Re: [gang8] PKT message on mathematics

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

Henry:

Re. the following:

> A general theory must deal with universal reality which poses the
> question whether capitlaism fits the definition.  Thus it is a logical
> question whether a general theory of capitalistic economics is possible.

Comment:

Agree - and, given their non-ergodic attributes, it strikes me as
self-evident that logic precludes the construction of a 'general theory' for
capitalistic economies.

Hence my conclusion posted on March 6, 2003:

My own view is that economic "theory" in the Newtonian sense is possible
ONLY with respect to a purely ANALYTICAL conceptualization of monetary
relations between economic agents cooperating in the production process.

And that is no small thing - for, insofar as economic scholars are concerned
with the architecture of real-world monetary systems whose primary task is
to serve the production process under conditions of near-full factor
employment and price stability, such "theory" is an essential point of
departure.

With respect to everything else, I submit that economic "theory" is common
sense applied to whatever circumstances the non-ergodicity of real-world
economies may generate at any given point in time and space.

Gunnar



----- Original Message -----
From: "Henry C.K. Liu" <hliu@xxxxxxxxxxxxxx>
To: <gang8@xxxxxxxxxxxxxxx>; <pkt@xxxxxxxxxxxxxxxx>
Sent: Monday, March 10, 2003 6:17 PM
Subject: Re: [gang8] PKT message on mathematics


> Mathematics is a language, not a realm.  Mathematical truth depends only
> consitency, even when it should be consistently false
>
> It is a Daoist axiom that intellectual scholarship and analytical logic
> can only serve to dissect and categorize information.  Knowledge,
> different from information, is achieved only through knowing.
> Ultimately, only intuitive understanding can provide wisdom.
> Truth, while elusive, exists.  But it is obscured by search, because
> purposeful search will inevitably mislead the searcher from truth.  By
> focusing on the purpose, the searcher can only find what he is looking
> for.  How does one know what questions to ask about truth if one does
> not know what the elusive answers should be?  Conversely, if one knows
> already what the answers should be, why does one need to ask questions?
>   Lewis Carrol’s Alice in Alice’s Adventures in Wonderland (1865) would
> unknowingly be a Daoist.
> Daoists believe that the dao (path) of life, since it eludes taxonomic
> definition and intellectual pursuit, can only be intuitively experienced
> through mystic meditation, by special breathing exercises and sexual
> techniques to enhance the mind and harmonize the body.  They believe
> that these mind-purifying undertakings, coupled with an ascetic
> lifestyle and lean diet, would also serve to prolong life.
> Daoist philosophy is referred to as Xuanxue, literally meaning: mystic
> learning.  The Dao of economics would focus on values rather than
> effciency, cooperation rather than competition, qualitative growth
> rather than quantiative growth.
>
> Aquinas would apply Aristotelian methods of logic to medieval mysticism
> of revelation.  His Summa Theologica (1267-1273) would be a systematic
> exposition of theology on rational philosophical principles.
> Up to that time, while Scholasticism, as advanced by St Augustine
> (354-430), would vindicate reason in theology, it would carefully
> differentiate between theology and philosophy.  It would do so by
> confining theology, proceeding from faith, to investigations of revealed
> truths, while it would limit philosophy, based on reason, from concern
> with truths that transcended reason.  Revealed truth would be proclaimed
> as discoverable only through faith.
> The thirteenth century would be a critical point in Christian thought
> regarding the relationship between faith and reason.
> The intellectual community in Christendom at that time would be torn
> between claims of followers of Averroes (1126-1198), Arabian philosopher
> from Cordoba in Spain, and claims of followers of St Augustine
> (354-430), troubled youth turned zealous convert, founder of Christian
> theology and spokesman for Christian mysticism.
> Efforts of followers of Averro‰s in the thirteenth century to separate
> absolutely faith from truth, would clash with the traditional claim that
> truth being exclusively a matter of faith.  Such claim has been made for
> the past nine centuries by followers of St Augustine whose contribution
> to the evolution of Christianity would be considered second only to that
> of St Paul, apostle to Gentiles and the greatest missionary apostle.
> Averroes, Latin name for Abu-al-Walid Ibn Rushd, whose commentaries on
> Aristotle would remain influential for four centuries, until the
> Renaissance, would attempt to circumscribe the separate limits of faith
> and reason, asserting that both could process truths and that the two
> separate realms need not be reconciled because they are not in conflict.
> Siger de Brabant of University of Paris, leader of Averroists, would
> claim in 1260 that it should be possible, as a matter of veracity, and
> tolerable, as a license in intellectual soundness, for a concept to be
> true in reason but false in faith or visa versa.
> The doctrines of Averroists, which include denying the immortality of
> the individual soul and upholding the eternity of matter, would end up
> being officially condemned by the Catholic Church.
> St Thomas Aquinas (1225-1274), nicknamed Dumb Ox because of his slow and
> deliberate manner of speech, brilliant father of Neo-Scholasticism,
> aiming to resolve the dispute between Averroists and Augustinians, would
> hold that reason and faith constitute 2 harmonious realms in which the
> truth of faith complements that of reason, both being gifts of God, but
> reason having an autonomy of its own.
> The existence of God could therefore be discovered through reason, with
> the grace of God.
> The theological significance of this momentous claim by Thomas Aquinas
> cannot be over-emphasized.  It would save Christianity from falling into
> irrelevance in the Age of Reason, sometimes referred to as the
> Enlightenment, and preserve tolerance for faith among rational thinkers
> in the scientific world.
> The Thomist claim would remain unchallenged for five centuries until
> David Hume (1711-1786) who would point out in his Inquiry into Human
> Understanding that since the conclusion of a valid inference could
> contain no information not found in the premise, there could be no valid
> conclusion from observed to unobserved phenomena.
> Hume would let the logic air out of the Thomist natural theology
> balloon, and in the process would show that even general laws of science
> could not be logically justified beyond their own limits, perhaps even
> including his own sweeping conclusion.
> Hume, the empiricist, would logically determine that logic is circular
> and goes nowhere: a classic position of Daoist skepticism.
> Immanuel Kant (1724-1804) would emancipate man’s command of knowledge
> from Humean skepticism.  In his Critique of Pure Reason (1781), Kant
> would emphasize the contribution of the knower to knowledge.  While
> acknowledging that the 3 great issues of metaphysics: God, freedom and
> immortality, could not be logically determined, he would assert that
> their essence is a necessary presupposition.  In his subsequent
> publications: Critique of Practical Reason (1788) and Critique of
> Judgement (1790), Kant would assert as a moral law his famous
> categorical imperative, which would require moral actions to be
> unconditionally and universally binding to absolute good will.
> Notwithstanding the enlightened breakthroughs of English Protestant
> empiricists like Hobbes, Locke and Hume, and perhaps in reaction to
> them, Pope Leo XIII would issue the encyclical Aeterni Patris in 1879.
> It would declare Scholasticism, as modified by Thomas Aquinas, to be
> official Catholic philosophy.  Unwittingly, Scholasticism would
> legitimize the independence of secular politics from Church control.  If
> reason and faith constitute 2 harmonious realms in which the truth of
> faith complements that of reason, both being gifts of God, but reason
> having an autonomy of its own, then politics and religion can also
> belong to separate realms in which morality of religion complements
> virtue in politics, but politics having an autonomy of its own.  It
> would provide the theological rationalization for the separation of
> Church and State.
> Unlike Christian theology, Daoism (Dao Jia), lacking the logic footing
> of Scholasticism, would remain unable to penetrate the primordial soup
> of its mysticism with a big bang of logic.  Consequently, it would fail
> to advance systematically as time goes on.  Consistent with its basic
> paradoxical outlook, Daoism with it’s long history of forty centuries,
> contents itself with circular insights on the mystery of life, the
> ultimate disclosure of which tends to recede with each flash of new
> insight, as if repelled by a fear that the final revelation of life’s
> secret would announce Daoism’s own death knell.
>
> A general theory must deal with universal reality which poses the
> question whether capitlaism fits the definition.  Thus it is a logical
> question whether a general theory of capitalistic economics is possible.
>
> HEnry C.K. Liu
>
> Gunnar Tomasson wrote:
> > I just posted the following to PKT.
> >
> > FYI.
> >
> > Gunnar
> >
> > ********
> >
> > 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
<mailto:rosserjb@xxxxxxx>>
> > To: "David Gleicher" <104201.2301@xxxxxxxxxxxxxx
> > <mailto:104201.2301@xxxxxxxxxxxxxx>>; "Ted Winslow"
> > <egwinslow@xxxxxxxxxx <mailto:egwinslow@xxxxxxxxxx>>
> > Cc: <pkt@xxxxxxxxxxxxxxxx <mailto: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
> >
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