Re: goedel

["Dr. Bruce R. McFarling" <ecbm@xxxxxxxxxxxxxxxxxxx>]

On Sun, 06 Oct 2002 12:34:04 -0500, Paul Davidson
<pdavidson@xxxxxxx> wrote:

> Therefore if I dispense with the ergodic axiom, it is for
> those who want to use it to prove that it is applicable to
> the real world!

Note, here, that there is a difference between saying,
"I will not assume that the economy is ergodic", and
saying, "I will assume that the economy is X, which
implies that it is not ergodic."

Between rival choices of axioms, there is only
appeals as to being more persuasive on various
grounds.  A collection of axioms that seem to
apply to a monetary exchange economy and another
that seem to apply to a monetary production
economy involving, for example, one side saying
that more rigorous analysis can be performed,
and the other saying that it is more rigorous
analysis of economies that do not in fact exist.
The merits of distinct and rival axiomatic systems
must be considered on non-analytic grounds.

However, between rival axiomatic systems in which
one is founded on a proper subset of the fundamental
axioms of the other, the analytical preference
has to be in favour of the system with the strictly
smaller axiomatic foundation.  That is why reproving
existing theorems with fewer axioms is one of the
academic games that mathematicians receive publications
for -- it broadens the potential relevance of the
theorem.

Goedel's theorem that for any axiomatic system
above a threshold level of complexity would
contain undecidable propositions (neither provable
nor disprovable) comes into play in evaluating the
19th century dream of a single unified deductive
science.  Deductive reasoning is seductive because
of the seeming certainty that it offers.  However,
the foundation axioms in use are always at stake
when reaching deductive conclusions, and their
relevance to the question at hand can never be
determined deductively.

The solution that much of economics relies on to handle
this problem is initiation institutions that train
novices to employ and to refrain from questioning a
certain deductive system, and then academic institutions
that reward those who are industrious and proficient in
their use of the deductive system.  So the
institutionalisation of existing habits of thought and
behavior in mainstream economics is used to provide the
glue to hold together a program of economic thought in
which social institutions are treated as phenomena in
which institutionalisation of existing habits of thought
and behavior does not take place.