Re: Article in the Chronicle of Higher Education

[pdavidso <pdavidso@xxxxxxx>]

.



>===== Original Message From 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.

I am not sure why you think this preface is relevant.

>
>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.
>


So what?

>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.


Also irrelevant as to how you reached your views.
>
>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."

Again I fail to see the rlevance of this Einstein statement relative to our
discussion.

 My argument relies on the  Hilbert discussion of the 1930s showing  that if
one has a consistent system a proposition will be true or false in that system
else that system will not be complete.  In the classical system with the gross
substitution axiom and the ergodic axiom, involuntary unemployment is false.
So the classical scholars must add another restrictive assumption, namely the
fixity of money wages and/or prices to get a complete system where involuntary
unemployment is true. The completeness of any system is tied to the
decidability ofits axiomatic propositions.

in Keynes general theory-- where gross substituion is not assumed (see chapter
17 of the GT) involuntary unemployment is true (possible) even if the system
has flexible wages and prices.-- therefore it does not require the additional
restrictive assumption of nominal fixities to demonstrate  the truth of
involuntary unemployment -- see Chapter 18 of the GT.

>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.

of course, so what?
>
>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."
>
Not true see my discussion of the fixity of nomiknal values above.

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

What I am saying id that the GT is more general than the classical theory and
what Keynes showed in Chapter 18 is that flexibility in money wages
exacerbated the problem of getting to full employment-- while the classical
system holds that such flexibility provides an automatic mechanism to
restoring equilibrium if the system is shocked off its full employmeny
equilibrium.


>
>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

What does Einstein's field axiom have to do with Keynes GT?

>
>> 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.

Here we have an obvious disagreement!

>
>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.
>



I am sorry to say but these comments below are irrelevant.  If Theories X, Y,
and Z do not share any common axioms then your point is correct --BUT
our discussion requires the recognition that all economic theories share some
common axiooms.  It is not that on the first Monday economics is a game of
bridge, on Tuesdays it is a game of gin rummy; on wednesday -- blackjack, etc,
Or ar you arguing that the rules of the economicgame change every day?


>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.

Not necessarily as my example of he classical fixity of money wages implies--
IF one removes the fixity assumption, the ergodic axiom [so that uncertainty
is the motivating force behind a demand for liquidity] and the lack of gross
substituion (only) between liquid assets and illiquid products of industry --
while stil permitting gross sunstition among the products of industry -- and
one has a comlete system (with fewer restrictive axioms) showing the truth of
the possibility of involuntary unemployent. The resulting complete logical
system known as THE GENERAL THEORY OF EMPLOYMENT INTEREST AND MONEY


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