I appreciate your thoughtful remarks. Before I respond to them, let me agree with Justin Schwartz's unhappiness that an overemphasis on pure technique can become an extremely sterile end in itself.
The point you raise Ted is indeed a very important and profound one. I discuss it in my paper _Aspects of Dialectics and Nonlinear Dynamics_ that appeared last May in the Cambridge Journal of Economics and which is available (sans figures) on my website. There really is a serious problem regarding the nature of variables that appear in equations and a far too great readiness of mathematical economists and others to attribute to much identity or reality to such things. Of course, the real question here does resolve around the nature of identity or reality.
I have at best a partial response for you, because I do not think there is any easy response to these questions. One is that in the modern theory of complexity provides ways of dealing with this emergence of new things. Now, in approaching this one is still partly stuck in the standard approach of having to assume some kinds of variables that have relations with each other (as opposed to "internal relations" of the sort you want). But then if one considers the system as a whole and its qualitative characteristics, this can evolve and can undergo discontinuous changes and even experience the emergence of qualitatively different structures. This was the sort of thing I was thinking about when I made my remark about new math techniques since the time of Keynes.
I might note that this particular problem is addressed in one of my favorite own papers, which did not appear in an economics journal at all. It is "Discontinuous Change in Multilevel Hierarchical Systems," (with Carl Folke, Folke Gunther, Heikki Isomaki, Charles Perrings, and Tonu Puu), Systems Research, 1994, vol. 11, no. 3, pp. 77-94. Unfortunately it is not available on my website (too old).
It opens with the quote: "For want of nail the shoe was lost. For want of the shoe the horse was lost. For want of the horse the rider was lost. For want of the rider the battle was lost. For want of the battle the war was lost. For want of the war the Kingdom was lost." (Benjajmin Franklin, Poor Richard's Almanac, 1735). This quote is a good example of a literary expression of something that the butterfly effect in chaos theory makes precise, how small events can have enormous effects. The paper then poses the "anagenetic moment" as arising from the synergetic entrainment of oscillators. I shall not bore you all with the subsequent math, although this gets applied to ecological economics issues and much is made of the distinction between bi-hierarchies where two parallel hierarchies cross-connect at each level, matrix hierarchy where the cross-connections can go across levels (a mess), and the more common single hierarchy that one encounters in corporate management, etc. A more ecological economics discussion (with less math) shows up in my article, "Systemic Crises in Hierarchical Ecological Economies," Land Economics, May 1995, vol. 72, no. 2, pp. 163-172, which can be accessed over on the Crashlist maintained on the marxism list at www.marxmail.org.
As a further biographical note, I was originally a physics major as an undergrad in the 60s at the University of Wisconsin, but also a self-styled beat poet as well. I turned off physics partly because of the Vietnam War and also had this crazy idea of doing something' more socially worthwhile in economics. My father was a math prof, indeed a pretty well known one (he was the director of the Army Math Research Center at UW that got bombed in 1970, big surprise, my father and I did not see eye to eye on politics), and so I had a strong background in math, raised to take it seriously as it were. I was partly attracted by the fact that econ did use math when I changed majors.
However, I soon came to be very frustrated by the kinds of math that econ did use, particularly the differential calculus with the presumption that everything is continuous and that one can then come up with justifications for the distribution of income according to marginal productivity theory. When I learned of the reswitching controversy in capital theory I immediately realized that it implied a deep discontinuity that undermined the whole apparatus of standard theory. I saw the vision of continuity as a cover for undermining the idea of sudden socioeconomic change. Thus I was quite excited when I first encountered catastrophe theory and I have gone on and on to the other "C's" ever since without ever looking back, as it were.
Of course my general take on all this is found in my main book, frequently cited on this list I believe, volume I of the second edition of which is now out, the one that was rejected by 13 publishers and which I viewed originally as this enormous critique/slam on standard economics but which is now viewed apparently by many as a sort of musty reference volume....
Well, enough of that personal musing for now. I am perhaps indulging in it as I am planning once again to leave the list sometime later today. Again it is the call of finishing that tedious volume and some other books I am working on (actually the second edition of Rosser and Rosser is the more immediately pressing item, way overdue at MIT Press). No, I am not protesting anything or anybody on the list. I like it and it is very lively. That is the problem. It is just too lively given my current work schedule. But, I'll be back.
Aside to kelley: Next time I'm around, I'll try to "assert harder." A big smooch to you, Snitgrrrl, and keep up that jingling, :-).
Also, I hope to see some of you in the next couple of days at the Eastern meetings in New York and especially at the Lynn Turgeon roundtable on Saturday at 2 at the Crowne Plaza. Still possible to get free badges from Mary Lesser at mlesser at iona.edu. J. Barkley Rosser, Jr. Professor of Economics James Madison University Harrisonburg, VA 22807 USA rosserjb at jmu.edu http://cob.jmu.edu/rosserjb
-----Original Message----- From: Ted Winslow <winslow at yorku.ca> To: lbo-talk at lists.panix.com <lbo-talk at lists.panix.com> Date: Tuesday, February 20, 2001 7:26 PM Subject: Re: "Volatility as Social Flaring"
>Barkley wrote:
>
>> Doug,
>> We have come a long way since Keynes' day.
>> These kinds of math techniques are exactly directed
>> at laying bare the nature of such interactions.
>
>Barkley and I have discussed this matter before on other lists.
>
>I don't think math techniques have developed in a way that invalidates
>Keynes's objection to their use in economics. Specifically, algebra cannot
>take account of the kind of interdependence to which Keynes points in the
>passage Doug quoted.
>
>This is the kind associated with "internal relations" i.e. with relations
>where the "identities" or "meanings" of the related things are the outcome
>of their relations. This idea was the subject of intense debate during
>Keynes's undergraduate years at Cambridge. Its main defender and
elaborator
>in that context was A.N. Whitehead.
>
>Whitehead explains the implications of internal relations for the use of
>algebra as follows:
>
>"Before we finally dismiss deductive logic [as the method of 'philosophy'
>understood as 'the search for premises'], 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, p. 107)
>
>In the case of the use of algebra to represent human behaviour, the
>maintenance of the requisite degree of self-identity (of the same
"meaning")
>of the "variables" in behavioural relations requires the maintenance of the
>requisite degree of self-identity in the individuals whose behaviour the
>algebra is to be used to represent. (This, by the way, is only one of the
>requirements the material must meet for algebra to be validly applicable to
>it.)
>
>Keynes's objection to its use in economics is based on the judgment that
>here (and in social theory - "psychics" - generally) the requirement is not
>met.
>
>"The atomic hypothesis which has worked so splendidly in physics breaks
down
>in psychics. We are faced at every turn with the problems of organic
unity,
>of discreteness, of discontinuity - the whole is not equal to the sum of
the
>parts, comparisons of quantity fail us, small changes produce large
effects,
>the assumptions of a uniform and homogeneous continuum are not satisfied."
>(Keynes, Collected Writings, vol. X, p. 262)
>
>He claims that, even in the short-term, as their relations change the
>"identities" of individuals change in ways that rule out algebraic
>representation of their behaviour. For instance, sudden changes in "the
>psychological attitude to liquidity" can transform the "meaning" of money.
>
>"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, 116)
>
>Such changes in individual psychology - expressed through changes in
>Keynes's "three fundamental psychological factors, namely, the
psychological
>propensity to consume, the psychological attitude to liquidity and the
>psychological expectation of future yield from capital-assets" - underpin
>Keynes's explanation of booms and busts in both the economy in general and
>the stock market in particular.
>
>Changes in the fundamental psychological factors are internally related:
>
>"The dismay and uncertainty as to the future which accompanies a collapse
in
>the marginal efficiency of capital naturally precipitates a sharp increase
>in liquidity-preference - and hence a rise in the rate of interest. Thus
>the fact that a collapse in the marginal efficiency of capital tends to be
>associated with a rise in the rate of interest may seriously aggravate the
>decline in investment." (Keynes, General Theory, p. 316)
>
>Whitehead himself drew out the implications of internal relations for
>political economy. He did so in the context of criticizing classical
>economists for their failure to take account of the variability of "human
>nature" in response to changes in "conditions".
>
>"Our sociological theories, our political philosophy, our practical maxims
>of business, our political economy, and our doctrines of education, are
>derived from an unbroken tradition of great thinkers and of practical
>examples, form the age of Plato in the fifth century before Christ to the
>end of the last century. The whole of this tradition is warped by the
>vicious assumption that each generation will substantially live amid the
>conditions governing the lives of its fathers and will transmit those
>conditions to mould with equal force the lives of its children. We are
>living in the first period of human history for which this assumption is
>false." (A.N. Whitehead, Adventures of Ideas, pp. 92-3)
>
>"Consider our main conclusions that our traditional doctrines of sociology,
>of political philosophy, of the practical conduct of large business, and of
>political economy are largely warped and vitiated by the implicit
assumption
>of a stable unchanging social system. With this assumption it is
>comparatively safe to base reasoning upon a simplified edition of human
>nature. For well-known stimuli working under well-known conditions produce
>well-known reactions. It is safe then to assume that human nature, for the
>purpose in hand, is adequately described in terms of some of the major
>reactions to some of the major stimuli. ...
> "In the present age, the element of novelty which life affords is too
>prominent to be omitted from our calculations. A deeper knowledge of the
>varieties of human nature is required to determine the reaction, in its
>character and its strength, to those elements of novelty which each decade
>of years introduces into social life." (Adventures of Ideas, pp.119-20)
>
>Best,
>
>Ted
>
>--
>Ted Winslow E-MAIL: WINSLOW at YORKU.CA
>Division of Social Science VOICE: (416) 736-5054
>York University FAX: (416) 736-5615
>4700 Keele St.
>Toronto, Ontario
>CANADA M3J 1P3
>
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