Science *explains*. Science is *explanation*. The scientific inquirer adopts a scientific heuristic. The scientist intends to explain.

On the one hand, there is the movement of empirical science from description to explanation, from proper domains of data to systems of laws that implicitly define the terms they relate; and at the end of this movement there is the ideal goal that is to be attained when all aspects of data, except the empirical residue, will have their intelligible counterpart in systems of explanatory conjugates and ideal frequencies. [CWl 3, 313/337]

Paraphrasing in part:

On the one hand, there is the movement of Functional Macroeconomic Dynamics from descriptive and statistical reporting to explanation, from proper domains of economic data to systems of laws that implicitly define the economic functionings they relate; and at the end of this movement there is the ideal goal: systems of explanatory conjugates, such as point-to-point and point-to-line functional correspendences, and ideal frequencies.

Now the principal technique in effecting the transition from description to explanation is measurement. We move away from colours as seen, from sounds as heard, from heat and pressure as felt. In their place, we determine the numbers named measurements. In virtue of this substitution, we are able to turn from the relations of sensible terms, which are correlative to our senses, to the relations of numbers, which are correlative to one another. Such is the fundamental significance of measurement. [CWL 3, 165/188-89]

We seek to explain the current, purely dynamic, concrete, economic process. The general theory will explain both equilibria and disequilibria in a unified and universally applicable coherent explanation. The analysis will result in a relating of interdependent, velocitous

functioningsto one another in a complete and coherent explanation of the economic process. Again, in order to explain, “The objective of the analysis is to discover the underlying intelligible and dynamic (accelerative) network offunctional, mutually conditioning, and interdependent relationships of these rates to one another.”[CWL 15, 26/27 ftnt 27 ]

National Income accounting and Functional Macroeconomic Dynamics envisage things in fundamentally different manners.

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. But despite their intimate connection, it remains that description and explanation envisage things in fundamentally different manners. The relations of things among themselves are, in general,

a different fieldfrom the relations of things to us. … Not only are description and explanation distinct, but there are two main varieties of description. There are the ordinary descriptions that can be cast in ordinary language. There are also the scientific descriptions for which ordinary language quickly proves inadequate and so is forced to yield its place to a special, technical terminology. (Now) both ordinary and scientific description are concerned with things as related to us, but both are not concerned with the same relations to us. The scientist selects the relations of things to us that lead more directly to knowledge of the relations of thingsamongthemselves. Ordinary description is free from this ulterior preoccupation. [CWL 3, 291-92/316-17]

“Functional”is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; it does not mean “who does what” in come commonsense realm of activity. … 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 themeaningof both point and straight line is fixed by the relation that two and only two points determine a straight line. … ‘In terms of the foregoing analysis, one may say that implicit definition consists in explanatory definition without nominal definition’ (CWL 3, 12/36-37). … Lonergan went on to identify the contemporary notion of a“function”as one of the most basic kinds of explanatory, implicit definition – one that specifies “things in their relations to one another” (CWL 3, 37-38/61-62)…In Lonergan’s circulation analysis, the basic terms are b – rates of productive activities and rates of payments. The objective of the analysis is to discover the underlying intelligible and dynamic (accelerative) network of functional, mutually conditioning, and interdependent relationships of these b. [CWL 15, 26-27 ftnt 27]

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, first by the advance of the sciences and, secondly, by full information on concrete situations. [CWL 3, 492/516] (In addition, read in the entirety [CWL 3, 490-96/514-520]

Paraphrasing in part:

The whole dynamical macroeconomic structure is relational: one cannot conceive the fundamental functional velocities without the relations defining them nor the relations without the fundamental functional velocities. Both terms and relations constitute a basic framework to be filled out, with concrete measurements

The explanation must be normative. It would be a framework for proper adaptation.

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. The framework would thus stand to the ordinary apprehension of the booms and slumps of the trade cycle in much the same way that the explanatory grasp of acceleration as the second derivative of a continuous function of distance and time stands to the ordinary, commonsense grasp of what it is to be going faster. [CWL 15, Editors’ Introduction lv]

Description states the relationship of things to our senses or perceptivity; e.g. hot, cold, red, gray, loud, sweet. In contrast, in our analysis one takes measurements and gathers data on *concrete events and processes*; then one advances from data and, by insight, develops abstract terms representing aggregate functionings having functional relations to one another and defined implicitly and mutually by their functional relations to one another; then one draws upon the forms of pure mathematics to formulate these relations as principles of the **Functional Macroeconomic Dynamics **which explain the process; finally one must verify these hypothetical formulations by returning to the concrete events and processes and testing the formulae against the patterns immanent in existing and new data.

The insights yielding terms of corporate accounting are indeed abstractive rather than descriptive, but they are abstraction at an elementary level in a commonsense activity; thus accounting classifications border practically on description, yielding categories familiar to us in our everyday experience such as wages, revenues, purchases, and sales, which serve to indicate both the past competitive performance and the prospects for survival of the individual firm. But the debits and credits of accounting classifications serve only in a plus or minus, source or use, profit or loss scheme. They are not mutually definitive and mutually conditioning. They are not purely relational. They cannot be used to **explain **the interdependent functionings of the macroeconomy. Conventional accounting does not explicitly include the functional classifications and relations required for explanation.

The whole structure (of functional macroeconomic dynamics) 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, first by the advance of the sciences and, secondly, by full information on concrete situations. [CWL 3, 492/516]

… an ‘accountant’s unity’: that is a category used in (conventional) accounting: For Lonergan, (conventional) accounting generally denotes an enterprise within common sense which uses descriptive, as contrasted with explanatory terms (on these terms see Insight 37-38/61-62, 178-79/201-3, 247-48/272-73). Insofar as that is true, the accountant’s unity is not an adequate index for the normative, explanatory analysis of the productive process. [CWL 15, page 26, ftnt. 26]

The explanation will be in a mathematical form isomorphic with the formal relations immanent in the data. The equation will faithfully represent the form intelligible in the functional phenomena. The functional terms will fix the functional relations and the functional relations will fix the functional terms. Thus, the meaning of the terms is provided by the equation. And the equation explains the pattern of elations immanent in the phenomena.

The abstract explanatory terms may be named “explanatory conjugates.”[1]

… one reaches explanatory conjugates by considering data as similar to other data; but the data, which are similar, also are concrete and individual; CWL3, 435/

Examples of explanation, constituted by an expression of terms-in-relation, from pure and applied mathematics with which the reader may be familiar are: C = πd; PV = nRT(The ideal gas law); F = ma; F = g (m_{1}m_{2})/d^{2}. Again,

On the one hand, there is the movement of empirical science from description to explanation, from proper domains of (pure economic data to

systems of lawsthat implicitly define the terms they relate; and at the end of this movement there is the ideal goal that is to be attained when all aspects of (pure economic) data, except the empirical residue, will have their intelligible counterpart in systems of explanatory conjugates and ideal frequencies. [CWl 3, 313/337]

The basic notions of physics are a mass that is distinct from weight, a temperature that differs from the intensity of the feeling of heat, and the electromagnetic vector fields. [CWL 3, 165/188-89]

Paraphrasing:

The basic notions of Functional Macroeconomic Dynamics are interdependent, mutually defining, velocitous functionings that are distinct from wages, salaries, indirect costs, legal fees, etc. [CWL 3, 165/188-89]

And one cannot conceive the functionings without the functional relations. Again,

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)

Thus, masses might be defined as the correlatives implicit in Newton’s law of inversesquares. Then there would be a pattern of relationships constituted by the verified equation; the pattern of relationships would fix the meaning of the pair of coefficients m

_{1}, m_{2}; and the meaning so determined would be the meaning of the name, mass. In like manner, heat might be defined implicitly by the first law of thermodynamics, and the electric and magnetic fields intensities, E and H, might be regarded as vector quantities defined by Maxwell’s equations for the electromagnetic field. [CWL 3, 80/103]

Basic to surplus, or point-to-point and point-to-line are precise analytical distinctions upon which a system of laws may be constructed. Paraphrasing:

Thus, *basic *and *surplus *or or point-to-point and point-to-line might be defined as the precise analytical correlatives implicit in Schumpeter’s description of economic expansion connecting capital expansion with booms and slumps. And *expenditures *and *costs *might be defined as the correlatives implicit in Lonergan’s observation that what limits so-called “profit” is macroeconomic costs. Then there would be a pattern of relationships constituted by the verified classical equation; the pattern of relationships would fix the meaning of basic vs. surplus, as well as macroeconomic costs vs. pure surplus income.

So, our search in scientific macroeconomics is for *explanatory, functional – not accounting –**interconnections *and *interdependencies*. We search for functional connections, dependencies and conditionings which implicitly condition and define one another, mutually determine one another and are determined by one another.

The investigator shifts his emphasis. We shift from premature analysis of prices and quantities to mutally defining functions containing prices and quantities

… Lonergan’s critique (shows that) by using the technique of implicit definition, the emphasis shifts from trying to

definethe relevant variables to searching heuristically for the maximum extent of interconnections and interdependence; and that the variables discovered in this way might not resemble very much the objects (or the aggregates) which, in the first instance, one was thinking about. [Gibbons 1987]

Gibbons is implying that the term “monetary function,” used as an abstract explanatory term, does “not resemble very much” the aggregates (wages, rent, profits, interest) which first occur to us in our responsibilities as corporate accountants or National Income accountants. Rather we end up with **explanatory **functional terms or concepts discovered by insights occurring at an adequate level of abstraction.

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]

The explanatory terms are terms which initially the scientist, like Newton or Clerk-Maxwell, had to imagine or fantasize about – rather than feel, smell, hear, or see in his everyday experience of accounting, purchasing, etc. Similarly, the terms *point-to-point, point-to-line, macroeconomic costs, *and *macroeconomic profits *are precise analytical and foundational distinctions and of scientific and systematic significance, unlike the accountants’ terms such as wages, direct costs, indirect costs, and profit after taxes.

Again, scientific explanation – whether in physics or macroeconomics – is to be distinguished from description. “Description and explanation envisage things in fundamentally different manners. The relations of things among themselves are, in general, a different field from the relations of things to us.”

… despite their intimate connection, it remains that description and explanation envisage things in fundamentally different manners. The relations of things among themselves are, in general, a different field from the relations of things to us. [CWL 3, 291/316]

Lonergan’s basic terms of systematic significance and scientific significance are functional velocities. One last time:

“Functional”is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; … Lonergan (identified) the contemporary notion of a“function”as one of the most basic kinds of explanatory, implicit definition – one that specifies “things in their relations to one another” … [CWL 15 26-27 ftnt 27]Now, at the root of classical method there are two heuristic principles. The first is that similar are understood similarly, that a difference of understanding presupposes a significant difference of data. The second is that similarities, relevant to explanation, lie not in the relations of things to our senses but in their relations to one another. Next, when these heuristic principles are applied, there result classifications by sensible similarity, then correlations, and finally the verification of correlations and of systems of correlations. But verified correlations necessarily involve the verification of terms implicitly defined by the correlations; and they do not involve more than such implicitly defined terms as related, for what is verified accurately is not this or that particular proposition but the general and abstract proposition on which ranges of ranges of particular propositions converge. … there is a fundamental heuristic structure that leads to the determination of conjugates, that is, of terms defined implicitly by their empirically and explanatory relations. Such terms as related are known by understanding, and so they are forms. [CWL 3, 435/460]

** **

[1]As a mnemonic: *Conjugate *stems from the Latin *iugum*, meaning the yoke that keeps two oxen together; and the prefix *con *from the Latin *cum*, meaning *with*. The idea is that the terms of the explanation are yoked together with each other in a system where the terms define the functional relations and the functional relations define the terms.