[OPE-L:2938] Re: Okishio and the poverty of mathematical economics

Gerald Lev (glevy@pratt.edu)
Sun, 1 Sep 1996 05:24:13 -0700 (PDT)

[ show plain text ]

Steve C wrote in [OPE-L:2928]:

> I get the feeling, however, that I may be missing something in your query.

Yes, I believe you missed a couple of points that I was trying to make.
This was probably my fault since I didn't make those points explicitly.

First: I was trying to get you to speak about the subject line for this
thread ("Okishio and the poverty of mathematical economics") which I
believe you spoke about in part in your recent book, _The Falling Rate of
Profit: Recasting the Marxian Debate_ (London, Pluto Press, 1994), but
did not refer to in [OPE-L:2924].

>"That the Okishio theorem is based on a methodological individualism and
>the Cartesian totality is a straightforward extension of the linear price
>of production model of the economy."
p. 59
>The characteristics of the "Cartesian theoretical program", the author of
>the above goes on to write (citing Levins and Lewontin), include: "1.
>*Ontological individualism* ... 2. *Pregiven rationality* ... 3.
>*Homogeneity* ... 4. *Reductionist explanation* ... 5. *Totality as a
>configuration of parts* ....".
p. 75

As you point out: "The linear price of production model is commonly used
by those advocates and critics alike of the Okishio theorem. As a result,
the debate over the Okishio theorem has occurred, and continues to occur,
almost exclusively on the terrain of the Cartesian totality" (p. 57).
Yet, "the mathematical result and logic of the Okishio theorem is
impeccable once the above assumptions (listed on p. 57, JL) are granted"
(p. 59).

Can't one then say, on the basis of the above, that the Okishio Theorem
is tied to the "poverty of mathematical economics" and that it should be
rejected if one can find: a) compelling reasons to reject the linear
price of production model; b) compelling reasons to reject the
assumptions of the model -- whether explicitly stated or implicit; or
c)) compelling reasons to reject methodological individualism and the
"Cartesian Totality"?

Second: the origin of this thread on "Okishio and the poverty of
mathematical economics" concerned, primarily, the question of what would
constitute a *refutation* of a theorem. It seems to me that unless a
theorem has a way of establishing its credibility, then it is a
*tautology* rather than a hypothesis. So: what would constitute a
refutation of the OT?

You will recall that in a previous post I took issue with, primarily: a)
the idea that economists should select particular types of mathematical
models precisely because they knew that such linear models could produce
"definite results" in the formal, mathematical sense; and b) Duncan's
suggestion concerning refutation: "if a hypothesis of a theorem does not
correspond to reality, it doesn't make the theorem wrong as a logical
construction, it makes the theorem irrelevant to explaining the
phenomenon at hand." To which I responded: "Using the above test, I
could develop a mathematical theorem which would have no relevance for
life in this or any other potential galaxy, yet could still not be
refuted (even though it was developed as a theorem to explain life in
*this* galaxy".

I interpreted Alan's post on "The tendency of rain to fall" to be an
attempt to do precisely what I claimed above that I could do. What would
constitute a _refutation_ of the "inevitable dryness theorem"? If you
reject the IDT based on logical reasons or because it "does not
correspond to reality", wouldn't that constitute a legitimate refutation?
If you can accept that point, then (_even though_, as Allin points
out, _it is an absurd theorem_) you at least would recognize that an
appeal to logic, evidence and reality can be used to attempt to refute
a theorem.

In OPE-L Solidarity,