Abstraction in Macroeconomics: Classical and Statistical Laws

Abstraction is enriching.  The relation of things to our senses must be transcended by abstraction; abstraction yields explanatory concepts implicitly defined by their functional relations to one another.

The commonsense accounting relations constituting historical Gross Domestic Product must be supplemented by the abstract explanatory formulation of Current Gross Domestic Functional Flows.  All participants must have the scientific guidance of a normative theory in order to properly adapt their personal conduct to the principles and laws of the objective process.

The normative theory will consist of abstract classical laws.

… classical laws are abstract

    1. in their heuristic anticipation,
    2. in the experimental techniques of their discovery,
    3. in their formulation, and
    4. in their verification

They are abstract in their heuristic anticipation.  For that anticipation rests on the detached and disinterested drive of inquiry, and it consists in a pure desire to understand.  Hence, the canon of relevance demands that one seek the immanent intelligibility of the data; the canon of parsimony demands that one add to the data no more than the formulation of what is grasped by understanding and verified; and the canon of complete explanation demands that this parsimonious addition of intelligibility be effected for all data.  Moreover, this anticipated enrichment is seen to be universal: the nature to be known will be the same for all data that are not significantly different, and the correlation to be specified is reached only if it holds for all parallel instances. (CWL 3, 89-90/112-13)

Secondly, classical laws are abstract in the experimental techniques of their discovery.  For the experimenter makes no pretense to deal with concrete situations in their native complexity; on the contrary he aims overtly at reducing that complexity to a minimum and so he does all he can to bring the concrete into some approximation to an ideal, typical, definable conjunction of materials and agents. … At every turn it seems that the concern of the experiment is to determine …  a theoretical correlation between definable and abstract entities. (CWL 3, 90/113)

Thirdly, classical laws are abstract in their formulation.  As laws, they are correlations linking correlatives, and the correlatives are never the unique data of some particular time and place.  Indeed they are not even generalized data, but generalized combinations of combinations of combinations of data.  Nor may one suppose that the data, take in these serial combinations, uniquely determine what the law must be.  For the discontinuous set of observations, represented, say, by points on a graph, can be satisfied by any number of laws, of which the scientist chooses the one that, all things considered, he reputes to be the simplestEnriching abstraction is still at work (CWL 3, 90/113-14)

Fourthly, classical laws are abstract in their verification.  For verification is reached, not by appealing to this or that isolated instance, but by securing as large and various a range of instances as both direct and indirect procedures make possible.  It follows that what is verified is, not this or that particular proposition, but the general, abstract formulation that alone admits the large and various range of applications.  Again, to repeat the argument from another viewpoint, what is verified is what can be refuted or revised.  What can be refuted or revised, is the general abstract formulation.  And so what is verified is the general, abstract formulation. (CWL 3, 90/114)

The abstract normative explanatory theory will dispel ignorance and it will silence much psychopolitical criticism.  It will be a normative theory of continuity, equilibrium, and a pure cycle of expansion in phases.

In equity (the basic expansion phase following the surplus expansion phase) should be directed to raising the standard of living of the whole society.  It does not.  And the reason why it does not is not the reason on which simple-minded moralists insist.  They blame greed.  But the prime cause is ignorance.  The dynamics of surplus and basic expansion, surplus and basic incomes are not understood, not formulated, not taught….. [CWL 15, 82]

… , besides the pricing system, there exists another economic mechanism, that relative to this (other) system man is not an internal factor but an external agent, and that the present economic problems are peculiarly baffling because man as external agent has not the systematic guidance he needs to operate successfully the machine he controls. [CWL 21, 109] 

Insight pivots between the descriptive terms of sensing and perceiving as arranged in some image and, by trial, error, manipulation of the image, and the genius of insight, reaches abstract terms related to and implicitly defining one another in a neat formula which explains the phenomena and is, thus, of purely scientific significance. Thus the everyday accountants’ revenues and costs get redefined as abstract pretio-quantital vectors implicitly defined by their functional relations to one another.

P’Q’ = p’a’Q’ + p”a”Q” (CWL 15, 157-60/)

There is a sense in which one may speak of the fraction of basic outlay that moves to basic income as the “costs” of basic production.  It is true that that sense is not at all an accountant’s sense of costs; … But however remote from the accountant’s meaning of the term “costs,” it remains that there is an aggregate and functional sense in which the fraction… is an index of costs.  For the greater the fraction that basic income is of total income (or total outlay), the less the remainder which constitutes the aggregate possibility of profit.  But what limits profit may be termed costs.  Hence we propose ….to speak of c’O’ and c”O” as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. (CWL 15, 156-57)

The basic distinction is between abstract system and particular cases.  Both are objects of insight.  But the particular case is the typical instance, presented by sense or imagination, and understood by insight into the presentation.  In contrast, the abstract system is neither sensible nor imaginable; it is a conceptual objectconstituted by terms and relations that, at least in the last resort, are defined implicitly. (CWL 3, 86/109)

Again, once abstract system is formulated, it can be applied to concrete situations only insofar as there occur insights into the situations as sensibly given; for without such insights there cannot be selected the relevant laws of abstract system, there cannot be determined the mode in which the laws combine in the concrete situation, and there cannot be substituted numerical values for the variables and undetermined constants of the general formulae. (CWL 3, 86/109-10)

Now let us suppose full knowledge of all classical principles and laws.  Then we suppose full knowledge of abstract system; for principles and laws are relations; such relations necessarily involve the terms that they define implicitly; and abstract system consists in terms implicitly defined by the relations expressed in verified principles and laws. (CWL 3, 86/110)

… abstract system is applied to concrete situations only and inasmuch as insight into the situations selects the relevant laws, determines the mode of their combination, and substitutes numerical values for the variables and undetermined constants of the laws. (CWL 3, 86/)110

Again, abstraction is enriching.

… to show that classical laws are not merely the macroscopic illusion resulting from a multitude of microscopic, random occurrences, a correct theory of the abstract is needed. … What is, then, the correct theory? (CWL 3, 88/112)

So far from being a mere impoverishment of the data of sense, abstraction in all its essential moments is enriching.  Its first moment is an enriching anticipation of an intelligibility to be added to sensible presentations; there is something to be known by insight.  Its second moment is the erection of heuristic structures and the attainment of insight to reveal in the data what is variously named as the significant, the relevant, the important, the essential, the idea, the form.  Its third moment is the formulation of the intelligibility that insight has revealed.  Only in this third moment does there appear the negative aspect of abstraction, namely the omission of the insignificant, the irrelevant, the negligible, the incidental, the merely empirical residue.  Moreover, this omission is neither absolute nor definitive.  For the empirical residue possesses the universal property of being what intelligence abstracts from.  Such a universal property provides the basis for a second set of heuristic procedures that take their stand on the simple premise that the non-systematic cannot be systematized. (CWL 3, 88-89/112)

Now our whole effort has been to draw attention to the fact of insight, to the enriching moments on which abstraction follows.  Accordingly, it is in this sense that we affirm classical laws to be abstract.  So far from being an impoverishment of sensible data, abstraction is an enrichment that goes beyond them.  Because abstraction goes beyond the sensible field, the frontiers of the abstract are not coterminous with the frontiers of the experienced.  Hence, full and exact knowledge of the systems to be reached by abstraction by no means denies the existence of an empirical residue that is non-systematic.  Again, just as in abstraction we prescind from the empirical residue, so when we come to the concrete applications of abstract principles and laws, we are forced to take into account the non-systematic conditions under which the systematic has its concrete realization. (CWL 3, 89/112)

Galileo recognized “primary qualities” but failed to recognize and thematize abstraction.

Galileo discovered our law of falling bodies, but he failed to recognize its abstractness.  Correctly, he recognized that explanation lies beyond description, that the relations of things to our senses must be transcended, that the relations of things to one another must be grasped, and that a geometrization of nature is the key tool in performing this task.  Still Galileo did not cast his methodological discoveries in the foregoing terms.  Instead of speaking of the relations of things to our senses, he spoke of the merely apparent, secondary qualities of things.  Instead of speaking of the relations of things to one another, he spoke of their real and objective primary qualities, and these he conceived as the mathematical dimensions of matter in motion. … The Galilean acknowledges … universality and necessity but cannot recognize its abstractness.  For him it is attached immediately to imaginable particles or an imaginable aether or both.  For him, it is already concrete, and so it is not in need of further determinations to reach concreteness.  For him, the further determinations, which would be non-systematically related to one another, simply do not exist.  Accordingly, since he has no doubt of the existence of classical laws, he cannot but regard statistical laws as mere formulations of our ignorance.  There is some vast aggregate of discrete or continuous but imaginable elements; they are subject to universal and necessary laws; and the business of the scientist is the hard task of determining those laws and so predicting what cannot but occur. (CWL 3, 130-31/152-53)

We seek systematic relationships in the abstract field.  Classical abstract laws and statistical laws are complementary.

This Galilean view … seems to have suffered a crippling wound from the overt claims of Quantum Mechanics.  Our argument, however, moves on a different terrain.  It appeals to Darwinism and to Quantum Mechanics only as illustrations of scientific intelligence.  Its proper premises lie in the dynamic structure of empirical inquiry and in the canons that govern its unfolding.  In that field it has noticed that abstraction is not impoverishing but enriching, that in the sense of enriching abstraction classical laws are abstract, that a systematic unification of classical laws does not imply the possibility of imaginative synthesis, that the concentration of systematic relationships in the abstract field leaves the further determinations, needed for concrete applications, non-systematically related to one another.  It follows that classical and statistical laws, so far from being opposed, are complementary.  It follows that the regularities of our universe result, not from classical laws alone, but from the combination of such laws with suitable constellations of concrete circumstances. (CWL 3, 131/154)

… the concentration of systematic relationships in the abstract field leaves the further determinations, needed for concrete applications, non-systematically related to one another.  It follows that classical and statistical laws, so far from being opposed, are complementary.  It follows that the regularities of our universe result, not from classical laws alone, but from the combination of such laws with suitable constellations of concrete circumstances. (CWL 3, 131/154)

Lonergan’s field-theoretic, explanatory mathematized relations are abstract and invariant.  They “are invariant and the ground of that invariance is that the expressions stand for abstract and generally valid propositions.”  The explanatory abstract expressions are generally applicable to any nation’s economic process, regardless of its particular culture, political system, or stage of growth.

When the symbolic form of a mathematical expression is unchanged by a transformation, the meaning of the expression is unchanged.  But a transformation is a shift from one spatial standpoint to another and, when expressions do not change their meanings under such shifts, then, … the expressions are invariant and the ground of that invariance is that the expressions stand for abstract and generally valid propositions. (CWL 3, 146/170)

Now, science is explanation rather than description.  Science proceeds in a systematic way, beginning with images of the phenomena of our sensing and perceiving and the measurements of these phenomena called data.  (Again) insight pivots between the descriptive terms of the sensing and perceiving as arranged in some image and, by trial, error, manipulation of the image, and the genius of insight, reaches abstract terms related to and implicitly defining one another in a neat formula which explains the phenomena and is, thus, of purely scientific significance.

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. … [CWL 3, 291/316]

The process of analysis moves from experiential, descriptive contents “through a process of redefinition towards terms implicitly defined by empirically established principles and laws.”

As the analysis reveals, there are only three basic alternatives. Either one’s terms are experiential conjugates or else they are pure conjugates based on combining contents alone or finally they are a special case of pure conjugates based on combining acts alone. … V. Lenzen in his Nature of Physical Theory emphasizes the genetic process that begins from experiential contents of force, heat, extension, duration, etc., to move through a process of redefinition towards terms implicitly defined by empirically established principles and laws.  .. Lindsay and Margenau in their Foundations of Physics, … may be said to exhibit a preference for terms implicitly defined by equations.  [CWL 3, 81-82/105]

Functional Macroeconomic Dynamics will take a heuristic cue from the empirical method and insights of explanatory science; the search will be for the general specification of the dynamic process in the form of differential equations d(x)/dt = …, and d2(x)/dt2 =

FMD is not a bunch of Walrasian supply-demand curves.  It is not a macrostatics. It is not a textbook efficient-cause theory of action and the reaction provoked by the action.  It is a dynamical theory.

Taking into account past and (expected) future values does not constitute the creative key transition to dynamics.  Those familiar with elementary statics and dynamics (in physical mechanics) will appreciate the shift in thinking involved in passing from equilibrium analysis (of for example a suspended weight or a steel bridge)…to an analysis where attention is focused on second-order differential equations, on d2θ/dt2, d2x/dt2, d2y/dt2, on a range of related forces, central, friction, whatever.  Particular boundary conditions, “past and future values” are relatively insignificant for the analysis.  What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

Ought there not to be introduced a technical term to denote this type of intelligibility?  … The intelligibility that is neither final nor material nor instrumental nor efficient causality is, of course, formal causality…What we have called the intelligibility immanent in sensible data and residing in the relations of things to one anothermight be named more briefly formal causality … [CWL  3, 78/101-102]

FMD is a theory of the immanent intelligibility or “formal cause” of the objective process.  It is a field theory of the relations of explanatory functionings among themselves.

This general specification will state the functional relations among the most basic explanatory variables – in this case, velocitous and accelerative “basic” point-to-point and “surplus” point-to-line functionings – which will explain by its abstract classical laws the interdependent functionings of the dynamic process.

The technique of implicit definition will be employed: Implicit definition will yield terms defined purely by their functional relations to one another.

An awareness and understanding of understanding, i.e. insight into insight is indispensible; a.) Insight pivotsbetween the observed concrete and the sought-after abstract immanent intelligibility of a thing or process. b.)Prescinding from exceptions in quantum mechanics, insight is into image: Insight into an image or a diagram of the observed concrete dynamic process will yield the abstract correlations of correlations constituting the immanent intelligibility among the interdependent functionings of the process.  c.) The initial struggle towards the insight yielding explanatory classical laws will be abstractive; it will disregard statistical notions such as non-systematic, probabilistic occurences such as the incidental levels of prices and quantities and irrelevant matters such as sociological categories, legal form, d.) Insight at an adequate level of abstraction will reach to the most basic terms and relations from which a superstructure comprising a complete theory of classical equations complemented by statistical laws may be deduced.

The model will be an idealized pure-cycle model for which the process has an exigence – like it or not – and by which we may measure random variances and significant disequilibrating maladaptations by external agents.

The general specification (formal cause) will be an objective and scientific relating of abstract terms to one another; it will be prior to and independent of the psychology (utility, disutility, intertemporal preference) and the conformal or maladaptive performance of human agents. The classical laws of purely objective economics are prior to the psychology or the anthropology of participants.  Participants must adapt to the classical laws of Functional Macroeconomic Dynamics.

We set out to indicate the existence of an objective mechanical structure of economic activity, of something independent of human psychology, of something to which human psychology must adapt itself if economic activity is not to become a matter of standing in a tub and trying to lift it. (CWL 21, 56)

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 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)

The classical laws represent the prior and more fundamental, immanent intelligibility, or formal cause, of the process, whereas the psyche-based activities of humans – outside of the process, as it were – constitute the external efficient cause of the process.

The particular results in the process will be given by the application of boundary conditions of prices and quantities. There exist statistical residues.

Read (3, 93 ff.)