## A. The Leibnitz-Newtonian Shift of Context and Scientific Economics; Basic Terms, Explanatory Conjugates, An adequate Level of Abstraction, No Premature Introduction of Boundary Conditions

Let us begin this subsection with an excerpt taken out of its context, but providing a preview or “trailer” to the entire subsection.

Taking into account past and (expected) future values does not constitute

the creative key transition to dynamics.Those familiar with elementary statics and dynamics (in physical mechanics) will appreciate the shift in thinking involved in passing from equilibrium analysis (of a suspended weight or a steel bridge)…to an analysis where attention is focused on second-order differential equations, on d^{2}θ/dt^{2}, d^{2}x/dt^{2}, d^{2}y/dt^{2}, on a range of related forces, central, friction, whatever. Particular boundary conditions, “past and future values” are relatively insignificant for the analysis. What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

Paraphrasing:

Taking into account past and (expected) future values does not constitute *the creative key transition to functional macroeconomic dynamics.* Those familiar with elementary statics and dynamics (in physical mechanics) will appreciate the shift in thinking involved in passing from (static) equilibrium analysis (of a suspended weight with subscripts for time not needed)…to a (dynamic equilibrium) analysis (of, say, planets or pendula) where attention is focused on second-order 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 in functional macroeconomic dynamics, past and future pricings and quantities (analogous to a planet’s particular past or future position, velocity, acceleration), are relatively insignificant for the analysis of the primary relativity. What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

Lonergan’s basic terms are velocities. There is a shift to dynamics. The creative shift is the Leibnitz-Newtonian shift.

In Lonergan’s circulation analysis, the basic terms are rates – rates of productive activities and rates of payments. The objective of the analysis is to discover the underlying intelligible and dynamic (accelerative) network of functional, mutually conditioning, and interdependent relationships of these rates to one another. [CWL 15 26-27 ftnt 27]

The Diagram of Rates of Flow represents the functional relations among these monetary velocities.

(the circulation analysis presented here) makes the use of a diagram particularly helpful, … (macroeconomics’) basic terms are defined by their functional relations. [CWL 15, 54]

The general law is universal; as general and universal, it is applicable to, but indifferent to, happenstantial combinations of particular secondary determinations.

Lonergan never used terms for magnitudes, only for rates and their accelerations (‘rates of rates’) in the

Essay in circulation Analysis. [CWL 15, 182]

The rates are rates of *economic activities* called *functionings*.

“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 26-27 ftnt 27]

- Functions, functions, functions.
- Functions not firms
- Functions, not profit-loss accounts
- Velocitous functions
- Rates of functional flows (activities)
- Relations of functionings to one another.
- Analytic, explanatory, theoretical relations.
- Mutually determining and determined functionings
- Functions implicitly defining one another by their functional relations to one another.

Lonergan’s “relations, and the terms they implicitly defined, were markedly different from either the terms of ordinary business parlance or the terms of neoclassical and Keynesian economic theory.” That ordinary business parlance is the accounts of ordinary profit-loss accounting.

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

In his Leibnitz-Newtonian shift, Lonergan’s basic terms are the velocities of interdependent, mutually-defining functionings. These functioning are defined by the functional relations in which they stand with one another. The terms and relations are diagrammed in the Diagram of Rates of Flow. Depending on one’s momentary interest and point of view, this schematic may alternately be called:

- The Diagram of Two Operative Circuits Connected by Operative Crossovers
- The Diagram of Functional Monetary Interdependencies
- The Diagram of Operative Functional Flows of Products, Payments, and Financings
- The Diagram of Monetary Transfers
- The Diagram of Monetary Channels
- The Diagram of the Monetary Correlates of the Productive Process
- The Diagram of Implicitly Defining, Mutually Conditioning, Velocitous Functionings
- The Diagram Sublating, Supervening, and Replacing the Single-Circuit Diagram of Macroeconomics Textbooks
- The Functional Framework
- (Colloquially, because of its shape) Lonergan’s Baseball Diamond

One can imagine the channels filled with functional flows; then one can grasp the interrelations and be well along the way to understanding and explaining the domestic economy. The diagram is of huge importance. But people underestimate it. It is clever. Its resemblance to a baseball diamond is intriguing. But it is to be understood, not described as clever and intriguing. With only slight exaggeration we say, “The diagram explains all equilibria and disequilibria.”

In the Leibnitz-Newtonian shift, the terms of the formulations of the analysis, explanation, hypothesis, theory are called *pure or explanatory conjugates*.

… verification is of formulations, and formulations state

- the relations of things to our senses, and
- the relations of things to one another.

… Pure or explanatory conjugates, … are correlatives defined implicitly by empirically established correlations, functions, laws, theories, systems. [CWL 3, 79-80/101-03]

… pure conjugates satisfy (empirical science’s) Canon of Parsimony. For the equations (stating the relations among the explanatory conjugates) are or can be established empirically. And by definition pure conjugates mean no more than necessarily is implicit in the meaning of such verified equations. [CWL 3, 80/103]

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 yard-stick; from the series of combinations I obtain a 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, 80/103-04 ]

A science of macroeconomic dynamics, if it is to be legitimate science of dynamics, demands the honoring of the principles of a dynamic and scientific heuristic, the discovery of the interdependent correlative velocities, and the verification of the relations among correlatives.

Now, at the root of classical (scientific) 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 the 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 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. [CWL 3, 435/ ]

the name, conjugate, brings out what we consider the essential feature of intelligible mutual relations that implicitly define conjugate forms. CWL 3, 437/

In seeking to discover the immanent intelligibility of the always current, purely dynamic economic process, one must operate at an adequate level of abstraction; one must not introduce particular boundary conditions – such as prices and quantities – prematurely and seek to build a primary theory upon secondary particular measurements. Particulars – such as prices and quantities – are relatively insignificant for the analysis. To understand and specify the purely dynamic process, one seeks to shift from the contexts of accounting and statistical reporting to the Leibnitz-Newtonian dynamics of differentials with respect to time.

We repeat:

Taking into account past and (expected) future values does not constitute

the creative key transition to dynamics.Those familiar with elementary statics and dynamics (in physical mechanics) will appreciate the shift in thinking involved in passing from equilibrium analysis (of a suspended weight or a steel bridge)…to an analysis where attention is focused on second-order differential equations, on d^{2}θ/dt^{2}, d^{2}x/dt^{2}, d^{2}y/dt^{2}, on a range of related forces, central, friction, whatever. Particular boundary conditions, “past and future values” are relatively insignificant for the analysis. What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

Paraphrasing:

Taking into account past and (expected) future values does not constitute *the creative key transition to functional macroeconomic dynamics.* Those familiar with elementary statics and dynamics (in physical mechanics) will appreciate the shift in thinking involved in passing from (static) equilibrium analysis (of a suspended weight with subscripts for time not needed)…to a (dynamic equilibrium) analysis (of, say, planets or pendula) where attention is focused on second-order 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 in functional macroeconomic dynamics, past and future pricings and quantities (analogous to a planet’s particular past or future position, velocity, acceleration), are relatively insignificant for the analysis of the primary relativity. What is significant is the Leibnitz-Newtonian shift of context. [McShane, 1980, 127]

We are doing Leibnitz-Newtonian economic science. We are seeking the general laws of a dynamic process of price-quantity flowings. The analysis will turn up both classical laws of central and normative tendency and statistical laws of probability that pertain to a non-systematic manifold.

General laws contain a primary relativity and are applied to the concrete “only through the addition of further determinations, and such further determinations pertain to a non-systematic manifold. … it is not enough to think about the general law; one has to add further determinations that are contingent from the very fact that they have to be obtained from a non-systematic manifold. [CWL 3, 492/516]

… conjugate forms are defined implicitly by their explanatory and empirically verified relations to one another. Still, such relations are general laws; they hold in any number of instances; they admit application to the concrete only through the addition of further determinations, and such further determinations pertain to a non-systematic manifold. There is, then, a primary relativity that is contained in the general law; it is inseparable from its base in the conjugate form which implicitly it defines;[1] and to reach the concrete relation that holds at a given place and time, it is not enough to think about the general law; one has to add further determinations[2] that are contingent from the very fact that they have to be obtained from a non-systematic manifold. [CWL 3, 492/516] (In addition, read in the entirety [CWL 3, 491-6/514-20])

Because classical systems are abstract, because they can be applied to the concrete only by appealing to a non-systematic manifold of further determinations, there are also statistical method and statistical laws. [CWL 3, 493-94/517]

The basic terms of the sciences … are defined by their respective relations to one another. To distinguish between the defining relation and the defined term can be no more than a notional operation; and even then it cannot be carried through, for if one prescinds from the defining relation, one no longer is thinking of the term as defined but of some other term that is mistakenly supposed to be absolute. [CWL 3, 496/520]

Ragnar Frisch could not see beyond particular boundary conditions to a general theory.[3] Boundary conditions such as pricings and quantities, which are secondary determinations pertaining to a non-systematic manifold, are relatively insignificant for the analysis.[4]

Frisch’s failure to develop a significant theory typifies the failure of economists who search for a dynamic heuristic. As well as a fundamental disorientation of approach there is also a tendency to shift to an inadequate level of abstraction with a premature introduction of boundary conditions in a determinate set of differential and difference equations. [McShane, 1980, 114]

McShane’s “inadequate level of abstraction” refers to the abstraction to the primary relativity among functional flows. This adequate level of abstraction yields the general laws. The secondary determinations – pricings and quantities in the coincidental manifold of the concrete process are the particular boundary conditions which may be applied to the general laws to get the particular relations of a particular instance. Thus, pricings and quantities have their intelligibility, or role so to speak, in the functional flows which they happen to compose in the concrete process. Pricings and quantities are no more interesting than a particular angle in the general law of cosines or than a particular position and velocity in a general theory of motion along a conic.

Finally, one seeks a general specification of the intelligibility of the process, a general explanatory specification universally applicable in any advanced exchanged economy in any political system to all equilibria and disequilibria; we do not seek the statistics of the Great Recession or a report of what the sales of tomatoes happened to be in the most recent quarter.

One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general conditions or worse, specific channel conditions, botches the analytic possibilities. [McShane 1980,124]

- In each period there are flows of capital and consumer goods.
- Capital goods are produced before their bounty becomes available; there is a temporality or rhythm to the process.
- Flows are velocities of so much or so many per period[5]
- Changes of velocities are accelerations.
- Second-order differential equations representating accelerations have algebraic solutions with two constants. First-order differential equations representing velocities have algebraic solutions with one constant.
- But, if our concern is economic velocities and we need only to find the first-order velocity function[6] as the solution to the second-order acceleration function, only one order of solving will be necessary. And if we can express the correlated accelerations in a first-order differential form (dv/dt) with respect to the same period of time, the solution stating the velocity will be an algebraic form.
- The possible general solutions to differential equations are infinite. One must employ a.) technical coefficients representing point-to-line or point-to-higher-dimension relationships, and b.) actual initial values or actual boundary values to get the precise solution or law.
- The Table on page 114 of CWL 15
*comparing*acceleration in the consumer-goods circuit (dQ’/Q’) vs. acceleration in the producer-goods circuit (dQ”/Q”) is a key table laying out possible sequences and combinations of accelerations as the economic process proceeds through its long-term expansion.. - These accelerations of productive flows of the two circuits are correlated with monetary accelerations of a.) spending on a standard of living, or of b.) investing in capital.
- Therefore, the general, universally applicable explanation of an objective economic process characterized by speedups and slowdowns of productive flows will consist of terms representing differently timed velocities and accelerations of the functional monetary correlates in their functional relations to one another.

See this website’s section entitled *McShanes Phrases:* *A Dynamic Heuristic; and the Creative Key Transition to the Leibnitz-Newtonian Context.*

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[1] That is, there is a general relation which is inseparable from the terms it relates; for the terms define the relations and the relations define the terms. The primary relativities are Productive point-to-point vs. point-to-line, and monetary P’Q’ = p’a’Q’ + p”a”Q” and Π”Κ” = π”α”Κ”.

[2] The further determinations are particular pricings-quantities combinations comprising the functional flows.

[3] Ragnar Frisch, 1895-1973, Nobel Memorial Prize in Economic Sciences in 1969

[4] See CWL 3, 492/516, and this website’s *Classical Laws and Concrete Probabilities; the Possibility of Deduction and Prediction*

[5] Lonergan never used terms for magnitudes, only for rates and their accelerations (‘rates of rates’) in the *Essay in circulation Analysis*. CWL 15, 182

[6] “function” here refers to the mathematical function, not to the monetary function or functioning