Re: Article in the Chronicle of Higher Education

[pdavidso <pdavidso@xxxxxxx>]

>===== Original Message From Gunnar Tomasson <gunnar.tomasson@xxxxxxxxxxx>
>An "axiom" is a metaphysical concept - it denotes what we take as "given"
>for some particular piece of deductive reasoning, be it A, B, or C.
>
>And, provided our reasoning is sound, it is meaningless to compare A, B, and
>C with one another.

an axiom is accept as a universal truth underlying an exercise in logical
deduction from axioms.

>As for Economic Theorems X, Y, and Z, they can be checked for (a) logical
>consistency with the underlying sets x, y, and z of axiomatic premises,
>and - if found to be logically coherent - (b) applicability to real-world
>economic conditions.



If X. Y , and Z share  common axioms, then what differentiates X from Y from Z
is any additional axioms added to the common axiomatic foundation. In choosing
which theory is the more general theory among X, Y and Z, the criteria is the
one theory with the smallest axiomatic base is the more general theory.
Unfortunately, Debreu's general [equilibrium]theory [as well as Samuelson's
FOUNDATIONS] does not search for the maximum generality[i.e., the theory with
the fewest required axioms] but rather what Debreu and Samuelson believe is
the "right generality".

For example Debreu in his THEORY OF VALUE" which is the benchmark
axiomatization for  mainstream micro (and macroeconomic) theory wrote:

"The theory of value is treated here with the standards of rigor ....The
effort towards rigor substitutes correct reasoning and results for incorrect
ones....leads to a deeper understanding of the problems to which it is
applied....Alliance to rigor determines the axiomatic form of analysis where
the theory, in the strict sense, is logically disconnected from its
interpretation". (Debreu, 1959 p. x)

For Debreu, as Roy Weintraub points out, the Walrasian equilibrium is the root
structure, i.e., the right level of generality from which all further works in
economics must start.

For Keynes, on the other hand, the classical system (including Walras) was a
special case of his general theory --because it had additional restrictive
axioms-- and the characteristics of this special case are "misleading and
disasterous" when applied to an entrepreneurial economy.
additional axioms.



 >Hence Samuelson's "attempt" in 'Foundations of Economic Analysis' to "show
>that there do exist meaningful theorems in diverse fields of economic
>affairs", where by "meaningful theorem" is "mean[t] simply a hypothesis
>about empirical data which could conceivably be refuted, if only under ideal
>conditions." (pp. 4-5)

Samuelson's meaningful theorems in the Foundations requires additional
restrictive axioms over the micro and macro-analysis of Keynes GT.

>An Economic Theorem is Good/Useful if it passes the test of real-world
>applicability - it is Bad/Useless if it does not.
>
>The number of axioms is immaterial in either case.


If you have two theories BOTH purporting to explain real world involuntary
unemployment equilibrium, the more general theory (i.e., the one with the
least number of restrictive axioms) MUST BE PREFERABLE OVER THE THE THOERY
THAT REQUIRES ADDITIONAL RESTRICTIVE AXIOMS-- see OCCAM's RAZOR, Gunnar!!

Paul

Paul Davidson
Editor, Journal of Post Keynesian Economics
University of Tennessee
SMC 503
Knoxville, Tennessee 37996-0550
phone # (561)369-1951; fax #(561)369-1951;
email pdavidson@xxxxxxx
http://econ.bus.utk.edu/davidsonextra/Davidson.html