Implicit Definition and Scientific Significance

Our main topic is Functions, Velocities, and the Achievement of Scientific Economics; and we first describe the economy’s constituent functionings so that we may advance to the explanatory formulation of their objective relations to one another.  The goal of macroeconomic dynamics is explanation of dynamic process in the form of terms functionally related to one another.  The whole structure of functional macroeconomic dynamics is purely relational.

A relation of terms to one another can be achieved by the technique of implicit definition, as exemplified by an implicit equation wherein the terms are defined by their relations to one another such as   x3+ y3+ x cos y = 1.

The name of Hilbert is associated with implicit definition in geometry:

an entirely new type of definition was introduced by Hilbert in his formulation of geometry.  He called it implicit definition.  An implicit definition express(es) only a relational form…. [CWL 10, 126][1]

Lonergan appropriates the technique of implicit definition to his macroeconomic dynamics:

Lonergan went on to identify the contemporary notion of a “function” as one of the most basic kinds of explanatory, implicit definition – one that specifies “things in their relations to one another” [CWL 3, 37-38/61-62]  [CWL 15  26-27 ftnt 27]

Field theory of modern physics uses implicit definition, rids itself of external efficient cause, and achieves the purely formal cause of immanent intelligible relations:

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 nobjects.  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.[2][CWL 10, 154]

Paraphrasing:

The academic economist conceived of psychological humans as efficient causes, but functional macroeconomic dynamics drops the notions of utility, indifference, and preference; it gets along perfectly well without them.  It thinks in terms of a field theory, the set of relationships between interdependent functionings.  Functional macroeconomic dynamics 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 functioning is known through its relations to all other functionings.

Thus, the macroeconomist seeking scientific, explanatory significance will seek “a set of intelligible relations linking what is implicitly defined by the relations themselves; (he seeks) a set of relational forms.  The form of any element is known through its relations to all other elements.”  And, in our case, the elements will be economic functionings linked according to a) relations of dependency within and between circuits, and b) relations of magnitude and timing between distinct functional accelerations.  Our science will be a set of pure relations whose terms are filled with functional economic content.

In functional macroeconomic dynamics, They are “the field of intelligible relations that implicitly define the elements.”  The immanent intelligibility is called the formal cause.  And it is only the application of functional macroeconomics, i.e. the management of the economy, that is concerned with efficiently causal human agents and goals.

modern science … is the perfecting of the very notion of science itself, of knowing things by their causes, by analysis and synthesis. What are the causes?  The field of intelligible relations that implicitly define the objects.  The objects with which a science deals are whatever is defined by its field of intelligible relations, whatever falls into that field.  The causes are formal causes; it is only applied science that is concerned with agents and ends. [C]WL 10, 155

Thus to belabor, the “formal cause” in functional macroeconomics is “the field of intelligible relations that implicitly define the objects.”  And the objects with which macroeconomics deals are the constituent functionings defined by their intelligible functional relations of dependency and interaction with one another.

To understand implicit definition, let us pause, cognizant of Lonergan’s investigations into science and scientific knowing in his seminal work Insight, and desirous of achieving scientific explanation, let us say some more about implicit definition, science and explanation, especially as they regard parallels between two different distinct sciences of geometry and macroeconomics.

In the subject of plane geometry, Hilbert employed the techniques of implicit definition.  “Point” has no meaning apart from the idea that two points determine a straight line.  And “line” has no meaning apart from the idea that a line is that which is determined by two points.  The terms “two points” and “line” are purely related, cleanly co-related or correlative. The definition of one term is implicit in the definition of the other term; the terms are mutually defined by their relations of one to the other; the relations define the terms and the terms define the relations.  The idea of one is the idea of the other.

Implicit definitions are not “nominal” definitions: they are not a matter of mere naming or of knowing how to use the terms in a declarative sentence.  Rather than nominal, the definitions are postulational stating an intelligible relationship.  They result from INSIGHT, the insight which grasps the real-terms-in-their-real-relations.

“Functional” is a technical term pertaining to the realm of explanation, analysis, theory; it does not mean “who does what” in some commonsense realm of activity………”Let us say, then, that for every basic insight there is a circle of terms and relations, such that the terms fix the relations, the relations fix the terms, and the insight fixes both…….Lonergan (identified) the contemporary notion of a “function” as one of the most basic kinds of explanatory, implicit definition – one that specifies “things in their relations to one another”…In Lonergan’s circulation analysis, the basic terms are rates – rates of productive activities and rates of payments.  The objective of the 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 26-27  ftnt 27]

And, if the terms and relations are foundational and of systematic significance, further insights may lead to further definitions and relations in the larger system of terms and relations known as plane geometry.

In the physical sciences, the scientist begins with the initial descriptive terms of experience.  These terms re-present; they state the relations of things to our senses, e.g. hot or cold, red or green, fast or slow.  Then the scientist performs measurements of the concrete process; then the initial descriptive terms undergo a revision; by trial and error and messing around with images (i.e. fantasizing about possible different interconnections in an image or phantasm) the scientist develops technical terms and formulates in a general rule the relations of these terms to one another to determine if they explain the patterns immanent in the measurements of the concrete process; finally he verifies his general rule or law applicable to the relations of the terms in every case.

Lonergan acts similarly.  He seeks what is “first-in-itself.”  Let us give several excerpts which indicate Lonergan’s purpose, dynamic heuristic, and technique.  We will be loading important ideas from CWL 3, Insight… into this treatment of functional macroeconomics.  In the following series of excerpts, note and compare the bookkeeper’s entities with the scientist’s preliminary classifications of functionings.  And note and compare the macroeconomic scientist’s insights into purely-relational, functional macrodynamics with the early scientist’s insights into “the nature of”.  For what is needed are

  1. A set of terms which wouldexpose similarities that reside in the relations of things to one another
  2. That the relations are the dynamic elements
  3. Which are the dynamic elements and the differentials of the system
  4. That these differentials reveal the significance of aggregate changes in prices that are themselves in need of interpretation…
  5. That prices – as either real and relative or monetary and absolute – are in need of interpretation.

Only at the end of the analysis do we come to the analytical framework needed to interpret price changes.  The academic economist’s beginning – prices – is functional macroeconomic dynamics’ end – prices as real and relative or monetary and absolute.

the set of terms and relations capable of explaining the phenomena of the business or trade cycle would not be the same as any given pricing system that automatically coordinates a vast coincidental manifold of decisions of demand and decisions of supply.  Such a system comes to sight as bookkeeper’s entities that form the basis of the preliminary descriptive classifications that need to be explained: they are the similarities “first-for-us.”  The relevant set of explanatory terms and relations would have to expose similarities that reside in the relations of things to one another or what is “first-in-itself”: namely both the dynamic elements and the differentials of the economic mechanism which reveal the significance of aggregate changes in prices that by themselves are in need of interpretation (as either real and relative or monetary and absolute). [CWL 15, Editors’ Introduction  lvi ]

Previously I have suggested a lack of adaptation in the free economies to the requirements of the pure cycle.  What that lack is can now be stated.  It is an inability to distinguish between the significance of a relative and an absolute rise or fall of monetary prices.  A relative (i.e. “real”) rise or fall is, indeed, a signal for a relatively increased or reduced production (of one product relative to another)…  (much)… (But) the rising prices of the surplus expansion are not real and relative but only monetary and absolute rising prices; to allow them to stimulate production is to convert the (normative) surplus expansion into a boom(which must be followed out of systematic necessity by a correlative and devastating slump). This I believe is the fundamental lack of adaptation to the productive cycle that our economies have to overcome. [CWL15, 139-140]

To repeat, then, Lonergan holds that prices as a concern for the bookkeepers or accountants are known- first-to-us by description and commonsense classification; and that his own functional analysis of production and circulation reveals an explanatory system known-first-in-itself.  Only such an explanatory framework will enable the all-important discrimination either of the causes and the variations in prices (MD:ECA 75-80, 113-20) or of a relative and an absolute rise or fall of monetary prices, only such an explanatory framework will make possible a correct interpretation of their significance. [CWL 15, Editors’ Introduction  lvi] [3]

There is a further type of insight that arises immediately from the data.  Such is the grasp (insight, or act of understanding) that precedes and grounds the definition of the circle.  Such was Galileo’s insight formulated in the law of falling bodies.  Such was Kepler’s insight formulated in the laws of planetary motion.  Such was Newton’s insight formulated in the theory of universal gravitation.  Such has been the point in the now well established technique of measuring and correlating measurements.  Such is the goal of classical heuristic structure that seeks to determine some unknown function by working out the differential equations, of which the unknown function will be a solution, and by imposing by postulation such principles as invariance and equivalence …Fourthly, it notes that this intelligibility, immanent in the [, resides in the relations of things, not to our senses, but to one another.  Thus, mechanics studies the relations of masses, not to our senses, but to one another. Chemistry defines its elements, not by their relations to our senses, but by their places in the pattern of relationships named the periodic table.  Biology has become an explanatory science by viewing all living forms as related to one another in that complex and comprehensive fashion that is summarily denoted by the single word, evolution. [CWL 3, 77-78; 100-102]

Galileo inaugurated modern science by insisting that the nature of weight was not enough; from sensible similarity, which resides in the relations of things to our senses, one must proceed to relations that hold directly between things themselves.  CWL 3, Insightp. 38/

Lonergan has six Canons of Empirical Method.[4]One is the Canon of Relevance, which states the type of understanding proper to empirical science:

“empirical inquiry aims at reaching the intelligibility immanent in the immediate data of sense.”  … This intelligibility resides in the relations of things, not to our senses, but to one another” …  “The technical term to denote this type of intelligibility is ‘formal causality.”  [CWL 3, 77-78/ 101-102]

At the root of classical method there are two heuristic principles.  The first is that similars are understood similarly…The second is that the similarities, relevant to explanation, lie not in the relation of things to our senses but in their relation to one another.  [CWL 3, 435/460]

Empirical inquiry has been conceived as a process from description to explanation.  We begin from things as related to our senses.  We end with things as related to one another.  Initial classifications are based upon sensible similarities.  But as correlations, laws, theories, systems are developed, initial classifications undergo a revision.  Sensible similarity has ceased to be significant, and definitions consist of technical terms that have been invented as a consequence of scientific advance. [CWL 3, 164/188]

First, there are preliminary classifications based on sense and common sense, such as the bookkeeper’s entities; then there are insights into “the nature of”:

Now sensible similarities, which occur in the relations of things to our senses, may be know before ‘the nature of …’ has been discovered.  They form the basis of preliminary classifications.  They specify the ‘nature of …’, so that one states that one is seeking the nature of colour, the nature of heat, the nature of change, the nature of life. … On the other hand, similarities that reside in the relations of things to one another are the proximate materials of insight into nature.  Hence, the empirical inquirer, to emphasize this fact, will say that his objective is not merely ‘the nature of …’ but more precisely, the unspecified correlation to be specified, the undetermined function to be determined. … The second step in the generalization is, then, that just as the mathematician states that he seeks an xwhich has such and such properties, so too the empirical inquirer states that he seeks a ‘nature  of …’ where the nature antecedently is specified by a classification based on sensible similarity and consequently will be known when some indeterminate function is determined.  [CWL 3, 38/62]

Whenever the scientist (economist) is seeking to determine some indeterminate function, he is relating things to one another.  And that is just what common sense does not do.  It understands things in their relations to us.  Thus we have Whitehead’s two worlds.  Eddington said that he had two tables in his room: there was a brown table, made of oak, solid, that had a certain shape, and then there was the scientific table that consisted of electrons bounding about and so on.  Most of it was empty space.  Where do the two tables come from?  They come from two approaches.  Common sense understands the table in its relations to us: a table is something you can lean on, something you do not bump into, something you can use for writing; it has a certain visible appearance, certain tactile qualities, and so on.  The table is integrated into the flow, the interests, the Sorge, the concern, of the subject.  But science relates measurements to one another; and it does not have to go very far along that route to discover that it is introducing an entirely new world…. Common sense, like grammar, is egocentric; it concerns the intelligibility of things for me.  In grammar, time and tense relate to mytime, mypresent.  The meaning of fundamental adverbs like ‘here’ and ‘there’ is related to me.  The first person is the point of reference. … The scientific procedure of relating things to one another builds up maps and clocks that leave the whole commonsense approach to things out of the picture. [CWL 10, 140]

Paraphrasing in part:

Whenever the economist is seeking to discover the immanent intelligibility of the current, purely dynamic process, he is relating functionings to one another.  And that is just what bookkeeping and National Income accounting do not do. They understand things in their relations to us. … But economics relates measurements of explanatory functional flows to one another; and it does not have to go very far along that route to discover that it is introducing an entirely new world…. It revises the whole commonsense approach of bookkeeping and National Income accounting to introduce an entirely new world.

Let’s keep going.  Sometimes it seems to this writer that conveying to the reader the background Lonergan brought to functional macroeconomic dynamics is more persuasive and convincing than conveying the actual content of functional macroeconomic dynamics in CWL 15, CWL 21, and McShane, 2017.  Intellectual background and historical context are hugely important. An appreciation of Lonergan’s background will convince the reader that surely this man must have achieved something significant by applying his learning to functional macroeconomic dynamics; just running through the functional macroeconomic dynamics of these three books may not inspire sufficient interest, especially to those mired in conventional macroeconomics.  The full context of all Lonergan’s work is vital to full appreciation of the achievement.

It follows that formulations contain two types of terms which may be named respectively, experiential and pure or explanatory conjugates.  [CWL 3, 79/101-102]

Experiential conjugates are correlatives whose meaning is expressed, at least in the last analysis, by appealing to the content of some human experience.

Thus “colors”…”sounds”…”heat”…”force”.… The fundamental set of such terms is verified, not only by scientists, but also by the secular experience of humanity. [CWL 3,  79/101-102]

Pure (or explanatory) conjugates, on the other hand, are correlatives defined implicitly by empirically established correlations, functions, laws, theories, systems. [CWL 3, 80/102-103]

Masses might be defined as the correlatives implicit in Newton’s law of inverse squares, .  Then there would be a pattern of relationships constituted by the verified equation; the pattern of relationships would fix the meaning of the pair of coefficients, m1, m2; and the meaning so determined would be the meaning of the name, mass.  In like manner, heat might be defined implicitly by the first law of thermodynamics, [5], and the electric and magnetic field intensities, E and H, might be regarded as vector quantities defined by Maxwell’s equations for the electromagnetic field.[6][CWL 3,  80/102-103][7]

Paraphrasing:

Functionings might be defined as the correlatives implicit in the equation of composition , the lagged technical accelerator kn[f’n(t-a)-Bn] = f”n-1(t) – An-1, and point-to-point vs. point-to-line.  Then there would be patterns of relationships constituted by the verified equations; the pattern of relationships would implicitly define the meaning of the dynamic functionings.

Understanding the last excerpt is the key to appreciating both the learning Lonergan brought to macroeconomics and Lonergan’s method and achievement in macroeconomics.  The meaning of the coefficients m1and m2is fixed by the pattern of relationships.   The word mass, as meant, does NOT denote a materiality which may be hefted.  The meaning of mass is determined exclusively by the relationship in the formulation.  The meaning of “heat” is determined by an abstract relationship among measured quantities, not by, in the same room, Smith’s feeling of being hot or Jones’ simultaneous feeling of being cold.  The meaning of intensities in the electromagnetic field is determined by an abstract relationship, not by my sense of a shock.

In these cases mass, heat, and intensity are abstract, yet real, terms in a system of real relations; they are abstract and recondite, not mere descriptions of sensations.  Further, they are ideal explanatory terms; they explain how the objective ideal mechanical, thermodynamic, or electromagnetic system really functions.  They present the immanent intelligibility of the functioning system.  They become the basis of the heating, ventilating, and air conditioning systems (HVAC) in buildings.

Right at the start of Macroeconomic Dynamics Lonergan illustrates scientific method by giving an example from chemistry of science advancing from description to explanation.[8]He will follow the lead of theoretical physicists and chemists, but he will do so intelligently because he is doing macroeconomics, not physics or chemistry; the data are the measurements of different phenomena.  He is clear enough to follow the lead and use the techniques of explanatory science only where these clues and techniques are useful and adaptable to this particular science.

One has to follow the lead of the successful scientists, the physicists and chemists, but one has to imitate them not slavishly but intelligently.  They employ insights of a particular type, namely the insights of the mathematician and of the curve fitter grasping in an aggregate of measurements a possible law. The student … also must employ insight, but he must not restrict himself to the particular types relevant to physics and chemistry.  On the contrary he has to work out his own structures of accumulating insights … [CWL 3, ?/?]

Lonergan is doing pure theoretical science and digging for scientific significance.

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.

“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 Keynesp. 313]

Whether it be physics, chemistry, or economics, the “whole scientific significance” is contained in the set of relationships. Since the objective economic process is a system of interdependent functionings, the economist seeks to discover the pattern of functionings implicitly defined by the functional relationships, otherwise his work is not of scientific or explanatory significance.

Lonergan avoided the traps that permanently ensnare others. He sought to discover the general principles – independent of human psychology – of the economic process in general terms; he did not go down the blind alley of using particular boundary terms such as particular prices or particular quantities to construct general principles.

Frish’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]

the Robinson-Eatwell analysis is hampered by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nosare last in analysis.[9][McShane 1980, 12 4]

But conjugate forms (FMC such as basic income flow, ordinary surplus income flow, and pure surplus income flow) are defined implicitly by their explanatory and empirically verified relations to one another.  Still, such (relations are general laws; correspondence with elements in the standard of living FMC); they hold in any number of instances; they admit application to the concrete only through the addition of further determinations (such as the coefficients of price and quantity FMC), and such further determinations pertain to a non-systematic manifold.  There is then, a primary relativity that is contained in the general law; it is inseparable from its base in the conjugate form which implicitly it defines; and to reach the concrete relation that holds at a given place and time, it is not enough to think about the general law; one has to add further determinations that are contingent from the very fact that they have to be obtained from a non-systematic manifold. [CWL 3, 492/516] (In addition, the student should read in the entirety CWL 3, 490-6/514-20)

Once again, he sought to generalize, to find a deeper unity in the disparateness.

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 hem; 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 ad interpretation of Kepler’s laws, so Einstein transforms the Newtonian laws of motion. … It is, we believe, 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]

Paraphrasing:

Generalization comes with Lonergan, who attacked the statics of Walras, laid down a purely relational general theory of functionings, and so found himself in a position to account for any equilibrium or disequilibrium of motions.  Others had all been busy with particular boundary conditions or secondary determinations in a coincidental manifold.  Lonergan dealt with the primary relativity of a purely relational structure of dynamic functioning.  He did so by turning to a field of greater generality and by finding a deeper unity in the apparent disparateness of microeconomics, neo-classical economics, Keynesian economics, etc. It is, we believe, a scientific generalization of modern economics that will yield the new political economy which we need. … Plainly the way out is through a more general field.

The “lack of ultimacy that Lonergan ascribes to prices and price theory can scarcely be overemphasized.”

Lonergan (emphasized) that prices and their changes are not explanatory but accountants’ entities. (He) insists that the mechanism of the pricing system does not furnish economists with distinctions among the significant variables, any more than Galileo Galilei’s discrete measurements of distances and times at the Tower of Pisa of themselves provided the law of the acceleration of falling bodies.  In short, the lack of ultimacy that Lonergan ascribes to prices and price theory can scarcely be overemphasized.  [Cwl 15, Editors’ Introduction xlvi]

The accountant’s everyday words “cost” and “profit” are assigned new meanings; they become technical terms implicitly defining one another and explaining the system of monetary flows congruent in transactings with the flows of products.

Lonergan was seeking the explanatory intelligibility underlying the ever-fluctuating rhythms of economic functioning.  To that end he worked out a set of terms and relations that ‘implicitly defined’ that intelligible pattern.  When all was said and done the relations, and the terms they implicitly defined, were markedly different from either the terms of ordinary business parlance or the terms of neoclassical and Keynesian economic theory. Moreover, not only did Lonergan’s terms differ, but he also indicated that these aforementioned (neoclassical and Keynesian) terms were permeated, as were the terms of Newton’s theory of gravitation, with descriptive, nonexplanatory residues.  Hence, just as a mathematical equation may be said to be the most adequate expression of purely intelligible relations among explanatory terms in certain instances – for example, Einstein’s gravitational field tensor equations    – something closely akin to Lonergan’s diagram seems necessary for the realm of dynamic economic functioning. So, for example, the existence and manner of dynamic mutual interdependence of the two circuits of payment, basic and surplus, is not adequately expressed either by descriptive terms (since this pattern does not directly relate to the senses of anyone operating in a common-sense way in a concretely functioning economy) nor by the series of (simultaneous) equations that do not explicitly manifest the interchanging of ‘flows.’ [CWL 15, 179]

Macroeconomic costs are functional flows correlated with the purchase of a standard of living; macroeconomic profits, i.e. pure surplus income are functional flows correlated with the purchase of expansionary capital.

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]

Now as the statistical approach differs from the descriptive, the analytic differs from both.  Out of endless classificatory possibilities it selects not the one sanctioned by ordinary speech nor again the one sanctioned by facility of measurement but the one that most rapidly yields terms which can be defined by the functional interrelations in which they stand. CWL 21, 112

In explanatory macroeconomics  –  as distinguished from descriptive corporate accounting and National Income accounting –  the correlative abstract terms “costs/consumption expenditures” and “profit/net aggregate savings/investment expenditure” represent functional flows of so much money per period.  They are flows of money payments.  They are rates mathematically represented as “velocities.”  Further, as flows of money within any circuit, outlays/compensation and expenditures/receipts constitute functional supply and demand.  Thus they constitute a monetary functioning or function.

By these functional relations to one another “macroeconomic aggregate functional costs” and “macroeconomic aggregate functional profits” are a.) abstract terms, b) implicitly and mutually definitive, c.) mutually exclusive, and d.) perfectly complementary in a pure dichotomy of the entire economic process.  They are not defined nominally so that one would know how to use them in a declarative sentence.   They are not terms describing sensations or perceptions.  Rather they are explanatory conjugates defined by the functional relations in which they stand with one another.  As terms related to one another they are the basic terms in an explanatory monetary theory.  This theory topples liberal monetary theories laden with sophisticated, but irrelevant, mathematics.

real analysis (is) identifying money with what money buys. … And that is the source of the problem in real analysis.  If you want to treat money that doesn’t make a difference, you can have a beautiful liberal monetary theory.  But it doesn’t say the way the thing works. [CWL 21, Editor’s Introduction, xxviii  (quoting Lonergan) ]

Costs are what comes to be spent on a standard of living and, thus, not invested; and net aggregate savings or investment or profit are what is not spent on a standard of living and, therefore, comes to be saved or invested. Costs flows and savings flows constitute a pure dichotomy: either A or B, but not both.

Costs and net aggregate savings are the monetary correlates of the exchanges of consumer goods and expansionary capital goods respectively.  Transactions in the real circuits of production and sale are enabled by payments. Payments are the doppelgangers[10]of real exchanges.  Money is the dummy of exchanges, with no purpose other than to enable and grease exchanges.

These differences and correlations (within the productive process) have now to be projected into their monetary correlates to set up classes of payments… The productive process (occurs) in an exchange economy.  It will be supposed to be an economy of notable size, complexity, and development, with property, exchange, prices, supply and demand, money.  [CWL 15, 39]

Implicit definition by functional relation constitutes a methodical shift from description to scientific explanation; i.e. from relating things to ourselves to relating them by their functional relations to one another. It moves the treatment of basic and surplus activities in the economy from the realm of description into the realm of explanation.  Rather than treating how the process appears to us, we come to understand how it really works!

Also, let us note here the norm that, since production is completed by sale, continuity and acceleration of the process requires that monetary demand keep pace with production supply.  There must be concomitance.

The concomitance of outlay and expenditure follows from the interaction of supply and demand.  The concomitance of income with outlay and expenditure is identical with the adjustment of the rate of saving to the requirements of the productive process. [CWL 15  144]

Concomitance is, I would claim, the key word in Lonergan’s economic thinking. Philip McShane[11]

An equivalent view of this notion of concomitance is “the adjustment of the rate of savings to the phase of the economic process.  A second equivalent view is that of “the crossovers balancing.”  The money that flows out of a circuit must be balanced by money that flows into a circuit.  These are all equivalent expressions of the same phenomenon; they are different ways of saying the same thing.

Our subtopic has been implicit definition and scientific significance.  To summarize: Implicit definition yields abstract macroeconomic terms defined by the functional relations in which they stand with one another.  Science is explanation in the form of terms in their relations to one another.  Therefore, implicit definition yields terms which have the potential to be of scientific significance.  Our basic terms are functional economic activities of so much per period implicitly defined by their functional relation with one another.  These terms and relations will be cast in equations which explain how the economy actually works.  There follows further measurements and testing for verification of the hypothesis.

[1]Two other examples of implicit definition are given by Lonergan as follows:

Let numbers be defined implicitly by operations, so that the result of any operation will be a number and any number can be the result of an operation.  ¶Let operations be defined implicitly by rules, so that what is done in accord with rules is an operation. [CWL 3, 16/]

[2]More fully, the excerpt is: 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 nobjects.  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]

[3]

[4]CWL 3, 77-78/

[5]The first law says that the change in the internal energy of a system  is equal to the sum of the heat gained or lostby the system and the work done  by or on the system.

[6]The basic specification of Clerk-Maxwell in electromagnetics employs the Del operator in the four-equation combination:

 

Del X E= (-1/c)H’

 

Del X H= (+1/c)E’

 

Del dot H= 0

 

Del dot E= 0

 

 

[7]Lonergan was aware that Newton’s mechanics was a theory of efficient causes and contained the residue of the experience of force and muscular effort in contrast to Einstein’s field equations.

☐  CWL 15, Appendix p. 180

 

Part Two … belongs almost entirely in what I call the Einsteinian context of Part Three, in contrast to the Newtonian achievement of Part One, (but) it is still somewhat transitional in system and expression. So, for example, to take the central character in the drama, pure surplus income is there named systematic profits. CWL 21, 325

 

[8]  And, perhaps at this point, the academic economist makes the fatal mistake of declaring that there will be nothing relevant to him and his investigations in this book.

[9]The full quote is: One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general boundary conditions or worse, specific channel conditions, botches the analytic possibilities….the Robinson-Eatwell analysis is hampered, not only by an absence of paradigmatic heuristic thinking in a field whose principles involve ends, but also by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nos are last in analysis. P 124

 

[10]In the sense of a doppelganger as the ghostly counterpart of a real person, so money is the dummy counterpart of a real product flow.

[11]Philip McShane, www.philipmcshane.com, Fusion 1  page 4 ftnt 10