# The System of Abstract Primary Relativities Applied to Secondary Determinations

There is required a shift of focus by academics from the concrete secondary determinations of prices and quantities in a non-systematic manifold to the immanent, abstract, primary relativities which may be applied to these secondary determinations to reach particular laws.

Paraphrasing [McShane, 1980, 127]: 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 will appreciate the shift in thinking involved in passing from equilibrium analysis to an analysis where attention is focused on second-order differential equations, on d2θ/dt2, d2x/dt2, d2y/dt2, on the primary relativities of a range of related forces, central, friction, whatever.  Particular secondary boundary conditions (such as) 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 Leibnitz-Newtonian shift of context.

Concrete relations contain a  primary relativity and secondary determinations.

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, 491-92/516]

The whole structure of the particular concrete law is relational.

The whole structure is relational: one cannot conceive the terms without the relations nor the relations without the terms. Both terms and relations constitute a basic framework to be filled out, [CWL 3, 492/516]  (In addition, read in the entirety [CWL 3, 491-6/514-20]

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 ‘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 in the concept of mass. [CWL 3, 493/]

The formal cause” of the economic process is its primary immanent intelligibility.  The formal cause consists in the primary relativities or general laws of the process , which hold in any number of instances.  The formal cause contains the normative theory and explains both normative equilibria and violative disequilibria.

Particular boundary conditions, such as past and future prices and quantities are relatively insignificant for the analysis; these boundary conditions are further determinations that are contingent from the very fact that they have to be obtained from a non-systematic manifold. (CWL 3, 491-6/)

In the formal cause we apprehend many things as one; we grasp all in a unified view.

Guided by a scientific and explanatory heuristic towards a systematic or analytic framework in order to discover general explanatory laws, 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 macroeconomic phenomena, and by finding a deeper unity at a more adequate level of abstraction in the apparent disparateness of neoclassicism, Keynesianism, monetarism, and behaviorism. … Lonergan went beyond the schools and the isms and the fads and the fancies by employing implicit definition, precise analytical distinctions, and functional analysis.

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. [Gibbons, 1987, 313]

Lonergan agreed with Schumpeter on the importance of systematic or analytic framework in order to explain, rather than merely record or describe, the aggregate phenomena of macroeconomics; … 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]

Paraphrasing [CWL 21, 6-7]: It is a scientific generalization of both the old political economy and modern economics that will sublate and transform the isms and yield the new sublation which we need. … Plainly the way out is through a more general field.

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

One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general boundary conditions or worse, specific channel conditions, botches the analytic possibilities….the Robinson-Eatwell analysis is hampered, not only by an absence of paradigmatic heuristic thinking in a field whose principles involve ends, but also by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nos are last in analysis: they require explanation.[McShane 1980, 124]

Again,

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 agreed with Schumpeter on the importance of 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]

We contrasted familiar textbook models  of macrostatic equilibrium, with Lonergan’s explanatory theory of macrodynamic equilibrium.  We contrasted a macrostatic toolkit with a purely relational field theory of macroeconomic dynamics. Lonergan discovered  a theory which is more fundamental than the traditional wisdom based upon human psychology and purported endogenous reactions to external forces.  His Functional Macroeconomic Dynamics is a set of relationships between n objects, a set of intelligible relations linking what is implicitly defined by the relations themselves, a set of relational forms wherein the form of any element is known through its relations to all other elements.  His field theory is a single explanatory unity; it is purely relational, completely general, and universally applicable to every configuration in any instance.

Let us repeat for emphasis two excerpts from not far above:

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

One might be reminded here of a parallel in hydrodynamics: if what is at issue is a general specification of the dynamics of free water waves, a premature introduction of general boundary conditions or worse, specific channel conditions, botches the analytic possibilities….the Robinson-Eatwell analysis is hampered, not only by an absence of paradigmatic heuristic thinking in a field whose principles involve ends, but also by their building the economic priora quoad nos of profits, wages, prices, etc., into explanation, when in fact the priora quoad nos are last in analysis: they require explanation.[McShane 1980, 124]

The textbook models employ comparative statics:  Certain quantities are accepted as given;  their determination is exogenous, i.e. they are static, or changed gradually, or traumatized by external shocks; they are parameters over which the endogenous participants have no control.  Other quantities are endogenous variables determined by adjustments effected by internal human agents within the comparative-statics framework.  For example: in an initial configuration, prices may be exogenously given and determinate of a certain endogenous intersection-equilibrium of quantities along the supply and demand curves.  Then, an exogenous, unexplained shock to prices is assumed, to which the internal human agents of supply and demand respond to effect a different intersection of the quantities of supply and demand.  Comparative statics is, thus, characterized by exogenous givens, unexplained shifts in the exogenous givens, and adjustments by endogenous participants to the endogenous variables such as to effect a new intersection of  the endogenous variables.

While comparative statics demonstrates the general principles of supply equaling demand and of quantities having prices, it does not explain the dynamic process in terms of the relations of constituent interdependent functionings among themselves.  In comparative statics there is a whole lot of assuming and guessing going on with respect to the shape of curves and the extent and direction of a reaction of entrepreneurs or their employees.  CS is a huge tangle a) of guesses – many of which are psychopolitical guesses motivated by preservation of reputation or pelf rather than by a search for truth – regarding profit-seeking firms contending with utility-seeking households, b) of reactions to change and to the expectations of change, and c) of the speed of the reactions.  And CS builds its edifice on windblown sands.  In such an imaginary tangle, so-called pundits can select strands in order to extrapolate as they will, and make predictions as they will when in the general case predictions of the longer term are impossible. (See CWL 3, 650-51, and here re Joseph Stiglitz )

So, instead of working our way out of the morass once and for all by discovering the immanent intelligibility of a general, universally relevant, explanatory theory, we have financial talk shows and meaningless political debates wallowing around in the premature introduction of the secondary determinations of a nonsystematic manifold.

In contrast, Functional Macroeconomic Dynamics is a theory of the formal cause or immanent intelligibility, or primary relativities, of a currentcontinuous or semicontinuous, purely dynamic process of interdependent, functional flows.  Its basic terms are few and easily handled; they are precisely defined by the functional relations in which they stand with one another; they are of scientific and explanatory significance; and their magnitudes are determinate.  FMD is purely relational.  It is a dynamical analysis of a dynamic process.  It is conceptually prior to, more fundamental than, and independent of the human psychology of preference and utility.  It is also a normative theory which provides the norms and precepts to which human psychology must adapt.

A final word regarding implicit definition:

Paraphrasing: [CWL 3, 492/516]   … conjugate terms or forms ( such as vectors P’Q’, and dot-product scalars [P’Q’ revenues], [p’a’Q’ basic “costs”], and [p”a”Q” surplus “costs”]) are defined implicitly by their explanatory and empirically verified relations to one another.  …  Such relations, e.g.

• P’Q’ = p’a’Q’ + p”a”Q”Basic circuit R&M [CWL 15, 158]
• da’ = a'(dq’/q’ – dQ’/Q’) [CWL 15, 159]
• d(P’Q”) = d(p’a’Q’) + d(p”a”Q”)  [CWL 15, 158]
• P’/p’ = a’ + a”p”Q”/p’Q’ [CWL 15, 158]
• J = a’ + a”R [CWL 15, 158]
• d(P’/p’) = dJ = da’ + a”dR + Rda”  [CWL 15, 158]
• kn[f’n(t-a)-Bn] = f”n-1(t) – An-1  [CWL 15, 37]
• dI’Σ(widni+ nidwi+dnidwi)yi  [CWL 15, 134]
• dΣFi= dvI”  [CWL 15, 150]
• f = vw [CWL 15, 148-49]
• df = vdw + wdv  [CWL 15, 148-49]
• DZ = PQ[(dP/P + dQ/Q + dPdQ/PQ) cos (A + dA) – 2 sin(dA/2) sin(A + dA/2)] [CWL 15, 108-9]

are general and universally applicable; they hold in any number of instances; the differential equations admit application to the concrete only through the addition of further determinations (such as the indices and coefficients of price and quantity), (however) such further determinations pertain to a non-systematic manifold.[3]  There is then, a primary relativity (correspondence of compensated factors of production with integral products [qi= ΣΣqijk [CWL 15, 30]] exiting into the standard of living and the correlation of dummy-money payments with accelerator and accelerated flows of products and services P’Q’ = p’a’Q’ + p”a”Q”; ) that is contained in the general law (dJ = da’ + a”dR + Rda”); it is inseparable from its base in the conjugate form which implicitly it defines; and to reach the concrete relation that holds at a given place and time, it is not enough to think about the general law; one has to add further determinations (such as coincidental pricings and quantities) that are contingent from the very fact that they have to be obtained from a non-systematic manifold. (In addition, read in the entirety CWL 3, 491-96/514-20)

The whole structure is relational: one cannot conceive the terms without the relations nor the relations without the terms. Both terms and relations constitute a basic framework to be filled out, [CWL 3, 492/516]  (In addition, read in the entirety [CWL 3, 491-6/514-20]