Re: Article in the Chronicle of Higher Education

["Gunnar Tomasson" <gunnar.tomasson@xxxxxxxxxxx>]

Paul:

Let me preface my comments on your points by noting that, when I proposed to
do my Ph. D. thesis at Harvard on "the epistemological foundations of
science in general and economics in particular" back in the 1970s, then
Department Chairman Dwight Perkins wrote back to advise that no Harvard
faculty member was qualified to supervise a thesis on the subject matter.  A
few days ago, a fellow Gang8 member based in Europe advised that he had
wanted to do a thesis on a similar topic in the early 1990s but that, after
searching far and wide (he contacted about 100 economics professors) for
someone with whom he could do such a thesis, the result was the same as in
my case.

Through the years, my attempts to engage top-rank economic scholars in
dialogue on the subject matter have yielded, inter alia, the following
responses:

1.  "There are few expert in both theoretical physics and economics, but I
am confident that any such will not agree that you have isolated a
contradiction in my Foundations." (P. A. Samuelson.)

2.  "Epistemology is a very hard subject." (F. H. Hahn.)

3.  And Milton Friedman advised that he had done no work on the subject
matter since his essay on 'The Methodology of Positive Economics' in the
early 1950s.

As for my own views on the subject matter, they reflect extensive research
over a quarter century into the epistemological aspects of theoretical
physics, key aspects of which came into clear focus through my own original
(intensive) research on atomic structure and related electromagnetic
phenomena in the 1970s.

All that being said, let me address your points one by one.

> 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".

Comment:

If Theorems X, Y, and Z are axiomatic structures in the sense that
Einstein's General Theory of Relativity is such, then they must share the
latter's distinguishing feature which Einstein summarized as follows in
1919:

"The chief attraction of the theory lies in its logical completeness."

That is to say, the "theory" is neither more nor less than a structure
constructed through deductive reasoning from a given set of axiomatic
premises.

With its 'logical completeness' assured, there remains the question of the
General Theory's applicability to real-world phenomena - on that point,
Einstein continued as follows:

"If a single one of the conclusions drawn from it proves wrong, it must be
given up; to modify it without destroying the whole structure seems to be
impossible."

That is to say, the question of the "theory's" real-world applicability
remains an open question.

Also, since the "theory's" logical completeness is defined with respect to a
given set of axiomatic premises, Einstein acknowledged a few months before
his death that "his castle in the air" - and "also most of current
physics" - would be reduced to "nothing" if the "field" axiom were judged to
be inadmissible in principle.

> 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!!

Comment:

The applicability of Occam's Razor remains to be established.

If, as I suggest, axiomatic structures become Theorems X, Y, and Z are
"non-overlapping" in the sense that the rules/games of (a) Chess, (b)
Contract Bridge, and (c) Gin Rummy may be said to be so, then the number of
axioms is immaterial.

Indeed, as indicated by Einstein's comments on the General Theory's "logical
completeness," remove one axiom and the whole axiomatic structure ("theory")
reduces to incoherence.

Gunnar




----- Original Message -----
From: "pdavidso" <pdavidso@xxxxxxx>
To: "Gunnar Tomasson" <gunnar.tomasson@xxxxxxxxxxx>
Cc: <pkt@xxxxxxxxxxxxxxxx>
Sent: Tuesday, January 28, 2003 4:22 PM
Subject: RE: Article in the Chronicle of Higher Education


> >===== 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
>
>