Re: The conflict at Notre Dame

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

Re. the following extract from Barkley's paper:

Overview
            After a prologue in which he summarizes several of his main
points, Weintraub focuses on the world of Alfred Marshall at Cambridge in
his opening chapter[1] and the mathematics that he studied.  The focus of
this chapter is the Mathematics Tripos that all students took at Cambridge
from the early 1800s on, described as "one of the most difficult
mathematical exams ever given."  The view of mathematics implicit in the
Tripos is that mathematics is a means to obtain absolute truth, with the
specific mathematics in question being largely derived from the celestial
mechanics of Isaac Newton, the greatest of all Cantabridgians.  Although
Marshall did very well on the Tripos, and nearly went into mathematics, in
his old age he becomes the defender of keeping mathematics in the background
of economic analysis, with Weintraub reproducing the part of his famous
letter to Bowley in which he recommends to "use mathematics as a short hand
language, rather than as an engine of inquiry" and culminates after having
emphasized providing "real life examples" with the fiery "Burn the
Mathematics" (p. 22), which also provides the title for the chapter.

            Weintraub argues that Marshall's attitude reflected more his
frustration with his perception of the changing nature of mathematics and
the importation of these changes into mathematical approaches in economics
rather than any ultimate opposition to using mathematics in economics.
Thus, Weintraub would appear to be vindicating Marshall from the charge that
he is one of those so sarcastically described in the quotation provided
above.  But it is hard to avoid seeing Weintraub as viewing him  as such
given that an inability to keep up with the latest changes in fashion in
mathematics is often posed later in the book as a reason why some reverted
to such attitudes.



----------------------------------------------------------------------------
----

[1] Another aspect of the book that this observer finds a bit disconcerting
is that several of the book's chapters were originally stand-alone articles.
He has clearly made an effort to integrate them into a coherent whole,
especially by laying them out in a more or less chronological order.  But
there are times when the overlaps and resulting oddities become a bit
peculiar.





Comment:

There is an alternative explanation of Marshall's attitude, namely, that he
understood the point which Bertrand Russell made in 'My Philosophical
Development' written towards the end of his long life.

Russell, after recalling his youthful enthusiastic embrace of mathematics as
universal language (or words to that effect), went on to state that he had
now "very reluctantly" come to conclude that such view of mathematics was
nonsense.

Instead, he had come to view mathematics as "tautological" and illustrated
the point with the following example:

"A four-legged animal is an animal."

Gunnar


----- Original Message -----
From: "J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>
To: "David Gleicher" <104201.2301@xxxxxxxxxxxxxx>; "Ted Winslow"
<egwinslow@xxxxxxxxxx>
Cc: <pkt@xxxxxxxxxxxxxxxx>
Sent: Monday, March 10, 2003 4:03 PM
Subject: Re: The conflict at Notre Dame


> Ted,
>        Sometimes variables in economics math models
> retain self identity and sometimes they don't.
>         BTW, although I think that Roy Weintraub overstates
> the defense of math in econ (my contribution to the
> symposium forthcoming in JPKE is available on my
> website at http://cob.jmu.edu/rosserjb, but you'll have
> to wait for the symposium to see Roy's reply), he does
> make a strong point that critics of math in econ often
> criticize math that they do not know very well, while
> accepting math that they know well.
>       Thus, are we not to use simple arithmetic?  Are
> such variables as the price of a commodity to be
> ruled out of being discussed because their self-
> identity might be changing over time?  Are we not
> allowed to use any numbers at all?
>      I think that it is
> very hard to draw a line, to say that arithmetic is OK,
> but topology is not.  What I think is incumbent upon
> those using more advanced math is to provide as good
> explanations as possible of what it is they are doing and
> why in "plain English," which unfortunately frequently is
> not done (often because some of the practitioners are
> terrible writers), although I see a trend to doing this in
> most of the more mathematically oriented journals, or
> at least trying to do so.
> Barkley Rosser
> ----- Original Message -----
> From: "Ted Winslow" <egwinslow@xxxxxxxxxx>
> To: "David Gleicher" <104201.2301@xxxxxxxxxxxxxx>
> Cc: <pkt@xxxxxxxxxxxxxxxx>; "J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>
> Sent: Saturday, March 08, 2003 4:50 PM
> Subject: Re: The conflict at Notre Dame
>
>
> >
> > David Gleicher wrote:
> >
> > > Does the mastery of a 'fruitful' mthematicl model not also reveal--the
> > > more
> > > deeply you pursue it--the model's limiitations, self-contradictions,
> > > etc,
> > > and in that way doesn't such a mathematical model force the
> > > 'ontoilogical
> > > fact of internal relations'  upon you in a way nothing else can?  That
> > > seems to me what gives the 'fruitful'models much of their value.
> > >
> > > It is ever thus that, in the words of Goethe:
> > >
> > > Gray, my friend, is every theory
> > > and green alone life's golden trees.
> >
> > It would be rather difficult for it to do this since the "mathematical"
> > models that dominate contemporary economics implicitly assume that
> > relations are "external" rather than "internal".  This is the point
> > made in Whitehead's discussion of the limitations of "algebra".
> >
> > "Before we finally dismiss deductive logic, it is well to note the
> > function of the 'variable' in logical reason.  In this connection the
> > term variable is applied to a symbol, occurring in a propositional form
> > which merely indicates any entity to which the propositional form can
> > be validly applied, so as to constitute a determinate proposition.
> > Also the variable, though undetermined, sustains its identity
> > throughout the arguments.  The notion originally assumed importance in
> > algebra, in the familiar letters such as x, y, z indicating any
> > numbers.  It also appears somewhat tentatively in the Aristotelian
> > syllogisms, where names such as 'Socrates,' indicate 'any man, the same
> > throughout the argument.'
> > "The use of the variable is to indicate the self-identity of some use
> > of 'any' throughout a train of reasoning.  For example in elementary
> > algebra when x first appears it means 'any number.'  But in that train
> > of reasoning, the reappearance of x always means 'the same number' as
> > in the original appearance.  Thus the variable is an ingenious
> > combination of the vagueness of any with the definiteness of a
> > particular indication.     "In logical reasoning, which proceeds by
> > the use of the variable, there are always two tacit presuppositions -
> > one is that the definite symbols of composition can retain the same
> > meaning as the reasoning elaborates novel compositions.  The other
> > presupposition is that this self-identity can be preserved when the
> > variable is replaced by some definite instance.  Complete self-identity
> > can never be preserved in any advance to novelty.  The only question
> > is, as to whether the loss is relevant to the purposes of the argument.
> >   The baby in the cradle, and the grown man in middle age, are in some
> > senses identical and in other senses diverse.  Is the train of argument
> > in its conclusions substantiated by the identity of vitiated by the
> > diversity?" (A.N. Whitehead, Modes of Thought, pp. 106-7)
> >
> > Ted
> >
> >
>
>