Galileo inaugurated modern science by insisting that the nature of weight was not enough; from sensible similarity, which resides in the relations of things to our senses, one must proceed to relations that hold directly between things themselves. [CWL 3, 38/62]
The relating of terms in geometry bears a resemblance to the relating of explanatory aggregates in economics. In both cases the terms define and explain one another by their intelligible relations. The intelligible relations define the causes. “The causes are formal causes; it is only applied science that is concerned with agents and ends.”
The point I wish to make is that modern science is not simply an addition to what was known before. It is the perfecting of the very notion of science itself, of knowing things by their causes, by analysis and synthesis. What are the causes? The field of intelligible relations that implicitly define the objects. The objects with which a science deals are whatever is defined by its field of intelligible relations, whatever falls into that field. The causes are formal causes; it is only applied science that is concerned with agents and ends.[CWL 10, 155]
Lonergan illustrates his basic meaning of ‘explanation’ by referring to D. Hilbert’s method of implicit definition: Let us say, then, that for every basic insight there is a circle of terms and relations, such that the terms fix the relations, the relations fix the terms, and the insight fixes both. ‘Thus the meaning of both point and straight line is fixed by the relation that two and only two points determine a straight line.“[CWL 15, 26-27 ftnt 27]
Scientific Functional Macroeconomic Dynamics is a field theory of intelligible relations, not an efficiently causal Newtonian mechanics with the interest rate as an external lever for application of force or efficient cause.
… 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 forms. The 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]
… again, as to the notion of cause, academics and government officials conceive of interest rates and other fixed pricing as efficient causes, and functional macroeconomic dynamics drops the notion of interest rates and other fixed pricing as efficient causes; it gets along perfectly well without them. It thinks in terms of a field theory, the set of relationships between interdependent functionings. The functional macroeconomics field theory is a set of intelligible relations linking what is implicitly defined by the relations themselves; it is a set of relational forms. The form of any functioning is known through its relations to all other functionings. What is a basic product? A basic product is any composite that satisfies the fundamental equations of the first degree that regard components with their composite product exiting the process into a standard of living. Consequently, when you add a new fundamental equation about functional relations, as functional macroeconomic dynamics does when it relates functionings to one another, you get a new theory of macroeconomics. Macroeconomic field theory is a matter of the immanent intelligibility of the overall functioning process. [from CWL 10, 154]
Dynamically science is the interplay of two factors: there are data revealed by experience, observation, experiment, measurement; and on the other hand, there is the constructive activity of mind. … Thus thought and experience are two complementary functions; thought constructs what experience reveals; and science is an exact equilibrium of the two. [CWL 21, 5 ]
Paraphrasing we may say, scientific economics consists of the experience of innovation and expansion experienced and formulated by the constructive activity of mind. It is understanding economic functionings by the intelligible relations which implicitly define them. The relations define the functionings and the functionings define the relations.
Science is explanation by relation of things to one another. The claim is being made that Lonergan made economics a science by formulating the dynamics of the overall functioning called the economy in terms implicitly defined by their functional relations to one another.
In the following excerpt, McShane speaks about “the creative key transition to dynamics.” He is speaking of the “shift of (analytical) thinking” exemplified in physics from the staticsof bridges and suspended weights, in which forces are exactly offsetting and in which there is no change or motion over time, to dynamics whose terms are the differentials of velocities and accelerations. He insists that a similar shift of analytic thinking is needed in the science of macroeconomics, which deals with velocities and accelerations of interdependent product movements and money movements. Also, boundary conditions such as the past or present valuesare “relatively insignificant for the analysis.” The compounding or discounting of values (secondary coincidental determinations) does not constitute an explanation (the primary relativity) of the macroeconomic field. Indeed the shift of analytical thinking to the primary relativity of the real economy is critical if economics is to qualify as a science of dynamics and transform discussion from nominal definition to implicit definition, from description to explanation, from hunch to specification of relational form, from economic mythmakingto economic truth-telling, and from political rant to intelligent reason.
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 mechanics) will appreciate the shift in thinking involved in passing from equilibrium analysis (of a system of balanced forces)… to an analysis where attention is focused on second-order differential equations, on
d2e/dt2 , d2x/dt2 , d2y/dt2
on a range of related forces, central, friction, whatever (in theoretical physics). 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]
And beyond the Leibnitz-Newtonian shift are the Lagrangean, Hamiltonian, and Einsteinian shifts.
Boundary values, such as particular quantities and prices, are “relatively insignificant.” Newtonian mechanics is not constructed from particular values for masses, positions, or times of particles or planets. It is a more general specification, a set of relations which hold for any particular time, place, or mass. Similarly in scientific macroeconomics, “Particular boundary conditions, “past and future values,” are relatively insignificant for the analysis. What is significant is the Leibnitz-Newtonian shift of context where attention is focused on a set of explanatory second-order differential equations interrelating flows of classes of products and their associated payments.
Discounting a future stream of expected future values to a present value does not constitute a dynamics that tells us how the functional velocities of the productive process and the functional velocities of the payments system interrelate. Nor does a similar discounting of expected utility, which contaminates the objective relations of scientific macroeconomics with speculative psychology. These discountings do not explain the formal functional relations of the interdependencies of the process, which is always the current process and is always a purely dynamic process.
The physicist says, Let the function stating the hypothesis be the solution to a differential equation. (See CWL 10) Then he attempts to understand all he can about the possible differential behavior of his data under different circumstances. Then he surveys the catalog of mathematical formalisms to select a general differential equation whose solutions will explain any and all behavior of particular data. Then he selects the appropriate differential equation from among the catalog of purely relational forms. Only after selecting a differential equation of the primary relativity of the data does he perform experiment after experiment using measured boundary values or initial values (both of which are coincidental secondary determinations) to verify that he has discovered an isomorphism of mathematical form accounting for a particular economic behavior and that his solution-function faithfully represents the contents of his insight and the behavior of the data.
Using this procedure, physical science has advanced through
- Galileo: laws and systems of laws in a geometry
- Newton: laws and systems of laws in differential equations
- Einstein: primary quantities space and time are to be explained or redefined in Special Relativity; the secondary qualities (color, sound, pressure, etc) are to be explained and redefined by electromagnetics and thermodynamics, gravity is to be explained and redefined by the General Theory of Gravitation as the curvature of space; and all observers have equal status by the principle of equivalence.
- Quantum Theory: system of states and probabilities (See CWL 10)
Now, the science of economics is not the science of physics. In both domains the scientist seeks explanation, but he examines different data possessing different intelligibilities to be represented by different sets of terms and relations. A scientific economist is confronted with a system of interdependent, conditioned velocities of production and sale of consumer goods and capital goods, and with accelerations in both normative growth and distorted boom and slump.
In the task of explaining, the scientific economist can profit by examining the orientation and insights of the physicist and the mathematician. He must know scientific method and he must adopt a scientific heuristic. It must be a dynamic heuristic. He must struggle to home in on his basic terms. Indeed a beneficial academic preparation for the scientific economist is the mastery of a) the relational forms provided by mathematicians, and b) potential application of such forms to express the intelligibilities of physics. Especially important, since economics deals with flows or velocities, would be the mastery of the differential equations of currents and fluids. Again, the scientific economist must have “a firmer grasp of the essentials of an effective theory”; he must have a dynamic heuristic to discover the classical laws of recurrent operations; i.e. he must achieve the classical laws of a theory of dynamics with its critical denominator dt2. Also important, since economic process like physical process has statistical laws which complement its classical laws of recurrent and expanding flows, would be the mastery of combinatorics, probability, and statistics explaining variability and risk.
No doubt Keynes was an economist first and a methodologist second but he was none the less very articulate about his theorizing……..Lonergan, for his part, is perhaps a methodologist first and an economist second, but, as we shall see, he was able to push his economic reflections further than Keynes because he had a firmer grasp of the essentials of an effective theory. [Gibbons, 1987]
Those familiar with elementary statics and dynamics (in mechanics) will appreciate the shift in thinking involved in passing … to an analysis where attention is focused on second-order differential equations, on d2e/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]
Note carefully that the objective of the scientific economist seeking scientific explanation is to discover the intelligible network of interdependent relationships of functional rates “to one another,” with a special focus on second-order differential equations specifying positive and negative accelerations referred to colloquially as progress and decline, boom and slump. Complete explanation will be achieved by a theory that comprehends all normative and distortive configurations of elements.
Also, there must be an affective response: If the economist is an academic ensconced in conventional statics, he must shift his psyche and motivation to embark on a different course of analysis, despite his history of involvement in descriptive statics.
The symbol for acceleration (d2s/dt2) perhaps hooks at you, an unwilling fish, shudderingly, suddenly, a threat. Not then, as in me (the me of Fusion 7, or of Beethoven’s 7thsymphony), a gentle “affect-laden image that evokes a feeling” (Method’smeaning of symbol). How are you to get over and beyond the shuddering, the sudden gripping of your psyche by that odd combination of letters and numbers? [McShane 2010, 86]
Finally, when the economist is dealing with others versed in calculus’ differential equations, the more math and the less politics the better. Equations are not political. The challenge to the opponent becomes, “Disprove the relations of my equations.” Political disagreements disguised as economic disagreements are to be avoided.
Mathematical verbosity, as opposed to verbosity of any other sort, could not have better suited the personal eccentricities of Kurt Gödel, a man who had so much to say on the nature of mathematical truth and knowledge and certainty, but wanted to say it using only the rigorous methodology of mathematics. With a proof in hand, he would not have to involve himself in the sorts of combative human conversations he regarded with distaste, maybe even with horror. There never was a man, I’ll wager, who combined so much conviction with so little inclination to argue his convictions by the normal means given to us, viz. human speech. ¶The irony of course is that while his theorems were accepted as of paramount importance, others did not always hear what he was attempting to say to them. They heard – and continue to hear – the voice of the Vienna Circle or of existentialism or postmodernism or of any other of the various fashionable outlooks of the twentieth century. They heard everything except what Godel was trying to say. [Goldstein, 2005, 135-36]
The word explain is derived from the Latin meaning make level or flat, as in two-dimensional space. However, the framework of our explanatory understanding may sometimes employ rectangular axes of many dimensions.