Re: [gang8] PKT message on mathematics

["Henry C.K. Liu" <hliu@xxxxxxxxxxxxxx>]

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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