Category Archives: Functions

A Closely Knit Frame of Reference; the Channels Account for Booms and Slumps, for Inflation and Deflation,

The interconnected channels of the Diagram of Rates of Flow provide a closely knit frame of reference.  The channels account for booms and slumps, inflation and deflation.

The method of circulation analysis resembles more the method of arithmetic than the method of botany.  It involves a minimum of description and classification, a maximum of interconnections and functional relations.  Perforce, some description and classification are necessary; but they are highly selective, and they contain the apparent arbitrariness inherent in all analysis.  For analytic thinking uses classes based on similarity only as a springboard to reach terms defined by the correlations in which they stand.  To take the arithmetic illustration, only a few of the integral numbers in the indefinite number series are classes derived from descriptive similarity; by definition, the whole series is a progression in which each successive term is a function of its predecessor.  It is this procedure that gives arithmetic its endless possibilities of accurate deduction; and, as has been well argued, it is an essentially analogous procedure that underlies all effective theory. [CWL 21, 111] Continue reading

An Einsteinian Relativistic Context: Space and Time Become Space-Time; Price and Quantity become Price-Quantity; An Abstract Set of Invariant Explanatory Relations


  • .I. Relations and Relativity in General
  • .II. Einstein’s Special Relativity and General Relativity
  • .III Lonergan’s Double-Circuited, Pretio-Quantital Relativity Theory
  • .IV. The Basic Price Spread; The Co-ordinated Relativity of Three Major Pretio-Quantital Flows and the Co-operative Relations Within Each Major Flow
  • .V. The Macroeconomic Field Theory Equations
  • .VI. Concerning Verification
  • .VII. Miscellaneous Selections
  • .VIII. Conclusion

Continue reading


Explanation By Gross Domestic Functional Flows To Supplement Description By Gross Domestic Product

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.  The two are not totally independent, for they deal with the same things and, as we have seen, 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]

The analysis of the overall dynamic functioning, which we call in nominal terms the economic process, must seek the explanation of the process.   It must seek the objective immanent intelligibility among the interdependent, dynamic “functionings” which altogether constitute the process.  The functionings are rates of so much or so many every so often, and, thus, they are velocities.  And the scientific analysis must be in terms of abstract, implicitly-defined, explanatory conjugates rather than in terms of the descriptive accountants’ unities of merely legal or proprietary entities called “firms.” (Continue reading)

Scientific Generalization by Functional Analysis of the Network of Interdependent Rates

The non-Euclideans moved geometry back to premises more remote than Euclid’s axioms, they developed methods of their own quite unlike Euclid’s, and though they did not impugn Euclid’s theorems, neither were they very interested in them; casually and incidentally they turn them up as particular cases in an enlarged and radically different field. Continue reading

Seminar on “Critical Thinking in Economics”

Presenters John Siegfried and David Colander, and discussants Daron Acemoglu, Melissa S. Kearney, John A List, N. Gregory Mankiw,  Deirdre McCloskey, and Betsey Stevenson recently collaborated in a virtual ASSA meeting entitled “What Does Critical Thinking Mean in Economics, the Big and Little of It?” Handouts from the meeting can be found in an Announcement in a blog of Saturday, January 2, 2021 on N. Gregory Mankiw’s website.

Preliminarily, note the subtitle in Lonergan’s seminal work, Insight: A Study of Human UnderstandingIn the present context we might reword the subtitle A Study of Critical ThinkingA very smart person – learned in  advanced mathematics and theoretical physics – called Lonergan’s book “The Most Significant Book of the Twentieth Century.”       (Continue reading)

Functions Are Not Seen, But Must Be Understood

Functions are not seen, but must be understood. (Catherine Blanche King, private communication)

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.  (CWL 15,  Editors’ Introduction, lv) (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 Philip McShane Sampler Relevant to Functional Macroeconomic Dynamics

Philip McShane had a strong background in mathematics and theoretical physics; thus he was able to understand the scientific significance of Bernard Lonergan’s macroeconomic field theory in an Einsteinian context.

First we display, in brief, key excerpts, many of which contain analogies from physics and chemistry, relevant to the science of Functional Macroeconomic Dynamics; then we show the same excerpts more fully within lengthier quotes. 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)