Re: The conflict at Notre Dame

["J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>]

Ted,
      Have been gone since last Tuesday.
      I accept that one can only operate math on objects
(or subjects) that are somehow able to maintain their
identities (and relations with each other, whether "external"
or "internal") long enough for those mathematical
operations or processes or concepts to be carried out
meaningfully.  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.
Barkley Rosser
----- Original Message -----
From: "Ted Winslow" <egwinslow@xxxxxxxxxx>
To: "J. Barkley Rosser, Jr." <rosserjb@xxxxxxx>
Cc: "David Gleicher" <104201.2301@xxxxxxxxxxxxxx>; <pkt@xxxxxxxxxxxxxxxx>
Sent: Wednesday, March 12, 2003 7:56 AM
Subject: Re: The conflict at Notre Dame



Barkley wrote:

>        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.

Weintraub ignores the ontological basis of Marshall's view of
mathematical methods and of the work on the philosophical foundations
of formal logic and mathematics at Cambridge in the early part of the
last century, work that, along with Marshall's critique, is critical to
understanding Keynes's view of formal logic and mathematics and their
role in economics. If I remember correctly, he doesn't even discuss
Keynes's view.  He also ignores the aspect of Whitehead to which I'm
pointing.  He can hardly be said to have demonstrated that criticism
having this ontological basis is based on ignorance.

The conception of the economy as "composed of individual,
self-interested agents - both utility-maximizing households and
profit-maximizing firms - pursuing their own self-interest" assumes
that "agents" remain self-identical through changes in their relations
i.e. it treats social relations as external rather than internal.

>       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.

The association of the position I'm elaborating with the claim that
arithmetic and numbers are useless is another straw man.  Internal
relations *limit* their applicability in the way indicated in the
following arguments of Whitehead and Russell.

"So far, this lecture has proceeded in the form of dogmatic statement.
What is the evidence to which it appeals?
"The only answer is the reaction of our own nature to the general
aspect of life in the Universe.
"This answer involves complete disagreement with a widespread
tradition of philosophic thought.  This erroneous tradition presupposes
independent existences; and this presupposition involves the
possibility of an adequate description of finite fact.  The result is
the presupposition of adequate separate premises from which argument
can proceed.
"For example, much philosophic thought is based upon the faked
adequacy of some account of various modes of human experience.  Thence
we reach some simple conclusion as to the essential character of human
knowledge, and of its essential limitation.  Namely, we know what we
cannot know.
"Understand that I am not denying the importance of the analysis of
experience: far from it.  The progress of human thought is derived from
the progressive enlightenment produced thereby.  What I am objecting to
is the absurd trust in the adequacy of our knowledge.  The
self-confidence of learned people is the comic tragedy of civilization.
"There is not a sentence which adequately states its own meaning.
There is always a background of presupposition which defies analysis by
reason of its infinitude.
"Let us take the simplest case; for example, the sentence, 'One and
one makes two.'
"Obviously this sentence omits a necessary limitation.  For one thing
and itself make one thing.  So we ought to say, 'One thing and another
thing make two things.'  This must mean the togetherness of one thing
with another thing issues in a group of two things.
"At this stage all sorts of difficulties arise.  There must be the
proper sort of things in the proper sort of togetherness.  The
togetherness of a spark and gunpowder produces an explosion, which is
very unlike two things.  Thus we should say, 'The proper sort of
togetherness of one thing and another thing produces the sort of group
which we call two things.'  Common sense at once tells you what is
meant.  But unfortunately there is no adequate analysis of common
sense, because it involves our relation to the infinity of the Universe.
"Also there is another difficulty.  When anything is placed in another
situation, it changes.  Every hostess takes account of this truth when
she invites suitable guests to a dinner party; and every cook
presupposes it as she proceeds to cook the dinner.  Of course, the
statement, 'One and one make two' assumes that the changes in the shift
of circumstances are unimportant.  But it is impossible for us to
analyse this notion of 'unimportant change.'  We have to rely upon
common sense.
"In fact, there is not a sentence, or a word, with a meaning which is
independent of the circumstances under which it is uttered.  The
essence of unscholarly thought consists in a neglect of this truth.
Also it is equally the essence of common sense to neglect these
differences of background when they are irrelevant to the immediate
purpose.  My point is that we cannot rely upon any adequate explicit
analysis.
"The conclusion is that Logic, conceived as an adequate analysis of
the advance of thought, is a fake.  It is a superb instrument, but it
requires a background of common sense.
"To take another example: Consider the 'exact' statements of the
various schools of Christian Theology.  If the leaders of any
ecclesiastical organization at present existing were transported back
to the sixteenth century, and stated their full beliefs, historical and
doctrinal, either in Geneva or in Spain, then Calvin, or the
Inquisitors, would have been profoundly shocked, and would have acted
according to their habits in such cases.  Perhaps, after some
explanation, both Calvin and the Inquisitors would have had the sense
to shift the emphasis of their own beliefs.  That is another question
which does not concern us.
"My point is that the final outlook of Philosophic thought cannot be
based upon the exact statements which form the basis of special
sciences.
"The exactness is a fake." (Whitehead "Immortality" in Essays in
Science and Philosophy, pp. 72-4)

"A metaphysical proposition - in the proper, general sense of the term
'metaphysical' - signifies a proposition which (i) has meaning for any
actual occasion as a subject entertaining it, and (ii) is 'general,' in
the sense that its predicate potentially relates any and every set of
actual occasions providing the suitable number of logical subjects for
the predicative pattern, and (iii) has a 'uniform' truth-value, in the
sense that by reason of its form and scope, its truth-value is
identical with the truth-value of each of the singular propositions to
be obtained by restricting the application of the predicate to any one
set of logical subjects. ...
"We certainly think that we entertain metaphysical propositions; but,
having regard to the mistakes of the past respecting the principles of
geometry, it is wise to reserve some scepticism on this point.  The
propositions which seem to be most obviously metaphysical are the
arithmetical theorems.  I will therefore illustrate the justification
both for the belief, and for the residual scepticism, by an examination
of one of the simplest of such theorems: One and one make two.
"Certainly, this proposition, construed in the sense 'one entity and
another entity make two entities,' seems to be properly metaphysical
without any shadow of limitation upon its generality, or truth.  But we
must hesitate even here, when we notice that it is usually asserted,
with equal confidence as to the generality of its metaphysical truth,
in a sense which is certainly limited, and sometimes untrue.  In our
reference to the actual world, we rarely consider an individual actual
entity.  The objects of our thoughts are almost always societies, or
looser groups of actual entities.  Now, for the sake of simplicity,
consider a society of the ‘personal’ type.  Such a society will be a
linear succession of actual occasions forming a historical route in
which some defining characteristic is inherited by each of its
predecessors.  A society of this sort is an ‘enduring object.’
Probably, a simple enduring object is simpler than anything which we
ordinarily perceive or think about.  It is the simplest type of
society; and for any duration of its existence it requires that its
environment be largely composed of analogous simple enduring objects.
What we normally consider is the wider society in which many strands of
enduring objects are to be found, a ‘corpuscular society.’
“Now, consider two enduring objects.  They will be easier to think
about if their defining characteristics are different.  We will call
these defining characteristics a and b, and also will use these
letters, a and b, as the names of the two enduring objects.  Now the
proposition ‘one entity and another entity make two entities’ is
usually construed in the sense that, given two enduring objects, any
act of attention which consciously comprehends an actual occasion from
each of the two historic routes will necessarily discover two actual
occasions, one from each of the two distinct routes.  For example,
suppose that a cup and a saucer are two such enduring objects, which of
course they are not; we always assume that, so long as they are both in
existence and are sufficiently close to be seen in one glance, any act
of attention, whereby we perceive the cup and perceive the saucer, will
thereby involve the perception of two actual occasions, one the cup in
one occasion of its existence and the other the saucer in one occasion
of its existence.  There can be no reasonable doubt as to the truth of
this assumption in this particular example.  But in making it, we are
very far from the metaphysical proposition from which we started.  We
are in fact stating a truth concerning the wide societies of entities
amid which our lives are placed.  It is a truth concerning this cosmos,
but not a metaphysical truth.
“Let us return to the two truly simple enduring objects, a and b.
Also let us assume that their defining characteristics, a and b, are
not contraries, so that both of them can qualify the same actual
occasion.  Indeed, having regard to the extreme generality of the
notion of a simple enduring object, it is practically certain that –
with the proper choice for the defining characteristics, a and b -
intersecting routes for a and b must have frequently come into
existence.  In such a contingency a being who could consciously
distinguish the two distinct enduring objects a and b, so as to have
knowledge of their distinct defining characteristics and their distinct
historic routes, might find a and b exemplified in one actual entity.
It is as though the cup and the saucer were at one instant identical;
and then, later on, resumed their distinct existence.
“We hardly ever apply arithmetic in its pure metaphysical sense,
without the addition of presumptions which depend for their truth on
the character of the societies dominating the cosmic epoch in which we
live.  It is hardly necessary to draw attention to the fact, that
ordinary verbal statements make no pretence of discriminating the
different senses in which an arithmetical statement can be understood.
There is no difficulty in imagining a world – i.e., a cosmic epoch –
in which arithmetic would be an interesting fanciful topic for
dreamers, but useless for practical people engrossed in the business of
life.  In fact, we seem to have been only barely rescued from such a
state of things.  For amid the actual occasions located in the wilds of
so-called ‘empty space,’ and well removed from the enduring objects
which go to form the enduring objects which go to form the enduring
material bodies, it is quite probable that the contemplation of
arithmetic would not direct attention to any very important relations
of things.  It is, of course, a mere speculation that any actual
entity, occurring in such an environment of faintly coordinated
achievement, achieves the intricacy of constitution required for
conscious mental operations.”  (Whitehead, Process and Reality
[Corrected Ed.], pp. 197-9)


"I began to develop a philosophy of my own during the year 1898, when,
with encouragement from my friend G.E. Moore, I threw over the
doctrines of Hegel.  If you watch a bus approaching you during a bad
London fog, you see first a vague blur of extra darkness, and you only
gradually become aware of it as a vehicle with parts and passengers.
According to Hegel, your first view as a vague blur is more correct
than your later impression, which is inspired by the misleading
impulses of the analytic intellect.  This point of view was
temperamentally unpleasing to me.  Like the philosophers of ancient
Greece, I prefer sharp outlines and definite separations such as the
landscapes of Greece afford.  When I first threw over Hegel, I was
delighted to be able to believe in the bizarre multiplicity of the
world.  I thought to myself, "Hegel says there is only the One, but
there really are twelve categories in Kant's philosophy." It may seem
queer that this was the example of plurality that specially impressed
me, but I am concerned to report the facts without distortion.
"For some years after throwing over Hegel I had an optimistic riot of
opposite beliefs.  I thought that whatever Hegel had denied must be
true.  He had maintained that there is no [38] absolute truth.  The
nearest approach (so he maintained) to absolute truth is truth about
the Absolute; but even that is not quite true, because it unduly
separates subject and object.  Consequently I, in rebellion, maintained
that there are innumerable absolute truths, more particularly in
mathematics.  Hegel had maintained that all separateness is illusory
and that the universe is more like a pot of treacle that a heap of
shot.  I therefore said, 'the universe is exactly like a heap of shot.'
Each separate shot, according to the creed I then held, had hard and
precise boundaries and was as absolute as Hegel's Absolute.  Hegel had
professed to prove by logic that number, space, time and matter are
illusions, but I developed a new logic which enabled me to think that
these things were as real as any mathematician could wish.  I read a
paper to a philosophical conference in Paris in 1900 in which I argued
that there really are points and instants.  Broadly speaking, I took
the view that, whenever Hegel's proof that some thing does not exist is
invalid, one may assume that the something in question does exist - at
any rate when that assumption is convenient to the mathematician.
Pythagoras and Plato had let their views of the universe be shaped by
mathematics, and I followed them gaily.
"It was Whitehead who was the serpent in this paradise of
Mediterranean clarity.  He said to me once: 'You think the world is
what it looks like in fine weather at noon day; I think it is what it
seems like in the early morning when one first wakes from deep sleep.'
I thought his remark horrid, but could not see how to prove that my
bias was any better than his.  At last he showed me how to apply the
technique of mathematical logic to his vague and higgledy-piggledy
world, and dress it up in Sunday clothes that the mathematician could
view without being shocked.  This technique which I learned from him
delighted me, and I no longer demanded that the naked truth should be
as good as the truth in its mathematical Sunday best.
"Although I still think that this is scientifically the right way to
deal with the world, I have come to think that the mathematical and
logical wrappings in which the naked truth is dressed go to deeper
layers than I had supposed, and that things which I had thought to be
skin are only well-made garments.  Take, for instance, numbers: when
you count, you count 'things,' but 'things' have been invented by human
beings for their own convenience.  This is not obvious on the earth's
surface because, owing to the low temperature, there is a certain
degree of apparent stability.  But it would be obvious if one could
live on the sun where there is nothing but perpetually changing
whirlwinds of gas.  If you lived on the sun, you would never have
thought of counting because there would be nothing to count.  In such
an environment, Hegel's philosophy would seem to be common sense, and
what we consider common sense would appear as fantastic metaphysical
speculation." (Bertrand Russell, "Beliefs: Discarded and Retained", in
Portraits from Memory, pp. 40-2)

Ted