Re: The conflict at Notre Dame

[Ted Winslow <egwinslow@xxxxxxxxxx>]

Barkley wrote:

> But unlike you I do not see this as nearly
> as big a problem in economics as you apparently do.
> One can go all Heraclitean and declare that everything is
> constantly changing and therefore we cannot do any math
> on anything (as Russell, or was it Whitehead? claims that
> we cannot do on the surface of the sun).  But I think that I
> have an identity that has been around for several decades,
> even if this is ultimately a metaphysical illusion.  Lots of
> economic agents have a self identity that persists.  Lots of
> objects are produced in the economy that have an identity
> and that can be measured quantitatively.  I guess I just
> find this continued reiteration of the Whitehead-Russell
> argument to be rather gaseous, and ultimately only useful
> to remind us that math has its limits, which I have already
> agreed with.
>       I would also note that there are simply incorrect statements
> in the lengthy pieces you have quoted, e.g. the claim that the
> universe is infinite.  But I do not see any point in you or me
> quoting either of these worthy gentlemen on this list at any
> further length.
>       As a final note, the nature of identity is very much in the eye
> of the beholder.  Thus, I am a single identity, but I am also
> composed of many individual cells, each of which is in turn a
> single identity.  And, Hegel is perfectly correct to assert the
> ultimate unity of the universe, but it nevertheless clearly possesses
> many individual sub-parts with their own identities, down to quarks
> and all kinds of other miniscule entities.  Big deal.

You ascribed to the position I was elaborating the view that
mathematics is "completely useless and should be completely avoided"
and  "pure sin and degradation" and that arithmetic and numbers are
also "useless".  The quotations were meant to demonstrate that this
misrepresents the position as well as to provide further elaboration
both of what is meant by the ontological idea of "internal relations"
and of the implications of the idea for the "axiomatic approach" in
general and for mathematics including arithmetic and numbers in
particular.  The quotations do what I say they do; they have this as
their "point".

They don't seem to be successfully making it, however, since you again
misrepresent the implications (and, in the final paragraph above, the
idea itself).  The idea is perfectly compatible, as the quotations
explicitly point out, with stability of individual character.

Such stability is assumed, for example, by Keynes's treatment of a
monetary crisis, a treatment to which I've previously pointed as
illustrative of the way in which the idea of internal relations limits
the use of mathematical methods.  The change in "identity" to which
Keynes points - the change that produces individuals "scared so stiff
as to be unable to move" - is characteristic of the kind of personality
Keynes takes as typical of participants in financial markets.

> "Why should anyone outside a lunatic asylum wish to use money as a
> store of wealth?
> 	"Because, partly on reasonable and partly on instinctive grounds, our
> desire to hold money as a store of wealth is a barometer of the degree
> of our distrust of our own calculations and conventions concerning the
> future.  Even though this feeling about money is itself conventional
> or instinctive, it operates, so to speak, at a deeper level of our
> motivation.  It takes charge at the moments when the higher, more
> precarious conventions have weakened.  The possession of actual money
> lulls our disquietude; and the premium which we require to make us
> part with money is the measure of the degree of our disquietude."
> (XIV, p. 116)
>
> Here is a description by Keynes of an actual crisis:
>
> "the most strking feature of the immediate situation is the
> extraordinary disparity between yields in London and yields in New
> York of comparable securities.  It seems to me quite impossible that
> the present situation can long persist.  And I should have supposed it
> to be probable that the readjustment would be brought about by a
> substantial rise in prices of prime fixed-interest securities in New
> York.  The present may be the chance of a lifetime for the purchase of
> the latter.  Obviously everyone in New York is scared so stiff as to
> be unable to move.  But that may be the opportunity of others away
> from any unsettling influence of the local atmosphere.  No serious
> risk can arise unless the existing financial system in America is
> going to peg out altogether.  I suppose that that is just possible,
> but I cannot believe that it is probable." (XXI, p. 113)

The change is associated with a change in the psychological "meaning"
of "money"; a "conventional or instinctive" "feeling about money"  that
"operates, so to speak, at a deeper level of our motivation" "takes
charge".  How can this be represented mathematically?

There are axiomatic and mathematical treatments of behaviour in
financial markets.  How do the axioms respecting agents on which these
treatments are based take account of the limits to the axiomatic
approach created by internal relations?

More generally, how are they taken account of in mathematical
elaborations of the assumption that the economy is "composed of
individual, self-interested agents - both utility-maximizing households
and profit-maximizing firms - pursuing their own self-interest"?

Ted