PKT message, A Future Economics

Gunnar

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The twin concepts of Determinacy and Indeterminacy are counterparts in theoretical economics to the NKS concepts of Computational Reducibility and Irreducibility ? an indeterminate theoretical proposition is one that may or may not be valid.

This has important implications in monetary economics for, as noted by David Hume in an essay ?Of Public Debt?, in which he reasoned in terms of Commodity Money, his conclusions were not valid for Money which lacks intrinsic commodity value.

Modern money lacks intrinsic commodity value ? that is to say, the Supply of Money, unlike that of Goods and Services, does not require Inputs of Factor Services, but is created with the proverbial stroke of a pen (or computer key).

In principle, therefore, the Supply of Money is indeterminate.

In turn, this implies that Computational Irreducibility is an intrinsic and inescapable attribute of real-world market economies ? a fact obfuscated by Paul A. Samuelson in formulating the concept of ?an operationally meaningful theorem? in ?Foundations of Economic Analysis? (1942).

?By a meaningful theorem,? Samuelson wrote, ?I mean simply a hypothesis about empirical data which could conceivably be refuted, if only under ideal conditions. A meaningful theorem may be false. It may be valid but of trivial importance. Its validity may be indeterminate [sic], and practically difficult or impossible to determine. Thus, with existing data, it may be difficult or impossible to check upon the hypothesis that the demand for salt is of elasticity ? 1.0. But it is meaningful because under ideal circumstances and experiment could be devised whereby one could hope to refute the hypothesis.? (Atheneum, New York, 1979, p. 4)

In the context, a ?meaningful theorem? which is also ?indeterminate? is an oxymoron on par with Reducible Computational Irreducibility!

Samuelson then proceeded to transform this oxymoron into the cornerstone of what, in due course, became orthodox mainstream economics as follows:

?In this study I attempt to show that there do exist meaningful theorems in diverse fields of economic affairs. They are not deduced from thin air or from a priori propositions of universal truth and vacuous applicability. The proceed almost wholly from two types of very general hypotheses [?a priori propositions of universal truth and vacuous applicability? ? insert]. The first is that the conditions of equilibrium are equivalent to the maximization (minimization) of some magnitude?.

?However, when we leave single economic units, the determination of unknowns is found to be unrelated to an extremum position. In even the simplest business cycle theories there is lacking symmetry in the conditions of equilibrium so that there is no possibility of directly reducing the problem to that of a maximum or minimum. Instead the dynamical properties of the system are specified, and the hypothesis [?a priori proposition of universal truth and vacuous applicability? ? insert] is made that the system is in ?stable? equilibrium or motion. By means of what I have called the Correspondence Principle between comparative statics and dynamics, definite operationally meaningful theorems can be derived from so simple a hypothesis. One interested only in fruitful statics must study dynamics.? (Op. cit., p. 5)

The fact that the Supply of Money does NOT require Inputs of Factor Services means that Samuelson?s hypothesis ?that the conditions of equilibrium are equivalent to the maximization (minimization) of some magnitude? cannot IN PRINCIPLE apply to real-world market economies.

I pointed this out to Samuelson in 1978 ? and now give him the last word:

??a scholar in economics who is fundamentally confused concerning the relationship of definition, tautology, logical implication, empirical hypothesis, and factual refutation may spend a lifetime shadow-boxing with reality.? (Op. cit., p. ix)

A Future Economics - Addendum