Category Archives: Functions

Abstraction in Macroeconomics; Classical and Statistical Laws

Abstraction is enriching.  The relation of things to our senses must be transcended by abstraction. Abstraction yields explanatory concepts implicitly defined by their functional relations to one another.

The commonsense accounting relations constituting historical Gross Domestic Product must be supplemented by the abstract explanatory formulation of Current Gross Domestic Functional Flows.  All participants must have the scientific guidance of a normative theory in order to properly adapt their personal conduct to the principles and laws of the objective process. (Continue reading)

The Significance of Zero in Functional Macroeconomic Dynamics: Dynamic Equilibrium, Implicit Definitions, Concomitance, Turning Points

It will be informative and thought-provoking to regard various instances of zero –  expressed or implied and each zero’s significance in the normative theory of Functional Macroeconomic Dynamics.  We may say that zeroes are “normatively forceful”, or, speaking metaphorically, “quasi-gravitational”;  They signify a systematic exigence for a “normative pull” on all interdependent pretio-quantital flows into their proper concomitance and solidarity, so as to provide a tightly knit framework and general explanation of the whole, intelligible, unitary, dynamic functioning.  

First, we simply list, without context or backup, 12 instances of zero; then second, we relist and add substantiation regarding each instance. We hope the reader will consult the context of the zeroes and their substantiation on the pages referenced at the end of the excerpts. Continue reading

Connecting the Notions of “Concomitance,” “Solidarity,” “Implicit Definition,” “Functional Relations,” and “Unification”

Concomitance is, I would claim, the key word in Lonergan’s economic thinking. (Philip McShane, Fusion 1, p. 4, ftnt 10)

“Concomitance,”solidarity,” “implicit definition,” “functional interdependence,” and “unification” are the key principles foundational to the equation(s) providing the scientific general explanation of the organic economic process. Proper adherence to the principles ensures a unification of all explanatory conjugates and relations of the unitary system. The patterns in the terms and relations of the explanatory equation(s) would be isomorphic with the actual patterns constituting the process of velocitous (dynamic) production and exchange. (Also click here)

Consider the theoretical significance and, thus, the explanatory significance of the following:

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. … 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’ and c”O” as costs of production, having warned the reader that the costs in question are aggregate and functional costs…. [CWL 15 156-57]  

Thus, we have basic Outlays-Incomes, c’O’ +c”O” = I’, explanatorily conjugate with – i.e. functionally related tobasic expenditures, E’ = P’Q’, which are implicitly defined in the following implicit equation: 

P’Q’ = p’a’Q’ + p”a”Q”  [CWL 15,156-62].

As was pointed out regarding Einstein’s general relativity equation – Gab = 8πTabin our treatment The Einsteinian Context: Curvature and Relativity (click here and here): Continue reading

A Greg Mankiw Blog

Introductory

Our concern, as always, is to understand and verify how money should circulate to meet the rectilinear primary process of production and sale.  We seek a normative theory which scientifically explains, rather than merely describes, the current, purely dynamic economic process.  The scientific explanation will be in the form of the objective relations of explanatory velocities and accelerations to one another.  These explanatory conjugates will be abstract correlations defined by their functional relations among themselves – rather than descriptions – no matter how literary and vivid –  of conditions, states, and events as they are related to us and affect us for better or worse.  Our goal is to achieve a scientific explanation yielding norms to which we must adapt. (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. (See Philip McShane in Categories in the right sidebar)

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

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)

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

Contents

  • .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

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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)