Re: Article in the Chronicle of Higher Education

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

Re. my statement:

> > For A, B, and C are non-overlapping - they are to one another
> > as, say, the rules/games of (a) Chess, (b) Contract Bridge,
> > and (c) Gin Rummy.

and Bruce's comments:

> Given the premise, stated at the last, the conclusion
> is sound. The point that Paul Davidson has been making
> for, what, thirty, forty years? has been regarding the
> alternative case where A and B overlap because A is a
> strict subset of B.  Of course, this aspect is not
> readily apparent as B as normally stated, and the
> substance of the type of argument that Paul is making
> is in making the translations.
>
> If you show that the mapping that he has drawn between
> the two sets of axioms are invalid, then you undermine
> his argument.

To the best of my knowledge, the first formal statement of key aspects of
the "alternative case where A and B overlap because A is a strict subset of
B" was made by Paul Samuelson in 'Foundations of Economic Analysis' as
follows:

"It is clear, however, that logically there is nothing fundamental about the
traditional boundaries of economic science.  In fact, a system may be as
broad or as narrow as we please depending upon the purpose at hand; and the
data of only system may be the variables of a wider system depending upon
expediency.  The fruitfulness of any theory will hinge upon the degree to
which factors relevant to the particular investigation at hand are brought
into sharp focus.  And if, for the understanding of the business cycle a
theory of governmental policy is demanded, the economist can ill afford to
neglect this need on the ground that such matters lie outside his province.
As for those who argue that special degrees of certainty and empirical
validity attach to the relations encompassed within the traditional limits
of economic theory, we may leave to them the task of proving their case."
(p. 9)

Note, (a) that Samuelson asserts - but does not prove - the validity of "the
alternative case," and (b) that, with his last sentence, Samuelson fudges
the point at issue and shifts onto others the burden of proof associated
with his assertion.

In the next paragraph, Samuelson effectively identifies the analytical
framework within which his assertion itself is either valid or invalid as
follows:

"It is not to be thought that the content of systems as described above must
be restricted to the variables usually considered in price and value theory.
On the contrary, one employs such constructions throughout the whole field
of theoretical economics including monetary and business cycle theory,
international trade, etc.  It goes without saying that the existence of such
systems in no way hinges upon the employment of symbolic or mathematical
methods.  In fact, any sector of economic theory which cannot be cast into
the mold of such a [general equilibrium] system must be regarded with
suspicion as suffering from haziness."

As for the essential attributes of such systems, Samuelson goes on to
explain:

"Within the framework of any system the relationships between our variables
are strictly those of mutual interdependence.  It is sterile and misleading
to speak of one variable as causing or determining another.  Once the
conditions of equilibrium are imposed, all variables are simultaneously
determined.  Indeed, from the standpoint of comparative statics equilibrium
is not something which is attained; it is something which, if attained,
displays certain properties.

"The only sense in which the use of the term causation is admissible is in
respect to changes in EXTERNAL data or parameters.  AS A FIGURE OF SPEECH,
it may be said that changes in these *cause* changes in the variables of our
system.  An increase in demand, i.e., a shift in the demand function due to
a change in the data, tastes, may be said to cause an increased output to be
sold.  Even here, when several parameters change simultaneously, it is
impossible to speak of causation attributable to each except in respect to
limiting rates of change (partial derivatives)." (pp. 9-10)

Comment:

1. The last paragraph lays out the WHOLE case for the admissibility in
principle of partial derivative analysis in general equilibrium reasoning
and, more generally, the use of Comparative Statics; the capitalized words
signal Samuelson's recognition that there exists NO CASE IN LOGIC for the
exception which he claims to exist with "respect to limiting rates of change
(partial derivatives)."

2.  For, as underscored by the 19th century Laplacian general-equilibrium
construction of Newtonian Universal Gravitational Mechanics, there is NO
place for "external data or parameters" (let alone "changes" therein) in
systems where "the relationships between our variables are strictly those of
mutual interdependence."

3.  Hence, irrespective of a possible "overlap" between A and B, where "A is
a strict subset of B", there is NO CASE IN LOGIC for applying partial
derivative analysis to "changes in external data or parameters" pertaining
to A and/or B, for NO such "external data or parameters" are admissible in
the first place.

4.  As for Samuelson's key assertion itself - that "a system may be as broad
or as narrow as we please depending upon the purpose at hand", that is to
say, a system may be sub-divided into A and B - it is inconsistent with the
Laplacian construction of Newtonian Universal Gravitational Mechanics.

5.  As for the Laplacian construction itself, it was mirrored precisely in
Leon Walras' statement late in life (reproduced in appendix to Don
Patinkin's book on 'Money, Prices, etc.') to the effect that, insofar as
real-world economies may be viewed as General Equilibrium Systems, they must
be judged to be in general equilibrium AT ALL POINTS IN TIME.

I conclude - and so advised Samuelson in the late 1970s - that the
methodological pre-suppositions of his 'Foundations of Economic Analysis',
as reflected in the modus operandi of contemporary mainstream, monetarist,
and PKT economists, are invalid.

Gunnar


----- Original Message -----
From: "Dr. Bruce R. McFarling" <Bruce.McFarling@xxxxxxxxxxxxxxxx>
To: <pkt@xxxxxxxxxxxxxxxx>
Sent: Wednesday, January 29, 2003 6:43 PM
Subject: Re: Article in the Chronicle of Higher Education