of the real world
simply cannot be totally rigorous; induction is not deduction.
In Karl Brunner’s view, the new-classical and “Minnesota” school
of macroeconomics, with its insistence on beginning from the supposed
beginning, commits what he called the “Cartesian fallacy.”
Ļe Cartesian tradition insisted that all statements be derived from
a small set of “first principles.” “Cogito ergo sum” and everything else