To reach a theory of macroeconomic dynamics we need, in the first place, a scientific and dynamic heuristic guiding us to a scientific explanation of the current, purely dynamic, concrete, economic process.
(Ragnar) Frisch’s failure to develop a significant theory typifies the failure of economists who search for a dynamic heuristic. As well as a fundamental disorientation of approach there is also a tendency to shift to an inadequate level of abstraction with a premature introduction of boundary conditions in a determinate set of differential and difference equations. [McShane, 1980, 114]
A heuristic is a guide to an inquiry. It will state both the general type of answer to be sought and the method to be used. Lonergan adopted a scientific and dynamic heuristic
… heuristic structures and canons of method constitute an a priori. They settle in advance the general determinations, not merely of the activities of knowing, but also of the content to be known. [CWL 3, 104-105/128]
In his search for a completely explanatory theory of macroeconomic dynamics, Lonergan developed a scientific and dynamic heuristic guiding his search for general laws that govern and explain the process. The process is always the current process; it is the process being conducted right now, or in this period. It is a concrete process in which we all participate in our daily producing and spending. And it is a process of interrelated, mutually conditioning, velocitous functionings. As velocitous, it is dynamic; it evolves over time. As an overall composite functioning, it consists of component functionings with different timings and conditioning interlockings. So, Lonergan’s heuristic had to be adequate to the nature of the process as current, purely dynamic, and compositely functional.
To avoid initial confusion and a subsequent divergence into contradictory propositions and faulty theories, there must be, in the first place, careful definition of precisely analytic terms. For the commonly used meanings of analysis, analytical, analytic, one may refer to the dictionary; for a gleaning of a meaning as it applies to scientific investigation and discovery one may start with the following excerpt.
So the first movement toward acquiring science begins from an ordinary prescientific description of things and ends in the knowledge of their causes. This first movement has been called: (1) analysis, because it starts from what is apprehended in a confused sort of way and moves to well-defined causes or reasons, (2) the way of resolution, because it resolves things into their causes, (3) the way of discovery, because previously unknown causes are discovered, (4) the way of certitude, because the ordinary prescientific knowledge of things is most obvious to us, and so the arguments we find most certain begin from such knowledge and to on to demonstrate matters that are more remote and more obscure to us, and (5) the temporal way, because causes are not usually discovered instantaneously, any more than they are discovered by just anyone or without a certain amount of good luck. ¶The other movement starts from the causes that have been discovered and ends by understanding things in their causes. This movement is called: (1) synthesis, because fundamental reasons are employed both to define things and to deduce their properties, (2) the way of composition, because causes are employed to produce things or constitute them, (3) the way of teaching or of learning, because it begins with concepts that are fundamental and especially simple, so that by adding a step at a time it may proceed in an orderly way to the understanding of an entire science, (4) the way of probability, partly because it often attains no more than probability, but also because people frequently have no clear discernment of just where or when they have reached certitude, and (5) the way of logical simultaneity, because, once the principles have been clearly laid down, all the rest takes comparatively little time; it can be accomplished in a few short deductions and applications. ¶For examples of the two ways, compare the history of a science like physics or chemistry with the textbooks from which these sciences are taught. History reveals that these sciences worked out their various demonstrations starting from the most obvious sensible data. But when one goes to a textbook, one finds at the beginning of the book in chemistry, only the periodic table of elements from which three hundred thousand compounds are derived, or, in physics, Newton’s laws, Riemannian geometry, or those remarkable quantum operators. The reason for this difference is, of course, that inquiring, investigating, and demonstrating begin with what is obvious, while teaching begins from those concepts that can be understood without understanding other elements. [CWL 12, 61-63]
Lonergan’s analysis began with “what is apprehended in a confused sort of way;” and the analysis moves to well-defined causes or reasons; e.g. booms and slumps seem to be correlated somehow with rates of capital spending. But his teaching in CWL 15 begins with “concepts that can be understood without (yet) understanding other elements.”
Point-to-point vs. point-to-line (Basic vs. surplus) are precise analytical distinctions. They are foundational distinctions between functionings. Preserving them as foundationals prevent us from veering off into a plethora of “schools,” “isms,” and pseudo-systems with their pseudo-problems.
… understanding is fruitful, so that when some first problem is solved, the remaining connected problems will be easily brought to a solution. This very fruitfulness, however, has its disadvantages. The same system that can be understood, grow, and keep improving can also be poorly understood or not understood at all, with the result that those who understand poorly in the first place will concoct pseudo-systems to solve pseudo-problems. [CWL 12, 29]
Upon a firm foundation of precise analytic terms at an adequate level of abstraction we may construct a system of general governing laws which are coherent with one another and completely explain the economic process. Thus these analytical terms are said to be of systematic significance. Paraphrasing [CWL 3, 80/103]:
Thus, basic and surplus or point-to-point and point-to-line might be defined as the precise analytical correlatives implicit in Schumpeter’s description of economic expansion connecting capital expansion with booms and slumps. And expenditures (classified as macroeconomic) costs might be defined as the correlatives implicit in Lonergan’s observation that what limits so-called “profit” is macroeconomic costs. (There is) a pattern of functional relationships constituted by the verified classical equation; the pattern of relationships would (implicitly define and) fix the meaning of basic vs. surplus, as well as macroeconomic costs vs. pure surplus income.
This pattern of relationships which fixes the meaning is purely relational so as to implicitly define.
again, as to the notion of cause, Newton conceived of his forces as efficient causes, and the modern mechanics drops the notion of force; it gets along perfectly well without it. It thinks in terms of a field theory, the set of relationships between n objects. The field theory is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms. The form of any element is known through its relations to all other elements. What is a mass? A mass is anything that satisfies the fundamental equations that regard masses. Consequently, when you add a new fundamental equation about mass, as Einstein did when he equated mass with energy, you get a new idea of mass. Field theory is a matter of the immanent intelligibility of the object. [CWL 10, 154]
again, as to the notion of cause, macroeconomists mistakenly conceive of (efficiently causal) subjective preferences as formal causes. Functional Macroeconomic Dynamics drops the notion of subjective preferences; it gets along perfectly well without it. It thinks in terms of a field theory, the set of relationships between n interdependent, implicitly defined functional activities. The field theory of FMD is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms. The form of any element is known through its relations to all other elements. …. Field theory is a matter of the immanent intelligibilityof the current, dynamic process under investigation.
In brief Lonergan is looking for an explanation in which the terms are defined by the relations in which they stand, that is, by a process of implicit definition. This technique (implicit definition) has been used to great effect by David Hilbert in his Foundations of Geometry in which, for example, the meaning of a point and a straight line is fixed by the relation that two, and only two points, determine a line. “The significance of implicit definition is its complete generality. The omission of nominal definition is the omission of a restriction to objects which, in the first instance, one happens to be thinking about. The exclusive use of explanatory or postulational elements concentrates attention upon the set of relationships in which the whole scientific significance is contained.” Michael Gibbons, Economic Theorizing in Lonergan and Keynes p. 313
One must avoid Frisch’s disorientation of approach, inadequate level of abstraction, and premature introduction of boundary conditions. One must operate from a profound point of view in order to achieve a deeper unity sublating the schools, isms, and pseudo-systems. One must generalize the disparate, non-coherent laws. One must recast the whole existing structure.
Now the movement from a less to a more general level of thought normally involves not only an enlargement but also a readaptation of the whole existing structure. A more profound viewpoint emerges, and this calls for a readjustment of the less general correlations.[CWL 21, 6]
Generalization comes with Newton, who attacked the general theory of motion, laid down its pure theory, identified Kepler’s and Galileo’s laws by inventing the calculus, and so found himself in a position to account for any corporeal motion known. Aristotle, Ptolemy, Copernicus, Galilei, and Kepler had all been busy with particular classes of moving bodies. Newton dealt in the same way with all. He did so by turning to a field of greater generality, the laws of motion, and by finding a deeper unity in the apparent disparateness of Kepler’s ellipse and Galilei’s time squared. … Similarly the non-Euclidean geometers and Einstein went beyond Euclid and Newton. … The non-Euclideans moved geometry back to premises more remote than Euclid’s axioms, they developed methods of their own quite unlike Euclid’s, and though they did not impugn Euclid’s theorems, neither were they very interested in them; casually and incidentally they turn them up as particular cases in an enlarged and radically different field. … Einstein went beyond Newton by employing the new geometries to make time an independent variable; and as Newton transformed the formulation and interpretation of Kepler’s laws, so Einstein transforms the Newtonian laws of motion. … It is, , a scientific generalization of the old political economy and of modern economics that will yield the new political economy which we need. … Plainly the way out is through a more general field. [CWL 21, 6-7]
Lonergan moved macroeconomics back to premises more remote than Walrasian statics, neoclassical macroeconomics and Keynesian macroeconomics; using the technique of implicit definition, he developed deeper, more comprehensive, explanatory formulae quite unlike others’, and though he did not impugn them, neither was he very interested in them; casually and incidentally combinations of prices and quantities turn up as particular coincidental cases in an enlarged and radically different, relativistic systematics. … Lonergan employed a new field-theory dynamics to make aggregate, mutually-defining, velocitous functionings the basic interdependent variables; and as Newton transformed the formulation and interpretation of Kepler’s laws, so Lonergan transforms the neoclassical and Keynesian laws of how economic flows functionally interrelate. … He achieved a scientific generalization of the old political economy and of modern economics that yields the new political economy of Functional Macroeconomic Dynamics which we need for guidance. … Plainly the way to settle pseudo-disputes about the intelligibility of the economic process is through a sublating, more general, dynamics of interrelated functionings.
…. Field theory is a matter of the immanent intelligibility of the object. [CWL 10, 154]
We are not going to discuss wealth or value, supply and demand, price levels and price patterns, capital and labor, interest and profits, production, distribution, and consumption. Because we are not, it certainly will be objected that our discussion has nothing to do with economic science, for economics is precisely the study of wealth and value, supply and demand, and so on. The answer is as follows. The discussion moves on a more general plane to terminate in a more general conclusion. Because the general includes the particular, a generalized economics cannot but include the particular economics. [CWL 21, 8]
Lonergan’s distinction between basic and surplus production and circulation enables him to envisage clearly those ‘further equilibria that have to be maintained’ in the normative framework of a pure theory of economic expansion and growth…. An explanatory account of the intrinsically evolutionary processes of any industrial exchange economy’s cycles of surplus (i.e. producer-goods) and basic (i.e. consumer-goods) production and exchange has to reveal how the different phases in the distinct cycles intermesh and coordinate in an intelligible sequence, by means of differential rates of crossover payments from basic to surplus and from surplus to basic, depending on what phase of aggregate expansion or leveling of the economy happens to be in at any given time. CWL 15, lxiii
Our three fundamental distinctions – 1) point-to-point vs. point-to-line (basic vs. surplus), 2) macroeconomic costs vs. pure surplus income for expansionary investment, 3) currently vs. later – contain virtually the superstructure of many equatings, which represent faithfully by isomorphism the dynamics of the process, and thus explain the process.
… one who reaches … understanding … that is most fruitful does not solve just one single problem in a sterile fashion …, but solves one problem directly in such a way that one simultaneously reaches a virtual solution of many others. CWL 12, 43
… if solving the first problem virtually solves all the others, the (systematically formed) concepts and terms in which the first problem and the first solution are defined and expressed cannot be significantly changed if they are to serve to define and express the later problems and solutions. Clearly, then, … the interconnected questions and solutions themselves demand both systematically formed concepts and a technical terminology that corresponds not to any concepts whatsoever but to systematic concepts.CWL 12, 25
To reach the needed distinctions and concepts the structure of the production-for-sale process must be analyzed first.
… , understanding is about principles. A principle is defined as what is first in some order. Therefore, it belongs to understanding to grasp the solution of that problem that is first in the order proposed by wisdom. Since this order is such that solving the first means that the others are expeditiously solved, the understanding should be such as virtually to contain in itself the answers to the rest of the questions. [CWL 12, 23]
… the questions are put in such an order that, once the first is solved, the solutions to the others follow with almost no difficulty. Therefore, because the later solutions are connected to the first as conclusions are connected to some principle, all solutions after the first seem to be the proper province of knowledge. [CWL 12, 25]
… a system of definitions is introduced through which the solutions can be formulated, and because a technical terminology is developed for expressing the defined concepts. [CWL 12, 25]
In the systematic way the understanding of some points is more necessary than the understanding of others: some points are such that, unless they are understood, nothing else in the entire treatise can be understood; neglecting to understand other points may deprive us only of part of the understanding of the entire treatise; and finally, some points are included just so that others may be more easily understood or that the connections with other questions may be clearer or that we may proceed more promptly to the applications. [CWL 12, 73]
The technique of implicit definition must be employed for the analysis to be scientific and functional. Corporate accounting and explanatory science envisage things in fundamentally different manners.
A distinction has been drawn between description and explanation. Description deals with things as related to us. Explanation deals with the same things as related among themselves. The two are not totally independent, for they deal with the same things and, as we have seen, description supplies, as it were, the tweezers by which we hold things while explanations are being discovered or verified, applied or revised. But despite their intimate connection, it remains that description and explanation envisage things in fundamentally different manners. The relations of things among themselves are, in general, a different field from the relations of things to us. … Not only are description and explanation distinct, but there are two main varieties of description. There are the ordinary descriptions that can be cast in ordinary language. There are also the scientific descriptions for which ordinary language quickly proves inadequate and so is forced to yield its place to a special, technical terminology. (Now) both ordinary and scientific description are concerned with things as related to us, but both are not concerned with the same relations to us. The scientist selects the relations of things to us that lead more directly to knowledge of the relations of things among themselves. Ordinary description is free from this ulterior preoccupation. [CWL 3, 291-92/316-17]
“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; Lonergan illustrates his basic meaning of ‘explanation’ by referring to D. Hilbert’s method of implicit definition: … In Lonergan’s circulation analysis, the basic (dynamical) terms are rates (of functional activities implicitly defined by their functional relations to one another) – rates of mutually conditioning, and interdependent productive activities and rates of mutually conditioning, and interdependent payments. The objective of analysis is to discover the … functional (inter)relationships (which implicitly define these rates and explain the dynamics of these rates to one another). [CWL 15, 26-27 ftnt 27]
So, Lonergan proceeds in wise order to reach a set of explanatory relations:
- He states the basic premise and goal of his analysis:
our inquiry differs radically from traditional economics, in which the ultimate premises are not production and exchange but rather exchange and self-interest, or later, exchange and a vaguely defined psychological situation. Our aim is to prescind from human psychology (so) that, in the first place, we may define the objective situation with which man has to deal, and, in the second place, define the psychological attitude that has to be adopted if man is to deal successfully with economic problems. Thus something of a Copernican revolution is attempted: instead of taking man as he is or as he may be thought to be and from that deducing what economic phenomena are going to be, we take the exchange process in its greatest generality and attempt to deduce the human adaptations necessary for survival. [CWL 21,42- 43]
- He makes a precise analytical distinction between point-to-line and point-to-line relations of products to the emergent standard of living.
- He states the postulate of the composition of a product. qi= ΣΣqijk; [CWL 15, 30]
- He postulates the law of lagged technical acceleration and analyzes the structure and rhythm of the productive process. kn[f’n(t-a)-Bn] = f”n-1(t) – An-1[CWL 15, 37]
- He discovers a normative pure cycle or central tendency for which the process has an exigence
- He constructs pricing and quantity vector indices, vectors being tensors of the first order; P2= Σpi2 [CWL 15, 108] Q2= Σqi2[CWL 15, 108] and he employs contraction of tensors to get values in what is always a process of value.
- He correlates the structure of the productive process with classes of payments
- He discovers a new theory of the velocity of money: Turnover magnitude and frequency are correlated with turnover dollar magnitude and frequency
- He analyzes and explains credit: why it is necessary and how it should enter the process
- He discovers a normative circulation of money
- He states a theorem of identity – or reciprocity – to equate the expenditure of incomes with the outlays of receipts. P’Q’ = p’a’Q’ +p”a”Q”
- On these basics and bases he can go on to discover the differential laws of the process as regards:
- Phases of a pure cycle and their equilibria
- Full realization of the potential of the process given a current state of culture and technology
- Crises and trade cycles called colloquially boomsand slumps
- The nature of credit and the norms of its use
- The ineptness of manipulation of interest rates
- The relativistic definition of prices and quantities
- The conflict of the criterion of ever increasing earnings and the cycle of the rising and falling of pure surplus income
- The occurrence of crises due to temporarily insufficient basic capacity and to failure to implement the basic expansion
To repeat, only by beginning with precise analytical distinctionscan one build up a coherent superstructure of terms and relations constituting a fully explanatory theory, devoid of pseudo-problems.
“Functional”is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; ¶Lonergan illustrates his basic meaning of ‘explanation’by referring to D. Hilbert’s method of implicit definition: … In Lonergan’s circulation analysis, the basic terms are rates – rates of productive activities and rates of payments. The objective of analysis is to discover the underlying, intelligible and indeed dynamic (accelerative) network of functional, mutually conditioning, and interdependent relationships of these rates to one another. CWL 15 26-26 ftnt 27