Category Archives: Implicit Definition

Explaining “Present Fact”: An Ever-Varying Process; A Never-Varying Systematics

The economic process is always the current, purely-dynamic, concrete functioning. The analysis of the dynamic process is always relevant to the present fact. The immanent intelligibility of such a dynamic, ever-varying process may itself be an invariant; i.e. though the differentials may change in magnitude, the relation of the differential velocities and accelerations among themselves is invariant.  So it is in the case of dynamic pendular motion, elliptic motion, the variables of electromagnetic phenomena, and in the dynamic economic process.  The general laws of the process are applicable in any instance.  These primary, abstract, general, field-theoretic laws may be applied to whatever may be the secondary determinations from the concrete non-systematic manifold.  Thus we can get the particular law explaining the particular concrete process under investigation.

The overall economic functioning has an objective immanent intelligibility.  This intelligibility is an invariant – a set of differential equations which implicitly define the explanatory, conjugate, differentials of the dynamic process. The explanatory terms are abstract functions defined by their functional relations to one another. In the implicit equations, the terms define the relations and the relations define the terms, and insight fixes both. And the equations cohere with one another to constitute a fully-explanatory field theory.

The point-to-line 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 indeterminacy is very much a present fact.  One has to await the future to have exact information.   And while estimates in the present may be esteemed accurate, the future has no intention of being ruled by them: owners do not junk equipment simply because it has outlasted the most reliable estimates; nor are bankrupts kept in business because their expectations, though mistaken, are proved to have been perfectly reasonable.  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 point-to-line and point-to-surface and higher correspondences. [CWL 15, 27-28]

in the long run, and especially in the very long run, such a correlation exists.  It is that surplus production is the accelerator of basic production.  In other words the correspondence between the two is not a point-to-point but a point-to-line correspondence; … Now such a correspondence, if it is to be expressed not in terms of expectations of the future but in terms of present fact, is a correspondence of accelerator to accelerated. … If the system is to move into a long-term expansion, this movement has to begin with a surplus quantity acceleration: surplus production has not merely to maintain or renew existing capital equipment but has to reach a level at which it turns out new units of production and maintains or renews a greater number of existing units; this gives the quantity surplus expansion. [CWL 21, 132]

(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) … 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 are concentrated in a redistributive function, whence may be derived changes in the stock of money (distinct process 3) 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 long-standing recurrence of crises in the modern expanding economy. [CWL 15, 53-54]

Five Why’s

Why Macroeconomists Don’t Flock to Functional Macroeconomic Dynamics

Why Study Peter Burley’s Models?

Why and How the Basic Expansion Fails To Be Implemented

Why Analyze The Productive Process First?

Why Revise The National Income and Product Accounts?

 

Insight Into The “Baseball Diamond”: Discovery For Implementation

Thus, if we want to have a comprehensive grasp of everything in a unified whole, we shall have to construct a diagram in which are symbolically represented all the various elements along with all the connections between them. [McShane 2014, 11 (quoting CWL 7, 151)]

We wish here to suggest the insights the reader should have to fully appreciate all that is contained in the Diagram of Rates of Flow. (Continue reading).

Lilley and Rogoff Recommending Negative Interest Rates

We are commenting with respect to Andrew Lilley and Kenneth Rogoff’s “conference draft” discussing the advisability of a FRB policy of negative interest rates:

 Lilley, Andrew and Kenneth Rogoff, April 24, 2019: “The Case for Implementing Effective Negative Interest Rate Policy” (Conference draft for presentation at Strategies For Monetary Policy: A Policy Conference, the Hoover Institution, Stanford University, May 4, 2019, 9:15 am PST) [Lilley and Rogoff, 2019]     (Continue reading)

A Comparative Note on Einstein’s Special-Relativity Field Theory and Lonergan’s Macroeconomic Field Theory

Special Relativity and Functional Macroeconomic Dynamics are field theories.  (Click here and here and here)  We wish to gain further appreciation of FMD as a field theory by juxtaposing it with Special Relativity.

… Special Relativity is primarily a field theory, that is, it is concerned not with efficient, instrumentalmaterial, 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. … Special Relativity is stated as a methodological doctrine that regards the mathematical expression of physical principles and laws, but Newtonian dynamics is stated as a doctrine about the objects subject to laws.  [3, 43/67] (Continue reading)

Theoretical Breakthroughs of Euclid, Newton, Hilbert, Einstein, and Lonergan

To help the reader gain an appreciation of Lonergan’s achievement of Modern Macroeconomic Field Theory we will, in each section, print leading excerpts, then highlight the key concepts of those excerpts. We will comment on the historically-significant advances in geometry of Euclid and Hilbert, in physics of Newton and Einstein, and in macroeconomics of Lonergan.

  • Euclid’s great achievement was his rigorous deduction of geometry.
  • Hilbert’s great achievement was his employment of implicit definition to reorder Euclid’s geometry.
  • Newton’s two great achievements were unifying the isolated insights of Galileo and Kepler into a unified system of mechanics and his invention of the calculus.
  • One of the great achievements of Einstein was the invention of the field theories of Special Relativity, General Relativity, and Gravitation.
  • One of Lonergan’s several great achievements was his systematization of macroeconomic phenomena in his Modern Macroeconomic Field Theory. He combined the technique of implicit definition introduced by Hilbert and the concept of a field theory developed by Faraday and Einstein; and he developed an explanatory macroeconomics, which is general, invariant, and relevant in any instance. (Continue reading)

A Contrast: Understanding Pricing in Macrostatic DSGE and in Macrodynamic FMD

.I.  Introduction: Contrasting Diagrams and What They Represent

We contrast an assumption and description with an explanation and interpretation.  We contrast the Dynamic Stochastic General Equilibrium (DSGE) assumption and description of pricing as exogenously given and acceptable as a lead item in analysis of economic problems with Functional Macroeconomic Dynamics’ (FMD’s) explanation and interpretation of pricing in the light of the significant functional pretio-quantital flows, which explain the dynamic economic process. (Continue reading)

Field Theory in Physics and Macroeconomics

We hope to inspire serious graduate students of economics a) to seek and achieve an understanding of “Macroeconomic Field Theory,” b) to verify empirically Lonergan’s field relations,  and c) to use the explanatory field relations as the basis of influential scholarly papers.

We trace developments

  • in physics from Newtonian mechanics to modern field theory, and
  • in economics from Walrasian supply-demand economics to purely relational, Modern Macroeconomic Field Theory.

Key ideas include a) abstraction and implicit definition as the basis and ground of invariance in both physics and macroeconomics, b) the concept of a purely relational field, c) immanent intelligibility and formal causality, and d) the canons of parsimony and of complete explanation. We highlight some key ideas: (continue reading)

Elements of The Analysis

Our aim is to prescind from human psychology that, in the first place, we may define the objective situation with which man has to deal, and, in the second place, define the psychological attitude that has to be adopted if man is to deal successfully with economic problems.  Thus something of a Copernican revolution is attempted: instead of taking man as he is or as he may be thought to be and from that deducing what economic phenomena are going to be, we take the exchange process in its greatest generality and attempt to deduce the human adaptations necessary for survival. [CWL 21,42- 43]

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 equilibrium analysis…to an analysis where attention is focused on second-order differential equations, on d2θ/dt2, d2x/dt2, d2y/dt2, on a range of related forces, central, friction, whatever….. What is significant is the Leibnitz-Newtonian shift of context. [McShane 1980, 127]

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.  …  description supplies, as it were, the tweezers by which we hold things while explanations are being discovered or verified, applied or revised. … [CWL 3, 291/316]

again, as to the notion of cause, Newton conceived of his forces as efficient causes, and the modern mechanics drops the notion of force; it gets along perfectly well without it.  It thinks in terms of a field theory, the set of relationships between n objects.  The field theory is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational formsThe form of any element is known through its relations to all other elements.  What is a mass?  A mass is anything that satisfies the fundamental equations that regard masses.  Consequently, when you add a new fundamental equation about mass, as Einstein did when he equated mass with energy, you get a new idea of mass.  Field theory is a matter of the immanent intelligibility of the object. [CWL 10, 154]