Contents
Part I –Introductory
.I.A Outline of the Analytic Process
Part II – List of Notions Underlying and Constituting FMD’s Explanatory Hypothesis
Part III – Substantiation of Related Notions
.III.A Arguments Relevant to the Notions of Truth and Verification of FMD
.III.B. List of Important Ideas and Arguments to be Substantiated
.III.C Substantiation of Important Ideas and Arguments
Part I –Introductory
Our title is The “Truth” or “Verification” of Macroeconomic Field Theory.
Truthaffirming judgment stands to understanding as verification stands to hypothesis. Thus, judgment, affirming virtuallyunconditioned truth, stands to the prior conception in the act of understanding as verification, based on wholly satisfactory empirical evidence, stands to hypothesis. Verification is the “quasitruthification” of that hypothesis which explains phenomena by conjugate terms implicitly defined by their functional relations among themselves.
The grounds of truth and of degree of probability in Functional Macroeconomic Dynamics are a) the precise analytic distinctions which virtually comprehend the whole dynamic functioning while identifying the basic foundational categories of the entire process, b) implicit definition, thus mutual definition, of explanatory conjugates by their interdependent functional relations to one another, c) rigorous deduction of the superstructure which comprises complete explanation d) the isomorphism of the purely relational abstract mathematical formulation with the real relational structure of the interdependencies of the pretioquantital process of production and exchange, e) accurate measurement of boundary values, f) cumulative verification of the hypothesis by repeated testing, g) absence of any unexplained phenomena, and h) absence of further questions about the explanatory adequacy of the hypothesis.
.I.A Outline of the Analytic Process
Key words and concepts in the Outline of the analysis below are
 Scientific, dynamic heuristic
 Precise analytic axiomatic distinctions
 Implicit definition of concepts among themselves
 Isomorphism of the formulation and the concrete process
 Rigorous deduction of superstructure
 Complete explanation
 Relations of correspondence
 Adequate level of abstraction
 Prescindence from human psychology
 Internal relations comprising a field theory
 Classical formulation
 Ideal frequency of occurrences
 Cumulative verification
Outline of the Analysis
In the bulleted Outline below (some bullets as statements, some as simple items in the outline), the analytic process culminating in a hypothetical explanation to be verified consists of the following items:
 the gathering of the alreadyknown facts of the objective economic process
Schumpeter had catalogued already known facts:
Lonergan was grateful for the way Schumpeter had shown slumps and crises were related to contraction of plant and equipment, and that there were ‘a hundred theories’ on why – so that in Schumpeter’s estimation there really existed no solid explanation. Lonergan claimed: ‘I have an explanation on that.’ [CWL 15, Editors’ Introduction, ftnt 86, liii]
 the adoption of a scientific, dynamic heuristic guiding the analyst to an objective, purely relational explanation of the dynamics of the economic process
our inquiry differs radically from traditional economics, in which the ultimate premises are not production and exchange but rather exchange and selfinterest, 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]
 the basis of the analysis must be the precise analytic axiomatic distinctions yielding fundamental, implicitlydefined terms and analytic postulates from which there may be rigorously deduced a superstructure of theorems constituting a complete explanation and a complete science.
 since science is formulated in the form of terms implicitly and functionally related among themselves, the employment of implicit definition to yield explanatory terms which are mutually defining, and purely functionally related among themselves
Excursus re internal vs. external relations:
… there follows a clarification of the problem of internal and external relations. Relations are said to be internal when the concept of the relation is intrinsic to the concept of its base;
(Reader: See CWL 3, 491/514 ff. re quantities and proportions)
… (relations) are external when the base remains essentially the same whether or not the relation accrues to it. Thus if ‘mass’ is conceived as a quantity of matter and matter is conceived as whatever satisfies the Kantian scheme of providing a filling for the empty form of time, then the law of inverse squares is external to the notion of mass. On the other hand, if masses are conceived as implicitly defined by their relations to one another and the law of inverse squares is the most fundamental of those relations, then the law is an internal relation, for the denial of the law would involve a change of the concept of mass. [CWL 3, 493]
Paraphrase:
There follows a clarification of the problem of internal and external relations. Relations are said to be internal when the concept of the relation is intrinsic to the concept of its base; they are external when the base remains essentially the same whether or not the relation accrues to it. Thus if ‘factor of production’ is conceived as a quantity of matter and matter is conceived as whatever satisfies the Kantian scheme of providing a filling for the empty form of space, then the law of velocitous factoral composition (q_{i} = q_{ijk}) is external to the notion of factor. On the other hand, a) if aggregates of current velocitouslyapplied factors of production (Q_{i}) are conceived as implicitly defined according to their functional relations of velocitous correspondence with aggregated integrated components exiting the process, and b) if the law of velocitous factoral composition is being related to velocitous exchange as the most basic and fundamental of those relations, then the law of the correspondence of composition and exit is an internal relation, for the denial of the law would involve a change in the concept of a velocitous composition implicitly related to velocitous exchange. (Paraphrase of CWL 3, 493)
Resume the bulleted outline:
 since efficientcausal humans make subjective, psychebased decisions, the abstract explanation must prescind from human psychology. It must operate at an adequate level of abstraction and be uncontaminated by intrusion of fickle human sentiments, bias, and psychopolitical decisions. It must be abstractive and objective so as to constitute the “pure formal cause” or “immanent intelligibility” of the process of production and exchange.
Lonergan agreed with Schumpeter on the importance of a systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; he agreed with Schumpeter that to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed that the economist had to know what are the significant variables in the light of which price changes are to be interpreted. According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]
 A mathematical formulating whose structure is isomorphic with the patterns and correlations constituting the immanent intelligibility of the data
 as it so happens, the already known facts of the macroeconomic process are that
 It is the current process constituted by flows of products and money. It is a dynamics.
 The flows are internallyconditioned and crossoverconditioned circulations in repetitive schemes and subschemes of recurrence.
Again,
Lonergan agreed with Schumpeter on the importance of a systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; he agreed with Schumpeter that to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed that the economist had to know what are the significant variables in the light of which price changes are to be interpreted. According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]
 thus, the perspective and analogies from the fluid dynamics of flows in both closed and open circuits may supply clues as to abstract forms applicable to the concrete process by isomorphism for explanation, verification, and proper management
 The complete explanation will have two components:

 The abstract formal intelligibility immanent in the intelligible correlatives of the measured data
 The ideal frequencies of the concrete events constituting the process, a) from which relative actual frequencies diverge nonsystematically, and b) but upon which relative actual frequencies converge
 as in other empirical sciences, econometricians must learn the abstract explanatory formulations in order to select wisely which data to measure in order to either verify, disprove, or declare probable the abstract classical hypothesis
 determination of the FMD hypothesis as fully explanatory in series of cases would constitute cumulative verification for analysis and for subsequent control of national and global economies
We will emphasize and honor the notions of truth and objectivity – independent of human psychology – as they must apply to alreadyknown facts of the macroeconomic process; and we focus on verification as it applies to the explanatory hypothesis of Macroeconomic Field Theory.
… 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. [CWL 3, 8182/105]
Indeed, (this particular) present study will offer an analysis of the macroeconomy that accounts for its successes and failures without attempting the historical and statistical research that would be necessary …. How is this possible? It is possible because knowledge of facts is one thing, and understanding known facts is another. The facts of the macroeconomy are already well known. What is lacking is a clear and precise understanding of the mechanism behind such obvious facts as the relations between expansion and contraction of the economy, employment and unemployment, inflation and deflation, and many other things that are just common knowledge. (CWL 15, 1112)
Again, because science is analytic and abstractive, its terms are exact; because its correlations purport to be generally valid, they must be determined with utmost precision; because its terms are exact and its correlations general, it must be ready to bear the weight of a vast superstructure of logical deductions in which each conclusion must be equally exact and valid generally. [CWL 3, 296/ ]
Functional Macroeconomic Dynamics is an explanatory theory. As science it employs a scientific heuristic, scientific method, and the technique of implicit definition.
… empirical method involves four distinct elements, namely
 the observation of data,
 insight into data,
 the formulation of the insight or set of insights, and
 the verification of the formulation. [CWL 3, 7879/102]
In the science of macroeconomic dynamics, an abstract hypothesis explaining the process is achieved by, first, measurements yielding data, second, insights correlating and precisely formulating the correlations in the data, and third, econometric verification of the hypothesis as a reliable explanation of the process. The theoretical hypothesis will be constituted by a) a general and abstract proposition consisting of a set of terms implicitly defined by their abstract functional correlations with one another, b) a set of ideal frequencies of the proposition’s constituent events upon which the relative actual frequencies converge, c) concrete measurable boundary values to which the abstract functional relations may be applied, and d) empirical verification that the abstract correlations and their application to boundary values explain the dynamic concrete process universally in any instance. We call the abstract terms of the explanatory correlations “explanatory conjugates”.
… verified correlations necessarily involve the verification of terms implicitly defined by the correlations; …what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empiricallyverified, explanatory relations. Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[quoted more fully below from CWL 3, 435/460]
Part II – List of Notions Underlying and Constituting FMD’s Explanatory Hypothesis
 The economic process always is the current, purely dynamic It is a process of “dynamical flows of products and payments.” Therefore its immanent intelligibility is the intelligibility among a set of interdependent rates or velocities.
 Science is explanation of a thing or a process by terms defined implicitly by their functional relations to one another.
 The scientific analyst must adapt a scientific heuristic and method to guide the search for explanation.
 The act of insight, also called the act of understanding, yields mutuallydefining explanatory termsrelated intrinsically to one another. Thus, when one is understanding by a single sweeping insight a Euclidean planar circle or a unified whole organic system of parts and functions solidary with one another, all the interrelated, interdependent, explanatory terms – both the precisely analytic foundational terms and the deduced superstructure of terms explaining the process – tumble out together and cohere with one another. They “hang together” in a single, solidary, unified whole.
 The abstract, general formulation of the economic process is The real is being; and being is the objective of the detached, disinterested, desire to know.
 Lonergan’s precise fundamental analytic terms are discovered to be the pointtopoint (basic), pointtoline (lowest surplus), pointtosurface (next lowest surplus), pointtovolume (next lowest surplus) and higher correspondences of the component, velocitouslyapplied, factors of production with the integral composition of factors flowing as a completed product out of the alwayscurrent system in a final sale.
 The precise, analyticallydistinguished, basic terms are those from which a superstructure comprising a purelyrelational, completelyexplanatory systematization of the process may be deduced.
 The concrete economic process is a threefold process – 1) a basic process, 2) a “surplus” process, and 3) a moneysupply process. It is explained by two components: 1) an invariant, abstract, explanatory, classical formulation, and 2) the ideal frequencies from which actual relative frequencies diverge at random in the nonsystematic manifold of human decisions.
 Each class of analytic productive activities – pointtopoint, pointtoline, etc. – has its own distinct circuit of monetary flows: Outlays, Incomes, Expenditures, Receipts repeated over and over again.
 For simplicity and pedagogy herein, all surplus levels are subsumed into a single surplus level. The resulting two distinct circuits of circulations – “basic” and “surplus” – have each their own circulations of OutlaysIncomes and ExpendituresReceipts. And they have crossover dealings with one another. The higher circuit sells producer (“capital”, pointtoline) goods to the next lower circuit, while the lowest circuit supplies (“basic”, pointtopoint) consumer goods to workers in the higher circuit(s).
 The condition of equilibrium in the doublecircuited, creditcentered system is that G = c”O” – i’O’ = 0. (See CWL 15, 534) The crossover dealings – c”O” and i’O’ – must balance; neither circuit can be allowed to drain or “rob” the other.
 Expansion occurs in phases: proportional, surplus, and basic; the phases are defined by the comparison of the accelerations dQ”/Q” and dQ’/Q’ of the two circuits. (See CWL 15, 114 ff.)
 Money is a dummy; it is an instrument invented by insightful human inventors to enable and lubricate a vast and complicated process of divided economic exchanges. Money is not a commodity to be hoarded.
 The functional role of credit is to fill the gap in time between payments made and payments received in justifiable activities such as shortterm workinprocess and socially or materiallybeneficial longterm investment projects undertaken by the private and government sectors. Though they are concomitant and theoretically “belonging together,” initial productive Outlays (payments made for production) normatively precede final Receipts (payments received for production). Credit fills the gap in time, and the word “credit” is used both abstractly and concretely.
 Money should be added to or withdrawn from the system by the Fed according only to the extent needed to accommodate the increasing or decreasing magnitudes and frequencies of transactions constituting justified expansion.
 Enlightened private and government sectors, not the Central Bank, are primarily responsible for managing a nation’s economic process in a continuous and equilibrated Repeat: “enlightened” by knowledge of the science. It is unwise to assign to the Fed responsibility for employment levels. Plus, the oftentouted Phillips Curve correlation has been proven by events to be bogus. Thus the insistence by FMD that the magnitudes and frequencies of monetary flows and the magnitudes and frequencies of productive turnovers must be correlated. with the
 The conformity to theoretical norms of continuity and equilibrium of the current, purely dynamic process must be measured and monitored by the Bureau of Economic Analysis and the Federal Reserve System; and divergences and disequilibria with respect to norms must be communicated to the private and government sectors with a clarity and a force which are understandable and, thus, enlightening and compelling for proper management of the process.
 The BEA and the Fed must, first, understand Lonergan’s explanatory formulation of the facts already known, i.e. the factual interrelations of basic and surplus processes constituting the alwayscurrent, purelydynamic economic process, and second, verify Lonergan’s hypothesis as universally applicable. Both must develop a) new datagathering techniques relative to the explanatory conjugates, b) new econometric verification techniques, , and c) procedures to continually monitor the concrete process to detect aberrant damaging divergences from the ideal frequencies implicit in the abstract theory.
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. If one grasps the necessary and sufficient conditions for the perfect roundness of this imagined plane curve, then one grasps not only the circle but also the point, the line, the circumference, the radii, the plane, and equality. All the concepts tumble out together, because all are needed to express adequately a single insight. All are coherent, for coherence basically means that all hang together from a single insight. [CWL 3, 12/36]
[Paraphrasing] Let us say, then, that for every basic insight in macroeconomic dynamics 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. If one grasps the necessary and sufficient conditions for concomitance, continuity, equilibrium, and organic solidarity among the constituent velocities and accelerations within this doublecircuited, creditcentered Representation and Model of interconnected Rates of Flow, then one grasps the Diagram as representing systematic interdependencies, conditionings, and mutual definings a) within circuits, b) between circuits, and c) between the moneysupply function and the operative circulations. All the concepts and relations constituting explanation and enlightenment tumble out together, because all are needed to express adequately the single comprehensive insight grasping the systematics of the process. The entire process is understood as a unified organic whole. All equations of terms and relations are coherent with one another, for coherence basically means that all hang together from a single comprehensive insight. [Paraphrasing CWL 3, 12/36]
Part III – Substantiation of Related Notions
.III.A Terms and Arguments Relevant to the Notions of Truth and Verification of FMD
Below is a) a brief list of important terminology, then b) a brief list of ideas and arguments relevant to the notions of truth and verification in Functional Macroeconomic Dynamics, followed by c) an expansion and substantiation of these same ideas and arguments.
Key terminology and important phrases include
 science and method
 purely functional analysis
 real analysis
 implicit definition
 concomitance
 interdependence
 mutual conditioning
 explanation
 foundational analytics
 logical deduction
 reality
 objectivity and truth
 positions and counterpositions
 true, false, or probable
 science as provisional
 generalization
 isomorphism
 organicism
 classical and statistical laws
 dynamics
 periodicity
 equilibrium
 macroeconomic “costs”
 credit
 complete explanation
 “truth” of electromagnetics
 “verification” of Functional Macroeconomic Dynamics as a Modern Field Theory:
.III.B. List of Important Ideas and Arguments to be Substantiated
 Adoption of a scientific heuristic and method
 Achieving precise, analytic basic terms and relations from which to deduce logically a coherent tightlyconnected superstructure of “theoretical” relations constituting a complete explanation isomorphic with the patterns of correlations among the measurements.
 The abstract, general, explanatory formulation is the reality to be verified as explaining the process.
 Explanation and explanatory conjugates: scientific and purely relational terms implicitly defining one another; whatever the variable magnitudes may be, the relations themselves among terms are made invariant by implicit definition of terms related among themselves. The cluster of coherent equations constitute a single explanatory unity, a system.
 Invariant classical laws, statistical laws of probability, and the implications for prediction
 Explanatory functional relations of significant (i.e. explanatory) variables “scientifically among themselves” in a closed, yet coherent and comprehensive set of equations Dynamics and secondorderdifferential equations
 Dynamics and secondorder differential equations
 The Periodicity of orderly, expansionary surges
 Implicit definition of abstract explanatory terms according to their functional relations to one another
 Humans participate in a formal field as efficient causes.
 Functional Relations of terms “scientifically among themselves” in a closed, yet coherent and comprehensive set of equations; and significant variables
 Lending rates
 The Isomorphism of the abstract, classical formulation of the economic process with the patterns grasped in the correlations of data. The isomorphism is explanatory of and “true to” the immanent intelligibility of the dynamic system
 Real Analysis of the economic process understands production and exchange of goods and services as primal and treats money as a functional dummy invented by humans to make possible a vast and intricate process rather than as a material commodity to be hoarded
 The central condition of equilibrium between circulations in two circuits, and the necessity of enlightened selfinterest to guide exchanges.
 The deficient efficientcause macrostatic the formal cause or immanent intelligibility
 Circulations in circuits; Costs and Expenditures are Implicitly Defined P’Q’ = p’a’Q’ + p”a” Q”. (CWL 15, 15659)
 The abstract meaning of credit to explain the implementation of the “quasiphysical” potentialincreased by invention and innovation, first, into the wideninganddeepening kinesis of surplus production, and subsequently, into the accelerated kinesis of basic production.
 Human knowing: Positions and counterpositions
 The notions of a) truth and b) objectivity as heuristic guides in the analysis and formulation of the objective economic process. Truth defined as the relation of knowing to being and constituted by the virtually unconditioned.
 The economist may assert that a proposition is true, false, or probable.
 True, truly, and truthful as adjectival or adverbial meanings
 Current established science as always provisional until a better explanation is discovered
 The Generalization called Macroeconomic Field Theory as the way out of the morass of arguments among macroeconomic “schools’ or “isms.”
 The Canon of Complete Explanation:
 What is the “truth” of electromagnetics? The character of its cumulative verification
 The process of empirical verification or (etymologically) “truthification” by econometricians of Lonergan’s abstract fieldtheoretic formulation of the current, purelydynamic, economic process
We seek the verification of a hypothesis which scientifically explains a system of measurable, pretioquantital flows. The hypothesis, a) by its precise analytic distinctions, b) its logical deductions, and c) its formulations of interrelations constitutes a “true” explanation of the objective, dynamic, concrete, economic process. The understanding, formulation, and teaching of this hypothesis is the paramount challenge to presentday economists and econometricians.
This would be the beginnings of a new economics of measurable flows, one that would yield norms of financing, of profit in both normal and innovative economies, etc., etc. [McShane, 2017, Preface v]
… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established. The most notable example is Pythagoras’ theorem on the hypotenuse of the rightangled triangle, which occurs at the end of book 1 of Euclid’s Elements. Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. … Similarly, mechanics became a system with Newton. Prior to Newton, Galileo’s law of the free fall and Kepler’s three laws of planetary motion were known. But these were isolated laws. Galileo’s prescription was that the system was to be a geometry; so there was something functioning as a system. But the system really emerged with Newton. This is what gave Newton his tremendous influence upon the enlightenment. He laid down a set of basic, definitions, and axioms, and proceeded to demonstrate and conclude from general principles and laws that had been established empirically by his predecessors. Mechanics became a science in the full sense at that point where it became an organized system. … Again, a great deal of chemistry was known prior to Mendeleev. But his discovery of the periodic table selected a set of basic chemical elements and selected them in such a way that further additions could be made to the basic elements. Since that time chemistry has been one single organized subject with a basic set of elements accounting for incredibly vast numbers of compounds. In other words, there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. [Method, 24142]
As Euclid, by his axioms, postulates and rigorous deduction, systematized previous geometry, and as Hilbert by his implicit definitions improved upon Euclid, and as Newton systematized Galileo and Kepler, and as ClerkMaxwell systematized Euler and Faraday, and as Einstein in his field theory of Special Relativity redefined space and time, so Lonergan by his analytic distinctions, implicit definitions, and differential equations, developed a field theoryof terms related purely among themselves – rather than related to an outside efficientcausal force or influence – and systematized the scattered insights of those many macroeconomists who went before.
… an entirely new type of definition was introduced by Hilbert in his formulation of geometry.[1] He called it implicit definition. An implicit definition drops the common matter to express only a relational form… The significance of implicit definition is that it does not pin down the meaning of the words ’point’ and ‘line’ to anything. Point, in Hilbert’s expression of geometry, can be a Euclidean position without magnitude, and a line can be a length without breadth or thickness lying evenly between its extremes. But a point can also be an ordered pair of numbers, where (a,b) is not the Cartesian notation for a Euclidean point, but just that ordered pair. And a straight line can be a firstdegree equation: y = mx + c is determined by two ordered pairs, and two ordered pairs will determine a firstdegree equation. Hilbert can mean by point and line the imaginable Euclidean point or line, the Cartesian algebraic expression for point and line, or anything else that will satisfy the relation “two of one determines one of the other,” no matter what they are. The definitions are in terms of relational form, with no attention to any common matter. The relational form selects any common matter that will be thought relevant. Implicit definition is a more abstract type of thinking that omits even the common matter. (CWL 10, 126)
Not all activities and services are coincident with the process of material objects to take their correspondencefrom that of the objects. It remains that the same general types of correspondence may be discerned. There is a pointtopoint correspondence between movements of trains and passengermiles, not indeed in the sense that there is some fixed ratio between trainmiles and passengermiles, but in the sense that the train has to move as often and as far as passengers move. … [CWL 15, 25]
The analysis must take into account two types of indeterminacy: 1) the nonsystematic divergencies of events from their ideal frequencies, and 2) the indeterminacy of current pointtoindeterminatefutureline in the phased expansion of the economic process.
… The analysis that insists on the indeterminacy is the analysis that insists on the present fact: estimates and expectations are proofs of the present indeterminacy and attempts to get round it; and, to come to the main point, an analysis based on such estimates and expectations can never arrive at a criticism of them; it would move in a vicious circle. It is to avoid that circle that we have divided the process in terms of indeterminate pointtoline and pointtosurface and higher correspondences. [CWL 15, 28]
Lonergan has formulated a tightlyknit explanation of the already known facts of a) capital expansion accelerating subsequent consumables expansion, b) excess investment constituting a boom, and c) economic contraction constituting a corrective slump or bust; and he puts forth this explanation as a hypothesis to the econometrics community and as a guide to all nations for management of their concrete economic process.
Indeed, the present study will offer an analysis of the macroeconomy that accounts for its successes and failureswithout attempting the historical and statistical research that would be necessary …. How is this possible? It is possible because knowledge of facts is one thing, and understanding known facts is another. The facts of the macroeconomy are already well known. What is lacking is a clear and precise understanding of the mechanismbehind such obvious facts as the relations between expansion and contraction of the economy, employment and unemployment, inflation and deflation, and many other things that are just common knowledge. (CWL 15, 1112)
Again, because science is analytic and abstractive, its terms are exact; because its correlations purport to be generally valid, they must be determined with utmost precision; because its terms are exact and its correlations general, it must be ready to bear the weight of a vast superstructure of logical deductions in which each conclusion must be equally exact and valid generally. [CWL 3, 296/ ]
.III.B Substantiation of Important Ideas and Arguments
.1. Adoption of a scientific heuristic and method
If the economic process is a dynamic process of so much or so many every so often, the critical thinker must adopt a scientific, dynamic heuristic and analytic method to reach answers of a certain type. The understanding would be in terms of the interrelations and interchanges of functional velocities among themselves.
There are classical laws and statistical laws; and there are canons of empirical method. (CWL 3, 70103/93126)
… there is a canon of complete explanation. Everything is to be explained. … … … The canon of complete explanation demands that the scientific world, which expresses the relation of things to one another, be constructed completely. It is not the world of common sense. (CWL 10, 144)
… if someone has a scientific, dynamic heuristic in is doing macroeconomics and you open his book, what do you find? You find just mathematical equations. He is solving problems, and what is it? It is more mathematics. Why do you say he is doing macroeconomics? He seems to be doing mathematics all the time. It is because there are regions of mathematics that are isomorphic with macrodynamic reality. There is the same relational structure between a given mathematical theory or system as there is between macroeconomic functionings that can be observed. This is another case, a big case, of isomorphism: on the one hand, mathematical expressions, and on the other hand, interdependent, mutually defining macroeconomic functionings. There is the same relational structure. But in the mathematical case, the relational structure links symbolic expressions, or mathematical concepts, with one another, while in the macroeconomics case what are related are concrete, interdependent, dynamic, macroeconomic functionings. ¶ So there is an isomorphism [Paraphrase of CWL 18, 3233]
An innate psychological bias towards glory and fame clouds economists’ purpose and obviates an objective dedicated search for explanation employing a strictly scientific, dynamic heuristic.
.2. Achieving precise, analytic basic terms and relations from which to deduce logically a coherent tightlyconnected superstructure of “theoretical” relations constituting a complete explanation isomorphic with the patterns of correlations among the measurements.
Now, at the root of classical method there are two heuristic principles. The first is that similars are understood similarly, that a difference of understanding presupposes a significant difference of data. The second is that similarities, relevant to explanation, lie not in the relations of things to our senses but in their relations to one another. Next, when these heuristic principles are applied, there (first) result classifications by sensible similarity, then correlations, and finally the verification of correlations and of systems of correlations. But verified correlations necessarily involve the verification of terms implicitly defined by the correlations; and they do not involve more than such implicitly defined terms as related, for what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically and explanatory relations. Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[CWL 3, 435/460]
Discovering a correspondence between elements and formulating the correspondences in a hypothesis for verification:
the correspondence between elements in the productive process and elements in the standard of living may be a pointtopoint, or a pointtoline, or a point to surface, or even some higher correspondence. (CWL 15, 23 for quote and context)
In the science of macroeconomics the everyday utterances “basic” and “surplus” become repurposed and redefined in equations as abstract technical, explanatory terms. The terms function as abstract terms in classical relations. Note Lenzen’s statement of a process of “redefinition.”
… 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, 8182/105]
Functional Macroeconomic Dynamics is an explanatory theory; as science it employs a scientific heuristic and the technique of implicit definition, and scientific method.
… empirical method involves four distinct elements, namely

 the observation of data,
 insight into data,
 the formulation of the insight or set of insights, and
 the verification of the formulation. [CWL 3, 7879/102]
We must not confuse two meanings of the word “basic”. The context usually makes it clear when a) “basic” means “fundamental” (as it might be defined in a dictionary), and b) “basic” is used as an abstract technical term of explanation to designate the velocitous economic activities in which factors of production are locked in an algebraic firstorder, pointtopoint correspondence to the factors integral to the completed composite products currently exiting the productive process, i.e. “out into” a standard of living. Both the current productive initial assembly of factors of production by compensated humans and the current final sale by compensated sellers of composite products are at rates, i.e. velocities. Basic refers to velocitous flows characterized by algebraic, pointtopoint, firstorder correspondences.
Lonergan establishes a precise, analytic foundation, upon which to build by rigorous deduction a completely explanatory superstructure and theory.
the correspondence between elements in the productive process and elements in the standard of living may be a pointtopoint, or a pointtoline, or a point to surface, or even some higher correspondence. (CWL 15, 23 )
Each correspondence – pointtopoint, pointtoline, etc. – has its own circulation of OutlaysIncomes and ExpendituresReceipts. Money circulates over and over again in these intelligible circuits to match up timely with the rhythms of the rectilinear (supplychain) process of production and sale. Money is outlaid by human entrepreneurs to human workers in supply and expended by human workers to human entrepreneurs in demand.
There can be several circuits in a hierarchy; however, for simplicity Lonergan subsumed all but the lowest, pointtopoint (final sale) circuit, into a single pointtoline (producergoods) circuit. Thus, to teach principles conveniently, yet satisfactorily, we usually speak of only two circuits, acknowledging, but subsuming, a likely hierarchy of circuits.
The pointtoline and higher correspondences are based upon the indeterminacy of the relation between certain (surplus) products and the (later ultimate basic) products that (exit the process and eventually) enter into the standard of living. … The analysis that insists on the indeterminacy is the analysis that insists on the present fact: estimates and expectations are proofs of the present indeterminacy and attempts to get round it; and, to come to the main point, an analysis based on such estimates and expectations can never arrive at a criticism of them; it would move in a vicious circle. It is to avoid that circle that we have divided the process in terms of indeterminate pointtoline and pointtosurface and higher correspondences. [CWL 15, 2728]
A valid scientific analysis of the productive process reveals a functional division of the structure of the productive process.
… the productive process was defined as a purely dynamic entity, a movement taking place between the potentialities of nature and products. In the present section, there has been attempted a dynamic division of that entity.. Elements in the process are in a pointtopoint, or pointtoline, or pointtosurface, or even some higher correspondence with elements in the standard of living. … The division is not based upon proprietary differences, … for the same firm may be engaged at once in different correspondences with the standard of living. Again, it is not a division based upon the properties of things; the same raw materials may be made into consumer goods or capital goods; and the capital goods may be pointtoline or pointtosurface or a higher correspondence; they may have one correspondence at one time and another at another. … the division is, then neither proprietary nor technical. It is a functional division of the structure of the productive process: it reveals the possibilities of the process as a dynamic system, though to bring out the full implications of such a system will require not only the next two sections, on the stages of the process, but also later sections on cycles. [CWL 15, 267]
“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; … 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” … [CWL 15 2627 ftnt 27]
All science begins from particular correlations, but the key discovery is the interdependence of the whole. … While it is true that a tableau or diagram cannot establish the uniqueness of a system or rigorously ground its universal relevance, it remains that the diagram (of the interconnections of a few precise aggregates) has compensating features that Quesnay’s system of simultaneous equations may imply but does not manifest. … There is the tremendous simplification (a diagram) effects. … The aims and limitations of macroeconomics make the use of a diagram particularly helpful, … For its basic terms are defined by their functional relations. The maintaining of a standard of living is attributed to a basic process (distinct process 1), an ongoing sequence of instances of so much every so often. The maintenance and acceleration (distinct process 2) of this basic process is brought about by a sequence of surplus stages, in which each lower stage is maintained and accelerated by the next higher. Finally, transactions that do no more than transfer titles to ownership (distinct process 3) are concentrated in a redistributive function, whence may be derived changes in the stock of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. … So there is to be discerned a threefold process in which a basic stage is maintained and accelerated by a series of surplus stages, while the needed additions to or subtractions from the stock of money in these processes is derived from the redistributive area. … it will be possible to distinguish stable and unstable combinations and sequences of rates in the three main areas and so gain some insight into the longstanding recurrence of crises in the modern expanding economy. [CWL 15, 53 and 177]
… 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 (and the equations of functionings it represents) 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 commonsense 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]
“By nature, inexorably determinate” and “by nature indeterminate” are opposites. Current activities may be classified as either one or the other, but not both, in a Porphyrean dichotomy of allinclusive genus into two mutually exclusive, but interacting in a correlated solidary symbiosis, “species” – accelerated basic pointtopoint and accelerator surplus pointtoline. Further, though simultaneous as to being under current process, they are not simultaneous or of uniform nature with respect to output effects. They are, so to speak, different species with different intelligible behavioral properties. They are of different natures.
The pointtoline and higher correspondences are based upon the indeterminacy of the relation between certain products and the ultimate products that enter into the standard of living. … the indeterminacy is very much a present fact. One has to await the future to have exact information. … estimates and expectations are proofs of the present indeterminacy. [CWL 15, 278]
Thus, FMD’s scientific classifications are exhaustively summary and totally comprehensive in the Porphyrean dichotomy. The pure dichotomy and the inextricable interdependence ensure a rock foundation for rigorous deduction into a superstructure of complete explanation.
On this model (of a search for significant basic variables), circulation analysis (in macroeconomic dynamics) raises a large superstructure of terms and theorems upon a summary classification and a few brief analyses of typical phenomena. (CWL 15, 18)
… a generalization proposed by common sense has quite a different meaning from a generalization proposed by science. The scientific generalization aims to offer a premise from which correct deductions can be drawn. (CWL 3, 17576 /199)
So, the utterance “basic” is used to analytically distinguish pointtopoint producing and selling from “surplus” pointtoline, orpointtosurface, or point to volume activities. These foundational abstract analytic distinctionsand relations are the bedrock for the deductions which constitute the abstract, superstructural, explanatory formulations which explain the system and can be applied to the concrete analytic boundary values. The objective explanatory system is constructed on an analytic “rock” rather than on descriptive sand. The coincidental probabilistic prices and quantities occurring in the nonsystematic manifold of everyday decisions constitute the boundary values to which the abstract explanatory formulations are applied so as to explain the particular concrete economic process as measurable and determinate at every point, yet flexible as a dynamic process.
And, of course, a complete explanation is called “theory” and a “system”.
… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established. The most notable example is Pythagoras’ theorem on the hypotenuse of the rightangled triangle, which occurs at the end of book 1 of Euclid’s Elements. Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. … Similarly, mechanics became a system with Newton. Prior to Newton, Galileo’s law of the free fall and Kepler’s three laws of planetary motion were known. But these were isolated laws. Galileo’s prescription was that the system was to be a geometry; so there was something functioning as a system. But the system really emerged with Newton. This is what gave Newton his tremendous influence upon the enlightenment. He laid down a set of basic, definitions, and axioms, and proceeded to demonstrate and conclude from general principles and laws that had been established empirically by his predecessors. Mechanics became a science in the full sense at that point where it became an organized system. … Again, a great deal of chemistry was known prior to Mendeleev. But his discovery of the periodic table selected a set of basic chemical elements and selected them in such a way that further additions could be made to the basic elements. Since that time chemistry has been one single organized subject with a basic set of elements accounting for incredibly vast numbers of compounds. In other words, there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. [Method, 24142]
.3. The abstract, general, explanatory formulation is the reality to be verified as explaining the process
The higher explanatory system is abstract. The underlying nonsystematic manifold is concrete. The economic process is a concrete process. So, what is “real?” What is reality? What is the reality to be verified? Is the reality only what can be kicked? Seen? Heard? Smelled? Tasted?
… an acknowledgement that the real is the verified makes it possible to affirm the reality of no less of the higher system than of the underlying manifold. The chemical is as real as the physical; the biological as real as the chemical; the psychic as real as the biological, and insight as real as the psychic. At once the psychogenic ceases to be merely a name, for the psychic becomes a real source of organization that controls underlying manifolds in a manner beyond the reach of their laws. (CWL 3, 206/)
These four further questions are one and the same. For the real is being, and apart from being there is nothing. Being is not known without reasonable affirmation, and existence is the respect in which being is known precisely inasmuch as it is affirmed reasonably. (CWL 3, 669/)
Knowledge of what is true or, in the case of a hypothesis, what is verified would consist a grasp of the virtually unconditioned, and as the grasp would answer the question, What? so the virtually unconditioned answers the question Whether? (See CWL 3, 670/)
Abstraction is enriching. Classical laws are abstract.
… the objection may be advanced by those that grant abstraction to be not impoverishing but enriching. They will point out that the canon of operations forces empirical inquiry to go beyond the mere aggregation of isolated laws to the development of systems. It is not enough to know the law of falling bodies, the law of air resistance, the law of friction. One also has to know how to apply these laws simultaneously if one is to solve practical problems. Hence, the discovery of laws has to be accompanied by the discovery of correlations between laws and, no less, of correlations between the correlations. There exists, then, a movement towards the systematic unification of classical laws and, as this unification is prompted by concrete problems, one may expect that, when all laws are known exactly and completely, there will also be known a systematic unification commensurate with world process in its concrete, historical unfolding. (CWL 3, 91/)
… 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.
The true aim of science is verification of understanding. Prediction and control are not, in and of themselves, verification.
For Lonergan, prediction and control are not legitimate ends of science because they are not the same as verified understanding, which is the true aim of science. [CWL 15, Editors’ Introduction, ftnt 32, xxxvii]
Verification is verification of the real. And the real is the verifiable.
… unlike his predecessors, (the contemporary scientist) has to think of knowledge, not as taking a look, but as experiencing, understanding and judging; he has to think of objectivity, not as mere extroversion, but as experiential, normative, and tending towards an absolute; he has to think of the real, not as a part of the ‘already out there now’, but as the verifiable. Clearly, the imagined as imagined can be verified only by actually seeing, and so there is no verifiable image of the elements of the mechanism. Moreover, what science does verify, does not lie in any particular affirmations, which are never more than approximate; what science verifies is to be found ingeneral affirmations, on which ranges of ranges of particular affirmations converge with an accuracy that increases with the precision of measurements and with the elimination of probable errors. (CWL 3, 42425/44950)
… first we must establish that as a matter of fact we know and that as a matter of fact there is some realityproportionate to our knowing. For only after the facts are known can we entertain any hope of reaching an explanation of the possibility of a correspondence between our inquiry and understanding, our reflection and judgment, and on the other hand the real as it really is. … As has been seen, our own unrestricted desire to know defines for us what we must mean when we speak of being; in the light of that notion we can settle by intelligent grasp and reasonable affirmation what in fact is and what in fact is not; and while this procedure des not explain why every possible and actual reality must be intelligible, it does settle what in fact already is known to be true and, at the same time, it gives rise to the further question that asks for complete explanation and complete intelligibility. (CWL 3, 6789/701)
… unlike the logical positivists, we are completely disillusioned of the notion that knowing the real is somehow looking at what is already out there now. Unlike them, we have much to say about the unconditioned and, indeed, it is in the unconditioned that we place the whole meaning and force of verification. (CWL 3/672/694)
If we ask why scientific hypothesis needs verification and why Thomist definition needs judgment, we meet with similar answers. The scientist will insist that it is a mistake to try and base science on a priori necessities, that the one fruitful procedure is to scrutinize things as in fact they are, to discern in them what possibly may be their laws, to formulate these possibilities as mere hypotheses, and to submit such hypotheses to every test before placing any great reliance on them. (Collection, 143) [CWL 4] Lonergan, Bernard J. F. (1993) Collection, ed. Frederick E. Crowe and Robert E. Doran, Toronto: University of Toronto Press [CWL 4] and[Collection, 1967] Lonergan, Bernard J. F., Collection, ed. Frederick E. Crowe S.J., (1967, London, Darton, Longman & Todd LTD [Collection, 1967]
… what occurred towards the end of the seventeenth century was the beginning not merely of much more and much better science but, basically, of a notion of science quite different from the notion worked out by Aristotle and taken for granted by his followers. To put the matter summarily, necessity was a key notion for Aristotle but today it is marginal; in its place is verifiable possibility. Causality was a key notion for Aristotle but today in effect, if not in name, it is replaced by correlation. The universal and abstract were normative in Aristotelian science, but modern science uses universals as tools in its unrelenting efforts to approximate to concrete process. Where the Aristotelian claimed certitude, the modern scientist disclaims anything more than probability … the prestige of this new idea of science is unquestioned, its effectiveness has been palpably demonstrated, its continuing necessity for the survival of the earth’s teeming population is beyond doubt. ( A Second Collection, pages 1034)
There are classical laws and statistical laws; and there are canons of empirical method. (CWL 3, 70103/93126)
… there is a canon of complete explanation. Everything is to be explained. … … … The canon of complete explanation demands that the scientific world, which expresses the relation of things to one another, be constructed completely. It is not the world of common sense. (CWL 10, 144)
Also,
… there is a canon of statistical residues. … (CWL 10, 144)
… exact and complete knowledge of classical laws not merely can leave room for possible statistical investigationbut also must do so. For such exact and complete knowledge would embrace all the systematic relations between determinate data; none the less, such knowledge would be abstract and so in need of further determinations to be applied to concrete instances; it follows that the further determinations cannot be systematically related to one another; and so there must be a field for statistical laws. (CWL 3, 11112)
… there is no need to interpret classical laws concretely. They can be statements of elements in abstract system where
 the abstract system is constituted by implicitly defined relations and terms,
 the abstract system is connected with data not directly but through the mediation of a complementary set of descriptive concepts, and
 the laws of the abstract system are said to be verified inasmuch as they assign limits on which, other things being equal, vast varieties of data converge.
On this showing, the completely determinate relations of classical laws are between the completely determinate terms they implicitly define. This closed structure is referred to data through a set of descriptive and so approximative concepts. Finally, the closed structure is proved relevant to data, not by exact coincidence, but by assigning the limits on which data converge. (CWL 3, 13637/)
… the canon of operations is a principle of cumulative verification. For laws guide operations successfully in the measure that they are correct. Hence, in so far as laws and their implications in a vast variety of situations are repeatedly successful guides of operations, their initial verification is cumulatively confirmed (CWL 3, 75/)
Regarding the notion of invariance irrespective of differences in coordinates: in field theory – whether in physics or in macroeconomics – the relations within mathematical equations remain invariant despite changes in the magnitudes of the variables.
physicists surmount their peculiar difficulty (of having to use reference frames) by expressing their principles and laws in mathematical equations that remain invariant under transformations of frames of reference. [CWL 3, 40/ ]
(The Canon of Parsimony) is at once obvious and difficult. … it forbids the empirical scientist to affirm what, as an empirical scientist, he does not know. … empirical method involves four distinct elements, namely

 the observation of data,
 insight into data,
 the formulation of the insight or set of insights, and
 the verification of the formulation. (CWL 3, 789/)
… verification is of formulations, and formulations state

 the relations of things to our senses, and
 the relations of things to one another. (CWL 3, 79/)
Scientific formulations are comprised of relations of things to one another.
Pure (or explanatory) conjugates … are correlatives defined implicitly by empirically established correlations, functions, laws, theories, systems. (CWL 3, 80)
On the other hand, the pure conjugate has its verification, not in contents of experience nor in their actual or potential correlatives, but only in combinations of such contents and correlatives. I see, for instance a series of extensions and alongside each I see a yardstick; from the series of combinations (of extension and yardstick) I see a series of measurements; from another series of combinations I obtain another series of measurements; from the correlation of the two series, together with a leap of insight, I am led to posit as probably realized some continuous function; pure conjugates are the minimal correlatives implicit in such functions; and their verification finds its ground, not in experience as such, but only in the combination of combinations, etc., etc., etc., of experiences. (CWL 3, 80/)
.4. Explanation and explanatory conjugates: scientific and purely relational terms implicitly defining one another; whatever the variable magnitudes may be, the relations themselves among terms are made invariant by implicit definition of terms among themselves. The cluster of coherent equations constitute a single explanatory unity, a system.
Already 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. … 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. (CWL 3, 291/316)
Our … main topic was the relation of common sense to science, and our fundamental assertion is that the two regard distinct and separate fields. Common sense is concerned with things as related to us. Science is concerned with things as related among themselves. (CWL 3, 293/318)
Purely functional relations and interconnections must be scientifically established.
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.” [Gibbons, 1987, 313]
Lonergan’s critique (shows that) by using the technique of implicit definition, the emphasis shifts from (first) trying to define the relevant variables to (first) searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects which, in the first instance, one was thinking about. [Gibbons, 1987]
To explain in the form of applied mathematics the current, purelydynamic, concrete economic process, Lonergan searched among purelyrelational formalisms for those formalisms which might in combination be isomorphic with (”true to”) the functional interrelations of the economic process. Thus, the applicable formalism would explain and systematize the scattered, but unsystematized, insights of macroeconomists. In particular, Schumpeter had observed that the level of capital spending seemed to be related to cyclical excesses and deficiencies colloquially called booms and slumps. Lonergan used the technique of implicit definition and the heuristic guide of the notion of a field theory; he identified abstract forms of a) inexorable pointtopoint functionings (“basic functionings”), b) pointtoindeterminatefutureline functionings (“surplus functionings”), c) temporal difference (t – a), d) rectilinear velocitous accumulation of factors of production (q_{i} = q_{ijk}), and e) velocities of circular fluid movements (O’ – I’ to E’ – R’) connected by crossover movements (c”O” – i’O’). These mathematical forms expressing purelyimplicit functional relations, are by themselves merely isolated abstractions; they exist prior to and independent of any consideration of application to any particular, “commonmatter” process. But, as general forms, found in part to be applicable to and explanatory of hydrodynamics, thermodynamics, electric circuits, survival activities, and social relations, they might be found to be applicable in combination to explain and systematize concrete schemes of recurrent circulations in a field such as periodicallyexpanding production for sale. Lonergan was able to discover equations, whose terms can represent economic functionings implicitly defined by their relations to one another; and these equations can be combined in a fieldtheoretic explanation of the objective economic process. Lonergan’s equations are isomorphic with, applicable to, and explanatory of rectilinear and circular processes constituting the field of macroeconomics.
Algebraic functions of the first degree are functions in which two terms implicitly define one another and thus mutually define one another. In Hilbert ‘s geometry two positions and a line implicitly define one another. Two points determine a line and a line determines two points.
By “algebraic functions of the first degree” is meant functions involving no exponential powers of the variables other than 1. … To give a simple example, if the number of loaves of bread is represented by the variable y, and the number of bushels of wheat by the variable x, then a relevant algebraic function might be where brepresents the number of loaves of bread which can be obtained from one bushel of wheat under current technological means, and c represents any fixed loss or gain which is independent of the number of bushels. [CWL 15, 23 ftnt. 25]
Thus, Hilbert’s technique of purelyrelational implicit definitions finds application to Lonergan’s treatment of the onetoone correspondence and concomitance of factors of current production with factors currently exiting the process.
“Basic” and “surplus”, i.e. pointtopoint and pointtoline, are general and universal formalisms. Upon these a superstructure of two circulations connected by crossover circulations may be deduced.
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]
On this model (of a search for significant basic variables), circulation analysis (in macroeconomic dynamics) raises a large superstructure of terms and theorems upon a summary classification and a few brief analyses of typical phenomena. (CWL 15, 18)
the relevant fact lies in the nature of the explanations that are applicable to our universe. It is to the effect that all such explanations are made up of general or universal elements [CWL 3, 29/ ]
It is clear that, for Lonergan, real internal relations are known by the sciences, which know created things ‘through their causes,’ that is, through their formal intelligibility. Prescientific knowledge of things does not know their real internal relations But that does not mean that it knows things without their relations. It does mean, though, that the connections or relations are not scientifically established. (CWL 12, 717, ftnt 5)
Now, at the root of classical method there are two heuristic principles. The first is that similars are understood similarly, that a difference of understanding presupposes a significant difference of data. The second is that similarities, relevant to explanation, lie not in the relations of things to our senses but in their relations to one another. Next, when these heuristic principles are applied, there (first) result classifications by sensible similarity, then correlations, and finally the verification of correlations and of systems of correlations. But verified correlations necessarily involve the verification of terms implicitly defined by the correlations; and they do not involve more than such implicitly defined terms as related, for what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically and explanatory relations. Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[CWL 3, 435/460]
The lack of ultimacy that Lonergan ascribes to prices and price theory can scarcely be overemphasized. (CWL 15 xlvixlvi)
Lonergan’s intention was ‘to formulate the laws of an economic mechanism more remote and, in a sense, more fundamental than the pricing system…laws which men themselves administrate in the personal conduct of their lives. In 1978 he began to refer to Nicholas Kaldor in support of his judgment that the significance traditionally accorded to price theory by conventional economics since Adam Smith’s Wealth of Nations (1776) amounted to a virtual derailment of economic theory……….Lonergan’s interest in Kaldor’s sweeping statement was to emphasize that prices and their changes are not explanatory but accountants’ entities………Lonergan insists that the mechanism of the pricing system does not furnish economists with distinctions among significant variables of aggregate surplus (or producergoods) and basic (or consumergoods) supply and demand with their determinate yet flexible velocities and accelerations, 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…….the lack of ultimacy that Lonergan ascribes to prices and price theory can scarcely be overemphasized. (CWL 15 xlvixlvi)
On this (methodological) model (i.e. implicit definition) circulation analysis raises a large superstructure of terms and theorems upon a summary classification and a few brief analyses of typical phenomena. Classes of payments quickly become rates of payment standing in the mutual conditioning of a circulation; to this mutual and, so to speak, internal conditioning there is added the external conditioning that arises out of transfers of money from one circulation to another; in turn this twofold conditioning in the monetary order is correlated with the conditioning constituted by productive rhythms of goods and services………There results a closely knit frame of reference that can envisage any total movement of an economy as a function of variations in rates of payment, and that can define the conditions of desirable movements as well as deduce the causes of breakdowns…CWL 15, 18
From insight into the insights of scientists, one grasps the characteristics of science: a) sets of basic terms defined by their relations to one another, b) sets of equations coherent with one another in a superstructure which constitutes a whole “system”; i.e. explains a whole systematic unity, such as mechanics, thermodynamics, electromagnetism, special relativity, and quantum mechanics.
… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established. The most notable example is Pythagoras’ theorem on the hypotenuse of the rightangled triangle, which occurs at the end of book 1 of Euclid’s Elements. Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. … Similarly, mechanics became a system with Newton. Prior to Newton, Galileo’s law of the free fall and Kepler’s three laws of planetary motion were known. But these were isolated laws. Galileo’s prescription was that the system was to be a geometry; so there was something functioning as a system. But the system really emerged with Newton. This is what gave Newton his tremendous influence upon the enlightenment. He laid down a set of basic, definitions, and axioms, and proceeded to demonstrate and conclude from general principles and laws that had been established empirically by his predecessors. Mechanics became a science in the full sense at that point where it became an organized system. … Again, a great deal of chemistry was known prior to Mendeleev. But his discovery of the periodic table selected a set of basic chemical elements and selected them in such a way that further additions could be made to the basic elements. Since that time chemistry has been one single organized subject with a basic set of elements accounting for incredibly vast numbers of compounds. In other words, there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. [Method, 24142]
Lonergan achieved a single explanatory unity, a system.
Newton set down laws of motion and proceeded to demonstrate that if a body moves in a field of central force, its trajectory is a conic section. He set out with a minimal cluster of insights, definitions, postulates, axioms and proceeded to account for the laws that had previously been empirically established, bringing them into a single explanatory unity. ¶A single insight yields a conception, a definition, an object of thought; but from a cluster of insights, you build up a system of definitions, axioms, postulates, and deductions. We have to note that a system is quite an achievement; systems are not numerous. There are Euclid’s geometry and subsequent developments in geometry, Newton’s mechanics and dynamics and the building upon Newton, and the Mendeleev table in chemistry. System, then, is the expression of a cluster of insights. [CWL 5, 52]
.5. Invariant classical laws, statistical laws of probability, and the implications for prediction
… The analysis that insists on the indeterminacy is the analysis that insists on the present fact: estimates and expectations are proofs of the present indeterminacy and attempts to get round it; and, to come to the main point, an analysis based on such estimates and expectations can never arrive at a criticism of them; it would move in a vicious circle. It is to avoid that circle that we have divided the process in terms of indeterminate pointtoline and pointtosurface and higher correspondences. [CWL 15, 28]
Explanation of the concrete process will contain two components: first, an invariant primary component consisting of abstract, invariant, internal, explanatory relations, relevant in any instance; plus, second, a secondary component of concrete determinations, such as actual prices and quantities incidently decided upon by participants in the nonsystematic manifold. The abstract and primary relativities can be applied to the boundary values of prices and quantities to reach explanation of the particular concrete instance of pretioquantital flows.
Thus, while FMD’s analysis of the primal process of velocitous production and sale of goods and services yields distinctions between pointtopoint and pointtoline, correspondences and correlations, and while its primary fieldtheoretic relativities are purely abstract, the complete explanation of the concrete process has two components; it consists of 1) primary abstract relations applied to 2) secondary concrete determinationsfrom the nonsystematic manifold. (See CWL 3, 49495/51516)
The converse to this difference in the meaning of verification appears in the difference between classical and statistical predictions. Classical predictions can be exact within assignable limits, because relations between measurements converge on the functional relations that formulate the classical laws. But because relative actual frequencies differ at random from probabilities, statistical predictions primarily regard the probabilities of events and only secondarily determine the corresponding frequencies that differ at random from probabilities. Hence, even when numbers are very great and probabilities high, as in the kinetic theory of gases, the possibility of exception has to be acknowledged; and when predictions rest on a statistical axiomatic structure, as in quantum mechanics, the structure itself seems to involve a principle of indeterminacy or uncertainty. [See CWL 3, 656/ ]
… 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, 8182/105]
In Functional Macroeconomic Dynamics there is a recognition and affirmation of both classical and statistical laws.
There are two heuristic principles and there is a heuristic structure. The two heuristic principles:
Now, at the root of classical method there are two heuristic principles. The first is that similars are understood similarly, that a difference of understanding presupposes a significant difference of data. The secondis that similarities, relevant to explanation, lie not in the relations of things to our senses but in their relations to one another. Next, when these heuristic principles are applied, there (first) result classifications by sensible similarity, then correlations, and finally the verification of correlations and of systems of correlations. But verified correlations necessarily involve the verification of terms implicitly defined by the correlations; and they do not involve more than such implicitly defined terms as related, for what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically and explanatory relations. Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[CWL 3, 435/460]
The heuristic structure:
… empirical method involves four distinct elements, namely

 the observation of data,
 insight into data,
 the formulation of the insight or set of insights, and
 the verification of the formulation. [CWL 3, 7879/102]
On the one hand, there is the movement of empirical science from description to explanation, from proper domains of data to systems of laws that implicitly define the terms they relate; and at the end of this movement there is the ideal goal that is to be attained when all aspects of data, except the empirical residue, will have their intelligible counterpart in systems of explanatory conjugates and ideal frequencies. [CWl 3, 313/337]
An analyst may stop to consider an apparent – but only apparent – problematic in Functional Macroeconomic Dynamics. It is claimed to be always the current process, yet it is also concerned with continuity and it plays out over time. If the human analyst feels an imperious need to predict the future, how can one confine oneself to the current process? Our answer is that, first, phenomena such as planetary, pendular, and trajectory always are a current process with classical laws, even though motions, as dynamical motions, play out over time. Second, we affirm that actual relations of measurements converge upon the functional relations, and that, in a nonsystematic manifold of human decisions, we must use the premise “ceteris paribus,” all other things being equal, and we must distinguish relative actual frequencies fro ideal frequencies. The analyst must grasp what presentlydivergent flows are intrinsically disequilibrating over time and must appreciate the systematic exigence and corresponding autonomous effort of the system to correct the divergence.
The productive process is, then, the (current) aggregate of activities proceeding from the potentialities of nature and terminating in a standard of living. Always it is the current process, and so it is distinguished both from the natural resources, which it presupposes, and from the durable effects of past production. [CWL 15, 20]
Lonergan’s analysis is a systematization of alreadyknown facts. His conclusions regard the intelligibility of a “mechanism.”
Indeed, the present study will offer an analysis of the macroeconomy that accounts for its successes and failures without attempting the historical and statistical research that would be necessary if any precise predictions were to be made. How is this possible? It is possible because knowledge of facts is one thing, and understanding known facts is another. The facts of the macroeconomy are already well known. What is lacking is a clear and precise understanding of the mechanism behind such obvious facts as the relations between expansion and contraction of the economy, employment and unemployment, inflation and deflation, and many other things that are just common knowledge. CWL 15, 1112
.6. Explanatory functional relations of significant (i.e. explanatory) variables “scientifically among themselves” in a closed, yet coherent and comprehensive set of equations
Explanatory science is neither commonsense corporate accounting nor the aggregation of corporate and management accountings to constitute the Gross Domestic Product. Functional Macroeconomic Dynamics is not National Income Accounting. Functional Macroeconomic Dynamics is explanatory science. The two disciplines are concerned with distinctly different fields. Their practice has different heuristics, methods, and purposes. The explanatory formulations constituting Functional Macroeconomic Dynamics consist of abstract terms defined by their functional relations to one another. The informative tallies of statements of income, cash flow, and net worth consist of compilations of commonsense categories of payments and receipts.
“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; … 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” … [CWL 15 2627 ftnt 27]
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 element is known through its relations to all other elements.” (CWL 10, 154)
Commonsense corporate and management accounting terms and their tally in aggregates – as used by the Bureau of Economic Analysis and the Federal Reserve Bank – are inadequate as indexes for use in scientific explanation.
An ‘accountant’s unity’ is a category used in (conventional) accounting. For Lonergan, (conventional) accounting generally denotes an enterprise within common sense which uses descriptive, as contrasted with explanatory terms (on these terms see CWL 3, 3738/6162, 17879/2013, 24748/27273). Insofar as that is true, the accountant’s unity is not an adequate index for the normative, explanatory analysis of the productive process. [CWL 15, 26, ftnt 26]
The nonEuclideans 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, 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, 67]
Science develops.
… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established. The most notable example is Pythagoras’ theorem on the hypotenuse of the rightangled triangle, which occurs at the end of book 1 of Euclid’s Elements. Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. … Similarly, mechanics became a system with Newton. Prior to Newton, Galileo’s law of the free fall and Kepler’s three laws of planetary motion were known. But these were isolated laws. Galileo’s prescription was that the system was to be a geometry; so there was something functioning as a system. But the system really emerged with Newton. This is what gave Newton his tremendous influence upon the enlightenment. He laid down a set of basic definitions, and axioms, and proceeded to demonstrate and conclude from general principles and laws that had been established empirically by his predecessors. Mechanics became a science in the full sense at that point where it became an organized system. … Again, a great deal of chemistry was known prior to Mendeleev. But his discovery of the periodic table selected a set of basic chemical elements and selected them in such a way that further additions could be made to the basic elements. Since that time chemistry has been one single organized subject with a basic set of elements accounting for incredibly vast numbers of compounds. In other words, there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. [CWL 10, 24142]
Science develops: it comes to understand what previously was not understood; (in contrast) logic unfolds: it states explicitly what already has been said implicitly. (CWL 15, 11)
… science rests upon two distinct grounds. As insight grasping possibility, it is science. As verification selecting the possibilities that in fact are realized, it is empirical. (CWL 3, 78/ )
… besides statistical predictions, there exist the fully accurate predictions that are exemplified by astronomy and that rest on the existence of schemes of recurrence. Moreover, the intelligent manner of making these predictions is to analyze the schemes into their component classical laws. Copernicus corrected Ptolemy’s imaginative scheme; Kepler corrected the circles of Copernicus; but it was Newton who worked out the underlying laws and Laplace who revealed the periodicity of the planetary system. From that discovery of laws the great movement of thought, named modern science, received its most powerful confirmation. It did so because it ended, at least for two centuries, the more common human tendency to speak, not of precise laws, but of the common run of events or the ordinary course of Nature. [CWL 3, 112/135]
Again,
The nonEuclideans 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, 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, 67]
Science is subject to revision.
Precisely because analysis is an ongoing process, it is subject to revision. In the measure that revision is radical, it involves new concepts and even new definitions. In this fashion the fact of revision displaces the old reliance on essential definitions and gives way to a search for significant basic variables. For variables, because it is process that is under investigation; for significant variables, because only significance contributes to the relevant acts of understanding; finally for basic variables, because others depend on them, and they depend on one another. In other words, basic variables form a closed circle, in which terms are fixed by their relations, relations fix the terms, and the whole is justified by the degree in which it and its implications are verified. (CWL 15, 9)
Functional Macroeconomic Dynamics applies implicit definition to achieve explanatory functional relations of terms among themselves.
Lonergan’s critique (shows that), by using the technique of implicit definition, the emphasis shifts from (first) trying to define the relevant variables to (first) searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects which, in the first instance, one was thinking about. [Gibbons, 1987]
The Porphyrean dichotomy resulting from the distinction of currentdeterminatepointtocurrentdeterminatepoint correspondence (basic) vs. currentdeterminatepointtofutureindeterminateseries correspondence(surplus) is the fundamental analytic division of the whole, current, dynamic, productive organism. From this distinction two distinct natures – differently timed but interrelated and ultimately solidary productive functions – are discovered and serve to form a “unitary basis.”. And, grounded in this relation of interdependent, mutuallyconditioning, productive activities, the intelligible system of normative monetary circulations may be deduced to yield the nuanced normative science of explanatory macroeconomics in Lonergan’s book, Macroeconomic Dynamics: An Essay in Circulation Analysis. The entire set of equations isomorphic with and explaining the entire dynamic economic process is logically deduced from the bedrock distinction between basic and surplus activities. That distinction between projectivegeometrical relations, i.e. between accelerator surplus functionings and accelerated basic functionings is, thus, said to be of systematic significance. Like Euclid’s axioms, Hilbert’s axioms. Maxwell’s equations, Einstein’s methodological doctrine in Special Relativity, it is the foundation or ground of a system.
… science rests upon two distinct grounds. As insight grasping possibility, it is science. As verification selecting the possibilities that in fact are realized, it is empirical. (CWL 3, 78/ )
Again in part:
… a science emerges when thinking in a given field moves to the level of system. … there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. . [CWL 10, 24142]
… real analysis (is) identifying money with what money buys. … 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, Editors’ Introduction, xxviii quoting Lonergan]
With a proper consideration of time and magnitude, the relation between accelerator surplus velocities and accelerated basic velocities is formulated as the lagged technical accelerator. (See CWL 15, 367)
k_{n}[f’_{n}(ta)B_{n}] = f”_{n1}(t) – A_{n1 [CWL 15, 367]}
Thus, one can, first, define the “mechanical”[2] structure of the functional production process and its internal conditions for continuity and equilibrium; then one correlates and projects this dynamical structure onto the correlated dynamic flow of the payments which make feasible the vast and intricate process of production and exchange; then one deduces ideal cyclic cooperation between the two monetary circulations themselves for concomitance, solidarity, continuity and equilibrium of the process. At the end of the analysis one has reached a systematic explanation –rather than a description – constituting a normative theory. Yet, by recognition of the nature of humans’ possibly effecting nonsystematic disequilibrating divergence from the norms, one has also a theory of equilibria and disequilibria, i.e. of excesses and deficiencies, booms and slumps, stagflations, and breakdowns These divergences can be captured in mathematical forms of correction back to a central tendency and exigence as stresses and strains or reversion to the mean, or divergences and convergences. Thus, booms, slumps, stagflations, and breakdowns. are not simply supposed, postulated, described, or labeled mysterious (having no rational explanation); rather they are explained as divergences from the ideal, normative continuity and equilibrium specified and prescribed by the a) abstract principles and laws, and b) ideal frequencies from which relative actual frequencies diverge nonsystematically.
… positive or negative transfers to basic demand (D’s”I’) and consequent similar transfers to surplus demand (D”s”I”) belong to the theory of booms and slumps. They involve changes in (aggregate basic or aggregate surplus) demand, with entrepreneurs receiving back more (or less) than they paid out in outlay (which includes profits of all kinds). The immediate effect (of these aberrational monetary transfers) is on the price levels at the final markets, and to these changes (in price), enterprise as a whole responds to release an upward (or downward) movement of the whole economy. But the initial increased transfers to demand [that is, excess transfers along (D’s’I’) and (D”s”I”) ] are not simply to be supposed. For that would be postulating without explaining the boom or slump. [CWL 15, 64]
Hilbert’s geometry and Lonergan’s Functional Macroeconomic Dynamics employ the technique of abstract implicit definition which, as abstract and general, expresses only a relational form… The significance of implicit definition is that it is purely relational and may be applied with intelligent selective applicability so as to reach a hypothetical explanation of a fieldtheoretic process with which they are isomorphic. Implicit definition applied to dynamical flows constitutes a more abstract and appropriate type of thinking than is employed in all the Walrasian macrostatic formalisms, which separate the economic process into internal reactions to inertial and extermal parameters over which they have no control.
.7. Dynamics and secondorder differential equations
We seek an explanatory understanding of the objective, dynamic, economic process. This understanding would yield a normative pattern of relations for which the process would have an exigence. The abstract, explanatory formulation would be universally valid and applicable in any instance. And, thus, we would be able to say, for example, that certain current levels of concrete activities diverge from the system’s norms and, thus by the nature of the departure, are intrinsically inflationary without our venturing to predict when and to what extent this moment’s departure may a) stand alone, b) combine with, or c) be offset by, other possible, coincidental, unpredictable departures, so as to sooner or later bring about actual inflation.
The overall process may be stable, simply reproducing itself period after period, thus constituted in the aggregateby constant velocities. Or it may enjoy intelligent invention, innovation, and implementation and, thus, change velocities and accelerate in some intelligible pattern. The acceleration would be expressed in secondorder differential equations.
Taking into account past and (expected) future values does not constitute the creative key transition to dynamics. Those familiar with elementary statics and dynamics will appreciate the shift in thinking involved in passing from (static) equilibrium analysis … to an analysis where attention is focused on secondorder differential equations, on d^{2}θ/dt^{2}, d^{2}x/dt^{2}, d^{2}y/dt^{2}, on the primary relativities of a range of related forces, central, friction, whatever. Particular secondary boundary conditions, past and future pricings and quantities, are relatively insignificant for the analysis of the primary relativity immanent in, and applicable to, every instance of the process. What is significant is the LeibnitzNewtonian shift of context. [McShane, 1980, 127]
Lonergan’s Diagram of Rates of Flow represents the intelligiblie explanatory interdependencies of functional flows. As interdependent constituents of the process, they are mutually conditioning and mutually defining.
… 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 (and the differential equations it represents) 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 commonsense 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]
Lonergan’s Diagram of Rates of Flow is an analytical framework. The mastery of this framework confers a definite benefit on the serious analyst.
Lonergan agreed with Schumpeter on the importance of a systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; he agreed with Schumpeter that to be able to explain the booms, slumps, and crashes of the trade or business cycles the economist’s analysis had to be as dynamic as the subject matter under investigation; and he agreed that the economist had to know what are the significant variables in the light of which price changes are to be interpreted. According to Lonergan, standard economic theory had successfully achieved none of these desiderata. [CWL 15, Editors’ Introduction liii]
.8. The periodicity of orderly, expansionary surges
There is a partial resemblance to the formal periodicity and repetition of other processes; however, the periodicity of the economic process consists uniquely of a series of velocitous surges and taperings, repeated when and as often as invention and improvement of methods provide, but having no necessity of decline. An individual pure cycle of expansion is a purely positive movement. The economic surge and tapering has not the rigidity of stricter wavelike processes such as electromagnetic or trigonometric waves, for each properlymanaged economic process has no intrinsic exigence for any type of decline. The pattern of any normative purecycle expansionof production and sale constitutes a purelyrelational field theory of strictly upward surges and taperings.
Further, individual surges and taperings with different temporal initiations and conclusions may be superposed on one another so as to effect a concurrent ”stack” of surges and taperings. And a more recent cycle may happen to partially replace an earlier upward movement.
There is such a thing as progress and its principle is liberty. … However, while there is progress and while its principle is liberty, there also is decline and its principle is bias. There is the minor principle of group bias which tends to generate its own corrective. There is the major principle of general bias and, though it too generates its own corrective, it does so only by confronting human intelligence with the alternative of adopting a higher viewpoint or perishing. To ignore the fact of decline was the error of the old liberal views of automatic progress. The far more confusing error of Marx was to lump together both progress and the two principles of decline under the impressive name of dialectical materialism, to grasp that the minor principle of decline would correct itself more rapidly through class war, and then to leap gaily to the sweeping conclusion that class war would accelerate progress. What, in fact, was accelerated was major decline which in Russia and Germany leaped to fairly thorough brands of totalitarianism. The basic service of the higher viewpoint will be a liberation from confusion through clear distinctions. Progress is not to be confused with decline; the corrective mechanism of the minor principle of decline is not to be thought capable of meeting the issues set by the major principle. [CWL 3, 234235/25960]
The pure cycle of expansion must not be confused with the “trade cycle” of ups and downs, excesses and their corrections, booms and slumps. The economic process has an exigence for its particular normative pure cyclefrom a lower level of abundance strictly upward to a higher level of abundance.
A systematic explanation, then, requires a normative theoretical framework. The basic terms and relations of such a framework would specify the distinctions and correlations that articulate the causes, which are not necessarily visible, of events that are apparent to all. The framework would thus stand to the ordinary apprehension of the booms and slumps of the trade cycle in much the same way that the explanatory grasp of acceleration as the second derivative of a continuous function of distance and time stands to the ordinary, commonsense grasp of what it is to be going faster. [CWL 15, Editors’ Introduction lv ]
Our immediate task is to work out the correlations that exist between the velocity and accelerator rhythms of production and the corresponding rhythms of income and expenditure. The set of such correlations constitutes the mechanical structure, a pattern of laws that stand to (purely experiential) economic activity as the laws of mechanics to buildings and machines. [CWL 21, 43]
In mechanics constant circular motions exhibit constant angular velocity. Pendular motions exhibit repetitive, though varying, angular velocity. Elliptical motion exhibits a constant sum of distances about two foci, a sweeping out of equal areas in equal times and a variable of eccentricity. Each particular “cyclical” economic expansion exhibits a pattern of positive surges, and taperings, and it may be represented mathematically so as to comprise a field theory of invariant relations among implicitly defined functional variables.
The great movement of thought, named modern science, has not reached the halls of the economics departments of our great universities. The Walrasian macrostatics of the textbooks is exact but not complete. A statics is not adequate to explain a dynamic process.
Though scattering conditions render certain prediction to be impossible in the general case, there exist classical schemes of recurrence that allow accurate statistical predictions.
For besides statistical predictions, there exist the fully accurate predictions that are exemplified by astronomy and that rest on the existence of schemes of recurrence. Moreover, the intelligent manner of making these predictions is to analyze the schemes into their component classical laws. Copernicus corrected Ptolemy’simaginative scheme; Kepler corrected the circles of Copernicus; but it was Newton who worked out the underlying laws and Laplace who revealed the periodicity of the planetary system. From that discovery of laws the great movement of thought, named modern science, received its most powerful confirmation. It did so because it ended, at least for two centuries, the more common human tendency to speak, not of precise laws, but of the common run of events or the ordinary course of Nature. [CWL 3, 112/135]
… without further clarification Schumpeter acknowledged that dynamic analysis called for a new light on equilibrium. Such new light arises when, over and above (DSGE’s) equilibria of supply and demand with respect to goods and services (classical microeconomics), there are recognized further equilibria (crossovers balancing, concomitance of outlays with income and of income with both outlays and expenditure, and actual technical coefficients conforming to normative coefficients) that have to be maintained if an economy chooses to remain in a stationary state, to embark on a longterm expansion, to distribute its benefits to the vast majority of its members, and so to return to a more affluent stationary state until such further time as further expansion (of surge and tapering) beckons. … Moreover, such macroequilibria are more fundamental than the microequilibriaassembled by Walras. (FMD’s macroequilibria) are the conditions of a properly functioning economy. (CWL 15, 92)
Taking into account past and (expected) future values does not constitute the creative key transition to dynamics. Those familiar with elementary statics and dynamics will appreciate the shift in thinking involved in passing from (static) equilibrium analysis … to an analysis where attention is focused on secondorder differential equations, on d^{2}θ/dt^{2}, d^{2}x/dt^{2}, d^{2}y/dt^{2}, on the primary relativities of a range of related forces, central, friction, whatever. Particular secondary boundary conditions, past and future pricings and quantities, are relatively insignificant for the analysis of the primary relativity immanent in, and applicable to, every instance of the process. What is significant is the LeibnitzNewtonian shift of context. [McShane, 1980, 127]
.9. Implicit definition of abstract explanatory terms according to their functional relations to one another
In Functional Macroeconomic Dynamics explanatory functionings implicitly define one another. (Click here and here and here)
“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; … 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” … [CWL 15 2627 ftnt 27]
… an entirely new type of definition was introduced by D. Hilbert in his formulation of geometry.[3] He called it implicit definition. An implicit definition drops the common matter to express only a relational form… The significance of implicit definition is that it does not pin down the meaning of the words ’point’ and ‘line’ to anything. Point, in Hilbert’s expression of geometry, can be a Euclidean position without magnitude, and a line can be a length without breadth or thickness lying evenly between its extremes. But a point can also be an ordered pair of numbers, where (a,b) is not the Cartesian notation for a Euclidean point, but just that ordered pair. And a straight line can be a firstdegree equation: y = mx + c is determined by two ordered pairs, and two ordered pairs will determine a firstdegree equation. Hilbert can mean by point and line the imaginable Euclidean point or line, the Cartesian algebraic expression for point and line, or anything else that will satisfy the relation “two of one determines one of the other,” no matter what they are. The definitions are in terms of relational form, with no attention to any common matter. The relational form selects any common matter that will be thought relevant. Implicit definition is a more abstract type of thinking that omits even the common matter. (CWL 10, ???)
The most basic implicit functional relations of Functional Macroeconomic Dynamics are the ground, foundation, or basis of the entire system and, thus, are said to be of systematic significance. They are the analytic foundation of the entire system. They are the bedrock on which the system has been built and stands; i.e. upon which the superstructure grows rather than the shifting sands on which the unsound schools or isms founder and into which the incoherent Babel of academia collapses and sinks.
In scientific macroeconomic dynamics we employ the technique of implicit definition by means of which we seek to grasp and formulate a core cluster of foundtional and superstructural explanatory terms and relations. The explanatory terms are called explanatory conjugates. Because they are mutually conditioning and mutually definitive of one another and thus “yoked together,” we call them conjugates. This core set of explanatory termsinrelation will virtually contain a derivable superstructure of relations constituting a system.
Lonergan’s critique (shows that) by using the technique of implicit definition, the emphasis shifts from (first) trying to define the relevant variables to (first) searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects which, in the first instance, one was thinking about. [Gibbons, 1987]
Not all activities and services are coincident with the process of material objects to take their correspondence from that of the objects. It remains that the same general types of correspondence may be discerned. There is a pointtopoint correspondence between movements of trains and passengermiles, not indeed in the sense that there is some fixed ratio between trainmiles and passengermiles, but in the sense that the train has to move as often and as far as passengers move. … [CWL 15, 25]
“Surplus” factors of production are in a currentdeterminatepointtoindeterminatefutureseries or higher relation with the factors constituting goods and services exiting the productive process at the moment of saleinto a standard of living. These relations are not determinate during the current process of production. They are then currently indeterminate and, so, there is indeterminacy in what always is the current process.
… The analysis that insists on the indeterminacy is the analysis that insists on the present fact: estimates and expectations are proofs of the present indeterminacy and attempts to get round it; and, to come to the main point, an analysis based on such estimates and expectations can never arrive at a criticism of them; it would move in a vicious circle. It is to avoid that circle that we have divided the process in terms of indeterminate pointtoline and pointtosurface and higher correspondences. [CWL 15, 28]
In Functional Macroeconomic dynamics the meaning of a term is fixed by the abstract, explanatory, functional relation in which it stands with other terms. Explanatory meaning is fixed by relation, not nominally by Webster or Oxford.
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 D. Hilbert in his Foundations of Geometry in which, for example, the meaning of a point and a straight line isfixed 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.” [Gibbons, 1987, 313]
In the science of macroeconomics, as in other sciences, conceptual objects are defined by the laws by which they are implicitly connected to one another.
… in physics objects are defined through the laws by which they are connected to one another; in chemistry elements are defined through the various series of relations that are found in the periodic table; in physiology organs are defined by the functions they have with regard to the whole body, and so on. (CWL 12, 717)
Again, the analysis is purely functional.
Lonergan’s critique (shows that) by using the technique of implicit definition, the emphasis shifts from (first) trying to define the relevant variables to (first) searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects which, in the first instance, one was thinking about. [Gibbons, 1987]
the terms are defined by the relations in which they stand, that is, by a process of implicit definition. [Gibbons 1987, 313]
The following are functional relations:
 Pointtopoint (CWL 15, 238)
 Pointtoline (CWL 15, 238)
 OutlaysIncomes to ExpendituresReceipts (CWL 15, 4555)
 P’Q’ = p’a’Q’ + p”a”Q” (and) G = c”O” – I’O’ = 0 (CWL 15, 15662)
 Crossovers between basic and surplus circuits in the condition of equilibrium: G = c”O” – I’O’ = 0 (CWL 15, 4555)
Again, in the science of macroeconomics, explanatory functionings are implicitly defined by empirically verified correlations; and we call such terms “explanatory conjugates”.
… verified correlations necessarily involve the verification of terms implicitly defined by the correlations; …what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically verified and explanatory relations. Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[quoted more fully below from CWL 3, 435/460]
.10. Humans participate in a formal field as efficient causes.
This section will require another entire review
https://functionalmacroeconomics.com/2019/05/24/efficientcausevsformalcause/
.11. Functional relations of terms “scientifically among themselves” in a closed, yet coherent and comprehensive set of equations and significant variables
As has been said, in the normative field theory of macroeconomics, magnitudes of explanatory terms are variables, but normative relations are invariant.
Functional Macroeconomic Dynamics is a normative theory of interdependencies and mutual conditionings, yet, because it involves efficientcausal humans characterized by ignorance optimism, desires and fears making sometimesfeckless and unpredictable decisions for themselves, it has not the rigidity of, say, [lanetary motion in Newtonian mechanics; participants are efficientcausal humans characterized by ignorance optimism, desires and fears.
A condition of circuit acceleration was seen in Section 15 to include the keeping in step of basic outlay, basic income, and basic expenditure, and on the other hand, the keeping in step of surplus outlay, surplus income, and surplus expenditure. Any of these rates may begin to vary independently of the others, and adjustment of the others may lag. But any systematic divergence brings automatic correctives to work. 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]
Consumer prices may rise for different reasons. There can be a normal rise because of scarcity, or a radically maladaptive rise because of maladjustments of incomes. A rise in consumer prices may be brought about as “a consequence and, as will appear, a corrective of disproportion between monetary and real consumer income.“
(CWL 15, 131) There would be, for instance, a radical maladjustment between circuit and productiveacceleration if, when surplus rates of production were increasing more rapidly than basic, basic rates of income were increasing more rapidly than surplus. Then interval after interval, an increasingly excessive amount of monetary income would be moving to the basic final market, and there would follow a rise in prices quite different in kind from the normal rise resulting from increasing scarcity. Such a rise would not be an ordinary scarcity but at once a consequence and, as will appear, a corrective of disproportion between monetary and real consumer income. ¶ Not only is it true that this second type of price variation is different from the first, but also one must give it a different kind of attention. When prices rise because of real scarcity, one may speak of a requirement for variation in E’ and E” over and above the variation postulated by dQ’/Q’ and dQ”/Q”. But when prices rise or fall because the distribution of income has not anticipated these requirements correctly, then price variation is not a postulate for variation in E’ and E” but rather a spontaneous effort at adjusting what should already have been adjusted. Accordingly, such adjustment variations in prices will be ignored for the moment to be considered more in detail in the next section (entitled The Cycle of Basic Income). (See the Cycle of Basic Income)
Present concern will be for the type of adjustment that the successive phases of the pure cycle postulate. (CWL 15, 131)
The central adjustment to the varying income requirements of the quantity curves of the successive phases of the expansion is variation in the rate of saving. This variation is an adjustment between the levels of income to be dedicated to a standard of living and the levels of income to be dedicated to expansionary investment. In the Diagram it is represented by flows in the crossovers between the two circuits.
The central adjustment is variation in the rate of saving. This rate may be defined, conveniently for present purposes, as the ratio of surplus income to total income. Assuming that the rate of saving will not differ appreciably because income is derived from basic or surplus outlay, we may denote this rate by the symbol w, so that
w = I”/I’ + I” (CWL 15, 13132)
.12. Lending rates
Depending on point of view, an interest rate could be called by the lender the rate of return, or by the borrower the rental price of money. And, in general, interest rates would differ depending upon maturity, credit risk, political risk, incidental costs of the lender, and supply and demand for rented money. And in a very general sense, interest payments could include dividends on preferred, convertible, or common stock. Thus both bonds and stocks would be viewed similarly and a loose expression of “the interest rate” would be a pretty useless rough average.
We state two everyday meanings and one theoretical meaning of the utterance “interest rate.”
 The interest rate charged by lenders to borrowers in the operative circuits based on supply and demand for loan money
 The bondmarket interest rate as priced in the stock and bond markets by money managers as the moneysupply in the markets sloshes back and forth between secondary stocks and bonds
 The rate of interest equal to the anticipated growth rate of an economic process; it could in practice be sliced into tranches of bank loans, bonds, convertibles, preferred stock and common stock characterized by different risk factors.
In the nonpandemic course of normative, wellmanaged events, prices would be stable; the Fed would supply the continuous economic process with the right amount of money to satisfy the requirements of the magnitudes and frequencies of turnover transactions. The three interest rates specified above would be approximately equal. However, in some combination of pandemic and/or theoretical ignorance and/or selfaggrandizing politicians, a flood of excess money into the system would force higherthannormative prices and lowerthannormative interest rates in the primary lending and secondary lending operations, despite highrisks warranting high risk premiums on top of a basic riskless lending rate. In that case, the nominal rate and the real rate might both go below zero. Welcome to 2021!
The flooding of the economic process by the government deficit, financed in large part by Fed purchases of government and governmentbacked securities is intrinsically inflationary and will – until the stresses and strains on quantities and prices get worked out to a proper relation once again among costs and incomes, and savings and investment – swindle the relatively vulnerable holders of cash, receivables, and fixedfee jobs, while artificially inflating prices in the primary operative circuits producing goods and services and in the secondary markets, which merely exchange titles of ownership of stocks, bonds, real estate, art. In these secondary markets, an exchange of, say, one million previouslyissued shares of General Motors does not produce a single automobile.
If inflation – caused by too much money chasing too few goods in the operative circuits – appeared, it could be cured by an adjustment of incomes, whether operationally in the private sector or operationally and by transfer payments by the government sector.
There would be, for instance, a radical maladjustment between circuit and productive acceleration if, when surplus rates of production were increasing more rapidly than basic, basic rates of income were increasing more rapidly than surplus. Then interval after interval, an increasingly excessive amount of monetary income would be moving to the basic final market, and there would follow a rise in prices quite different in kind from the normal rise resulting from increasing scarcity. Such a rise would not be an ordinary scarcity but at once a consequence and, as will appear, a corrective of disproportion between monetary and real consumer income. ¶ Not only is it true that this second type of price variation is different from the first, but also one must give it a different kind of attention. When prices rise because of real scarcity, one may speak of a requirement for variation in E’ and E” over and above the variation postulated by dQ’/Q’ and dQ”/Q”. But when prices rise or fall because the distribution of income has not anticipated these requirements correctly, then price variation is not a postulate for variation in E’ and E” but rather a spontaneous effort at adjusting what should already have been adjusted. Accordingly, such adjustment variations in prices will be ignored for the moment to be considered more in detail in the next section (entitled The Cycle of Basic Income). (CWL 15, 131)
Lonergan addresses the problem of inflation in a nuanced expansion of the productive process in phases. And he treats the ineptitude of manipulation of interest rates. The central adjustment to the disequilibria of inflationand deflation is not the manipulation of interest rates, rather it is variation of the rate of consuming vs. saving for investment, i.e. the adjustment of the distribution of incomes for that consumption or investment.
The purpose of this section is to inquire into the manner in which the rate of saving W is adjusted to the phases of the pure cycle of the productive process. Traditional theory looked to shifting interest rates to provide suitable adjustment. In the main we shall be concerned with factors that are prior to changing interest rates and more effective. [CWL 15, 133]
Recall that Outlays are normatively concomitant with Expenditures, and Incomes are normatively concomitant with both Outlays and Expenditures. So, to speak of a corrective adjustment of specific class of Incomes is to speak of a concomitant adjustment of specific class of Outlays and a specific class of Expenditures.
The central adjustment is variation in the rate of saving. This rate may be defined, conveniently for present purposes, as the ratio of surplus income to total income. Assuming that the rate of saving will not differ appreciably because income is derived from basic or surplus outlay, we may denote this rate by the symbol w, so that
w = I”/I’ + I” (CWL 15, 13132)
Basic income and the average propensity to purchase pointtopoint “basic” products is expressed well by a stratification of incomes:
I’ = Σw_{i}n_{i}y_{i} (35) [CWL 15, 134]
The adjustment of basic incomes to cure inflation or deflation is
dI’ = Σ(w_{i}dn_{i} + n_{i}dw_{i})y_{i} (36) [CWL 15, 134].
Evidently, then, suitable migrations are a means of providing adjustments in the community’s rate of saving. To increase the rate of saving (for expansionary investment), increase the income of the rich. … to decrease the rate of saving (to expand consumption and fully utilize new capital providing greater capacity for production and a more abundant standard of living), increase the income of the poor. … The foregoing is the fundamental modeof adjusting the rate of saving to the phases of the productive cycle. It reveals that the surplus expansion is antiegalitarian, inasmuch as that expansion postulates that increments in income go to high incomes. But it also reveals the basic expansion to be egalitarian, for that expansion postulates that increments go to low incomes [CWL 15, 13537]
For further elaboration, see in Table of Topics on the Home Page the following entries on the website:
Facing Facts: The Ideal of Constant Value vs. the Fact of Inflation
Revison of the NIPA Into Explanatory Form
*Revision of the NIPA into Explanatory Form
Notes Regarding FRB Monetary Policy and a Theoretic of Credit
*Notes Regarding FRB Monetary Policy and a Theoretic of Credit
*Money: Notes on the Nature and Purpose of Money
Our culture does not grasp the relativistic, fieldtheoretic basis of functional basic income, functional pure surplus income, magnitudes and frequencies of turnovers, the velocity of money, etc. It has not an understanding of the framework of the Diagram of Rates of Flow.
Now it is true that our culture cannot be accused of mistaken ideas on pure surplus income as it has been defined in this essay; for on that precise topic it has . … there exists, in the mentality of our culture, no ideas, and in the procedures of our economies, no mechanisms, directed to smoothly and equitably bringing about the reversal of net aggregate savings to zero as the basic expansion proceeds. (CWL 15, 153)
The subtitle of CWL 15 is “An Essay in Circulation Analysis.” Lonergan typically makes the reader focus on the real productive process, its concomitant circulations of money, its implied condition of equilibrium, its classes of initial, transitional, and final payments, and nonoperative payments of Smith to Jones.
Insert Diagram
In the third place, it will be best to consider financial operations, that is any exchange in which a sum of money is paid for a sum of money to be received. Now either the two sums of money are equal, or else one is greater than the other. If the two are equal, the transaction is purely redistributive. If one is greater than the other, then, generally speaking, the difference is the payment for a service of some specific type; rendering such service is as much a part of current production as rendering any other service, while the payment will be divided up, perhaps among different entrepreneurial units, and commonly the initial payments of wages, salaries, rents, dividends, reserve funds, and so forth. In other words, financial operations are partly redistributive payments and partly payments for services rendered; thus in banking, payments of principal are redistributive, but payments of interest are operative, with interest paid to the banks as a final operative payment (for their services) and interest paid by the banks to depositors an initial operative payment; again, in insurance the payment of policies isredistributive, but the payment of premiums on policies is partly redistributive and partly operative; it is redistributive to the extent it balances the payment of policies; and it is (a final operative payment) to the extent it pays insurance companies for their services. (CWL 15, 4445)
Lonergan argued that previous depressions could be understood in terms of a tendency by producerbanker combinations with price fixing powers to hang onto the K^{N} accumulation profit cum interest rather than raise wages, even after the economy was tooled up to the requirements of the new stationary state. Peter Burley and Laszlo Csapo, Money Information in Lonerganvon Neumann Systems, Economic Systems Research, vol. 4, No. 2, 1992 p. 139
One could rework the calculations of this paper replacing the c by s>c, where sc would correspond to goods and money taken outside our equilibrium relative price and production model via an exogenous interest rate ‘ claimed by the bankerproducer combination….Then the endogenous growth and interest rate…falls to
r=i={k(k’d’1)s[(k’d’1)l+dl’]}/{k+s[(k’d’2)+(1+d)l}
This would become negative if c corresponded to the stationary state values of r=i=0. The relative price and activity vectors would then become
y_{i}=Y[k’d’1i, l’s(1+i)](1=i)^{Ht}
x_{i}=X(k’d’1r, d+r)(1=r)^{t}
This ongoing growth in unemployment would seem important to note in a world of high interest debt problems….it would seem important for analysis to be clear about the growing cost of an ongoing extraction of surpluses when living standards of employed workers are downward rigid. Peter Burley and Laszlo Csapo, Money Information in Lonerganvon Neumann Systems, Economic Systems Research, vol. 4, No. 2, 1992 pp.139ff
When the proper action for the Fed to take – e.g. add to or withdraw money in the system only in conformity to the requirements of the magnitudes and frequencies of current transactions – the Fed must, rather than bow to a reelectiondespitetheoreticalignoranceandcommonsensemessups Congress, make itself unpopular to the legislative and executive branches and force both branches to obey the principles and laws of scientific macroeconomics and, so, effect a balanced budget. The Fed must not effect either or both of a harmful money supply or a harmful price of money (interest rate) just to please those seeking reelection and glory. The Fed must be independent rather than in obeisance. It must announce to ignorants in the government that the mandate for full employment should be directed to the private and government sectors, not to the issuer of dummy money and wise regulator of the banking system.
We refer the reader to CWL 15, Section 20 “Misadventures”, where Lonergan addresses aspects of the subject of ineffective basic demand arising from the failure of a) academe to understand and communicate economic science, and b) the enlightened private and government sectors to effect a balanced budget, for which the economic process has an exigence. The private and government sectors must implement the basic expansion. Lonergan treats a “series of palliatives that, in one way or another, divert attention away from the ineffective demand for basic goods and services and, at times, mitigate it.” In “Misadventures” he briefly critiques – from a strictly, strictly, strictly economic point of view of normativelybalanced flows in a wellmanaged economy – the economic similarity in
 Foreign trade surpluses
 Anticipated and actual warfare
 Socalled wars on illiteracy, on poverty, on ill health, on unemployment, on insecurity
Now this type of surplus is not confined to warlike concerns. Once the possibility of an unbalanced budget is established, the precedent can be invoked to persuade politicians to carry on other wars: wars on illiteracy, on poverty, on ill health, on unemployment, on insecurity. Where the profit motive does not prove efficacious, the state must intervene. … the increasing volume of transactions requires a larger money supply, and the central bank can be persuaded to meet the demand. … it appears to be less evident that a vicious circle of ever more demands for a larger money supply with no increase in real income is inflationary … In any case there has emerged in fact if not in name the welfare state. … Its mechanism is rather strikingly similar to that of the favorable balance of foreign trade. The debt once owed by colonies to richer countries now is replaced by the national debt. … now the long overdue basic expansion is doled out to one’s fellow countrymen under the haughty name of welfare. [CWL 15, 8586]
A final note: As everyone who has worked on the timevalue of money knows and as Lonergan points out, the interest rate has different effects on short vs. longterm projects.
The effect of rising interest rates on turnover magnitudes depends upon the turnover frequency of the enterprise. (In simple terms,) if the frequency is once every two years, 1% increase in the rate of interest is a 2% increase in costs; if the frequency is once every month, 1% increase in the rate of interest is 1/12 of 1% increase in costs. (CWL 15, 143)
See
Malkiel, Burton Gordon (1962). “Expectations, Bond Prices, and the Term Structure of Interest Rates”. The Quarterly Journal of Economics.
.13. The Isomorphism of the abstract, classical formulation of the economic process with the patterns grasped in the correlations of data. The isomorphism is explanatory of and “true to” the immanent intelligibility of the dynamic system
The mathematical explanation of the objective, dynamical, economic process is constituted by a) terms whose meanings are fixed by their functional relations, b) relations which are fixed by the terms, and thus c) terms and meanings which are both fixed by conceptconnecting insight. As in other sciences, the terms are implicitly defined by their relations to one another. The formalisms are abstract and the explanatory meanings of their terms (explanatory conjugates) are, in the manner of Hilbert, implicitly determined by their functional relations to one another.
Rather than descriptive terms describing relations to us in our concrete experience, the functionallydefined terms qualify as explanatory conjugates to explain by their relations an isomorphic process of functional relations.
The formulation of the explanation will be isomorphic with the patterns in the data of the measurements of the constituent interdependent, mutually conditioning, mutually defining functional velocities and accelerations. It will express combinations of combinations and correlations of correlations. Insight into macoeconomics’ functional interrelations finds its adequate expression in an abstract formulation. The terms and relations can be set in a mathematical form which is isomorphic with, and thus, faithfully represents, nd fully explains, the interrelations of the concrete economic process.
Again, to take perhaps a simpler and more familiar example, if someone is doing physics and you open his book, what do you find? You find just mathematical equations. He is solving problems, and what is it? It is more mathematics.
Why do you say he is doing physics? He seems to be doing mathematics all the time. It is because there are regions of mathematics that are isomorphic with physical reality. There is the same relational structurebetween a given mathematical theory or system as there is between events that can be observed. This is another case, a big case, of isomorphism: on the one hand, mathematical expressions, and on the other hand, physical events. There is the same relational structure. But in the mathematical case, the relational structure links symbolic expressions, or mathematical concepts, with one another, while in the physical case what are related are concrete physical events, wave lengths that you observe through a machine and so on. ¶ So there is an isomorphism of geometry, algebra, physics; the same relational structure can be found in all three. Consequently, one’s symbolism can be given a geometrical interpretation, or an algebraic interpretation, or a physical interpretation. [CWL 18, 3233]
In the following we have paraphrased, and we have substituted “macroeconomics” and “economics” for “physics” and “macroeconomic” and “economic” for “physical.” We thereby gain a good idea of Lonergan’s dynamic heuristic.
… if someone has a scientific, dynamic heuristic in is doing macroeconomics and you open his book, what do you find? You find just mathematical equations. He is solving problems, and what is it? It is more mathematics. Why do you say he is doing macroeconomics? He seems to be doing mathematics all the time. It is because there are regions of mathematics that are isomorphic with macrodynamic reality. There is the same relational structure between a given mathematical theory or system as there is between macroeconomic functionings that can be observed. This is another case, a big case, of isomorphism: on the one hand, mathematical expressions, and on the other hand, interdependent, mutually defining macroeconomic functionings. There is the same relational structure. But in the mathematical case, the relational structure links symbolic expressions, or mathematical concepts, with one another, while in the macroeconomics case what are related are concrete, interdependent, dynamic, macroeconomic functionings. ¶ So there is an isomorphism [Paraphrase of CWL 18, 3233]
… just as a mathematical equation may be said to be the most adequate expression of purely intelligible relations among explanatory termsin certain instances – for example, Einstein’s gravitational field tensor equations – something closely akin to Lonergan’s diagram (and the equations it represents) 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 commonsense 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]
… The mathematical meaning of an expression resides in the distinction between constants and variables and in the sign or collocations that dictate operations of combining, multiplying, summing, differentiating, integrating, and so forth. It follows that, as long as the symbolic pattern of a mathematical expression is unchanged, it’s mathematical meaning is unchanged. Further, it follows that if a symbolic pattern is unchanged by any substitutions of a determinate group, then the mathematical meaning of the pattern is independent of the meaning of the substitutions. [CWL 3, 1819/43]
Mathematical symbolism of constants, variables, operators and their collocations is, of course, different from poetic symbolism or the psychological symbolism of feelings, emotions, and dreams. Paraphrasing the first excerpt above, we have substituted “macroeconomics” and “economics” for “physics” and “macroeconomic” and “economic” for “physical.” We thereby gain a good idea of Lonergan’s dynamic heuristic and of the scientificnessof Functional Macroeconomic dynamics.
.14. Real Analysis of the economic process understands production and exchange of goods and services as primal and treats money as a functional dummy invented by humans to make possible and to lubricate a vast and intricate process rather than as a material commodity to be hoarded
Functional Macroeconomic Dynamics is explanatory rather than descriptive. Its basic terms are velocities of explanatory functionings. Its basic terms are classes of velocitous functional flows of products; these functional flows are mutually defined by the functional relations in which they stand with one another. The explanatory conjugates are purely relational – implicitly defined by their functional relations of interdependence with one another – and the theory is a field theory of explanatory functional relations among n objects. In a system of flows – such as the flows of products and payments — scientific and explanatory analysis is in terms of the relations of these flows to one another. Unexplained external price shifts, such as those given primacy by the ISLM and ADAS models, are not the primary analyzand. And pretioquantital Incomes and Expenditures must be interpreted in the light of the primal relations of the interdependent explanatory flows which they compose.
… real analysis (is) identifying money with what money buys. … 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, Editors’ Introduction, xxviii quoting Lonergan]
… money is an instrument invented to fulfill a definite task; it is not the ultimate master of the situation. … Accordingly money has to conform to the objective exigencies of the economic process, and not vice versa. (CWL 21, 101)
Criticism requires sound premises and verified theory.
A study of the mechanics of motorcars yields premises for a criticism of drivers, precisely because the motorcars, as distinct from the drivers, have laws of their own which drivers must respect. But if the mechanics of motors included, in a single piece, the anthropology of drivers, criticism could be no more than haphazard. (CWL 21, 109)
Similarly
A study of the mechanisms of macroeconomic dynamics yields premises for a criticism of efficientcausal human participants, precisely because the macroeconomic system, as distinct from the participants, has laws of iys own which participants must respect. But if the mechanisms of macroeconomic dynamics included, in a single piece, the anthropology of participants, criticism could be no more than haphazard. (paraphrase of CWL 21, 109)
Money is understood as a dummy invented by humans to enable a vast and intricate exchange process; it greases the process; it enables divided exchange – producing this here and buying that there.
the necessary and sufficient condition of constant value in the dummy lies in its concomitant variation with the real flow. (CWL 21, 3839)
Money is not a commodity to be hoarded. The everyday concrete economic process consists of velocitous concrete production and exchange of concrete goods and services for money. Money is a fellowtraveler – a correlative and a concomitant – in the primary process of production and sale. The abstract intelligibility of velocitous production and sale is the primary fundamental analyzand. And money plays the role of a dummy invented by humans to enable and grease the divided exchanges in the large, aggregated, complex, productionandexchange process.
It is now necessary to state the necessary and sufficient condition of constancy or variation in the exchange value of the dummy. To this end we compare two flows of the circulation: the real flow of property, goods, and services, and the dummy flow being given and taken in exchange for the real flow….Accordingly, the necessary and sufficient condition of constant value in the dummy lies in its concomitant variation with the real flow. (CWL 21, 3839)
The real flows are flows of goods and services which underlie the flow of dummy money payments. Again,
… real analysis (is) identifying money with what money buys. … 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, Editors’ Introduction, xxviii quoting Lonergan]
Ideally the dummy money would be constant in exchange value. If its value is not as, ideally, it “must” be, then it constitutes inflation or deflation, both of which are swindles.
… the dummy must be constant in exchange value, so that equal quantities continue to exchange, in the general case, for equal quantities of goods and services. The alternative to constant value in the dummy is the alternative of inflation and deflation. Of these famous twins, inflation swindles those with cash to enrich those with property or debts, while deflation swindles those with property or debts to enrich those with cash; in addition to the swindle each of these twins has his own way of torturing the dynamic flows; deflation gives producers a steady stream of losses; inflation yields a steady stream of gains to give production a druglike stimulus. [CWL 21, 3738]
In seeking to understand the economic process, one must be constantly aware of the difference between the scientific vs. the symbolic way of knowing. In doing macroeconomic dynamics one must intend science, not emotional symbol and mythmaking.
No less than scientific language, symbolic language intends a truth yet can be wrong. Just as there are truths known scientifically, so also are there truths communicated symbolically; and just as there are scientific opinions that have long been totally abandoned, so also are there myths … things have only one way of being, but humans do not have only one way of knowing. One who knows scientifically knows universally; but this universality does not belong to things (as if universals subsisted) but to the scientific way of knowing. One who apprehends and speaks symbolically is using a way of knowing that is full of vivid imagery and feeling, but nevertheless by reflecting one can distinguish between what are to be attributed to the things themselves and what are to be ascribed to this way of knowing. (CWL 11, 381)
.15. The central condition of equilibrium between circulations in two circuits, and the necessity of enlightened selfinterest to guide exchanges
The equilibrium between distinct but interdependent circulations of payments has a partial resemblance to the equilibrium in fluid dynamics. The condition of equilibrium is represented in the doublecircuited, creditcentered Diagram of Rates of Flow. Based upon the principles of organicconcomitance and implicit definition, there is discovered a solidary, organic, macroeconomic system, with an exigence for equilibrium formulated as the balance of the crossovers.
G = c”O” – i’O’ = 0 (CWL 15, 5355)
In a stationary economy, one without innovation or development, the crossovers balance when allowances are made for seasonal and minor fluctuations. In that state, the crossovers are, of course constant. But in a surge the crossovers vary, and the problem of macrodynamic equilibrium is that the crossovers must remain dynamically balanced. If they do not remain so, then one circuit is being drained in a way that might seem to benefit the other. [McShane, 2017, 69]
Insert Diagram
Adjustments are required as the economic process advances in phases from an initial stationary state of production and leisure to a more bountiful, higher stationary state of production and leisure. Lonergan treats the cycles of basic and surplus incomes and investments in the transitional phases constituting the longterm cycle of expansion. See in Sections 268 of CWL 15: The Cycle of Basic Income (pp. 133 ff.); The Cycle of Pure Surplus Income (pp 144 ff.); The Cycle of the Aggregate Basic Price Spread. (pp. 136 ff.)
Lonergan’s “Summary of the Argument” adumbrates the systematics of monetary circulations and the necessity of enlightened selfinterest:
The present inquiry is concerned with relations between the productive process and the monetary circulation. It will be shown 1) that the acceleration of the process postulates modifications in the circulation, 2) that there exist ‘systematic,’ as opposed to, windfall profits, 3) that systematic profits increase in the earlier stages of longterm accelerations but revert to zero in later stages – a phenomenon underlying the variations in marginal efficiency of capital of Keynesian General Theory, 4) that the increase and decrease of systematic profits necessitate corresponding changes in subordinate rates of spending – a correlation underlying the significance of the Keynesian propensity to consume, … From the premises and conclusions of this analysis it will the be argued 9) that prices can not be regarded (by the stewards of the economy) as ultimate norms guiding strategic economic decisions, 10) that the function of prices is merely to provide a mechanism for overcoming the divergence of strategically indifferent decisions or preferences, and 11) that, since not all decisions and preferences possess this indifference, the exchange economy is confronted with the dilemma either of eliminating itself by suppressing the freedom of exchange or of certain classes of exchanges, or else of effectively augmenting the enlightenment of the enlightened selfinterest that guides exchanges. [CWL 15, 56]
As items 1) – 4) above affirm, in an intelligentlymonitored and properly managed economy, the ratio of rates of flows of “basic incomes” for consumption and “surplus incomes” for investment require active modification or rebalancing. Note that, since certain classes of Outlays, Incomes, Expenditures, and Receipts are concomitant with one another, to speak explicitly of only one of the four aspects is to speak implicitly of the other three.
The central adjustment is variation in the rate of saving. This rate may be defined, conveniently for present purposes, as the ratio of surplus income to total income. Assuming that the rate of saving will not differ appreciably because income is derived from basic or surplus outlay, we may denote this rate by the symbol w, so that
w = I”/I’ + I” (CWL 15, 13132)
… without further clarification Schumpeter acknowledged that dynamic analysis called for a new light on equilibrium. Such new light arises when, over and above (DSGE’s) equilibria of supply and demand with respect to goods and services (in classical MACROeconomics), there are recognized further equilibria (crossovers in balance between circuits, and concomitance of outlays with income and of income with both Outlays and Expenditures in each circuit) that have to be maintained if an economy chooses to remain in a stationary state, to embark on a longterm expansion, to distribute its benefits to the vast majority of its members, and so to return to a more affluent stationary state until such further time as further expansion beckons. … Moreover, such macroequilibria are more fundamental than the microequilibria assembled by Walras. (FMD’s macroequilibria) are the conditions of a properly functioning economy. (CWL 15, 92)
And the condition of equilibrium is
G = c”O” – i’O’ = 0 (CWL 15, 5355)
.16. The deficient efficientcause macrostatic vs. the formal cause or immanent intelligibility
Functional Macroeconomic dynamics is also called Macroeconomic Field Theory. Textbook macroeconomics is primarily an efficientcause theory of prices, their action, and the reaction evoked by action.
Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumental, material, or final causes of events, but with the intelligibility immanent in data; but Newtonian dynamics seems primarily a theory of efficient causes, of forces, their action, and the reaction evoked by action. … [3, 43/67]
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 another, might be named more briefly formal causality… [CWL 3, 78/101102]
our inquiry differs radically from traditional economics, in which the ultimate premises are not production and exchange but rather exchange and selfinterest, 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]
Lonergan’s intention was ‘to formulate the laws of an economic mechanism more remote and, in a sense, more fundamental than the pricing system…laws which men themselves administrate in the personal conduct of their lives. In 1978 he began to refer to Nicholas Kaldor in support of his judgment that the significance traditionally accorded to price theory by conventional economics since Adam Smith’s Wealth of Nations (1776) amounted to a virtual derailment of economic theory……….Lonergan’s interest in Kaldor’s sweeping statement was to emphasize that prices and their changes are not explanatory but accountants’ entities………Lonergan insists that the mechanism of the pricing system does not furnish economists with distinctions among significant variables of aggregate surplus (or producergoods) and basic (or consumergoods) supply and demand with their determinate yet flexible velocities and accelerations, 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…….the lack of ultimacy that Lonergan ascribes to prices and price theory can scarcely be overemphasized. (CWL 15, Editors Introduction, xlvixlvi )
Private and government criteria, policies, and activities are the ignorant efficient causes, from, so to speak, outside the formal process. In a doublecircuited expansionary economic process, the flows of basic and surplus incomes and the ratio of each to the other and of each to total deserves careful scrutiny.
The flow of income in a functional analysis, however, requires somewhat more attention: it is the corner of the analysis which holds the key to the sublation both of Keynes’ problems of consumption, savings and investments, and of Kalecki’s dictum that the workers spend what they get and the capitalists get what they spend. [McShane 1980, 120]
Macroeconomists in academia, at the Bureau of Economic Analysis, and at the Federal Reserve Board mistakenly ground explanation of the objective economic process upon psychic elements – such as utility, time preference, expectations, hunches about the effectiveness of interest rate manipulations, which are, as it were, external to the immanent formalintelligibility of the objective process as a unitary pointtopoint and pointtoline system of circulations – solidary with one another – of production and exchange.
… real analysis (is) identifying money with what money buys. … 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, Editors’ Introduction, xxviii quoting Lonergan]
A study of the mechanics of motorcars yields premises for a criticism of drivers, precisely because the motorcars, as distinct from the drivers, have laws of their own which drivers must respect. But if the mechanics of motorsincluded, in a single piece, the anthropology of drivers, criticism could be no more than haphazard. CWL 21, 109
The psyche of the human driver is not the immanent intelligibility of the thing called an automobile; the psyche of the switcher is not the immanent intelligibility of the the electric circuit. The psyche of the operator is not the immanent intelligibility of the objective hydrodynamic system. Functional Macroeconomic Dynamics drops the notion of psychic motive and consequent efficient cause; it gets along perfectly well without it. It thinks in terms of a field theory, the set of internal relationships among the n interdependent, implicitlydefined, objective functionings which constitute the process. The field theory of Functional Macroeconomic Dynamics explains the objective process prior to its being operated. Functional Macroeconomic Dynamics is a set of intelligible functional relations linking interdependent functionings which are implicitly defined by their functional relations of immanent functioning among themselves; it is a set of relational forms. The form of any inner functioning is known through its relations to all other inner functionings, rather than being known through its relation to an external and psychological efficient cause. …. The field theory of macroeconomics is a matter of the immanent intelligibility of the objective, dynamic functional process.
Taking into account past and (expected) future values does not constitute the creative key transition to dynamics. Those familiar with elementary statics and dynamics will appreciate the shift in thinking involved in passing from (static) equilibrium analysis … to an analysis where attention is focused on secondorder differential equations, on d^{2}θ/dt^{2}, d^{2}x/dt^{2}, d^{2}y/dt^{2}, on the primary relativities of a range of related forces, central, friction, whatever. Particular secondary boundary conditions, past and future pricings and quantities, are relatively insignificant for the analysis of the primary relativity immanent in, and applicable to, every instance of the process. What is significant is the LeibnitzNewtonian shift of context. [McShane, 1980, 127]
… It will be well at once to draw attention to J.A. Schumpeter’s insistence on the merits of the diagram as a tool. (Schumpeter, History 24043, on the CantillonQuesnay tableau.) … First, there is the tremendous simplification it effects. From millions of exchanges one advances to precise aggregates, relatively few in number, and hence easy to follow up and handle. … Next come the possibilities of advancing to numerical theory. In this respect, despite profound differences in their respective achievements, the contemporary work of Leontieff may be viewed as a revival of Francois Quesnay’s tableau economique. Most important is the fact that this procedure was the first to make explicit the concept of economic equilibrium. All science begins from particular correlations, but the key discovery is the interdependence of the whole.… While it is true that a tableau or diagram cannot establish the uniqueness of a system or rigorously ground its universal relevance, it remains that the diagram (of the interconnections of a few precise aggregates) has compensating features that Quesnay’s system of simultaneous equations may imply but does not manifest. … There is the tremendous simplification (a diagram) effects. The aims and limitations of macroeconomics make the use of a diagram particularly helpful, … For its basic terms are defined by their functional relations. The maintaining of a standard of living (distinct process 1) is attributed to a basic process, an ongoing sequence of instances of so much every so often. The maintenance and acceleration (distinct process 2) of this basic process is brought about by a sequence of surplus stages, in which each lower stage is maintained and accelerated by the next higher. Finally, transactions that do no more than transfer titles to ownership (distinct process 3) are concentrated in a redistributive function, whence may be derived changes in the stock of money dictated by the acceleration (positive or negative) in the basic and surplus stages of the process. … So there is to be discerned a threefold process in which a basic stage is maintained and accelerated by a series of surplus stages, while the needed additions to or subtractions from the stock of money in these processes is derived from the redistributive area. … it will be possible to distinguish stable and unstable combinations and sequences of rates in the three main areas and so gain some insight into the longstanding recurrence of crises in the modern expanding economy. [CWL 15, 53 and 177] [#66]
While we agree with Schumpeter that Walras’s system implicitly includes the aggregates commonly considered in macroanalysis, (Walras’s system) can hardly be credited with distinctions between basic and surplus Expenditure, Receipts, Outlay, Income, and much less with an account of their various dynamic relations. But until such distinctions are drawn and their dynamic significance understood, the aggregates and relations cannot be contained implicitly in any (explanatory) system. [CWL 15, 9192]
.17. Circulations in circuits; Costs and Expenditures are Implicitly Defined P’Q’ = p’a’Q’ + p”a” Q”. (CWL 15, 15659)
Basic Expenditures are equal to Macroeconomic Costs, as both are defined below; and Basic Incomes for Expenditures are generated as the obverse of Macroeconomic Costs.
P’Q’ = p’a’Q’ + p”a” Q”. (CWL 15, 15659)
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’ = p’a’Q’) and (c”O” = p”a”Q”) as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. [CWL 15, 15657]
P’Q’ = p’a’Q’ + p”a” Q”. (CWL 15, 15659)
P’/p’ = a’ + a”(p”Q”/p’Q’)
Or, utilizing the symbols J and R,
 J = a’ + a”R
 dJ = da” + Rda” + a”dR
 da’ = a’(dq’/q’ – dQ’/Q’
And, by changing (’) to (”) one has the parallel equation for da”.
.18. The abstract meaning of credit to explain the implementation of the “quasiphysical” potential increased by invention and innovation, first, into the wideninganddeepening kinesis of surplus production, and subsequently, into the accelerated kinesis of basic production.
The proper role of credit is to bridge the gap in time between payments made and payments received. Just as inflation may be explained as normally caused by scarcity or as abnormally caused by failure to anticipate the need for higher incomes balancing higher production, so credit may exist properly in the proper amount according to the requirements of economic expansion or improperly in the improper amount in the case of irresponsible lendingborrowing in a boom.
We have treated the subject of credit elsewhere on this website, and we direct the reader to those treatments:
*Notes Regarding FRB Monetary Policy and a Theoretic of Credit
 Re Correcting Excess Investment and Inadequate Demand
 The Financial Problem: Supplying the Money Needed for Transactions
 Towards a Theoretic of Credit; How Money Should enter and Circulate Within the System
 Preliminary Guidance
 The Broad Context of Interest Rates
 Credit Money and its Circulation; the Return OF Investment
 Interest Payments and Their Circulation
 Equations for Expansion
 The Formal Cause
 Circulating Principal as Intrinsic to the Process
 Price Changes: Real and Relative vs.Monetary and Absolute
 Circular Return: Intrinsic, Inevitable, and Good
 The General Governs the Particular Generally
 Interest Rate Changes Are DoubleEdged; Manipulation is Inept
 General and Concluding Remarks
 Burley’s Evolutionary Model
*Money: Notes on the Nature and Purpose of Money
 The Nature and Purpose of Money
 Fiat Money as a Promise to Pay
 The Norms Guiding the Flows of Money
 The Norms Guiding the Creation of Money
 Contra the Gold Standard
 Money, the Stock Market and the Bifurcation of Purchasing Power
 Burley’s Essays (in Money: Notes on its Nature and Purchase)
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The serious reader of CWL 15 is by now familiar with the following three equations; he can understand the second in light of the first; and he can grasp in the third their combination in Gross Domestic Functional Flows.
P’Q’ = p’a’Q’ + p”a”Q”_{Basic R&M }(CWL 15, 15662)
Π”Κ”=π”α”Κ”_{Pure expansionary surplus}+ π”α”Κ”_{R&M to self}
GDFF = P’Q’ + Π”Κ”= p’a’Q’ + p”a”Q”_{Basic R&M }+ π”α”Κ”_{Pure expansionary surplus}+ π”α”Κ”_{Surplus R&M costs to self}
Prior to scrutinizing our revision of the NIPAs, the reader is encouraged to review CWL 15, 535.
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So, we have for primary normative monetary circulations in the two circuits of the Diagram, assuming
 that all expansionary money enters the system through Supply (S’s’O’) and (S”s”O”),
 that “the variables O’, O”, I’, and I” are to be regarded as aggregates that are ‘completed’ only after all redistributive transactions have been taken into account” (CWL 15, 200), and
 (D’s’I’) and (D”s”I”) equal zero because we are prescinding here from CWL 15, 64’s “theory of booms and slumps.”
The elements of the fieldtheoretic circulations:
 R’ = E’ (CWL 15, 54) Receipts and Expenditures are two elements of the same transaction
 R” = E” (CWL 15, 54)
 I’ = O’ + M’ (CWL 15, 54)
 I” = O” + M” (CWL 15, 54)
 G = c”O” – i’O’ (CWL 15, 54) Monetary transfers between the two circuits
 G = c”O” – i’O’ = 0 (CWL 16, 50) The condition of dynamic equilibrium of 2 circuits
 M’ = (S’ – s’O’) + (D’ – s’I’) + G (CWL 15, 54) Net basic monetary dealings w R function and G
 M” = (S” – s”O”) + (D” – s”I”) – G (CWL 15, 54)
 (S’s’O’) = ΔT’ + (O’ – R’) + ΔR’ (CWL 16, 67) Micro basis of monetary transfers to supply
 (S” s”O”) = ΔT” + (O” – R”) + ΔR” (CWL 16, 67)
Thus, for example, assuming that the crossovers balance so as to satisfy the condition of dynamic equilibrium, G = c”O” – i’O’ = 0, by the principle of concomitance and the role of credit to bridge brief time gaps, we would have for the basic circuit (denoted by single superscripts):
 P’Q’: R’ = E’ = I’ = O’ +M’ (CWL 15, 54)
 P’Q’: R’ = E’ = I’ = O’ +[S’ – s’O’] + [D’ – s’I’] (CWL 15, 54)
 P’Q’: R’ = E’ = I’ = O’ + [ΔT’ + (O’ – R’) + ΔR’] + [D’ – s’I’] (CWL 15, 54, and 6667)
Similarly, by changing the basic circuit’s single superscript (‘) to the surplus circuit’s double superscript (“), we would have for the surplus circuit:
 Π”Κ”: R” = E” = I” = O” +M” (CWL 15, 54)
 Π”Κ”: R” = E” = I” = O” +[S”’ – s”O”] + [D” – s”I”] (CWL 15, 54)
 Π”Κ”: R” = E” = I” = O” + [ΔT” + (O” – R”) + ΔR”’] + [D” – s”I”] (CWL 15, 54, and 6667)
More simply, we consider final Gross Domestic Explanatory Pretioquantital Functional Flows (GDEPQFF) in a stable (“static nonexpanding”) economy, fully funded so as to not require flows to or from the Redistributive Function, and explained in terms of functional Expenditures and Outlays rather than described by GDP.
GDEPQFF = P’Q’ + Π”Κ”
GDEPQFF = P’Q’ + Π”Κ”= p’a’Q’ + p”a”Q”_{Basic R&M }+ π”α”Κ”_{Pure expansionary surplus}+ π”α”Κ”_{Surplus R&M costs to self}
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But, in general, we are not dealing with a stable, static, nongrowing economy; and our focus is credit as an explanatory conjugate. One must distinguish a) the rate of interest charged by lending banks in the operative circuits from b) the stock and bond markets’ riskladen rate of return, from c) the theoretical rate of interest identical to the anticipated rate of growth. (See, for example, Burley Burley, Peter (1992) Evolutionary von Neumann Models, Journal of Evolutionary Economics 2 , 26980 [Burley, 19922]
Burley, Peter (2002), Lonergan and Interest Rates, Australian Lonergan Workshop 2, ed. Matthew C. Ogilvie and William J. Danaher, Sydney: Novum Organum 6167 [Burley, 20022] )
In practice all maturitized rates may differ, depending upon the money supply and the money demand in different arenas. A flood of stimulus money which winds up in the secondary stock and bond markets when capacity is not fully utilized and there is, thus, no need to borrow for expansion or improvement is intrinsically inflationary and will eventually constitute an inflationary force.
One may object that, if the principle of “concomitance” is valid, the four aspects of the supplydemand monetary circulation – OutlaysIncomes, ExpendituresReceipts – must go together of flow simultaneously.
A condition of circuit acceleration was seen in Section 15 to include the keeping in step of basic outlay, basic income, and basic expenditure, and on the other hand, the keeping in step of surplus outlay, surplus income, and surplus expenditure. Any of these rates may begin to vary independently of the others, and adjustment of the others may lag. But any systematic divergence brings automatic correctives to work. 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]
However, in reply, Concomitance is a principle of organization and theoretical togetherness; it is not a strict temporal simultaneity; it is a theoretic and explanatory coordination comprised of existing dummy moneypluscredit associated functionally with what can be, and is, bought. A constituent of actual concomitance is credit, whose purpose is to bridge the gap between payments made and payments received in both the shorterterm inventory turns and the longerterm projects of capital expansion.(Click here.)
In placing OI production principally prior to ER sale. (See Appendix to Section 15, CWL 15, 6570)
To study the exchange equilibrium it is necessary to introduce a system of reference, a method of listing the different funds or accumulations that are standing in equilibrium. … Such a system may be any degree of generality. The absolute minimum of generality would be to list all the individual persons, firms, banking institutions, etc. that possessed funds. Such a procedure would be very thorough, but it would not be science, for science is of the general and it is guided not by quantitative considerations but by the selection of significant differences. … Let us define a balance as a sum of money or credit held in view of some definite purpose or indefinite eventuality. Then, from the viewpoint of our analysis, there exist five types, and so five aggregates, of balances. … First there are redistributional balances (like) the reserves assuring the liquidity of banks, insurance companies, underwriters, dealers in stocks and bonds, and the accumulations for the purchase of land, used capital equipment, and secondhand products such as houses, used motorcars, and the like. … Second and third, there are trader balances … to bridge the gap between the initiation of his turnover and its completion: he has to purchase materials, pay wages, and it is only when he has sold his product that the monetary return of his outlay begins. To bridge this gap he must have circulating capital. (Thus we have) primary (basic) trader balances and secondary (surplus) trader balances. Fourth and fifth there are primary consumer balances and secondary consumer balances. On the principle of equilibrium, defined in the preceding section, there must be in the general case an equilibrium between movements into each of these and movements out to all the others. [CWL 21, 5859]
Further, the government ‘s elected and appointed officials effecting of selfaggrandizement, economic waste, and chickenhearted low taxation posses a particular problem.
https://functionalmacroeconomics.com/2021/11/06/aviciouscircle/
Deficit spending arises when government expenditure exceeds its revenues. It may be represented by payments made to the circuits from the redistributional area in excess of payments made from the circuits to the redistributional area. [CWL 15, 17374]
An existing money supply should be being correctly monitored and calibrated according to the magnitudes and frequencies of the current dynamic process, and fully Outlaid and fully Expended in the operative circuits for current basic and surplus production and exchange. Additional money required for acceleration in both the basic and surplus circuits should enter the system as credit money to the supply function, not as purelyinflationary money to the demand function.
the supposition that circuit acceleration to some extent postulates increments in the quantity of money in the circuits … points to excess transfers to supply, to (S’s’O’) and (S”s”O”), as the mode in which increments in quantities of money enter the circuits. [CWL 15, 61]
Further, the normal entry and exit of quantities of money to the circuits or from them is by the transfers from the Redistributive to the Supply functions. [CWL 15, 64]
Equations (4a) and (3a) are mathematically similar. They then give us a simple model of how all exchange money enters and leaves the system as credit money … . Burley, Evolutionary von Neumann Models, p. 272
One cannot identify a reduction of basic income (by savings) with an increase in the supply of money (for investment), – (such a reduction is normally a misdirective drain of the basic circuit, not an increase) – for a reduction of basic income is only one source of such supply; moreover, it is neither the normal nor the principal source of such supply; … principally the increase in the supply of money is due to the expansion of bank credit, which is necessary to provide the positive (S’s’O’) and (S”s”O”) needed interval after interval to enable the circuits to keep pace with the expanding productive process. [CWL 15, 142]
Again, an existing money supply should be being correctly monitored and calibrated according to the magnitudes and frequencies of the current dynamic process, and fully Outlaid and fully Expended in the operative circuits for current basic and surplus production and exchange. Additional money required for acceleration in both the basic and surplus circuits should enter the system as credit money to the supply function, not as purelyinflationary money to the demand function.
This cumulative action of C‘ and C” reveals an iron law regarding consumer expenditure, namely unless both primary and secondary consumers in the aggregate spend all their income, then they are decreasing their income by the amounts they are failing to spend. In other words, in the aggregate, neither primary nor secondary consumers should save; if they do, they exchange a rate for a mere quantity, and income for an equal lump sum, a dollar for a dollar; moreover, they change a real (basic) expansion into a static phase, and a static phase into economic decline. The slogan is, then, Spend what you get or you won’t get it (back) to spend. (CWL 21, 72)
The Interest rate is a relation between factors. Credit’s purpose is to bridge the gap in time between payments made and payments received. This time gap may be short, as in the case of the working capital cycle or long as in a multiyear capital project.
The gap in time may correspond to the potential for higher production. Soo, it would have the coordinates of time and production or productivity.
.19. Human knowing: positions and counterpositions
Lonergan’s gnoseology distinguishes between positions and counterpositions. One’s philosophical positionson human knowing must be coherent with one’s own actual knowing, which consists of a) acts of experiencing and imagining, b) insight and understanding, c) judgment and reasonable affirmation, d) deliberation and choice. (See CWL 3, 388, which McShane called “the challenge page”)
It will be a basic position, [ on a) reality, b) knowing reality,and c) objectivity in one’s knowing]
 if the real is the concrete universe of being and not a subdivision of the ‘already out there now’;
 if the (human) subject becomes known when it affirms itself intelligently and reasonably and so is not known yet in any prior ‘existential’ state; and
 if objectivity is conceived as a consequence of intelligent inquiry and critical reflection, and not as a property of (the nonhuman animal’s) vital anticipation, extroversion and satisfaction
… On the other hand, it will be a basic counterposition, if it contradicts one or more of the basic positions. … all counterpositions invite reversal; for any lack of coherence prompts the intelligent and reasonable inquirer to introduce coherence. But counterpositions, though coherent with one another, though the insertion of their symbolic equivalents into an electric computer would not lead to breakdown, none the less are incoherent with the activitiesof grasping them intelligently and affirming them reasonably. For these activities contain the basic positions; and the basic positions are incoherent with any counterposition. … The only coherent way to maintain a counterposition is that of the animal; for animals not only do not speak but also do not make excuses for their silence. [CWL 3, 388/413]
The concrete universe of being is defined to be the objective of the detached, disinterested desire to know, and its range is unrestricted. Being is the anything and everything that is the objective of that desire. Being is what is known truly. Inversely, then, knowing is true by its relation to being, and truth is a relation of knowing to being.
Being, then, includes both the abstract and concrete intelligibility of both space and time, as well as the intelligible classical laws comprising the abstract immanent intelligibility of the productive process and the statistical ideal frequencies of events in the schemes of recurrence of the process from which actual relative frequencies do not systematically diverge.
The definition of truth was introduced implicitly in our account of the notion of being. For being was identifiedwith what is to be known through intelligent grasp and reasonable affirmation; but the only reasonable affirmation is the true affirmation, and so being is what is known truly. Inversely, then, knowing is true by its relation to being, and truth is a relation of knowing to being. (CWL 3, 552/)
The proximate criterion of truth is the virtually unconditioned. Thus,
Not only, then, is judgment absolute, not only does it rest upon a grasp of the unconditioned, not only does reflection set the dichotomy, Is it or is it not? But at the root of the cognitional process there is a cool, detached, disinterested desire to know and its range is unrestricted. Being is the anything and everything that is the objective of that desire. (CWL 3, 352/)
and so being is what is known truly. Inversely, then, knowing is true by its relation to being, and truth is a relation of knowing to being. (CWL 3, 552)
The remote criterion (of truth) is the proper unfolding of the detached and disinterested desire to know. In negative terms this proper unfolding is the absence of interference from other desires that inhibit or reinforce and in either case distort the guidance given by the pure desire. (CWL 3, 550)
There is a normative aspect (of objectivity) that is contained in the contrast between the detached and unrestricted desire to know and, on the other hand, merely subjective desires and fears. (CWL 3, 375/ )
Thus, the animal, whose living consists of “vital anticipation, extroversion and satisfaction” in “the already out there now”, does not seek to know the concrete universe of being.
See CWL 3, 3889 for examples of counterpositions of Descartes,Hobbes, and Hume.
.20. The notions of a) truth and b) objectivity as heuristic guides in the analysis and formulation of the objective economic process. Truth defined as the relation of knowing to being and constituted by the virtually unconditioned.
 A) Truth
So we are brought to the profound disillusionment of modern man and to the focal point of his horror. He had hoped through knowledge to ensure a development that was always progress and never decline. He has discovered that the advance of human knowledge is ambivalent, that it places in man’s hands stupendous power without necessarily adding proportionate wisdom and virtue, that the fact of advance and the evidence of power are not guarantees of truth, that myth is the permanent alternative to mystery and mystery is what his hubris rejected. The real issue, then, is truth. (CWL 3, 549/57273)
Being is the objective of the pure desire to know. (CWL 3, 348/)
The definition of truth was introduced implicitly in our account of the notion of being. For being was identifiedwith what is to be known through intelligent grasp and reasonable affirmation; but the only reasonable affirmation is the true affirmation, and so being is what is known truly. Inversely, then, knowing is true by its relation to being, and truth is a relation of knowing to being. (CWL 3, 552/)
Not only, then, is judgment absolute, not only does it rest upon a grasp of the unconditioned, not only does reflection set the dichotomy, Is it or is it not? But at the root of the cognitional process there is a cool, detached, disinterested desire to know and its range is unrestricted. Being is the anything and everything that is the objective of that desire. (CWL 3, 352/)
The real issue, then, is truth. Though it has concerned us all along, it will not be amiss to bring together at least the main points made on different occasions and in different chapters. Accordingly, we distinguish

 the criterion of truth,
 the definition of truth,
 the ontology of truth,
 truth in expression,
 the appropriation of truth, and
 the truth of interpretation. (CWL 3, 549/57273)
The proximate criterion of truth is reflective grasp of the virtually unconditioned … Essentially, then, because the content of judgment is unconditioned, it is independent of the judging subject. Essentially, again, rational consciousness is what issues in a product that is independent of itself. Such is the meaning of absolute objectivity, and from it there follows a public or common terrain through which different subjects can and do communicate and agree. (CWL 3, 54950)
The remote criterion (of truth) is the proper unfolding of the detached and disinterested desire to know. In negative terms this proper unfolding is the absence of interference from other desires that inhibit or reinforce and in either case distort the guidance given by the pure desire. (CWL 3, 550)
The ground of absolute objectivity is the virtually unconditioned that is grasped by reflective understanding and posited in judgment. The formally unconditioned, which has no conditions at all, stands outside the interlocked field of conditioning and conditioned; it is intrinsically absolute. The virtually unconditioned stands within that field; it has conditions; it itself is among the conditions of other instances of the conditioned; still its conditions are fulfilled; it is a de facto absolute. ¶ Because the content of the judgment is an absolute, it is withdrawn from relativity to the subject that utters it, the place in which he utters it, the time at which he utters it. Caesar’s crossing of the Rubicon was a contingent event occurring at a particular place and time. But a true affirmation of that event is an eternal, immutable, definitive validity. For if it is true that he did cross, then no one whatever at any place or time can truly deny that he did. ¶ Again, … ¶ It is important not to confuse the absolute objectivity of any correct judgment with the invariance proper to the expression of universal judgments. Both universal and particular judgments, if correct, are absolutely objective. But the former are expressed invariantly because the expression is independent of variations in spatiotemporal reference frames, while the latter are expressed relatively because their expression does not enjoy such independence. …(CWL 3, 3779)
In one’s insight into insights of mathematicians and scientists one notes a fourlevel structure of knowing: first, experience and imagination; second, insight or act of understanding yielding concepts and provisional definitions; third, judgment or affirmation of “is”ness or existence or equality or definition or identity or affirmation; fourth, in the case of what to do, decision; and finally, caritas.
… 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, 8182/105]
Thus, Functional Macroeconomic Dynamics is an explanatory theory of the process of production and sale; as a science of dynamic flows it employs a scientific heuristic, scientific method, and the technique of implicit definition to reach precise basic analytic terms from which there may be rigorously and logically deduced a superstructure constituting a completely explanatory theory.
… empirical method involves four distinct elements, namely

 the observation of data,
 insight into data,
 the formulation of the insight or set of insights, and
 the verification of the formulation. [CWL 3, 7879/102]
These four distinct elements of scientific method correspond to 1) experience and imagination, 2) act of insight, 3) conception of the insight, and 4) validation of the conception by testing.
The theory called Functional Macroeconomic Dynamics is an organized system. It has a unitary basis of precise basic analytic distinctions. It has a rigorous logicallydeduced superstructure accounting universally for equilibria and disequilibria. It has a determinate systematic structure to which corresponds a determinate field.
… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established. The most notable example is Pythagoras’ theorem on the hypotenuse of the rightangled triangle, which occurs at the end of book 1 of Euclid’s Elements. Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. … Similarly, mechanics became a system with Newton. Prior to Newton, Galileo’s law of the free fall and Kepler’s three laws of planetary motion were known. But these were isolated laws. Galileo’s prescription was that the system was to be a geometry; so there was something functioning as a system. But the system really emerged with Newton. This is what gave Newton his tremendous influence upon the enlightenment. He laid down a set of basic, definitions, and axioms, and proceeded to demonstrate and conclude from general principles and laws that had been established empirically by his predecessors. Mechanics became a science in the full sense at that point where it became an organized system. … Again, a great deal of chemistry was known prior to Mendeleev. But his discovery of the periodic table selected a set of basic chemical elements and selected them in such a way that further additions could be made to the basic elements. Since that time chemistry has been one single organized subject with a basic set of elements accounting for incredibly vast numbers of compounds. In other words, there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. [Method, 24142]
One knows by the act of understanding called insight, which generates concepts implicitly defined by their functional interrelations to one another. The interrelations may be those which constitute in geometry and in other sciences the relations of axioms, explanatory postulates, genera, species, implicit definitions, logical deductions, explanations, existence, “isness”, whose terms are functionally related to one another. The insight determining functional interrelations is distinguished from the insight determining the relations of things to usand from the symbols which arise from, and represent, feelings and the hue of one’s temperament. The confirmation of the act of understanding as true is the content of what is called by us judgment based on insight into the sufficiency of the evidence. The ultimate goal of wonder, insight, and judgment is truth. The initial insight is an act of understanding; the second insight is the act of judgment regarding the sufficiency of evidence which determines whether the understanding is true, false, or probable.
In macroeconomic dynamics, as in other sciences, basic foundational terms – such as pointtopoint, pointtoline, aggregate macroeconomic costs, aggregate macroeconomic pure surplus income – must be defined unambiguously. Basic terms must be precisely implicitly defined by their functional relations to one another – not by Webster, not by Oxford – but rather by their mutual functional relations.
… the heuristic assumptions of science anticipate the determination of natures that always act in the same fashion under similar circumstances, and as well the determinations of ideal norms of probability from events diverge only in a nonsystematic manner. … Terms, then, must be defined unambiguously, and they must always be employed exactly in that unambiguous meaning. (CWL 3, 17576 /199)
 B) Objectivity
See CWL 3, 375ff/ . re objectivity.
The second of the partial aspects of objectivity is the normative. It is objectivity as opposed to the subjectivity of wishful thinking, of rash or excessively cautious judgments, of allowing joy or sadness, hope or fear, love or detestation, to interfere with the proper march of cognitional process. (CWL 3, 380/
There is a normative aspect (of objectivity) that is contained in the contrast between the detached and unrestricted desire to know and, on the other hand, merely subjective desires and fears. (CWL 3, 375/ )
Again, see CWL 3, 375ff/ . re objectivity.
.21. The economist may assert that a proposition is true, false, or probable.
See Prediction is Impossible in the General Case.
One knows by the insight that generates the concepts and their interrelations that constitute relations of definitions, deductions, and explanations rather than by the symbols which arise from feelings and the hue of one’s temperament. The goal of wonder, insight, and judgment is objective truth
The real issue, then, is truth. Though it has concerned us all along, it will not be amiss to bring together at least the main points made on different occasions and in different chapters. Accordingly, we distinguish

 the criterion of truth,
 the definition of truth,
 the ontology of truth,
 truth in expression,
 the appropriation of truth, and
 the truth of interpretation. (CWL 3, 549/57273)
The proximate criterion of truth is reflective grasp of the virtually unconditioned … Essentially, then, because the content of judgment is unconditioned, it is independent of the judging subject. Essentially, again, rational consciousness is what issues in a product that is independent of itself. Such is the meaning of absolute objectivity, and from it there follows a public or common terrain through which different subjects can and do communicate and agree. (CWL 3, 54950)
But the outstanding feature of modern science is that it is not certain. It is increasingly probable. … If one does not grasp the unconditioned, one doubts; one says, “It might be so,” and talks about possibility and probability and high probability. But one does not simply say, “It is.” (CWL 10, 14647)
There is a more radical difficulty. The period from 18701914 and later was still under the spell of classical mechanics with its ideal of exact prediction and with the complementary notion that probability was no more than a cloak for ignorance. But for us the quantum theory has made it possible to grasp that classical laws are abstract inasmuch as they hold only ceteris paribus, and that statistical laws provide a natural complementsince they can reveal how often other things are likely to be equal. In a universe such as ours, with its vast numbers and its enormous time intervals, one is led to think of schemes of recurrence, whose several carriers severally follow their own classical laws, whose assembly follows the probability of their emergence, and whose continued functioning follows the probability of their survival. Such in a nutshell is the evolutionary view that in Insight I sketched out under the name of emergent probability and, earlier in this essay, I have applied to economics. (CWL 15, 9293)
For a human society, like an ecology, is an assembly of assemblies of schemes of recurrence. As interdependent they support one another. As subordinate they underpin higher orders of schemes. As higher they bring to fuller fruition their subordinates. Every scheme has had its probability of emergence, and it will last in accord with its probability of survival. CWL 15, 93
Clearly schemes of recurrence exist and function. No less clearly, their functioning is not inevitable. A population can decline, dwindle, vanish. A vast technological expansion, robbed of its technicians, would become a monument more intricate but no more useful than the pyramids. An economy can falter, though resources and capital equipment abound, though skill cries for its opportunity and desire for skill’s product, though labour asks for work and industry is eager to employ it; then one can prime the pumps and make X occur; but because the schemes are not functioning properly, X fails to recur. As the economy, so too the polity can fall apart. … much …in a twilight of straitened but gracious living men await the catalytic trifle that will reveal to a surprised world the end of a once brilliant day. (CWL 3, 209210/235)
.22. True, truly, and truthful as adjectival and adverbial meanings
True
See Webster
 Being true as fidelity to norms, precepts, and oneself and other people
 True to one’s responsibility to do good and avoid evil
 True to an ideal
 True to one’s spouse
 True to one’s word
 The true aim of science is verification of understanding.
 Being is what is known truly.
The definition of truth was introduced implicitly in our account of the notion of being. For being was identified with what is to be known through intelligent grasp and reasonable affirmation; but the only reasonable affirmation is the true affirmation, and so being is what is known truly. Inversely, then, knowing is true by its relation to being, and truth is a relation of knowing to being. (CWL 3, 552)
Truly
 Without feigning, falsity, or inaccuracy in truth or fact (Webster)
Truthful and fully truthful
 Not lying
 Not otherwise deceiving
 Telling the whole truth and nothing but the truth
.23. Current established science is always provisional until a better explanation is discovered
Scientific thought involves a more exact anticipation. What is to be known inasmuch as data are understood is some correlation or function that states universally the relations of things … to one another. Hence the scientific anticipation is of some unspecified correlation to be specified, some indeterminate function to be determined; and now the task of specifying or determining is carried out by measuring, by tabulating measurements, by reaching an insight into the tabulated measurements, and by expressing the insight through some general correlation or function that, if verified, will define a limit on which converge the relations between all subsequent appropriate measurements. [CWL 3, 44/68]
The history of science, from the Greeks to the present day, manifests that a scientific theory is provisional. “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, 67]
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 nonEuclidean geometers and Einstein went beyond Euclid and Newton. … The nonEuclideans 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, we believe, a scientific generalization of the old political economy and of modern economics that will yield the new political economywhich we need. … Plainly the way out is through a more general field. [CWL 21, 67]
Precisely because analysis is an ongoing process, it is subject to revision. In the measure that revision is radical, it involves new concepts and even new definitions. In this fashion the fact of revision displaces the old reliance on essential definitions and gives way to a search for significant basic variables. For variables, because it is process that is under investigation; for significant variables, because only significance contributes to the relevant acts of understanding; finally for basic variables, because others depend on them, and they depend on one another. In other words, basic variables form a closed circle, in which terms are fixed by their relations, relations fix the terms, and the whole is justified by the degree in which it and its implications are verified. (CWL 15, p. 9)
… statistical laws presuppose some classification of events. One is not going to advance quantum theory by investigating baseball averages. Hence definitive statistical laws suppose definitive classifications. The future discovery of new kinds or of new subdivisions of subatomic elements will invite a revision of the statistical laws. Similarly more accurate investigations may lead to discernment within the statistical law of a systematic element that can be abstracted in classical form to leave a new statistical residue. [CWL 3, 302/ ]
A theory in science or economics is tentative or provisional and subject to continued verification by experiment. It is accepted as long as it explains or accounts for the data. If it fails to do so, by leaving some questions unanswered, further questions are raised and the scientist seeks a new and better explanation or a new and more satisfactory theory to explain or account for the data.
Science develops: it comes to understand what previously was not understood; (in contrast) logic unfolds: it states explicitly what already has been said implicitly. (CWL 15, 11)
… science rests upon two distinct grounds. As insight grasping possibility, it is science. As verification selecting the possibilities that in fact are realized, it is empirical. (CWL 3, 78/ )
Basic (foundational) terms must be precisely defined.
Inversely, because science seeks knowledge of the things as related among themselves, because such relations lie outside our immediate experience, because the ultimates in such relations are to be reached only when ultimate explanation is reached, each great forward step of scientific knowledge involves a more or less profound revision of its fundamental terms. Again, because science is analytic and abstractive, its terms are exact; because its correlations purport to be generally valid, they must be determined with utmost precision; because its terms are exact and its correlations general, it must be ready to bear the weight of a vast superstructure of logical deductions in which each conclusion must be equally exact and valid generally. [CWL 3, 296/ ]
…, (Lonergan) approaches the focus armed with precise analytic distinctions upon which a superstructure of laws, coherent with one another and comprising a complete theory, may be constructed. Paraphrasing [CWL 3, 80/103]:
A new idea lives for a period that is long or short according to its generality, but it may be succeeded by other alternatives, and in any case it will be transformed, perhaps beyond recognition, by higher generalizations. Thus the current textbook macrostatics will give way to Functional Macroeconomic Dynamics, also known as Macroeconomic Field Theory.
CWL 21, 20 each stage of the long process is ushered in by a new idea that has to overcome the interests vested in old ideas, that has to seek realization through the risks of enterprise, that can yield its full fruit only when adapted and modified by a thousand strokes of creative imagination. And every idea, once it has borne its fruit, has to reconcile itself to death. A new idea is new only when it first appears. It comes to man not as a possession forever but only as a transient servant; it has its day, glorious or foul; it lives for a period that is long or short according to its generality, but it may be succeeded by other alternatives, and in any case it will be transformed, perhaps beyond recognition, by higher generalizations. Thus the stagecoach disappeared before the train, the clipper ships gave way to steamers, domestic spinning wheels and looms were concentrated in powerdriven factories, money changers yielded place to bill brokers, brokers to banks and financiers. Nor is it impossible that further developments in science should make small units selfsufficient on an ultramodern standard of living to eliminate commerce and industry, to transform agriculture into a superchemistry, to clear away finance and even money, to make economic solidarity a memory, and power over nature the only difference between high civilization and primitive gardening. … But we are not there yet. And for society to progress towards that or any other goal it must fulfill one condition. It cannot be a titanothore, a beast with a threeton body and a tenounce brain. It must not direct its main effort to the ordinary final product of standard of living but to the overhead final product of cultural implements. It must not glory in its widening, in adding industry to industry, and feeding the soul of man with an abundant demand for labor. It must glory in the deepening, in the pure deepening that adds to aggregate leisure, to liberate many entirely and all increasingly to the field of cultural activities.
the Canon of Operations is a principle of systematization. Insights yield simple laws, but simple laws are applicable only in pure cases. The law of free fall holds in a vacuum. But operations do not occur in a vacuum. Hence, one is driven to determine the law of air resistance and the laws of friction. Similarly, Boyle’s law has to be complemented with Charles’ and GayLussac’s, and all three need to be corrected by Van der Waals’ formula. (CWL 3, 75/)
… unlike the logical positivists, we are completely disillusioned of the notion that knowing the real is somehow looking at what is already out there now. Unlike them, we have much to say about the unconditioned and, indeed, it is in the unconditioned that we place the whole meaning and force of verification. (CWL 3/672/)
A knowledge of cognitional theory is helpful for readers seeking to make macroeconomics a legitimate science. In one’s insight into scientists’ insights one notes a fourlevel structure of knowing: first, experience and imagination; second, insight or act of understanding yielding concepts and provisional definitions; third, judgment or affirmation of “is”ness or existence or equality or identity or affirmation or truth; fourth, in the case of what to do, decision; and finally, caritas.
… 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, 8182/105]
Functional Macroeconomic Dynamics is an explanatory theory; as science it employs a heuristic, the technique of implicit definition, and scientific method.
… empirical method involves four distinct elements, namely

 the observation of data,
 insight into data,
 the formulation of the insight or set of insights, and
 the verification of the formulation. [CWL 3, 7879/102]
.24. The Generalization called Macroeconomic Field Theory as the way out of the morass of arguments among macroeconomic “schools’ or “isms
Macroeconomic Field Theory sublates the arguments among macroeconomic “schools’ or “isms. Many of those arguments are isolated and lack coherence; they cannot identify the state of the process; they are nondynamic, insufficiently nuanced as to price and quantity interactions; and they do not comprise a completely explanatory systematics.
… a science emerges when thinking in a given field moves to the level of system. Prior to Euclid there were many geometrical theorems that had been established. The most notable example is Pythagoras’ theorem on the hypotenuse of the rightangled triangle, which occurs at the end of book 1 of Euclid’s Elements. Euclid’s achievement was to bring together all these scattered theorems by setting up a unitary basis that would handle all of them and a great number of others as well. … Similarly, mechanics became a system with Newton. Prior to Newton, Galileo’s law of the free fall and Kepler’s three laws of planetary motion were known. But these were isolated laws. Galileo’s prescription was that the system was to be a geometry; so there was something functioning as a system. But the system really emerged with Newton. This is what gave Newton his tremendous influence upon the enlightenment. He laid down a set of basic, definitions, and axioms, and proceeded to demonstrate and conclude from general principles and laws that had been established empirically by his predecessors. Mechanics became a science in the full sense at that point where it became an organized system. … Again, a great deal of chemistry was known prior to Mendeleev. But his discovery of the periodic table selected a set of basic chemical elements and selected them in such a way that further additions could be made to the basic elements. Since that time chemistry has been one single organized subject with a basic set of elements accounting for incredibly vast numbers of compounds. In other words, there is a point in the history of any science when it comes of age, when it has a determinate systematic structure to which corresponds a determinate field. [Method, 24142]
(In physics) 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 nonEuclidean geometers and Einstein went beyond Euclid and Newton. … The nonEuclideans 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, 67]
Paraphrasing
Lonergan dealt in the same way with all macroeconomic phenomena. He did so by turning to a field of greater generality, the field theory of dynamic macroeconomic phenomena, and by finding a deeper unity at a more adequate level of abstraction in the apparent disparateness of Walrasian macrostatics, neoclassical selfcorrectionism, Keynesian interventionism, monetary moneysupplyism, rational behaviorism, Federal Reserve Phillipscurveism, Marxian classism and victimism, and Laissezfaire egoism. … Lonergan went beyond the schools and isms by employing implicit definition, precise analytical distinctions, and functional analysis and rigorous deduction towards complete explanation of interdependent, implicitlydefined, functional flows. It is this scientific generalization of the old political economy and of modern economics that will sublate and transform the isms so as to yield the new political economy which we need. … Plainly the way out is through a more general field. [CWL 21, 67]
Clearly, we have to do with another aspect of the empirical residue and, no less clearly, this aspect is coupled with the most powerful of all scientific techniques, generalization. [ CWL 3, 28/ ]
Macroeconomic Field Theory is universal and applicable in any instance.
The basis of the theoretical contention is that, just as the same act of understanding is repeated when the same setof data is apprehended a second time, so also the same act of understanding is repeated when one apprehends a second set of data that is similar to the first in all respects.… … much … …merely that singular combinations of universal explanatory elements may be set in correspondence with singular combinations of common properties or aspects in each individual. (CWL 3, 2930/ )
Again, … common sense vs.science:
may seem to generalize. But a generalization proposed by common sense has quite a different meaning from a generalization proposed by science. The scientific generalization aims to offer a premise from which correct deductions can be drawn. But the generalizations issued by common sense are not meant to be premises for deductions. Rather they would communicate pointers that ordinarily is is well to bear in mind. Proverbs are older far than principles and, like the rules of grammar, they do not lose their validity because of their numerous exceptions. For they aim to express, not the scientist’s rounded set of insights that either holds in every instance or in none at all, but the incomplete set of insights which is called upon in every concrete instance … [CWL 3, 176/ ]
Functional Macroeconomic Dynamics sublates all other macroeconomic theories by reaching an adequate level of abstraction, or a deeper unity, or a more profound point of view, or a purely relational, fully explanatory, scientific macroeconomics. This general intelligibility, based on precise analytic distinctions and rigorous deduction, fully explains the economic process and eliminates at a stroke much of what is contained in the current popular 700page textbooks.
Ragnar Frisch was a Norwegian economist and the corecipient of the first Nobel Memorial Prize in Economic Sciences in 1969. He failed to develop a significant theory.
“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 (price and quantity) in a determinate set of differential and difference equations.” [McShane, 1980, 114] [29]
A rigidly egalitarian system belongs to a perfectly egalitarian world; (but) a world in which men are, in fact, unequal must find a different system. What system? If the idealism is sentiment without intelligence, it is as likely as not to mate with the underground cynicism of the revolutionaries to foist upon us a dictatorship of the proletariat in which the proletariat does not dictate, a dictatorship of the Herrenvolk in which the Volk obeys the Fuhrer. But if that idealism can be brought too learn the discipline of logic and of scientific reflection, then it will impose a generalization of the exchange economy. To determine the nature of such a generalization is the aim of this inquiry; but at once this is at least evident. The vast forces of human benevolence can no longer be left to tumble down the Niagara of fine sentiments and noble dreams. They have to be assigned a function and harnessed within the exchange system, for in no other way can that system shake off its fictitious fetters to move consistently towards its maximum. [CWL 21, 36]
.25. The Canon of Complete Explanation:
See CWL 3, 846/107109
.26. What is the “truth” of electromagnetics? The character of its “cumulative verification”
Empirical verification stands to the formulated hypothesis as judgment of virtuallyunconditioned truthstands to insightful understanding.
Science develops. Its initial propositions may be true, false, or probable. It is subject to revision; i.e. it is provisional, until a better explanation is discovered.
ClerkMaxwell’s 4equation cluster of the laws of electromagnetics has heuristically guided productive operationssuccessfully in a vast variety of situations. Verification of ClerkMaxwell’s theory doesn’t ask, Is it true?, rather it asks, Are the terms and relations of the (mathematical) correlations of measurements isomorphic with the patterns in the data? That is, are they true to the data? Is the theory validated or cumulatively verified or “truthified” in every instance?
… the Canon of Operations is a principle of cumulative verification. For laws guide operations successfully in the measure that they are correct. Hence, in so far as laws and their implications in a vast variety of situationsare repeatedly successful guides of operations, their initial verification is cumulatively confirmed (CWL 3, 75/)
… science rests upon two distinct grounds. As insight grasping possibility, it is science. As verificationselecting the possibilities that in fact are realized, it is empirical. (CWL 3, 78)
Also,
the Canon of Operations is a principle of systematization. Insights yield simple laws, but simple laws are applicable only in pure cases. The law of free fall holds in a vacuum. But operations do not occur in a vacuum. Hence, one is driven to determine the law of air resistance and the laws of friction. Similarly, Boyle’s law (relating the volume, pressure, and temperature of a gas) has to be complemented with Charles’ and GayLussac’s, and all three need to be corrected by Van der Waals’ formula. (CWL 3, 75/)
ClerkMaxwell’s abstract, purely relational laws may be named “positions.” CM’s equations are real; they are objectively conceived as a consequence of intelligent inquiry and critical reflection; his laws constitute a verified reality when they are repeatedly successful guides of operations and are affirmed intelligently and reasonably.
Scientific thought involves a more exact anticipation. What is to be known inasmuch as data are understood is some correlation or function that states universally the relations of things … to one another. Hence the scientific anticipation is of some unspecified correlation to be specified, some indeterminate function to be determined; and now the task of specifying or determining is carried out by measuring, by tabulating measurements, by reaching an insight into the tabulated measurements, and by expressing the insight through some general correlation or function that, if verified, will define a limit on which converge the relations between all subsequent appropriate measurements. [CWL 3, 44/68]
Now, at the root of classical method there are two heuristic principles. The first is that similars are understood similarly, that a difference of understanding presupposes a significant difference of data. The second is that similarities, relevant to explanation, lie not in the relations of things to our senses but in their relations to one another. Next, when these heuristic principles are applied, there (first) result classifications by sensible similarity, then correlations, and finally the verification of correlations and of systems of correlations. But verified correlations necessarily involve the verification of terms implicitly defined by the correlations; and they do not involve more than such implicitly defined terms as related, for what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically and explanatory relations. Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[CWL 3, 435/460]
Again, because science seeks knowledge of the things as related among themselves, because such relations lie outside our immediate experience, because the ultimates in such relations are to be reached only when ultimate explanation is reached, each great forward step of scientific knowledge involves a more or less profound revision of its fundamental terms. Again, because science is analytic and abstractive, its terms are exact; because its correlations purport to be generally valid, they must be determined with utmost precision; because its terms are exact and its correlations general, it must be ready to bear the weight of a vast superstructure of logical deductions in which each conclusion must be equally exact and valid generally. [CWL 3, 296/ ]
.27. The process of empirical verification or (etymologically) “truthification” by econometricians of Lonergan’s abstract fieldtheoretic formulation of the current, purelydynamic, economic process
Professional economists, econometricians, and financial analysts owe it to themselves and their clients to set aside time to, first, master the explanatory science of Functional Macroeconomic Dynamics (FMD), also called Macroeconomic Field Theory (MFT). Academic economists must come to understand and teach FMD, being careful to rigorously compare and contrast textbook Walrasian macroSTATIC, efficientcause, economics against Lonergan’s universal, formalcause, immanentintelligibility Macroeconomic Field Theory. Consultant economists must communicate and advise based upon FMD. Econometricians – after first mastering FMD’s correlations and relativistic field theory – must verify FMD’s correlations as explanatory.
The disorientating Walrasian macrostatics, which is a staple of university textbooks, is in need of sublation by a generalization to a higher dynamical viewpoint at a more adequate level of abstraction. Accepting the Latin “altus” as meaning both high or deep, depending on the context, Functional Macroeconomic Dynamics provides a both higher and more profound point of view and discovers a higher synthesis and deeper unity in a more general field. This deeper unity is also called Macroeconomic Field Theory.
As Newton discovered a deeper unity that generalized the isolated insights of Galileo and Kepler, so Lonergan sought to discover a deeper unity that generalized the insights of S.M. Longfield, John Rae, Nassau Senior, Eugen von BöhmBawerk, and Piero Sraffa[2]; a deeper unity in the relations among economic functionings. [CWL 25, Editors’ Introduction lxii]
Theorists and econometricians must courageously enter a new realm. They must have a confident scientific spirit. They must accept and be guided by new and precise foundational functional distinctions in their verification of a new hypothesis.
Back, then, to the parallel with physics. The introduction of a new distinction places a huge burden on the physics community to shuffle previous data, to take a new and precise view on present and future data. Is this one of the reasons why Lonergan’s present distinction is not yet welcome in economics? … I am inclined to think that the main difficulty is the subtle absence of the scientific spirit in contemporary economics. … There is nothing wrong with mathematical subtlety or rigor: the rigor mortis belongs to the absence of significant variables coupled regularly with the absence of empirical and pragmatic perspective; a case in point is the sophistications of rational expectations theory. … The real difficulty is in the scientific perspective that can come to grips with precise functional distinctions. [McShane 20022, 2122]
On one hand, the analyst may work from the top down, gather alreadyknown facts and fit a theory to the known facts. On the other hand, the analyst may work from the bottom up, conduct experiments, measure data, gather new facts, seek and discover new correlations in the data and further correlations in the initial correlations, and formulate a fully explanatory classical theory. In the former case, a gathering of alreadyknown facts cries out for the explanatory formulafitting; in the latter case, experimental determination of previouslyunknown facts precedes the formulafitting.
The history of science reveals successive improvements in theory. Science develops and is subject to revision; i.e.initially and beyond it remains provisional, until a better explanation is discovered.
Precisely because analysis is an ongoing process, it is subject to revision. In the measure that revision is radical, it involves new concepts and even new definitions. In this fashion the fact of revision displaces the old reliance on essential definitions and gives way to a search for significant basic variables. For variables, because it is process that is under investigation; for significant variables, because only significance contributes to the relevant acts of understanding; finally for basic variables, because others depend on them, and they depend on one another. In other words, basic variables form a closed circle, in which terms are fixed by their relations, relations fix the terms, and the whole is justified by the degree in which it and its implications are verified. (CWL 15, 9)
… science rests upon two distinct grounds. As insight grasping possibility, it is science. As verification selecting the possibilities that in fact are realized, it is empirical. (CWL 3, 78)
Economists and econometricians must grasp the heuristic principles of classical scientific method in order to discover abstract, explanatory formulations which they will try to cumulatively verify, “truthify”, substantiate. (See .1. “Adoption of a scientific heuristic and method” subsection in this subtopic)
Scientific thought involves a more exact anticipation. What is to be known inasmuch as data are understood is some correlation or function that states universally the relations of things … to one another. Hence the scientific anticipation is of some unspecified correlation to be specified, some indeterminate function to be determined; and now the task of specifying or determining is carried out by measuring, by tabulating measurements, by reaching an insight into the tabulated measurements, and by expressing the insight through some general correlation or function that, if verified, will define a limit on which converge the relations between all subsequent appropriate measurements. [CWL 3, 44/68]
each stage of the long process is ushered in by a new idea that has to overcome the interests vested in old ideas, that has to seek realization through the risks of enterprise, that can yield its full fruit only when adapted and modified by a thousand strokes of creative imagination. And every idea, once it has borne its fruit, has to reconcile itself to death. A new idea is new only when it first appears. It comes to man not as a possession forever but only as a transient servant; it has its day, glorious or foul; it lives for a period that is long or short according to its generality, but it may be succeeded by other alternatives, and in any case it will be transformed, perhaps beyond recognition, by higher generalizations. Thus the stagecoach disappeared before the train, the clipper shipsgave way to steamers, domestic spinning wheels and looms were concentrated in powerdriven factories, money changers yielded place to bill brokers, brokers to banks and financiers. Nor is it impossible that further developments in science should make small units selfsufficient on an ultramodern standard of living to eliminate commerce and industry, to transform agriculture into a superchemistry, to clear away finance and even money, to make economic solidarity a memory, and power over nature the only difference between high civilization and primitive gardening. … But we are not there yet. And for society to progress towards that or any other goal it must fulfill one condition. It cannot be a titanothore, a beast with a threeton body and a tenounce brain. It must not direct its main effort to the ordinary final product of standard of living but to the overhead final product of cultural implements. It must not glory in its widening, in adding industry to industry, and feeding the soul of man with an abundant demand for labor. It must glory in the deepening, in the pure deepening that adds to aggregate leisure, to liberate many entirely and all increasingly to the field of cultural activities. (CWL 21, 20)
Verification is of correlations and of terms implicitly defined by the correlations.
Now, at the root of classical method there are two heuristic principles. The first is that similars are understood similarly… . The second is that similarities, relevant to explanation, lie not in the relations of things to our senses but in their relations to one another. Next, when these heuristic principles are applied, there (first) result classifications by sensible similarity, then correlations, and finally the verification of correlations and of systems of correlations. But verified correlations necessarily involve the verification of terms implicitly defined by the correlations; and they do not involve more than such implicitly defined terms as related, for what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically and explanatory relations. Such terms as related are known by understanding, and so they are forms. Let us name them conjugate forms.[CWL 3, 435/460]
Again, because science seeks knowledge of the things as related among themselves, because such relations lie outside our immediate experience, because the ultimates in such relations are to be reached only when ultimate explanation is reached, each great forward step of scientific knowledge involves a more or less profound revision of its fundamental terms. Again, because science is analytic and abstractive, its terms are exact; because its correlations purport to be generally valid, they must be determined with utmost precision; because its terms are exact and its correlations general, it must be ready to bear the weight of a vast superstructure of logical deductions in which each conclusion must be equally exact and valid generally. [CWL 3, 296/ ]
The explanation of the concrete economic process consists of both abstract classical laws and statistical laws. There are both classical formulations and ideal frequencies from which actual frequencies will differ at random. The classical laws of Functional Macroeconomic Dynamics are constituted by functional relations of abstract general terms to one another expressed in general and abstract propositions on which ranges of ranges of particular propositions converge. Classical predictions can be exact within assignable limits, because relations between measurements of concrete events in the nonsystematic manifold of events just converge on the functional relations that formulate the classical laws.
… though both classical and statistical hypotheses need verification, verification has not the same meaning in both cases. Because the relations between measurements converge on the functional relations that express classical laws, it is possible to substitute the numerical values determined by the measurements for the variables that are functionally related by the laws. In contrast, because relative actual frequencies differ at random from probabilities, it is not possible to deduce the probabilities from any fully determinate mathematical formula by substituting for the variables of the formula the fractions that correspond to relative actual frequencies. (CWL 3, 656/)
The converse to this difference in the meaning of verification appears in the difference between classical and statistical predictions. Classical predictions can be exact only within assignable limits, because relations between measurements converge on the functional relations that formulate the classical laws. But because relative actual frequencies differ at random from probabilities, statistical predictions primarily regard the probabilities of events and only secondarily determine the corresponding frequencies that differ at random from probabilities. Hence, even when numbers are very great and probabilities high, as in the kinetic theory of gases, the possibility of exception has to be acknowledged; … [CWL 3, 66/ ]
The Functional Macroeconomic Dynamics to be “certified,” “truthified,” “validated” is a Macroeconomic Field Theory. It is not a theory of efficient causes, where some outside cause, over which participants have no control, is the primary parameter. Rather it is an invariant set of internal relations of terms among themselves.
The economic process to be experimentally verified expands in phases. Magnitudes of the variables change as the process expands phase by phase. Production quantities and incomes should increase normatively according to the invariant normative relations of the terms of the process. So, econometricians must, first, understand the process, so that they can properly select the quantities to be measured. Then, they must discern where in the series of phases the process is and whether or not the real quantities and the dummy money supply are properly equilibrated. Finally, they must verify the invariance in the relations among the terms.
See Explanation by Gross Domestic Functional Flows to Supplement Description by Gross Domestic Product,
and see Gross Domestic Functional Flows: GDFF = P’Q’ + Π”Κ”; Revision and Technicalities.
[2] By “mechanical” we mean having to do with the science of motion. Note that Newton’s three laws of motion plus his inverse squares law plus the deduced superstructure of principles of work, kinetic and potential energy, etc are grouped under the heading “mechanics.” By “mechanical” we do not mean rigidly “mechanistic” like the simplest piece of metal machinery.