> 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