Re: The conflict at Notre Dame

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

Barkley:

I appreciate your thoughtful comments, but wish to question the following:

>         As for the claim that "all" math is tautological, I fear that
> I disagree with this one.  Is it tautological that two plus two
> equals four?   I would remind everyone that the issue of what
> kind of geometry is relevant turned out to be an empirical question.

While the proposition that "what kind of geometry is relevant turned out to
be an empirical question" is not disputed by the vast majority of
theoretical physicists, the following statement made by Einstein in August
1954 underscores that the proposition is CONTINGENT on an affirmative
finding with respect to the admissibility of the "field concept" in
theoretical physics:

"I concede that it is quite possible that physics cannot be founded on the
concept of field - that is to say, on continuous elements.  But then, out of
my whole castle in the air - including the theory of gravitation, but also
most of current physics - there would remain almost nothing." (Private
letter, August 10th, 1954, reprinted in *Einstein, A Centenary Volume*,
published by Harvard University Press, 1979, p. 269)

For what it is worth, I should note that I exchanged views with a post-doc
theoretical physicist, who was moderator of The New York Times Science Forum
on the admissibility of the "field concept" - my view was that, in light of
such and such, it appeared crystal clear that the concept was NOT
admissible.

"Precisely," he replied, adding that his post-doc research program aimed at
finding some, even if seemingly "crazy", idea which might resolve the
problem involved.

 Gunnar


----- Original Message -----
From: "J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>
To: "Gunnar Tomasson" <gunnar.tomasson@xxxxxxxxxxx>; "David Gleicher"
<104201.2301@xxxxxxxxxxxxxx>; "Ted Winslow" <egwinslow@xxxxxxxxxx>
Cc: <pkt@xxxxxxxxxxxxxxxx>
Sent: Tuesday, March 11, 2003 10:53 AM
Subject: Re: The conflict at Notre Dame


> Gunnar,
>        First, I regret that you have quoted me on the argument
> that the book is a bunch of articles.  This is apparently mistaken
> and Roy Weintraub very much took me to task for making that
> statement.  It is the most incorrect remark in my entire paper.
> I have apologized to him privately for making that mistake, and
> here make that apology public.
>        As regards Marshall, I suspect that you are at least partly
> right about the influences on Marshall.  Certainly he knew both
> Russell and Whitehead, as Keynes knew Wittgenstein; indeed
> Keynes knew Wittgenstein very well.  I noted that there is a lot
> of ambivalence with all of these figures regarding the use of
> mathematics, and I believe that I have made it clear that I
> agree with Henry Liu that math most definitely has its limits.
> Knowing what those are is one of the greatest challenges in
> using math in any discipline, and certainly in economics.
>         As for the claim that "all" math is tautological, I fear that
> I disagree with this one.  Is it tautological that two plus two
> equals four?   I would remind everyone that the issue of what
> kind of geometry is relevant turned out to be an empirical question.
> But certainly a lot of Bourbakist formalism does devolve into
> tautology.  Joan Robinson's old wisecrack about the economic
> theoretician taking the rabbit out of the hat with great drama after
> having put it into the hat in full view of the audience is all too
> frequently very valid.
> Barkley Rosser
> ----- Original Message -----
> From: "Gunnar Tomasson" <gunnar.tomasson@xxxxxxxxxxx>
> To: "J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>; "David Gleicher"
> <104201.2301@xxxxxxxxxxxxxx>; "Ted Winslow" <egwinslow@xxxxxxxxxx>
> Cc: <pkt@xxxxxxxxxxxxxxxx>
> Sent: Monday, March 10, 2003 5:22 PM
> Subject: Re: The conflict at Notre Dame
>
>
> > 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
> > > >
> > > >
> > >
> > >
> >
> >
> >
>